Multivarite Deep Learning for Ice of Power Lines
10
Research Article Multivariable Time Series Prediction for the Icing Process on Overhead Power Transmission Line Peng Li, 1,2,3 Na Zhao, 1 Donghua Zhou, 2 Min Cao, 3 Jingjie Li, 1 and Xinling Shi 1 1 Department of Electronic Engineering, Yunnan University, Kunming 650091, China 2 Department of Automation, Tsinghua University, Beijing 100084, China 3 Yunnan Electric Power Research Institute, China Southern Power Grid Corp., Kunming 650217, China Correspondence should be addressed to Peng Li; [email protected] Received 27 January 2014; Accepted 14 June 2014; Published 17 July 2014 Academic Editor: Martin Riera-Guasp Copyright © 2014 Peng Li et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. e design of monitoring and predictive alarm systems is necessary for successful overhead power transmission line icing. Given the characteristics of complexity, nonlinearity, and fitfulness in the line icing process, a model based on a multivariable time series is presented here to predict the icing load of a transmission line. In this model, the time effects of micrometeorology parameters for the icing process have been analyzed. e phase-space reconstruction theory and machine learning method were then applied to establish the prediction model, which fully utilized the history of multivariable time series data in local monitoring systems to represent the mapping relationship between icing load and micrometeorology factors. Relevant to the characteristic of fitfulness in line icing, the simulations were carried out during the same icing process or different process to test the model’s prediction precision and robustness. According to the simulation results for the Tao-Luo-Xiong Transmission Line, this model demonstrates a good accuracy of prediction in different process, if the prediction length is less than two hours, and would be helpful for power grid departments when deciding to take action in advance to address potential icing disasters. 1. Introduction With rapid societal and economic development, human beings have come to rely more and more on all kinds of energy sources, but especially on electric power. Consequently, reli- ability, maintainability, and safety requirements have become more and more important for electric power plants and grids. In recent years, global greenhouse effects have resulted in atrocious weather events, including freezes, windstorms, severe thunderstorms, fog, floods, and mudslides. ese events have threatened the safety of power grid systems. In the Southern of China, most notably in Yunnan, Guizhou, Sichuan, Chongqing, and Hunan, frozen disasters occur frequently in winter; overhead power lines pass through high altitude and low latitude areas across complex landscapes and through changing climates, such as the Qinling Mountains, the Hengduan Mountains, and the Wumeng Mountains. During the winter months, these are areas where cold air from the North meets warm, humid air from Southern, and under special micrometeorology conditions, water will ice across the surface of overhead power lines, eventually causing problems, such as tower collapse, line breakage, flashover of insulators, or conductor gallop. In early 2008, in Central Southern and Southwest China, an ice storm caused more than 120,000 towers to collapse, downed more than 7,000 electrical lines, and shut down 859 substations, according to statistics from the Southern Power Grid Corp. of China [1]. ese accidents resulted in significant financial losses to domestic and industrial electrical power users. It is always preferable to take preventative actions instead reacting to events aſter an accident has already happened. Line icing has caused a lot of problems to grid systems in the past; obviously, if it is possible to monitor and predict potential icing threats to transmission lines, timely alarms could improve the power grid’s reliability. e models and methods for monitoring and predicting icing vary. In the area of research focused on monitoring the icing process online, Savadjiev and Farzaneh [2] presented the IRM (icing rate meter) method, which indirectly describes the ice’s rate of increase through the use of an instrument Hindawi Publishing Corporation e Scientific World Journal Volume 2014, Article ID 256815, 9 pages http://dx.doi.org/10.1155/2014/256815
description
Multivarite Deep Learning for Ice of Power Lines
Transcript of Multivarite Deep Learning for Ice of Power Lines
Research ArticleMultivariable Time Series Prediction for the Icing Process onOverhead Power Transmission Line
Peng Li123 Na Zhao1 Donghua Zhou2 Min Cao3 Jingjie Li1 and Xinling Shi1
1 Department of Electronic Engineering Yunnan University Kunming 650091 China2Department of Automation Tsinghua University Beijing 100084 China3 Yunnan Electric Power Research Institute China Southern Power Grid Corp Kunming 650217 China
Correspondence should be addressed to Peng Li lipengynueducn
Received 27 January 2014 Accepted 14 June 2014 Published 17 July 2014
Academic Editor Martin Riera-Guasp
Copyright copy 2014 Peng Li et al This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The design of monitoring and predictive alarm systems is necessary for successful overhead power transmission line icing Giventhe characteristics of complexity nonlinearity and fitfulness in the line icing process a model based on a multivariable time seriesis presented here to predict the icing load of a transmission line In this model the time effects of micrometeorology parametersfor the icing process have been analyzed The phase-space reconstruction theory and machine learning method were then appliedto establish the prediction model which fully utilized the history of multivariable time series data in local monitoring systems torepresent the mapping relationship between icing load and micrometeorology factors Relevant to the characteristic of fitfulnessin line icing the simulations were carried out during the same icing process or different process to test the modelrsquos predictionprecision and robustness According to the simulation results for the Tao-Luo-Xiong Transmission Line this model demonstratesa good accuracy of prediction in different process if the prediction length is less than two hours and would be helpful for powergrid departments when deciding to take action in advance to address potential icing disasters
1 Introduction
With rapid societal and economic development humanbeings have come to relymore andmore on all kinds of energysources but especially on electric power Consequently reli-ability maintainability and safety requirements have becomemore and more important for electric power plants andgrids In recent years global greenhouse effects have resultedin atrocious weather events including freezes windstormssevere thunderstorms fog floods and mudslides Theseevents have threatened the safety of power grid systems Inthe Southern of China most notably in Yunnan GuizhouSichuan Chongqing and Hunan frozen disasters occurfrequently in winter overhead power lines pass through highaltitude and low latitude areas across complex landscapes andthrough changing climates such as the Qinling Mountainsthe Hengduan Mountains and the Wumeng MountainsDuring the winter months these are areas where cold airfrom the North meets warm humid air from Southern andunder special micrometeorology conditions water will ice
across the surface of overhead power lines eventually causingproblems such as tower collapse line breakage flashoverof insulators or conductor gallop In early 2008 in CentralSouthern and Southwest China an ice storm caused morethan 120000 towers to collapse downed more than 7000electrical lines and shut down 859 substations accordingto statistics from the Southern Power Grid Corp of China[1] These accidents resulted in significant financial losses todomestic and industrial electrical power users
It is always preferable to take preventative actions insteadreacting to events after an accident has already happenedLine icing has caused a lot of problems to grid systems inthe past obviously if it is possible to monitor and predictpotential icing threats to transmission lines timely alarmscould improve the power gridrsquos reliability
The models and methods for monitoring and predictingicing vary In the area of research focused on monitoring theicing process online Savadjiev andFarzaneh [2] presented theIRM (icing rate meter) method which indirectly describesthe icersquos rate of increase through the use of an instrument
Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 256815 9 pageshttpdxdoiorg1011552014256815
2 The Scientific World Journal
Safety diagnosis prediction and
decision-making for maintenance
Controller
Detecting
Maintenance Power grid
Monitoringsystem
ObjectSafety targetsfor power grid State
Figure 1 Maintenance based on safety status prediction
installed near the transmission line This method is conve-nient but imprecise when measuring the load of line icingHuang and Sun [3] and Yang et al [4] presented amechanicalmodel that has advantages in timely and exact estimates forthe load of lines icing but the instruments for sampling theforce data are expensive This method is unable to forecastthe icing status it can only display the real-time status of theicing process The Glouba model [5] and the edge of imageextraction model [6] succeed in practice they can estimatethe icing load at a low cost but their precision is less than themechanical model and they are also unable to forecast icingstatus
As shown in Figure 1 it is obvious that decision-makingbased on a predictive status for maintenance is better thanone based on a current status because the predictive controlhas the advantage of reducing unsafe factors in advancecompared to a simple feedback control loopTherefore if thetransmission linersquos icing status has been predicted and unsafeparts of it have been assessed the departments of power gridmaintenance can actively optimize a schedule to deice thelines
Consequently it is imperative to find methods to predictthe icing threat of power grid usingmeteorology informationforecasted by the weather bureau
In the area of research focused on predicting the icingprocess an experiment model [7] and a statistical analysismodel [8] based on micrometeorology parameters predictedicing loads using certain micrometeorology parameters suchas the environmental temperature humidity wind veloc-ity and direction rainfall and snowfall The Makkonenmodel [9] is based on a thermodynamic mechanism butits variables such as the content of liquid state water anda distributing dripping parameter can be obtained in alaboratory but are difficult to measure at local monitoringpoints along a transmission line so it is not generally suitablefor the icing process
Even though the mathematical models above have beenobtained they are founded in special conditions either bystatistical analysis methods or thermodynamic mechanismsand are not robust enough to withstand if the environmentchanges because the micrometeorology conditions are dif-ferent in each instance when lines ice over for example in
a valley versus along a hillside Furthermore because of thecomplexity and nonlinearity of the icing models it is difficultto acquire all of them to predict icing process in differentlocations because themapping relationship changes betweenthe independent variables and dependent variables
In the northeast area of Yunnan Province in China icingdisasters happen frequently [10] Plentiful advanced forcemeasurements andmicroweather stations have been installedfor the online monitoring of power grids and the real-time icing load status and micrometeorology parameters aretransmitted concurrently to a surveillance center by wiredandwireless sensor networks But as a result of the complexityin microlandforms and micrometeorology in this area it isdifficult to find a specific mathematics model to predict theicing process in different transmission lines
On the one hand the cost of an onlinemonitoring systemis expensive to establish and maintain and they are unableto predict disasters in advance On the other hand themass history of mechanical data and meteorology data fromonline monitoring system has been recorded continuouslythis history reflects the real mapping relationship betweendisasters and factors
Consequently it is significant tomine helpful informationfrom mass history data using intelligent algorithms [11ndash14]By these means we not only can take full advantage of themass data from expensive instruments but can also deter-mine the prediction models for icing threats McComberet al [15] Larouche et al [16] and others [17] presented amodel based on an artificial neural network to predict theicing process using history data but those models do nottake into consideration the relationship between icing loadsand the time effects of micrometeorology Li et al [18] andLi et al [19] established a model describing the time effectsof micrometeorology on line icing based on a time seriesanalysis and machine learning methods but did not definehow best to find the multivariable time series
In this paper we have presented a model based on amultivariable time series to predict the icing load of a powertransmission line which utilizes the historymeteorology datafrom the icing monitoring system of China Southern PowerGrid Corp (CSPGC) and takes into account the time effectsof meteorology factors using the phase-space reconstruction
The Scientific World Journal 3
theory to establish it According to the simulation results thismodel accurately predicted the icing load in the Tao-Luo-Xiong Transmission Line and would prove helpful for powergrid departments in their efforts to take action against icingdisasters
2 Prediction Model Based onMultivariable Time Series
21 Time Effects Analysis of Influence Factors in the IcingProcess Due to the huge damage of freezes disaster inJanuary 2008 CSPGC has built the icing monitoring systemsin some important overhead transmission lines in the north-east area of Yunnan Province The micrometeorology andforce data are collected by field sensors and synchronouslytransmitted to monitoring center through GSM (globalsystem for mobile) communication system Figure 2 showsthree icing processes two of which are serious in the Tao-Luo-Xiong Transmission Line from December 14th of 2009to January 25th of 2010 There is an obvious relationshipbetween the icing load (weight) and influence factors suchas the environment temperature humidity wind speed winddirection air pressure and sunlight intensity
Following are the approximate increasing conditions forthe icing process in this line
(1) humidity is above 90
(2) wind direction is about 70∘
(3) wind speed is close to 0ms
(4) air pressure is above 735 Pa
(5) sunlight is minimal during the day
(6) temperature is below 0∘C
If those conditions continue and temperature continuesto drop the ice rain will continue for a significant amountof time consequently the degree of icing will become moreserious
As the Makkonen model [9 20] describes the icingaccretion process is formulated as follows
119889119902119882
(119905) = 2119877 (119905) 1205721
(119905) 1205722
(119905) 1205723
(119905) 119867 (119905) 119882119878
(119905) 119889119905 (1)
where 119877(119905) is the equivalent radius of the icing line whichrestricts the surface area of the icing line that the ice rain cancling to 120572
1(119905) is the collision efficiency which is determined
by forces of aerodynamic drag and inertia for water droplets1205722(119905) is the sticking efficiency which denotes the efficiency
with which a water droplet hits an iced-over surface such thatit rapidly freezes and does not bounce 120572
3(119905) is the accretion
efficiency During the dry-growth icing process 1205723(119905) = 1
during wet-growth icing the freezing rate is controlled by therate at which the latent heat is released during the freezingprocess 0 lt 120572
3(119905) lt 1 119867(119905) is the environment humidity and
119882119878(119905) is the wind speed
500 1000 1500 2000 2500 3000
minus200
20
050
100Humidity ()
0
01020
Wind speed (ms)
0200400
720740760
Air pressure (Pa)
010002000
0500
1000Icing load (kg)
The first seriousicing process
The second seriousicing process
Temperature (∘C)
Sunlight (Wm2)
Wind direction (∘)
Figure 2 Meteorology data and icing load curves I (20091214ndash2010125)
Assuming 1198770is the radius of the line without icing we
can obtain the following estimation formula
119902119882
(119905) = int
119905
1199050
2119877 (120591) 1205721
(120591) 1205722
(120591) 1205723
(120591) 119867 (120591) 119882119878
(120591) 119889120591
+ 1199020
119877 (119905) =
(1198770
minus radic(4119902119882
(119905) 98120587120574) + 11987720
)
2+ 1198770
(2)
where 1199020is the weight of ice per unit length for the transmis-
sion line at initial time 1199050and 120574 is the average density of the
iceUsing formula (2) (3) is deduced
1199021015840
119882
(119905) = (31198770
minus radic4119902119882
(119905)
98120587120574+ 11987720
)
times 1205721
(119905) 1205722
(119905) 1205723
(119905) 119867 (119905) 119882119878
(119905)
(3)
If defining 119906(119905) = 1205721(119905)1205722(119905)1205723(119905)119867(119905)119882
119878(119905) 119879 as the
sampling period and assuming 119879 = 1 then the state equationof the icing process is shown as the following formula
1199021015840
119882
(119896) = 119891 (119902119882
(119896 minus 1) 119906 (119896 minus 1)) 119896 = 1 2 119899 (4)
As formula (4) shows the state of the icing process isdriven by time series 119906(119896) and 119906(119896) is related to micrometeo-rology factors including environment temperature humid-ity wind speed wind direction air pressure and sunlightintensity [19] as formula (5) shows
119906 (119905) = Γ (119879119875
(119905) 119867 (119905) 119882119878
(119905) 119882119863
(119905) 119860119875
(119905) 119878119868(119905)) (5)
It is also possible to describe formula (4) using formula(6) as a discrete state equation
119902119882
(119896) = 119892 (119902119882
(119896 minus 1) 119879119875
(119896 minus 1) 119867 (119896 minus 1)
119882119878
(119896 minus 1) 119882119863
(119896 minus 1) 119860119875
(119896 minus 1) 119878119868(119896 minus 1))
(6)
4 The Scientific World Journal
where the variables are defined as follows 119902119882 icing load
(weight) of transmission line 119879119875 environment temperature
119867 environment humidity 119882119878 wind speed 119882
119863 wind direc-
tion (clockwise angle departure fromnorth)119860119875 air pressure
119878119868 sunlight intensity 119896 sampling time 119892(lowast) mapping
functionThe process of line icing can be regarded as the icing load
at time 119896 which is decided by icing load and micrometeorol-ogy factors at time 119896 minus 1 that is a multivariate time seriesprocess
22 Icing Load Time Series Model Based on Phase-SpaceReconstruction and Machine Learning But as shown inFigure 2 it is evident that the process of transmission lineicing is fitful and complex icing or melting often hap-pens alternately over several months and the increasing ordecreasing of the icing process is nonlinear and nonstation-ary Thus it is difficult to find the mapping function 119892(lowast) in(6)
A chaos time series prediction theory based on phase-space reconstruction has been widely applied in predictionfor multivariable and nonlinear time series [21 22] In thispaper it is the theoretical foundation for modeling the icingprocess
221 Phase-Space Reconstruction of Multivarious Time Seri-ous for Icing Process According to Takensrsquo embedding the-orem [23] for chaos time series modeling a time series canbe defined as 119909
119894119897
119894=1
where 119897 is the length of the time serieswhich can be reconstructed from a 119863-dimensional phasespace described by the following formula
x119894(119905) = [119909
119894(119905) 119909119894(119905 minus 120591) 119909
119894(119905 minus (119898 minus 1) 120591)]
119879
(7)
where 119898 is known as the embedding dimension of recon-structed phase space and 120591 is the delay constant Becausethe power transmission line icing is a multivariate timeseries described by formula (6) according to the phase-spacereconstruction model shown as formula (7) the time seriesprediction model of power transmission line icing can befound as the following formula
119881 (119899) = [119902119882
(119899) 119902119882
(119899 minus 1205911) 119902
119882(119899 minus (119889
1minus 1) 120591
1)
119879119875
(119899) 119879119875
(119899 minus 1205912) 119879
119875(119899 minus (119889
2minus 1) 120591
2)
119867 (119899) 119867 (119899 minus 1205913) 119867 (119899 minus (119889
3minus 1) 120591
3)
119882119878
(119899) 119882119878
(119899 minus 1205914) 119882
119878(119899 minus (119889
4minus 1) 120591
4)
119882119863
(119899) 119882119863
(119899 minus 1205915) 119882
119863(119899 minus (119889
5minus 1) 120591
5)
119860119875
(119899) 119860119875
(119899 minus 1205916) 119860
119875(119899 minus (119889
6minus 1) 120591
6)
119878119871
(119899) 119878119871
(119899 minus 1205917) 119878
119871(119899 minus (119889
7minus 1) 120591
7)]119879
(8)
where 119899 is the total number of sampling for icing processtime series and 120591
119894and 119889
119894are the time delay and embedding
dimension for each variable respectively 119894 = 1 2 7
Table 1 Delay time 120591119894
and embedding dimension 119889119894
Various 119902119908
119879119875
119867 119882119878
119882119863
119860119901
119878119871
120591119894
2 0 0 0 0 0 0119889119894
5 1 1 1 1 1 1
Based on Takensrsquo embedding theorem [23] if 119889 = sum7
119894=1
119889119894is
large enough and 1 le 119896 le 119886 119886 is the most step length forprediction and the mapping function Φ
(119889) is available
119881 (119899 + 119896) = Φ(119889)
(119881 (119899)) (9)
Formula (9) is equal to (10) as follows
119902119882
(119899 + 119896) = Φ1
(119881 (119899))
119879119875
(119899 + 119896) = Φ2
(119881 (119899))
119878119871
(119899 + 119896) = Φ7
(119881 (119899))
(10)
Therefore the mapping for 119902119882
(119899 + 119896) and 119881(119899) can bedescribed as the following formula
119902119882
(119899 + 119896) = Φ1
(119881 (119899)) (11)
As Takensrsquo embedding principle based on chaos theoryindicates selecting 120591
119894and 119889119894is important for (8) because they
decide the degree of approximation for the phase space andthe size of the attractor In this paper the autocorrelationalgorithm [24] was applied to estimate the delay time 120591
119894
and the saturated correlation dimension algorithm (G-Palgorithm) [25] was used to select the embedding dimension119889119894However if there is no noise in this time series then Tak-
ensrsquo embedding principle [23] figures that an unoptimizable120591119894is not influential in its performance for phase space to
describe the dynamic characteristics of a complex processSo owing to decreasing complexity of computing we confirm1205911
= 2 and 120591119894= 0 (119894 = 1)
Values of delay time 120591119894and embedding dimension 119889
119894are
shown in Table 1The mapping between 119902
119882(119899 + 119896) and 119881(119899) is obtained as
the following formula
119902119882
(119899 + 119896) = Φ1
(119902119882
(119899) 119902119882
(119899 minus 2) 119902119882
(119899 minus 4)
119902119882
(119899 minus 10) 119879119875
(119899) 119867 (119899) 119882119878
(119899)
119882119863
(119899) 119860119875
(119899) 119878119871
(119899))
(12)
Function Φ1(sdot) is the optimization mapping which can
be obtained using the following formula
min 119869 =
119873
sum
119899=1
[119902119882
(119899 + 119896) minus Φ1
(119881 (119899))]2
(13)
where Φ1(sdot) is the optimal estimate for Φ
1(sdot)
The Scientific World Journal 5
Adjust related weight or factor
Rated load of tower
Prediction icing load
BPNN or SVM(modeling)
More than the setting training steps or the average of whole
error less than the set point
No
Yes
History meteorological data and icing load
Stop training
BPNN or SVM(established)
Forecast data of meteorological
Results of prediction for
icing threat
(a) Modeling (b) Prediction
Fuzzy reasoning
Pretreatment
Figure 3 The process of modeling and prediction
222 Optimization Mapping Modeling of Icing Process BasedonMachine Learning As Φ
1(sdot) is multivariate and nonlinear
we can obtain it using BPNN (back propagation neuralnetwork) [26ndash28] SVM (support vector machine) [29 30]and other data-driven methods Here Φ
1(sdot) is founded by
BPNN it is a machine learning process as shown in Figure 3After training that is also the prediction model of the icingload time series
As formula (13) shows the output of BPNN is the resultof a prediction at time 119899 which denotes the value of icingload at time 119899 + 119896 119879
119875(119899) 119867(119899) 119882
119878(119899) 119882
119863(119899) 119860
119875(119899) and
119878119871(119899) denote the meteorology factors such as temperature
humidity wind speed wind direction and sunlight whichimpact the process of icing at time 119899
119902119882
(119899) 119902119882
(119899 minus 2) 119902119882
(119899 minus 4) 119902119882
(119899 minus 6) 119902119882
(119899 minus 8) and119902119882
(119899 minus 10) are the history icing loads at time 119899 119899 minus 2 119899 minus 4119899 minus 6 119899 minus 8 and 119899 minus 10 which are achieved by the mechanicalmodel [3 4]
In this method given the ability to approximate anynonlinear mapping using learning in BPNN the functionΦ1(sdot)was found using themodel in Figure 3(a) After training
the BBPN the predictionmodel could be applied as shown inFigure 3(b) Determining the icing prediction values allowsthe relevant departments to assess the threat of inclementweather to the power grid and take some deicing or main-tenance actions in advance
3 Simulation and Analysis
Micrometeorology data including environment temperaturehumidity wind velocity wind direction sunlight intensityand air pressure in addition to the insulatorrsquos mechanicaldata such as pull force wind angle and lean angle wereacquired from an online monitoring system tracking theTao-Luo-Xiong Transmission Line in the northwest area ofYunnan Province China
The data were collected from a variety of sensors andrecorded every 20 minutes from November 2009 to January2010 as shown in Figure 2 which shows the twomost seriousicing processes
For the purposes of this paper in testing the modelrsquosprecision and robustness the simulations were carried outduring the same icing process or different process
However the prediction model in this paper has beenbased on phase-space reconstruction it is a multivariabletime series prediction model which considers multidimen-sional meteorology factors If we take the icing process asa single variable time series and predict it using ARIMA(autoregressive integrated moving average) model [22] thedifferences between the two icing process predictionmethodshave also been analyzed in this paper
As Figure 3(a) shows the first step for finding the icingthreat prediction model based on data-driven methods is to
6 The Scientific World Journal
pretreat the data Because the model is based on methodsincluding BPNN SVM [29] and other machine learningalgorithms the quality of data determines the precision ofthemodel Data pretreatment can reduce uncertain effects formodeling through the use of a filter or smoothing methodsGiven that formula (12) was found without noise datapretreatment is necessary for a prediction model based onphase-space reconstruction
31 Data Pretreatment As shown in Figure 2 wind speedwinddirection sunlight intensity and icing loads are unstablewhen comparing temperature humidity and air pressureThat can result in some disadvantages for modeling asdescribed in the following in which case we only performedpretreatment for those four variations
(1) The sunlight intensity changes periodically Duringthe daytime there is an obvious difference when the weatheris clear or raining but at night regardless whether theweather is clear or raining the sunlight intensity is the sameequaling zero which impacts the learning of BPNN Havingbeen filtered using the wavelets algorithm [31] the curve ofsunlight is displayed in Figure 4 It holds certain relativitywith the icing load the icing begins and increases when thesunlight intensity is close to zero
(2) Owing to uncertain shelling during the icing processthere exist some noise and outliers in the value of the icingload These are determined by the shape and distribution ofice along the transmission line and not only by meteorologyfactors The precision would be influenced if training withthose noise and outliers In Figure 4 the icing load has beensmoothed by using weighted linear least squares model [32]
(3) As shown in the analysis in Section 21 the icingbegins and rises when the wind direction is about 70∘ andwind speed is close to zero Although wind speed and winddirection have some stability over a limited period theychange with the air currentThis also impacts the training forthemodel In Figure 4 thewinddirection and speed have alsobeen smoothed using the weighted linear least squares model[31]
32 Icing Load Prediction in Same Icing Process In this casewe predicted the icing load in the same process whichmeansthe simulation data for training and for prediction exist in thesame icing process In this icing process as shown in Figure 2the number of data is 230 from December 17th to 20th in2009 the frontal 192 data were used as the training inputnot including the shelling (melting) phase The modelingflow chart of the BPNN is shown in Figure 3(a) the maximalsetting of training steps is 1000 the error value of set point is001 and the earning rate parameter is 01
After finding the model the remainder data were availedto prediction As a result we achieved the prediction resultsas Figure 5 when the prediction length 119896 is 1
In Figure 5 the trend of change for the icing process hasbeen predicted accurately the error variance of prediction is1086 kg which is about 14 ofmax icing load in this process
If prediction length 119896 increases the prediction errorvariances will rise rapidly as Table 2 shows But if 119896 le 4
0500
1000Filter result of icing load (kg)
05
1015
Filter result of wind speed (ms)
0100200300
0 500 1000 1500 2000 2500 30000200400600
The first serious icing process The second serious icing process
Filter result of sunlight (Wm2)
Filter result of wind direction (∘)
Figure 4 Filter results of 119902119882
119882119875
119882119863
and 119878119871
0 5 10 15 20 25 30 35 40minus200
0
200
400
600
800
1000
Icin
g lo
ad (k
g)
Prediction valueActual valueError
Figure 5 Results of prediction in the same icing process (119896 = 1) forthe first serious icing process (20091217ndash20091220)
Table 2 The error variances of icing load prediction in sameicing process for the first serious icing process from (12172009sim
12202009)
Prediction length 119896 1 2 3 4 5 6Standard deviation(multivariable predictionbased on BPNN)
1086 1345 1428 1817 2556 2975
Standard deviation (singlevariable prediction basedon ARIMA)
1519 1947 2635 2893 3201 3862
the error variance will be less than 30 of the max icingload This is available prediction information for power griddepartment to use against icing disasters
If we do predict using the ARIMA model it is obviousthat the error variances will be greater than in the model wehave shown in this paperThe results can be found in Table 2
Similarly if we predict the second serious icing process asFigure 2 shows where the number of training data is 109 fromJanuary 10th to 12th in 2010 the number of prediction data is41 on January 12th in 2010 Results are shown in Figure 6 andTable 3
The Scientific World Journal 7
minus200
0
200
400
600
800
1000
Icin
g lo
ad (k
g)
0 5 10 15 20 25 30 35 4540
Prediction valueActual valueError
Figure 6 Results of prediction in same icing process (119896 = 1) for thesecond serious icing process (1102010sim1122010)
Table 3 The error variances of icing load prediction in same icingprocess for the second serious icing process (1102010sim1122010)
Prediction length 119896 1 2 3 4 5 6Standard deviation(multivariable predictionbased on BPNN)
1361 1494 1725 2106 2821 3136
Standard deviation (singlevariable prediction basedon ARIMA)
1452 2049 2887 2936 3684 4074
33 Icing Load Prediction in Different Icing Process As shownin Figure 2 we have selected the full process of the firstserious icing as the training input data which is also shownin Figure 4 The training process involves three phasesincluding inexistence rising and shelling (melting) UnlikeSection 32 the shelling phase is used to train the BPNNThenumber of training data is 310 fromDecember 17th to 20th in2009 the maximal setting steps of training are 1000 the errorvalue of set point is 001 and the earning rate parameter is 01
The second serious icing process is used to make predic-tions The number of predictions is 150 from January 10thto 12th in 2010 which is shown in Figure 2 The results ofsimulation are as shown in Figure 7
In Figure 7 the trend of change for the icing process ispredicted more accurately because the error in the shellingphase is less than found in Figure 6 The error variance ofprediction is 712 kg which is about 10 of max icing loadin this process
This is similar to Section 32 in that the prediction errorvariances will rise rapidly if prediction length 119896 increases asshown in Table 4 If 119896 ge 5 the error variance will be morethan 30 of the max icing load
If we perform a prediction using ARIMA model it isevident that the error variances are greater than found inthe model with the multivariable time series On the otherhand the error variances that were predicted in the different
0 50 100 150minus400
minus200
0
200
400
600
800
1000
Icin
g lo
ad (k
g)
Prediction valueActual valueError
Figure 7 Results of prediction in different icing process (119896 = 1)
Table 4 The error variances of icing load prediction in differenticing process
Prediction length 119896 1 2 3 4 5 6Standard deviation(multivariable predictionbased on BPNN)
712 935 1358 1789 2666 3247
Standard deviation (singlevariable prediction basedon ARIMA)
1263 1333 1711 2299 3172 3568
processes are all less than in the same process and can beobtained if we compare Table 3 to Table 4
34 Analysis and Summary
(1) ThePrecision of the PredictionModel Based on Time SeriesData-Driven Depends on the Integrality and Sufficiency ofHistory Data Machine learning algorithms such as BPNNand SVM are effective methods for utilizing history datato find the prediction model but the modelrsquos precision isdecided by the training data If the data used for the modeldo not include all possible inputs and outputs the model willnot be suitable to describe the mapping relationship betweenthem
In Section 32 the simulation is during the same processof icing it is obvious that the precision is satisfactory beforethe shelling phase and the error is less than 200 kg Howeverin the shelling phase that is unacceptable especially inFigure 6 where the error is greater than 600 kg This isdependent on the training data which does not cover theshelling phase so it is imprecise
When compared with the results of Section 33 thesimulation is performed during different stages in the icingprocess consequently the error variances are less than thoseof Section 32 whether the prediction length is short or longIt is because of this the data for training input involves wholephases of the icing process including inexistence rising andshelling (melting) As the shelling process is very important
8 The Scientific World Journal
for diagnosing the safety of power transmission line [32] theintegrality and sufficiency of history data is very necessary forprediction of it
(2) The Precision of Prediction Model Is Related to the Lengthof Prediction If Prediction Length Were Short the PredictionError Would Be Small According to the information theory[33] that the correlativity would increase if the time distancedecreases This means the value of the icing load at time 119899
is correlative to the value at time 119899 minus 119896 and the correlativitywould decrease if 119896 increased
As the results of Tables 2ndash4 show when 119896 increases theprediction error will also increase If 119896 lt 5 the error variancewill be less than 30 of max icing load That means if theprediction length is less than two hours it will be helpfulfor power grid departments to take actions in advance forpotential icing disasters along the Tao-Luo-Xiong Line But ifthe length of prediction is more than two hours the methodabout deep learning [34] maybe is a good choice
(3) The Precision of the Prediction Model Based on a Data-Driven Multivariable Time Series Is Better Than One Basedon a Single Variable Time Series According to Takensrsquoembedding principle [23] if time delay and embeddingdimensions are suitable the results of a prediction based ona single variable time series would be satisfactory Howeverthere exist some uncertainty and immaturity in the singlevariable time series so we cannot confirm that the phasespace adequately describes the process of a complex dynamicssystem Multivariable time series are comprised of moredynamic information than a single variable
As the analysis of Section 21 shows the icing processalong the transmission line is complex and decided by multi-meteorological factors Therefore if only based on a singlevariable time series such as the ARIMA model it could notdescribe the icing process exactly The results of Tables 2ndash4also indicate the analysis above
4 Conclusions
The transmission line icing is a nonlinear and high dimensionprocess The advantage of using an automatic monitoringsystem for power transmission lines is that a large amountof process data is available to diagnose Because complex lineicing processes cannot be easily represented using accuratemathematical models a data-driven method must be con-sidered After analyzing the Makkonen model of the icingprocess we determined that the line icing is a multivariatetime series process
Consequently in this paper a model based on multi-variable time series has been presented to predict the icingload of the transmission line In this model time effectsof micrometeorology parameters for the icing process wereanalyzed and the phase-space reconstruction theory andmachine learning methods were applied which utilized thehistoric multivariable time series data to establish the modelAs the characteristic of fitfulness in line icing the simulationswere carried out during the same icing process or differentprocess for testing the precision and robustness of the model
According to the results of simulation for the Tao-Luo-Xiong Transmission Line this model has a good accuracyof prediction in different processes if the prediction lengthis less than five That means the maximal prediction time isapproximately two hours which would be helpful for powergrid departments when deciding to take action in advance toaddress potential icing disasters
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This paper was supported by the National High TechnologyResearch and Development Program (ldquo863rdquo Program) ofChina under Grant no 2011AA05A120 the National Natu-ral Science Foundation of China (NSFC) under Grant no61364024 and the 5th Training Program for the Key YoungTeachers of Yunnan University
References
[1] H Hou X Yin Q Chen D You G Tong andD Shao ldquoReviewon the wide area blackout of 500 kV main power grid in someareas of south china in 2008 snow disasterrdquo Automation ofElectric Power Systems vol 32 no 11 pp 12ndash15 2008
[2] K Savadjiev and M Farzaneh ldquoAnalysis and interpretation oficing rate meter and load cell measurements on the MtBelairicing siterdquo in Proceedings of the 9th International Offshore PolarEngineering Conference vol 2 pp 607ndash611 Brest France 1999
[3] X B Huang and Q D Sun ldquoMechanical analysis on transmis-sion line conductor icing and application of online monitoringsystemrdquoAutomation of Electric Power Systems vol 13 no 14 pp98ndash101 2007
[4] L Yang Y Hao W Li et al ldquoA mechanical calculation modelfor on-line icing-monitoring system of overhead transmissionlinesrdquo Proceedings of the Chinese Society of Electrical Engineer-ing vol 30 no 19 pp 100ndash105 2010
[5] Y Xu and R G Bosisio ldquoGoubau ice sensor transitions forelectric power linesrdquo Sensing and Imaging vol 10 no 1-2 pp31ndash40 2009
[6] I Y H Gu U Sistiaga M Sonja et al ldquoAutomatic surveillanceand analysis of snow and ice coverage on electrical insulatorsof power transmission linesrdquo in Proceedings of the InternationalConference (ICCVG rsquo08) vol 5337 of Lecture Notes in ComputerScience pp 368ndash379 Springer 2008
[7] Y Sakamoto ldquoSnow accretion on overhead wiresrdquo PhilosophicalTransactions of the Royal Society A vol 358 no 1776 pp 2941ndash2970 2000
[8] M Farzaneh and K Savadjiev ldquoStatistical analysis of field datafor precipitation icing accretion on overhead power linesrdquo IEEETransactions on Power Delivery vol 20 no 2 pp 1080ndash10872005
[9] L Makkonen ldquoModeling power line icing in freezing precipita-tionrdquo Atmospheric Research vol 46 no 1-2 pp 131ndash142 1998
[10] X Wu L Li and X M Rui ldquoIcing load accretion prognosisfor power transmission linewithmodified hidden semi-Markov
The Scientific World Journal 9
modelrdquo IET Generation Transmission ampDistribution vol 8 no3 pp 480ndash485 2014
[11] S Rajakarunakaran D Devaraj G S Venkatratnam and KSurja Prakasa Rao ldquoArticial neural network approach for faultdetection in LPG transfer systemrdquo Applied Soft Computing vol8 no 1 pp 740ndash748 2008
[12] A Quteishat and C P Lim ldquoA modified fuzzy min-maxneural network with rule extraction and its application to faultdetection and classificationrdquo Applied Soft Computing Journalvol 8 no 2 pp 985ndash995 2008
[13] J Xu and Z Hou ldquoNotes on data-driven system approachesrdquoActa Automatica Sinica vol 35 no 6 pp 668ndash675 2009
[14] E Zio and F Di Maio ldquoA data-driven fuzzy approach forpredicting the remaining useful life in dynamic failure scenariosof a nuclear systemrdquo Reliability Engineering and System Safetyvol 95 no 1 pp 49ndash57 2010
[15] P McComber J De Lafontaine and J Laflamme ldquoA neuralsystem to estimate transmission line icingrdquo in Proceedings of the8th International Workshop on Atmospheric Icing on Structures(IWAIS rsquo98) pp 101ndash106 Reykjavik Iceland 1998
[16] E Larouche J Rouat and G Bouchard ldquoExploration ofstatic and time dependent neural network techniques for thepredicion of ice accertion on overhead line conductorsrdquo inProceedings of the 4th International Workshop on AtmosphericIcing of Structures (IWAIS rsquo00) Chester UK 2000
[17] P Li N Li Q Li M Cao and H Chen ldquoPrediction modelfor power transmission line icing load based on data-drivenrdquoAdvanced Materials Research vol 144 pp 1295ndash1299 2011
[18] P Li Q Li M Cao S Gao and H Huang ldquoTime seriesprediction for icing process of overhead power transmissionline based on BP neural networksrdquo in Proceedings of the 30thChinese Control Conference (CCC rsquo11) pp 5315ndash5318 YantaiChina July 2011
[19] Q Li P Li Q Zhang W Ren M Cao and S Gao ldquoIcingload prediction for overhead power lines based on SVMrdquoin Proceedings of the International Conference on ModellingIdentification and Control (ICMIC rsquo11) vol 6 pp 104ndash108 June2011
[20] L Makkonen ldquoModels for the growth of rime glaze icicles andwet snow on structuresrdquo Philosophical Transactions of the RoyalSociety A Mathematical Physical and Engineering Sciences vol358 no 1776 pp 2913ndash2939 2000
[21] L Cao AMees andK Judd ldquoDynamics frommultivariate timeseriesrdquoPhysicaDNonlinear Phenomena vol 121 no 1-2 pp 75ndash88 1998
[22] J Fan and Q Yao Nonlinear Time Series Nonparametric andParametric Methods Springer Berlin Germany 2002
[23] F Takens Daynamical Systems and Turbulence Lecture Notesin Mathematics Sringer Berlin Germany 1981
[24] L AAguirre ldquoAnonlinear correlation function for selecting thedelay time in dynamical reconstructionsrdquo Physics Letters A vol203 no 2-3 pp 88ndash94 1995
[25] P Grassberger and I Procaccia ldquoMeasuring the strangeness ofstrange attractorsrdquo Physica D Nonlinear Phenomena vol 9 no1-2 pp 189ndash208 1983
[26] G Zhexue and S Zhiqiang Neural Network Theory and ItsApplication Publishing House of Electronics Industry BeijingChina 2008
[27] C Chuang S Su and C Hsiao ldquoThe Annealing Robust Back-propagation (ARBP) learning algorithmrdquo IEEE Transactions onNeural Networks vol 11 no 5 pp 1067ndash1077 2000
[28] H Tsukimoto ldquoExtracting rules from trained neural networksrdquoIEEE Transactions on Neural Networks vol 11 no 2 pp 377ndash389 2000
[29] VN VapnikTheNature of Statistical LearningTheory SpringerBerlin Germany 1998
[30] Z Y Hu Y K Bao and T Xiong ldquoElectricity load forecastingusing support vector regression with memetic algorithmsrdquoTheScientific World Journal vol 2013 Article ID 292575 10 pages2013
[31] R A Johnson Applied Multivariate Statistical Analysis Pren-tice-Hall New York NY USA 1988
[32] L E Kollar M Farzaneh and P van Dyke ldquoModeling iceshedding propagation on transmission lines with or withoutinterphase spacersrdquo IEEE Transactions on Power Delivery vol28 no 1 pp 261ndash267 2013
[33] J A van der Lubbe Information Theory Cambridge UniversityPress Cambridge UK 1997
[34] J Schmidhuber ldquoDeep learning in neural networks anoverviewrdquo Tech Rep University of Lugano amp SUPS I MannoSwitzerland 2014
Submit your manuscripts athttpwwwhindawicom
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Distributed Sensor Networks
International Journal of
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SensorsJournal of
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Advances inOptoElectronics
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Navigation and Observation
International Journal of
2 The Scientific World Journal
Safety diagnosis prediction and
decision-making for maintenance
Controller
Detecting
Maintenance Power grid
Monitoringsystem
ObjectSafety targetsfor power grid State
Figure 1 Maintenance based on safety status prediction
installed near the transmission line This method is conve-nient but imprecise when measuring the load of line icingHuang and Sun [3] and Yang et al [4] presented amechanicalmodel that has advantages in timely and exact estimates forthe load of lines icing but the instruments for sampling theforce data are expensive This method is unable to forecastthe icing status it can only display the real-time status of theicing process The Glouba model [5] and the edge of imageextraction model [6] succeed in practice they can estimatethe icing load at a low cost but their precision is less than themechanical model and they are also unable to forecast icingstatus
As shown in Figure 1 it is obvious that decision-makingbased on a predictive status for maintenance is better thanone based on a current status because the predictive controlhas the advantage of reducing unsafe factors in advancecompared to a simple feedback control loopTherefore if thetransmission linersquos icing status has been predicted and unsafeparts of it have been assessed the departments of power gridmaintenance can actively optimize a schedule to deice thelines
Consequently it is imperative to find methods to predictthe icing threat of power grid usingmeteorology informationforecasted by the weather bureau
In the area of research focused on predicting the icingprocess an experiment model [7] and a statistical analysismodel [8] based on micrometeorology parameters predictedicing loads using certain micrometeorology parameters suchas the environmental temperature humidity wind veloc-ity and direction rainfall and snowfall The Makkonenmodel [9] is based on a thermodynamic mechanism butits variables such as the content of liquid state water anda distributing dripping parameter can be obtained in alaboratory but are difficult to measure at local monitoringpoints along a transmission line so it is not generally suitablefor the icing process
Even though the mathematical models above have beenobtained they are founded in special conditions either bystatistical analysis methods or thermodynamic mechanismsand are not robust enough to withstand if the environmentchanges because the micrometeorology conditions are dif-ferent in each instance when lines ice over for example in
a valley versus along a hillside Furthermore because of thecomplexity and nonlinearity of the icing models it is difficultto acquire all of them to predict icing process in differentlocations because themapping relationship changes betweenthe independent variables and dependent variables
In the northeast area of Yunnan Province in China icingdisasters happen frequently [10] Plentiful advanced forcemeasurements andmicroweather stations have been installedfor the online monitoring of power grids and the real-time icing load status and micrometeorology parameters aretransmitted concurrently to a surveillance center by wiredandwireless sensor networks But as a result of the complexityin microlandforms and micrometeorology in this area it isdifficult to find a specific mathematics model to predict theicing process in different transmission lines
On the one hand the cost of an onlinemonitoring systemis expensive to establish and maintain and they are unableto predict disasters in advance On the other hand themass history of mechanical data and meteorology data fromonline monitoring system has been recorded continuouslythis history reflects the real mapping relationship betweendisasters and factors
Consequently it is significant tomine helpful informationfrom mass history data using intelligent algorithms [11ndash14]By these means we not only can take full advantage of themass data from expensive instruments but can also deter-mine the prediction models for icing threats McComberet al [15] Larouche et al [16] and others [17] presented amodel based on an artificial neural network to predict theicing process using history data but those models do nottake into consideration the relationship between icing loadsand the time effects of micrometeorology Li et al [18] andLi et al [19] established a model describing the time effectsof micrometeorology on line icing based on a time seriesanalysis and machine learning methods but did not definehow best to find the multivariable time series
In this paper we have presented a model based on amultivariable time series to predict the icing load of a powertransmission line which utilizes the historymeteorology datafrom the icing monitoring system of China Southern PowerGrid Corp (CSPGC) and takes into account the time effectsof meteorology factors using the phase-space reconstruction
The Scientific World Journal 3
theory to establish it According to the simulation results thismodel accurately predicted the icing load in the Tao-Luo-Xiong Transmission Line and would prove helpful for powergrid departments in their efforts to take action against icingdisasters
2 Prediction Model Based onMultivariable Time Series
21 Time Effects Analysis of Influence Factors in the IcingProcess Due to the huge damage of freezes disaster inJanuary 2008 CSPGC has built the icing monitoring systemsin some important overhead transmission lines in the north-east area of Yunnan Province The micrometeorology andforce data are collected by field sensors and synchronouslytransmitted to monitoring center through GSM (globalsystem for mobile) communication system Figure 2 showsthree icing processes two of which are serious in the Tao-Luo-Xiong Transmission Line from December 14th of 2009to January 25th of 2010 There is an obvious relationshipbetween the icing load (weight) and influence factors suchas the environment temperature humidity wind speed winddirection air pressure and sunlight intensity
Following are the approximate increasing conditions forthe icing process in this line
(1) humidity is above 90
(2) wind direction is about 70∘
(3) wind speed is close to 0ms
(4) air pressure is above 735 Pa
(5) sunlight is minimal during the day
(6) temperature is below 0∘C
If those conditions continue and temperature continuesto drop the ice rain will continue for a significant amountof time consequently the degree of icing will become moreserious
As the Makkonen model [9 20] describes the icingaccretion process is formulated as follows
119889119902119882
(119905) = 2119877 (119905) 1205721
(119905) 1205722
(119905) 1205723
(119905) 119867 (119905) 119882119878
(119905) 119889119905 (1)
where 119877(119905) is the equivalent radius of the icing line whichrestricts the surface area of the icing line that the ice rain cancling to 120572
1(119905) is the collision efficiency which is determined
by forces of aerodynamic drag and inertia for water droplets1205722(119905) is the sticking efficiency which denotes the efficiency
with which a water droplet hits an iced-over surface such thatit rapidly freezes and does not bounce 120572
3(119905) is the accretion
efficiency During the dry-growth icing process 1205723(119905) = 1
during wet-growth icing the freezing rate is controlled by therate at which the latent heat is released during the freezingprocess 0 lt 120572
3(119905) lt 1 119867(119905) is the environment humidity and
119882119878(119905) is the wind speed
500 1000 1500 2000 2500 3000
minus200
20
050
100Humidity ()
0
01020
Wind speed (ms)
0200400
720740760
Air pressure (Pa)
010002000
0500
1000Icing load (kg)
The first seriousicing process
The second seriousicing process
Temperature (∘C)
Sunlight (Wm2)
Wind direction (∘)
Figure 2 Meteorology data and icing load curves I (20091214ndash2010125)
Assuming 1198770is the radius of the line without icing we
can obtain the following estimation formula
119902119882
(119905) = int
119905
1199050
2119877 (120591) 1205721
(120591) 1205722
(120591) 1205723
(120591) 119867 (120591) 119882119878
(120591) 119889120591
+ 1199020
119877 (119905) =
(1198770
minus radic(4119902119882
(119905) 98120587120574) + 11987720
)
2+ 1198770
(2)
where 1199020is the weight of ice per unit length for the transmis-
sion line at initial time 1199050and 120574 is the average density of the
iceUsing formula (2) (3) is deduced
1199021015840
119882
(119905) = (31198770
minus radic4119902119882
(119905)
98120587120574+ 11987720
)
times 1205721
(119905) 1205722
(119905) 1205723
(119905) 119867 (119905) 119882119878
(119905)
(3)
If defining 119906(119905) = 1205721(119905)1205722(119905)1205723(119905)119867(119905)119882
119878(119905) 119879 as the
sampling period and assuming 119879 = 1 then the state equationof the icing process is shown as the following formula
1199021015840
119882
(119896) = 119891 (119902119882
(119896 minus 1) 119906 (119896 minus 1)) 119896 = 1 2 119899 (4)
As formula (4) shows the state of the icing process isdriven by time series 119906(119896) and 119906(119896) is related to micrometeo-rology factors including environment temperature humid-ity wind speed wind direction air pressure and sunlightintensity [19] as formula (5) shows
119906 (119905) = Γ (119879119875
(119905) 119867 (119905) 119882119878
(119905) 119882119863
(119905) 119860119875
(119905) 119878119868(119905)) (5)
It is also possible to describe formula (4) using formula(6) as a discrete state equation
119902119882
(119896) = 119892 (119902119882
(119896 minus 1) 119879119875
(119896 minus 1) 119867 (119896 minus 1)
119882119878
(119896 minus 1) 119882119863
(119896 minus 1) 119860119875
(119896 minus 1) 119878119868(119896 minus 1))
(6)
4 The Scientific World Journal
where the variables are defined as follows 119902119882 icing load
(weight) of transmission line 119879119875 environment temperature
119867 environment humidity 119882119878 wind speed 119882
119863 wind direc-
tion (clockwise angle departure fromnorth)119860119875 air pressure
119878119868 sunlight intensity 119896 sampling time 119892(lowast) mapping
functionThe process of line icing can be regarded as the icing load
at time 119896 which is decided by icing load and micrometeorol-ogy factors at time 119896 minus 1 that is a multivariate time seriesprocess
22 Icing Load Time Series Model Based on Phase-SpaceReconstruction and Machine Learning But as shown inFigure 2 it is evident that the process of transmission lineicing is fitful and complex icing or melting often hap-pens alternately over several months and the increasing ordecreasing of the icing process is nonlinear and nonstation-ary Thus it is difficult to find the mapping function 119892(lowast) in(6)
A chaos time series prediction theory based on phase-space reconstruction has been widely applied in predictionfor multivariable and nonlinear time series [21 22] In thispaper it is the theoretical foundation for modeling the icingprocess
221 Phase-Space Reconstruction of Multivarious Time Seri-ous for Icing Process According to Takensrsquo embedding the-orem [23] for chaos time series modeling a time series canbe defined as 119909
119894119897
119894=1
where 119897 is the length of the time serieswhich can be reconstructed from a 119863-dimensional phasespace described by the following formula
x119894(119905) = [119909
119894(119905) 119909119894(119905 minus 120591) 119909
119894(119905 minus (119898 minus 1) 120591)]
119879
(7)
where 119898 is known as the embedding dimension of recon-structed phase space and 120591 is the delay constant Becausethe power transmission line icing is a multivariate timeseries described by formula (6) according to the phase-spacereconstruction model shown as formula (7) the time seriesprediction model of power transmission line icing can befound as the following formula
119881 (119899) = [119902119882
(119899) 119902119882
(119899 minus 1205911) 119902
119882(119899 minus (119889
1minus 1) 120591
1)
119879119875
(119899) 119879119875
(119899 minus 1205912) 119879
119875(119899 minus (119889
2minus 1) 120591
2)
119867 (119899) 119867 (119899 minus 1205913) 119867 (119899 minus (119889
3minus 1) 120591
3)
119882119878
(119899) 119882119878
(119899 minus 1205914) 119882
119878(119899 minus (119889
4minus 1) 120591
4)
119882119863
(119899) 119882119863
(119899 minus 1205915) 119882
119863(119899 minus (119889
5minus 1) 120591
5)
119860119875
(119899) 119860119875
(119899 minus 1205916) 119860
119875(119899 minus (119889
6minus 1) 120591
6)
119878119871
(119899) 119878119871
(119899 minus 1205917) 119878
119871(119899 minus (119889
7minus 1) 120591
7)]119879
(8)
where 119899 is the total number of sampling for icing processtime series and 120591
119894and 119889
119894are the time delay and embedding
dimension for each variable respectively 119894 = 1 2 7
Table 1 Delay time 120591119894
and embedding dimension 119889119894
Various 119902119908
119879119875
119867 119882119878
119882119863
119860119901
119878119871
120591119894
2 0 0 0 0 0 0119889119894
5 1 1 1 1 1 1
Based on Takensrsquo embedding theorem [23] if 119889 = sum7
119894=1
119889119894is
large enough and 1 le 119896 le 119886 119886 is the most step length forprediction and the mapping function Φ
(119889) is available
119881 (119899 + 119896) = Φ(119889)
(119881 (119899)) (9)
Formula (9) is equal to (10) as follows
119902119882
(119899 + 119896) = Φ1
(119881 (119899))
119879119875
(119899 + 119896) = Φ2
(119881 (119899))
119878119871
(119899 + 119896) = Φ7
(119881 (119899))
(10)
Therefore the mapping for 119902119882
(119899 + 119896) and 119881(119899) can bedescribed as the following formula
119902119882
(119899 + 119896) = Φ1
(119881 (119899)) (11)
As Takensrsquo embedding principle based on chaos theoryindicates selecting 120591
119894and 119889119894is important for (8) because they
decide the degree of approximation for the phase space andthe size of the attractor In this paper the autocorrelationalgorithm [24] was applied to estimate the delay time 120591
119894
and the saturated correlation dimension algorithm (G-Palgorithm) [25] was used to select the embedding dimension119889119894However if there is no noise in this time series then Tak-
ensrsquo embedding principle [23] figures that an unoptimizable120591119894is not influential in its performance for phase space to
describe the dynamic characteristics of a complex processSo owing to decreasing complexity of computing we confirm1205911
= 2 and 120591119894= 0 (119894 = 1)
Values of delay time 120591119894and embedding dimension 119889
119894are
shown in Table 1The mapping between 119902
119882(119899 + 119896) and 119881(119899) is obtained as
the following formula
119902119882
(119899 + 119896) = Φ1
(119902119882
(119899) 119902119882
(119899 minus 2) 119902119882
(119899 minus 4)
119902119882
(119899 minus 10) 119879119875
(119899) 119867 (119899) 119882119878
(119899)
119882119863
(119899) 119860119875
(119899) 119878119871
(119899))
(12)
Function Φ1(sdot) is the optimization mapping which can
be obtained using the following formula
min 119869 =
119873
sum
119899=1
[119902119882
(119899 + 119896) minus Φ1
(119881 (119899))]2
(13)
where Φ1(sdot) is the optimal estimate for Φ
1(sdot)
The Scientific World Journal 5
Adjust related weight or factor
Rated load of tower
Prediction icing load
BPNN or SVM(modeling)
More than the setting training steps or the average of whole
error less than the set point
No
Yes
History meteorological data and icing load
Stop training
BPNN or SVM(established)
Forecast data of meteorological
Results of prediction for
icing threat
(a) Modeling (b) Prediction
Fuzzy reasoning
Pretreatment
Figure 3 The process of modeling and prediction
222 Optimization Mapping Modeling of Icing Process BasedonMachine Learning As Φ
1(sdot) is multivariate and nonlinear
we can obtain it using BPNN (back propagation neuralnetwork) [26ndash28] SVM (support vector machine) [29 30]and other data-driven methods Here Φ
1(sdot) is founded by
BPNN it is a machine learning process as shown in Figure 3After training that is also the prediction model of the icingload time series
As formula (13) shows the output of BPNN is the resultof a prediction at time 119899 which denotes the value of icingload at time 119899 + 119896 119879
119875(119899) 119867(119899) 119882
119878(119899) 119882
119863(119899) 119860
119875(119899) and
119878119871(119899) denote the meteorology factors such as temperature
humidity wind speed wind direction and sunlight whichimpact the process of icing at time 119899
119902119882
(119899) 119902119882
(119899 minus 2) 119902119882
(119899 minus 4) 119902119882
(119899 minus 6) 119902119882
(119899 minus 8) and119902119882
(119899 minus 10) are the history icing loads at time 119899 119899 minus 2 119899 minus 4119899 minus 6 119899 minus 8 and 119899 minus 10 which are achieved by the mechanicalmodel [3 4]
In this method given the ability to approximate anynonlinear mapping using learning in BPNN the functionΦ1(sdot)was found using themodel in Figure 3(a) After training
the BBPN the predictionmodel could be applied as shown inFigure 3(b) Determining the icing prediction values allowsthe relevant departments to assess the threat of inclementweather to the power grid and take some deicing or main-tenance actions in advance
3 Simulation and Analysis
Micrometeorology data including environment temperaturehumidity wind velocity wind direction sunlight intensityand air pressure in addition to the insulatorrsquos mechanicaldata such as pull force wind angle and lean angle wereacquired from an online monitoring system tracking theTao-Luo-Xiong Transmission Line in the northwest area ofYunnan Province China
The data were collected from a variety of sensors andrecorded every 20 minutes from November 2009 to January2010 as shown in Figure 2 which shows the twomost seriousicing processes
For the purposes of this paper in testing the modelrsquosprecision and robustness the simulations were carried outduring the same icing process or different process
However the prediction model in this paper has beenbased on phase-space reconstruction it is a multivariabletime series prediction model which considers multidimen-sional meteorology factors If we take the icing process asa single variable time series and predict it using ARIMA(autoregressive integrated moving average) model [22] thedifferences between the two icing process predictionmethodshave also been analyzed in this paper
As Figure 3(a) shows the first step for finding the icingthreat prediction model based on data-driven methods is to
6 The Scientific World Journal
pretreat the data Because the model is based on methodsincluding BPNN SVM [29] and other machine learningalgorithms the quality of data determines the precision ofthemodel Data pretreatment can reduce uncertain effects formodeling through the use of a filter or smoothing methodsGiven that formula (12) was found without noise datapretreatment is necessary for a prediction model based onphase-space reconstruction
31 Data Pretreatment As shown in Figure 2 wind speedwinddirection sunlight intensity and icing loads are unstablewhen comparing temperature humidity and air pressureThat can result in some disadvantages for modeling asdescribed in the following in which case we only performedpretreatment for those four variations
(1) The sunlight intensity changes periodically Duringthe daytime there is an obvious difference when the weatheris clear or raining but at night regardless whether theweather is clear or raining the sunlight intensity is the sameequaling zero which impacts the learning of BPNN Havingbeen filtered using the wavelets algorithm [31] the curve ofsunlight is displayed in Figure 4 It holds certain relativitywith the icing load the icing begins and increases when thesunlight intensity is close to zero
(2) Owing to uncertain shelling during the icing processthere exist some noise and outliers in the value of the icingload These are determined by the shape and distribution ofice along the transmission line and not only by meteorologyfactors The precision would be influenced if training withthose noise and outliers In Figure 4 the icing load has beensmoothed by using weighted linear least squares model [32]
(3) As shown in the analysis in Section 21 the icingbegins and rises when the wind direction is about 70∘ andwind speed is close to zero Although wind speed and winddirection have some stability over a limited period theychange with the air currentThis also impacts the training forthemodel In Figure 4 thewinddirection and speed have alsobeen smoothed using the weighted linear least squares model[31]
32 Icing Load Prediction in Same Icing Process In this casewe predicted the icing load in the same process whichmeansthe simulation data for training and for prediction exist in thesame icing process In this icing process as shown in Figure 2the number of data is 230 from December 17th to 20th in2009 the frontal 192 data were used as the training inputnot including the shelling (melting) phase The modelingflow chart of the BPNN is shown in Figure 3(a) the maximalsetting of training steps is 1000 the error value of set point is001 and the earning rate parameter is 01
After finding the model the remainder data were availedto prediction As a result we achieved the prediction resultsas Figure 5 when the prediction length 119896 is 1
In Figure 5 the trend of change for the icing process hasbeen predicted accurately the error variance of prediction is1086 kg which is about 14 ofmax icing load in this process
If prediction length 119896 increases the prediction errorvariances will rise rapidly as Table 2 shows But if 119896 le 4
0500
1000Filter result of icing load (kg)
05
1015
Filter result of wind speed (ms)
0100200300
0 500 1000 1500 2000 2500 30000200400600
The first serious icing process The second serious icing process
Filter result of sunlight (Wm2)
Filter result of wind direction (∘)
Figure 4 Filter results of 119902119882
119882119875
119882119863
and 119878119871
0 5 10 15 20 25 30 35 40minus200
0
200
400
600
800
1000
Icin
g lo
ad (k
g)
Prediction valueActual valueError
Figure 5 Results of prediction in the same icing process (119896 = 1) forthe first serious icing process (20091217ndash20091220)
Table 2 The error variances of icing load prediction in sameicing process for the first serious icing process from (12172009sim
12202009)
Prediction length 119896 1 2 3 4 5 6Standard deviation(multivariable predictionbased on BPNN)
1086 1345 1428 1817 2556 2975
Standard deviation (singlevariable prediction basedon ARIMA)
1519 1947 2635 2893 3201 3862
the error variance will be less than 30 of the max icingload This is available prediction information for power griddepartment to use against icing disasters
If we do predict using the ARIMA model it is obviousthat the error variances will be greater than in the model wehave shown in this paperThe results can be found in Table 2
Similarly if we predict the second serious icing process asFigure 2 shows where the number of training data is 109 fromJanuary 10th to 12th in 2010 the number of prediction data is41 on January 12th in 2010 Results are shown in Figure 6 andTable 3
The Scientific World Journal 7
minus200
0
200
400
600
800
1000
Icin
g lo
ad (k
g)
0 5 10 15 20 25 30 35 4540
Prediction valueActual valueError
Figure 6 Results of prediction in same icing process (119896 = 1) for thesecond serious icing process (1102010sim1122010)
Table 3 The error variances of icing load prediction in same icingprocess for the second serious icing process (1102010sim1122010)
Prediction length 119896 1 2 3 4 5 6Standard deviation(multivariable predictionbased on BPNN)
1361 1494 1725 2106 2821 3136
Standard deviation (singlevariable prediction basedon ARIMA)
1452 2049 2887 2936 3684 4074
33 Icing Load Prediction in Different Icing Process As shownin Figure 2 we have selected the full process of the firstserious icing as the training input data which is also shownin Figure 4 The training process involves three phasesincluding inexistence rising and shelling (melting) UnlikeSection 32 the shelling phase is used to train the BPNNThenumber of training data is 310 fromDecember 17th to 20th in2009 the maximal setting steps of training are 1000 the errorvalue of set point is 001 and the earning rate parameter is 01
The second serious icing process is used to make predic-tions The number of predictions is 150 from January 10thto 12th in 2010 which is shown in Figure 2 The results ofsimulation are as shown in Figure 7
In Figure 7 the trend of change for the icing process ispredicted more accurately because the error in the shellingphase is less than found in Figure 6 The error variance ofprediction is 712 kg which is about 10 of max icing loadin this process
This is similar to Section 32 in that the prediction errorvariances will rise rapidly if prediction length 119896 increases asshown in Table 4 If 119896 ge 5 the error variance will be morethan 30 of the max icing load
If we perform a prediction using ARIMA model it isevident that the error variances are greater than found inthe model with the multivariable time series On the otherhand the error variances that were predicted in the different
0 50 100 150minus400
minus200
0
200
400
600
800
1000
Icin
g lo
ad (k
g)
Prediction valueActual valueError
Figure 7 Results of prediction in different icing process (119896 = 1)
Table 4 The error variances of icing load prediction in differenticing process
Prediction length 119896 1 2 3 4 5 6Standard deviation(multivariable predictionbased on BPNN)
712 935 1358 1789 2666 3247
Standard deviation (singlevariable prediction basedon ARIMA)
1263 1333 1711 2299 3172 3568
processes are all less than in the same process and can beobtained if we compare Table 3 to Table 4
34 Analysis and Summary
(1) ThePrecision of the PredictionModel Based on Time SeriesData-Driven Depends on the Integrality and Sufficiency ofHistory Data Machine learning algorithms such as BPNNand SVM are effective methods for utilizing history datato find the prediction model but the modelrsquos precision isdecided by the training data If the data used for the modeldo not include all possible inputs and outputs the model willnot be suitable to describe the mapping relationship betweenthem
In Section 32 the simulation is during the same processof icing it is obvious that the precision is satisfactory beforethe shelling phase and the error is less than 200 kg Howeverin the shelling phase that is unacceptable especially inFigure 6 where the error is greater than 600 kg This isdependent on the training data which does not cover theshelling phase so it is imprecise
When compared with the results of Section 33 thesimulation is performed during different stages in the icingprocess consequently the error variances are less than thoseof Section 32 whether the prediction length is short or longIt is because of this the data for training input involves wholephases of the icing process including inexistence rising andshelling (melting) As the shelling process is very important
8 The Scientific World Journal
for diagnosing the safety of power transmission line [32] theintegrality and sufficiency of history data is very necessary forprediction of it
(2) The Precision of Prediction Model Is Related to the Lengthof Prediction If Prediction Length Were Short the PredictionError Would Be Small According to the information theory[33] that the correlativity would increase if the time distancedecreases This means the value of the icing load at time 119899
is correlative to the value at time 119899 minus 119896 and the correlativitywould decrease if 119896 increased
As the results of Tables 2ndash4 show when 119896 increases theprediction error will also increase If 119896 lt 5 the error variancewill be less than 30 of max icing load That means if theprediction length is less than two hours it will be helpfulfor power grid departments to take actions in advance forpotential icing disasters along the Tao-Luo-Xiong Line But ifthe length of prediction is more than two hours the methodabout deep learning [34] maybe is a good choice
(3) The Precision of the Prediction Model Based on a Data-Driven Multivariable Time Series Is Better Than One Basedon a Single Variable Time Series According to Takensrsquoembedding principle [23] if time delay and embeddingdimensions are suitable the results of a prediction based ona single variable time series would be satisfactory Howeverthere exist some uncertainty and immaturity in the singlevariable time series so we cannot confirm that the phasespace adequately describes the process of a complex dynamicssystem Multivariable time series are comprised of moredynamic information than a single variable
As the analysis of Section 21 shows the icing processalong the transmission line is complex and decided by multi-meteorological factors Therefore if only based on a singlevariable time series such as the ARIMA model it could notdescribe the icing process exactly The results of Tables 2ndash4also indicate the analysis above
4 Conclusions
The transmission line icing is a nonlinear and high dimensionprocess The advantage of using an automatic monitoringsystem for power transmission lines is that a large amountof process data is available to diagnose Because complex lineicing processes cannot be easily represented using accuratemathematical models a data-driven method must be con-sidered After analyzing the Makkonen model of the icingprocess we determined that the line icing is a multivariatetime series process
Consequently in this paper a model based on multi-variable time series has been presented to predict the icingload of the transmission line In this model time effectsof micrometeorology parameters for the icing process wereanalyzed and the phase-space reconstruction theory andmachine learning methods were applied which utilized thehistoric multivariable time series data to establish the modelAs the characteristic of fitfulness in line icing the simulationswere carried out during the same icing process or differentprocess for testing the precision and robustness of the model
According to the results of simulation for the Tao-Luo-Xiong Transmission Line this model has a good accuracyof prediction in different processes if the prediction lengthis less than five That means the maximal prediction time isapproximately two hours which would be helpful for powergrid departments when deciding to take action in advance toaddress potential icing disasters
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This paper was supported by the National High TechnologyResearch and Development Program (ldquo863rdquo Program) ofChina under Grant no 2011AA05A120 the National Natu-ral Science Foundation of China (NSFC) under Grant no61364024 and the 5th Training Program for the Key YoungTeachers of Yunnan University
References
[1] H Hou X Yin Q Chen D You G Tong andD Shao ldquoReviewon the wide area blackout of 500 kV main power grid in someareas of south china in 2008 snow disasterrdquo Automation ofElectric Power Systems vol 32 no 11 pp 12ndash15 2008
[2] K Savadjiev and M Farzaneh ldquoAnalysis and interpretation oficing rate meter and load cell measurements on the MtBelairicing siterdquo in Proceedings of the 9th International Offshore PolarEngineering Conference vol 2 pp 607ndash611 Brest France 1999
[3] X B Huang and Q D Sun ldquoMechanical analysis on transmis-sion line conductor icing and application of online monitoringsystemrdquoAutomation of Electric Power Systems vol 13 no 14 pp98ndash101 2007
[4] L Yang Y Hao W Li et al ldquoA mechanical calculation modelfor on-line icing-monitoring system of overhead transmissionlinesrdquo Proceedings of the Chinese Society of Electrical Engineer-ing vol 30 no 19 pp 100ndash105 2010
[5] Y Xu and R G Bosisio ldquoGoubau ice sensor transitions forelectric power linesrdquo Sensing and Imaging vol 10 no 1-2 pp31ndash40 2009
[6] I Y H Gu U Sistiaga M Sonja et al ldquoAutomatic surveillanceand analysis of snow and ice coverage on electrical insulatorsof power transmission linesrdquo in Proceedings of the InternationalConference (ICCVG rsquo08) vol 5337 of Lecture Notes in ComputerScience pp 368ndash379 Springer 2008
[7] Y Sakamoto ldquoSnow accretion on overhead wiresrdquo PhilosophicalTransactions of the Royal Society A vol 358 no 1776 pp 2941ndash2970 2000
[8] M Farzaneh and K Savadjiev ldquoStatistical analysis of field datafor precipitation icing accretion on overhead power linesrdquo IEEETransactions on Power Delivery vol 20 no 2 pp 1080ndash10872005
[9] L Makkonen ldquoModeling power line icing in freezing precipita-tionrdquo Atmospheric Research vol 46 no 1-2 pp 131ndash142 1998
[10] X Wu L Li and X M Rui ldquoIcing load accretion prognosisfor power transmission linewithmodified hidden semi-Markov
The Scientific World Journal 9
modelrdquo IET Generation Transmission ampDistribution vol 8 no3 pp 480ndash485 2014
[11] S Rajakarunakaran D Devaraj G S Venkatratnam and KSurja Prakasa Rao ldquoArticial neural network approach for faultdetection in LPG transfer systemrdquo Applied Soft Computing vol8 no 1 pp 740ndash748 2008
[12] A Quteishat and C P Lim ldquoA modified fuzzy min-maxneural network with rule extraction and its application to faultdetection and classificationrdquo Applied Soft Computing Journalvol 8 no 2 pp 985ndash995 2008
[13] J Xu and Z Hou ldquoNotes on data-driven system approachesrdquoActa Automatica Sinica vol 35 no 6 pp 668ndash675 2009
[14] E Zio and F Di Maio ldquoA data-driven fuzzy approach forpredicting the remaining useful life in dynamic failure scenariosof a nuclear systemrdquo Reliability Engineering and System Safetyvol 95 no 1 pp 49ndash57 2010
[15] P McComber J De Lafontaine and J Laflamme ldquoA neuralsystem to estimate transmission line icingrdquo in Proceedings of the8th International Workshop on Atmospheric Icing on Structures(IWAIS rsquo98) pp 101ndash106 Reykjavik Iceland 1998
[16] E Larouche J Rouat and G Bouchard ldquoExploration ofstatic and time dependent neural network techniques for thepredicion of ice accertion on overhead line conductorsrdquo inProceedings of the 4th International Workshop on AtmosphericIcing of Structures (IWAIS rsquo00) Chester UK 2000
[17] P Li N Li Q Li M Cao and H Chen ldquoPrediction modelfor power transmission line icing load based on data-drivenrdquoAdvanced Materials Research vol 144 pp 1295ndash1299 2011
[18] P Li Q Li M Cao S Gao and H Huang ldquoTime seriesprediction for icing process of overhead power transmissionline based on BP neural networksrdquo in Proceedings of the 30thChinese Control Conference (CCC rsquo11) pp 5315ndash5318 YantaiChina July 2011
[19] Q Li P Li Q Zhang W Ren M Cao and S Gao ldquoIcingload prediction for overhead power lines based on SVMrdquoin Proceedings of the International Conference on ModellingIdentification and Control (ICMIC rsquo11) vol 6 pp 104ndash108 June2011
[20] L Makkonen ldquoModels for the growth of rime glaze icicles andwet snow on structuresrdquo Philosophical Transactions of the RoyalSociety A Mathematical Physical and Engineering Sciences vol358 no 1776 pp 2913ndash2939 2000
[21] L Cao AMees andK Judd ldquoDynamics frommultivariate timeseriesrdquoPhysicaDNonlinear Phenomena vol 121 no 1-2 pp 75ndash88 1998
[22] J Fan and Q Yao Nonlinear Time Series Nonparametric andParametric Methods Springer Berlin Germany 2002
[23] F Takens Daynamical Systems and Turbulence Lecture Notesin Mathematics Sringer Berlin Germany 1981
[24] L AAguirre ldquoAnonlinear correlation function for selecting thedelay time in dynamical reconstructionsrdquo Physics Letters A vol203 no 2-3 pp 88ndash94 1995
[25] P Grassberger and I Procaccia ldquoMeasuring the strangeness ofstrange attractorsrdquo Physica D Nonlinear Phenomena vol 9 no1-2 pp 189ndash208 1983
[26] G Zhexue and S Zhiqiang Neural Network Theory and ItsApplication Publishing House of Electronics Industry BeijingChina 2008
[27] C Chuang S Su and C Hsiao ldquoThe Annealing Robust Back-propagation (ARBP) learning algorithmrdquo IEEE Transactions onNeural Networks vol 11 no 5 pp 1067ndash1077 2000
[28] H Tsukimoto ldquoExtracting rules from trained neural networksrdquoIEEE Transactions on Neural Networks vol 11 no 2 pp 377ndash389 2000
[29] VN VapnikTheNature of Statistical LearningTheory SpringerBerlin Germany 1998
[30] Z Y Hu Y K Bao and T Xiong ldquoElectricity load forecastingusing support vector regression with memetic algorithmsrdquoTheScientific World Journal vol 2013 Article ID 292575 10 pages2013
[31] R A Johnson Applied Multivariate Statistical Analysis Pren-tice-Hall New York NY USA 1988
[32] L E Kollar M Farzaneh and P van Dyke ldquoModeling iceshedding propagation on transmission lines with or withoutinterphase spacersrdquo IEEE Transactions on Power Delivery vol28 no 1 pp 261ndash267 2013
[33] J A van der Lubbe Information Theory Cambridge UniversityPress Cambridge UK 1997
[34] J Schmidhuber ldquoDeep learning in neural networks anoverviewrdquo Tech Rep University of Lugano amp SUPS I MannoSwitzerland 2014
Submit your manuscripts athttpwwwhindawicom
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International Journal of
The Scientific World Journal 3
theory to establish it According to the simulation results thismodel accurately predicted the icing load in the Tao-Luo-Xiong Transmission Line and would prove helpful for powergrid departments in their efforts to take action against icingdisasters
2 Prediction Model Based onMultivariable Time Series
21 Time Effects Analysis of Influence Factors in the IcingProcess Due to the huge damage of freezes disaster inJanuary 2008 CSPGC has built the icing monitoring systemsin some important overhead transmission lines in the north-east area of Yunnan Province The micrometeorology andforce data are collected by field sensors and synchronouslytransmitted to monitoring center through GSM (globalsystem for mobile) communication system Figure 2 showsthree icing processes two of which are serious in the Tao-Luo-Xiong Transmission Line from December 14th of 2009to January 25th of 2010 There is an obvious relationshipbetween the icing load (weight) and influence factors suchas the environment temperature humidity wind speed winddirection air pressure and sunlight intensity
Following are the approximate increasing conditions forthe icing process in this line
(1) humidity is above 90
(2) wind direction is about 70∘
(3) wind speed is close to 0ms
(4) air pressure is above 735 Pa
(5) sunlight is minimal during the day
(6) temperature is below 0∘C
If those conditions continue and temperature continuesto drop the ice rain will continue for a significant amountof time consequently the degree of icing will become moreserious
As the Makkonen model [9 20] describes the icingaccretion process is formulated as follows
119889119902119882
(119905) = 2119877 (119905) 1205721
(119905) 1205722
(119905) 1205723
(119905) 119867 (119905) 119882119878
(119905) 119889119905 (1)
where 119877(119905) is the equivalent radius of the icing line whichrestricts the surface area of the icing line that the ice rain cancling to 120572
1(119905) is the collision efficiency which is determined
by forces of aerodynamic drag and inertia for water droplets1205722(119905) is the sticking efficiency which denotes the efficiency
with which a water droplet hits an iced-over surface such thatit rapidly freezes and does not bounce 120572
3(119905) is the accretion
efficiency During the dry-growth icing process 1205723(119905) = 1
during wet-growth icing the freezing rate is controlled by therate at which the latent heat is released during the freezingprocess 0 lt 120572
3(119905) lt 1 119867(119905) is the environment humidity and
119882119878(119905) is the wind speed
500 1000 1500 2000 2500 3000
minus200
20
050
100Humidity ()
0
01020
Wind speed (ms)
0200400
720740760
Air pressure (Pa)
010002000
0500
1000Icing load (kg)
The first seriousicing process
The second seriousicing process
Temperature (∘C)
Sunlight (Wm2)
Wind direction (∘)
Figure 2 Meteorology data and icing load curves I (20091214ndash2010125)
Assuming 1198770is the radius of the line without icing we
can obtain the following estimation formula
119902119882
(119905) = int
119905
1199050
2119877 (120591) 1205721
(120591) 1205722
(120591) 1205723
(120591) 119867 (120591) 119882119878
(120591) 119889120591
+ 1199020
119877 (119905) =
(1198770
minus radic(4119902119882
(119905) 98120587120574) + 11987720
)
2+ 1198770
(2)
where 1199020is the weight of ice per unit length for the transmis-
sion line at initial time 1199050and 120574 is the average density of the
iceUsing formula (2) (3) is deduced
1199021015840
119882
(119905) = (31198770
minus radic4119902119882
(119905)
98120587120574+ 11987720
)
times 1205721
(119905) 1205722
(119905) 1205723
(119905) 119867 (119905) 119882119878
(119905)
(3)
If defining 119906(119905) = 1205721(119905)1205722(119905)1205723(119905)119867(119905)119882
119878(119905) 119879 as the
sampling period and assuming 119879 = 1 then the state equationof the icing process is shown as the following formula
1199021015840
119882
(119896) = 119891 (119902119882
(119896 minus 1) 119906 (119896 minus 1)) 119896 = 1 2 119899 (4)
As formula (4) shows the state of the icing process isdriven by time series 119906(119896) and 119906(119896) is related to micrometeo-rology factors including environment temperature humid-ity wind speed wind direction air pressure and sunlightintensity [19] as formula (5) shows
119906 (119905) = Γ (119879119875
(119905) 119867 (119905) 119882119878
(119905) 119882119863
(119905) 119860119875
(119905) 119878119868(119905)) (5)
It is also possible to describe formula (4) using formula(6) as a discrete state equation
119902119882
(119896) = 119892 (119902119882
(119896 minus 1) 119879119875
(119896 minus 1) 119867 (119896 minus 1)
119882119878
(119896 minus 1) 119882119863
(119896 minus 1) 119860119875
(119896 minus 1) 119878119868(119896 minus 1))
(6)
4 The Scientific World Journal
where the variables are defined as follows 119902119882 icing load
(weight) of transmission line 119879119875 environment temperature
119867 environment humidity 119882119878 wind speed 119882
119863 wind direc-
tion (clockwise angle departure fromnorth)119860119875 air pressure
119878119868 sunlight intensity 119896 sampling time 119892(lowast) mapping
functionThe process of line icing can be regarded as the icing load
at time 119896 which is decided by icing load and micrometeorol-ogy factors at time 119896 minus 1 that is a multivariate time seriesprocess
22 Icing Load Time Series Model Based on Phase-SpaceReconstruction and Machine Learning But as shown inFigure 2 it is evident that the process of transmission lineicing is fitful and complex icing or melting often hap-pens alternately over several months and the increasing ordecreasing of the icing process is nonlinear and nonstation-ary Thus it is difficult to find the mapping function 119892(lowast) in(6)
A chaos time series prediction theory based on phase-space reconstruction has been widely applied in predictionfor multivariable and nonlinear time series [21 22] In thispaper it is the theoretical foundation for modeling the icingprocess
221 Phase-Space Reconstruction of Multivarious Time Seri-ous for Icing Process According to Takensrsquo embedding the-orem [23] for chaos time series modeling a time series canbe defined as 119909
119894119897
119894=1
where 119897 is the length of the time serieswhich can be reconstructed from a 119863-dimensional phasespace described by the following formula
x119894(119905) = [119909
119894(119905) 119909119894(119905 minus 120591) 119909
119894(119905 minus (119898 minus 1) 120591)]
119879
(7)
where 119898 is known as the embedding dimension of recon-structed phase space and 120591 is the delay constant Becausethe power transmission line icing is a multivariate timeseries described by formula (6) according to the phase-spacereconstruction model shown as formula (7) the time seriesprediction model of power transmission line icing can befound as the following formula
119881 (119899) = [119902119882
(119899) 119902119882
(119899 minus 1205911) 119902
119882(119899 minus (119889
1minus 1) 120591
1)
119879119875
(119899) 119879119875
(119899 minus 1205912) 119879
119875(119899 minus (119889
2minus 1) 120591
2)
119867 (119899) 119867 (119899 minus 1205913) 119867 (119899 minus (119889
3minus 1) 120591
3)
119882119878
(119899) 119882119878
(119899 minus 1205914) 119882
119878(119899 minus (119889
4minus 1) 120591
4)
119882119863
(119899) 119882119863
(119899 minus 1205915) 119882
119863(119899 minus (119889
5minus 1) 120591
5)
119860119875
(119899) 119860119875
(119899 minus 1205916) 119860
119875(119899 minus (119889
6minus 1) 120591
6)
119878119871
(119899) 119878119871
(119899 minus 1205917) 119878
119871(119899 minus (119889
7minus 1) 120591
7)]119879
(8)
where 119899 is the total number of sampling for icing processtime series and 120591
119894and 119889
119894are the time delay and embedding
dimension for each variable respectively 119894 = 1 2 7
Table 1 Delay time 120591119894
and embedding dimension 119889119894
Various 119902119908
119879119875
119867 119882119878
119882119863
119860119901
119878119871
120591119894
2 0 0 0 0 0 0119889119894
5 1 1 1 1 1 1
Based on Takensrsquo embedding theorem [23] if 119889 = sum7
119894=1
119889119894is
large enough and 1 le 119896 le 119886 119886 is the most step length forprediction and the mapping function Φ
(119889) is available
119881 (119899 + 119896) = Φ(119889)
(119881 (119899)) (9)
Formula (9) is equal to (10) as follows
119902119882
(119899 + 119896) = Φ1
(119881 (119899))
119879119875
(119899 + 119896) = Φ2
(119881 (119899))
119878119871
(119899 + 119896) = Φ7
(119881 (119899))
(10)
Therefore the mapping for 119902119882
(119899 + 119896) and 119881(119899) can bedescribed as the following formula
119902119882
(119899 + 119896) = Φ1
(119881 (119899)) (11)
As Takensrsquo embedding principle based on chaos theoryindicates selecting 120591
119894and 119889119894is important for (8) because they
decide the degree of approximation for the phase space andthe size of the attractor In this paper the autocorrelationalgorithm [24] was applied to estimate the delay time 120591
119894
and the saturated correlation dimension algorithm (G-Palgorithm) [25] was used to select the embedding dimension119889119894However if there is no noise in this time series then Tak-
ensrsquo embedding principle [23] figures that an unoptimizable120591119894is not influential in its performance for phase space to
describe the dynamic characteristics of a complex processSo owing to decreasing complexity of computing we confirm1205911
= 2 and 120591119894= 0 (119894 = 1)
Values of delay time 120591119894and embedding dimension 119889
119894are
shown in Table 1The mapping between 119902
119882(119899 + 119896) and 119881(119899) is obtained as
the following formula
119902119882
(119899 + 119896) = Φ1
(119902119882
(119899) 119902119882
(119899 minus 2) 119902119882
(119899 minus 4)
119902119882
(119899 minus 10) 119879119875
(119899) 119867 (119899) 119882119878
(119899)
119882119863
(119899) 119860119875
(119899) 119878119871
(119899))
(12)
Function Φ1(sdot) is the optimization mapping which can
be obtained using the following formula
min 119869 =
119873
sum
119899=1
[119902119882
(119899 + 119896) minus Φ1
(119881 (119899))]2
(13)
where Φ1(sdot) is the optimal estimate for Φ
1(sdot)
The Scientific World Journal 5
Adjust related weight or factor
Rated load of tower
Prediction icing load
BPNN or SVM(modeling)
More than the setting training steps or the average of whole
error less than the set point
No
Yes
History meteorological data and icing load
Stop training
BPNN or SVM(established)
Forecast data of meteorological
Results of prediction for
icing threat
(a) Modeling (b) Prediction
Fuzzy reasoning
Pretreatment
Figure 3 The process of modeling and prediction
222 Optimization Mapping Modeling of Icing Process BasedonMachine Learning As Φ
1(sdot) is multivariate and nonlinear
we can obtain it using BPNN (back propagation neuralnetwork) [26ndash28] SVM (support vector machine) [29 30]and other data-driven methods Here Φ
1(sdot) is founded by
BPNN it is a machine learning process as shown in Figure 3After training that is also the prediction model of the icingload time series
As formula (13) shows the output of BPNN is the resultof a prediction at time 119899 which denotes the value of icingload at time 119899 + 119896 119879
119875(119899) 119867(119899) 119882
119878(119899) 119882
119863(119899) 119860
119875(119899) and
119878119871(119899) denote the meteorology factors such as temperature
humidity wind speed wind direction and sunlight whichimpact the process of icing at time 119899
119902119882
(119899) 119902119882
(119899 minus 2) 119902119882
(119899 minus 4) 119902119882
(119899 minus 6) 119902119882
(119899 minus 8) and119902119882
(119899 minus 10) are the history icing loads at time 119899 119899 minus 2 119899 minus 4119899 minus 6 119899 minus 8 and 119899 minus 10 which are achieved by the mechanicalmodel [3 4]
In this method given the ability to approximate anynonlinear mapping using learning in BPNN the functionΦ1(sdot)was found using themodel in Figure 3(a) After training
the BBPN the predictionmodel could be applied as shown inFigure 3(b) Determining the icing prediction values allowsthe relevant departments to assess the threat of inclementweather to the power grid and take some deicing or main-tenance actions in advance
3 Simulation and Analysis
Micrometeorology data including environment temperaturehumidity wind velocity wind direction sunlight intensityand air pressure in addition to the insulatorrsquos mechanicaldata such as pull force wind angle and lean angle wereacquired from an online monitoring system tracking theTao-Luo-Xiong Transmission Line in the northwest area ofYunnan Province China
The data were collected from a variety of sensors andrecorded every 20 minutes from November 2009 to January2010 as shown in Figure 2 which shows the twomost seriousicing processes
For the purposes of this paper in testing the modelrsquosprecision and robustness the simulations were carried outduring the same icing process or different process
However the prediction model in this paper has beenbased on phase-space reconstruction it is a multivariabletime series prediction model which considers multidimen-sional meteorology factors If we take the icing process asa single variable time series and predict it using ARIMA(autoregressive integrated moving average) model [22] thedifferences between the two icing process predictionmethodshave also been analyzed in this paper
As Figure 3(a) shows the first step for finding the icingthreat prediction model based on data-driven methods is to
6 The Scientific World Journal
pretreat the data Because the model is based on methodsincluding BPNN SVM [29] and other machine learningalgorithms the quality of data determines the precision ofthemodel Data pretreatment can reduce uncertain effects formodeling through the use of a filter or smoothing methodsGiven that formula (12) was found without noise datapretreatment is necessary for a prediction model based onphase-space reconstruction
31 Data Pretreatment As shown in Figure 2 wind speedwinddirection sunlight intensity and icing loads are unstablewhen comparing temperature humidity and air pressureThat can result in some disadvantages for modeling asdescribed in the following in which case we only performedpretreatment for those four variations
(1) The sunlight intensity changes periodically Duringthe daytime there is an obvious difference when the weatheris clear or raining but at night regardless whether theweather is clear or raining the sunlight intensity is the sameequaling zero which impacts the learning of BPNN Havingbeen filtered using the wavelets algorithm [31] the curve ofsunlight is displayed in Figure 4 It holds certain relativitywith the icing load the icing begins and increases when thesunlight intensity is close to zero
(2) Owing to uncertain shelling during the icing processthere exist some noise and outliers in the value of the icingload These are determined by the shape and distribution ofice along the transmission line and not only by meteorologyfactors The precision would be influenced if training withthose noise and outliers In Figure 4 the icing load has beensmoothed by using weighted linear least squares model [32]
(3) As shown in the analysis in Section 21 the icingbegins and rises when the wind direction is about 70∘ andwind speed is close to zero Although wind speed and winddirection have some stability over a limited period theychange with the air currentThis also impacts the training forthemodel In Figure 4 thewinddirection and speed have alsobeen smoothed using the weighted linear least squares model[31]
32 Icing Load Prediction in Same Icing Process In this casewe predicted the icing load in the same process whichmeansthe simulation data for training and for prediction exist in thesame icing process In this icing process as shown in Figure 2the number of data is 230 from December 17th to 20th in2009 the frontal 192 data were used as the training inputnot including the shelling (melting) phase The modelingflow chart of the BPNN is shown in Figure 3(a) the maximalsetting of training steps is 1000 the error value of set point is001 and the earning rate parameter is 01
After finding the model the remainder data were availedto prediction As a result we achieved the prediction resultsas Figure 5 when the prediction length 119896 is 1
In Figure 5 the trend of change for the icing process hasbeen predicted accurately the error variance of prediction is1086 kg which is about 14 ofmax icing load in this process
If prediction length 119896 increases the prediction errorvariances will rise rapidly as Table 2 shows But if 119896 le 4
0500
1000Filter result of icing load (kg)
05
1015
Filter result of wind speed (ms)
0100200300
0 500 1000 1500 2000 2500 30000200400600
The first serious icing process The second serious icing process
Filter result of sunlight (Wm2)
Filter result of wind direction (∘)
Figure 4 Filter results of 119902119882
119882119875
119882119863
and 119878119871
0 5 10 15 20 25 30 35 40minus200
0
200
400
600
800
1000
Icin
g lo
ad (k
g)
Prediction valueActual valueError
Figure 5 Results of prediction in the same icing process (119896 = 1) forthe first serious icing process (20091217ndash20091220)
Table 2 The error variances of icing load prediction in sameicing process for the first serious icing process from (12172009sim
12202009)
Prediction length 119896 1 2 3 4 5 6Standard deviation(multivariable predictionbased on BPNN)
1086 1345 1428 1817 2556 2975
Standard deviation (singlevariable prediction basedon ARIMA)
1519 1947 2635 2893 3201 3862
the error variance will be less than 30 of the max icingload This is available prediction information for power griddepartment to use against icing disasters
If we do predict using the ARIMA model it is obviousthat the error variances will be greater than in the model wehave shown in this paperThe results can be found in Table 2
Similarly if we predict the second serious icing process asFigure 2 shows where the number of training data is 109 fromJanuary 10th to 12th in 2010 the number of prediction data is41 on January 12th in 2010 Results are shown in Figure 6 andTable 3
The Scientific World Journal 7
minus200
0
200
400
600
800
1000
Icin
g lo
ad (k
g)
0 5 10 15 20 25 30 35 4540
Prediction valueActual valueError
Figure 6 Results of prediction in same icing process (119896 = 1) for thesecond serious icing process (1102010sim1122010)
Table 3 The error variances of icing load prediction in same icingprocess for the second serious icing process (1102010sim1122010)
Prediction length 119896 1 2 3 4 5 6Standard deviation(multivariable predictionbased on BPNN)
1361 1494 1725 2106 2821 3136
Standard deviation (singlevariable prediction basedon ARIMA)
1452 2049 2887 2936 3684 4074
33 Icing Load Prediction in Different Icing Process As shownin Figure 2 we have selected the full process of the firstserious icing as the training input data which is also shownin Figure 4 The training process involves three phasesincluding inexistence rising and shelling (melting) UnlikeSection 32 the shelling phase is used to train the BPNNThenumber of training data is 310 fromDecember 17th to 20th in2009 the maximal setting steps of training are 1000 the errorvalue of set point is 001 and the earning rate parameter is 01
The second serious icing process is used to make predic-tions The number of predictions is 150 from January 10thto 12th in 2010 which is shown in Figure 2 The results ofsimulation are as shown in Figure 7
In Figure 7 the trend of change for the icing process ispredicted more accurately because the error in the shellingphase is less than found in Figure 6 The error variance ofprediction is 712 kg which is about 10 of max icing loadin this process
This is similar to Section 32 in that the prediction errorvariances will rise rapidly if prediction length 119896 increases asshown in Table 4 If 119896 ge 5 the error variance will be morethan 30 of the max icing load
If we perform a prediction using ARIMA model it isevident that the error variances are greater than found inthe model with the multivariable time series On the otherhand the error variances that were predicted in the different
0 50 100 150minus400
minus200
0
200
400
600
800
1000
Icin
g lo
ad (k
g)
Prediction valueActual valueError
Figure 7 Results of prediction in different icing process (119896 = 1)
Table 4 The error variances of icing load prediction in differenticing process
Prediction length 119896 1 2 3 4 5 6Standard deviation(multivariable predictionbased on BPNN)
712 935 1358 1789 2666 3247
Standard deviation (singlevariable prediction basedon ARIMA)
1263 1333 1711 2299 3172 3568
processes are all less than in the same process and can beobtained if we compare Table 3 to Table 4
34 Analysis and Summary
(1) ThePrecision of the PredictionModel Based on Time SeriesData-Driven Depends on the Integrality and Sufficiency ofHistory Data Machine learning algorithms such as BPNNand SVM are effective methods for utilizing history datato find the prediction model but the modelrsquos precision isdecided by the training data If the data used for the modeldo not include all possible inputs and outputs the model willnot be suitable to describe the mapping relationship betweenthem
In Section 32 the simulation is during the same processof icing it is obvious that the precision is satisfactory beforethe shelling phase and the error is less than 200 kg Howeverin the shelling phase that is unacceptable especially inFigure 6 where the error is greater than 600 kg This isdependent on the training data which does not cover theshelling phase so it is imprecise
When compared with the results of Section 33 thesimulation is performed during different stages in the icingprocess consequently the error variances are less than thoseof Section 32 whether the prediction length is short or longIt is because of this the data for training input involves wholephases of the icing process including inexistence rising andshelling (melting) As the shelling process is very important
8 The Scientific World Journal
for diagnosing the safety of power transmission line [32] theintegrality and sufficiency of history data is very necessary forprediction of it
(2) The Precision of Prediction Model Is Related to the Lengthof Prediction If Prediction Length Were Short the PredictionError Would Be Small According to the information theory[33] that the correlativity would increase if the time distancedecreases This means the value of the icing load at time 119899
is correlative to the value at time 119899 minus 119896 and the correlativitywould decrease if 119896 increased
As the results of Tables 2ndash4 show when 119896 increases theprediction error will also increase If 119896 lt 5 the error variancewill be less than 30 of max icing load That means if theprediction length is less than two hours it will be helpfulfor power grid departments to take actions in advance forpotential icing disasters along the Tao-Luo-Xiong Line But ifthe length of prediction is more than two hours the methodabout deep learning [34] maybe is a good choice
(3) The Precision of the Prediction Model Based on a Data-Driven Multivariable Time Series Is Better Than One Basedon a Single Variable Time Series According to Takensrsquoembedding principle [23] if time delay and embeddingdimensions are suitable the results of a prediction based ona single variable time series would be satisfactory Howeverthere exist some uncertainty and immaturity in the singlevariable time series so we cannot confirm that the phasespace adequately describes the process of a complex dynamicssystem Multivariable time series are comprised of moredynamic information than a single variable
As the analysis of Section 21 shows the icing processalong the transmission line is complex and decided by multi-meteorological factors Therefore if only based on a singlevariable time series such as the ARIMA model it could notdescribe the icing process exactly The results of Tables 2ndash4also indicate the analysis above
4 Conclusions
The transmission line icing is a nonlinear and high dimensionprocess The advantage of using an automatic monitoringsystem for power transmission lines is that a large amountof process data is available to diagnose Because complex lineicing processes cannot be easily represented using accuratemathematical models a data-driven method must be con-sidered After analyzing the Makkonen model of the icingprocess we determined that the line icing is a multivariatetime series process
Consequently in this paper a model based on multi-variable time series has been presented to predict the icingload of the transmission line In this model time effectsof micrometeorology parameters for the icing process wereanalyzed and the phase-space reconstruction theory andmachine learning methods were applied which utilized thehistoric multivariable time series data to establish the modelAs the characteristic of fitfulness in line icing the simulationswere carried out during the same icing process or differentprocess for testing the precision and robustness of the model
According to the results of simulation for the Tao-Luo-Xiong Transmission Line this model has a good accuracyof prediction in different processes if the prediction lengthis less than five That means the maximal prediction time isapproximately two hours which would be helpful for powergrid departments when deciding to take action in advance toaddress potential icing disasters
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This paper was supported by the National High TechnologyResearch and Development Program (ldquo863rdquo Program) ofChina under Grant no 2011AA05A120 the National Natu-ral Science Foundation of China (NSFC) under Grant no61364024 and the 5th Training Program for the Key YoungTeachers of Yunnan University
References
[1] H Hou X Yin Q Chen D You G Tong andD Shao ldquoReviewon the wide area blackout of 500 kV main power grid in someareas of south china in 2008 snow disasterrdquo Automation ofElectric Power Systems vol 32 no 11 pp 12ndash15 2008
[2] K Savadjiev and M Farzaneh ldquoAnalysis and interpretation oficing rate meter and load cell measurements on the MtBelairicing siterdquo in Proceedings of the 9th International Offshore PolarEngineering Conference vol 2 pp 607ndash611 Brest France 1999
[3] X B Huang and Q D Sun ldquoMechanical analysis on transmis-sion line conductor icing and application of online monitoringsystemrdquoAutomation of Electric Power Systems vol 13 no 14 pp98ndash101 2007
[4] L Yang Y Hao W Li et al ldquoA mechanical calculation modelfor on-line icing-monitoring system of overhead transmissionlinesrdquo Proceedings of the Chinese Society of Electrical Engineer-ing vol 30 no 19 pp 100ndash105 2010
[5] Y Xu and R G Bosisio ldquoGoubau ice sensor transitions forelectric power linesrdquo Sensing and Imaging vol 10 no 1-2 pp31ndash40 2009
[6] I Y H Gu U Sistiaga M Sonja et al ldquoAutomatic surveillanceand analysis of snow and ice coverage on electrical insulatorsof power transmission linesrdquo in Proceedings of the InternationalConference (ICCVG rsquo08) vol 5337 of Lecture Notes in ComputerScience pp 368ndash379 Springer 2008
[7] Y Sakamoto ldquoSnow accretion on overhead wiresrdquo PhilosophicalTransactions of the Royal Society A vol 358 no 1776 pp 2941ndash2970 2000
[8] M Farzaneh and K Savadjiev ldquoStatistical analysis of field datafor precipitation icing accretion on overhead power linesrdquo IEEETransactions on Power Delivery vol 20 no 2 pp 1080ndash10872005
[9] L Makkonen ldquoModeling power line icing in freezing precipita-tionrdquo Atmospheric Research vol 46 no 1-2 pp 131ndash142 1998
[10] X Wu L Li and X M Rui ldquoIcing load accretion prognosisfor power transmission linewithmodified hidden semi-Markov
The Scientific World Journal 9
modelrdquo IET Generation Transmission ampDistribution vol 8 no3 pp 480ndash485 2014
[11] S Rajakarunakaran D Devaraj G S Venkatratnam and KSurja Prakasa Rao ldquoArticial neural network approach for faultdetection in LPG transfer systemrdquo Applied Soft Computing vol8 no 1 pp 740ndash748 2008
[12] A Quteishat and C P Lim ldquoA modified fuzzy min-maxneural network with rule extraction and its application to faultdetection and classificationrdquo Applied Soft Computing Journalvol 8 no 2 pp 985ndash995 2008
[13] J Xu and Z Hou ldquoNotes on data-driven system approachesrdquoActa Automatica Sinica vol 35 no 6 pp 668ndash675 2009
[14] E Zio and F Di Maio ldquoA data-driven fuzzy approach forpredicting the remaining useful life in dynamic failure scenariosof a nuclear systemrdquo Reliability Engineering and System Safetyvol 95 no 1 pp 49ndash57 2010
[15] P McComber J De Lafontaine and J Laflamme ldquoA neuralsystem to estimate transmission line icingrdquo in Proceedings of the8th International Workshop on Atmospheric Icing on Structures(IWAIS rsquo98) pp 101ndash106 Reykjavik Iceland 1998
[16] E Larouche J Rouat and G Bouchard ldquoExploration ofstatic and time dependent neural network techniques for thepredicion of ice accertion on overhead line conductorsrdquo inProceedings of the 4th International Workshop on AtmosphericIcing of Structures (IWAIS rsquo00) Chester UK 2000
[17] P Li N Li Q Li M Cao and H Chen ldquoPrediction modelfor power transmission line icing load based on data-drivenrdquoAdvanced Materials Research vol 144 pp 1295ndash1299 2011
[18] P Li Q Li M Cao S Gao and H Huang ldquoTime seriesprediction for icing process of overhead power transmissionline based on BP neural networksrdquo in Proceedings of the 30thChinese Control Conference (CCC rsquo11) pp 5315ndash5318 YantaiChina July 2011
[19] Q Li P Li Q Zhang W Ren M Cao and S Gao ldquoIcingload prediction for overhead power lines based on SVMrdquoin Proceedings of the International Conference on ModellingIdentification and Control (ICMIC rsquo11) vol 6 pp 104ndash108 June2011
[20] L Makkonen ldquoModels for the growth of rime glaze icicles andwet snow on structuresrdquo Philosophical Transactions of the RoyalSociety A Mathematical Physical and Engineering Sciences vol358 no 1776 pp 2913ndash2939 2000
[21] L Cao AMees andK Judd ldquoDynamics frommultivariate timeseriesrdquoPhysicaDNonlinear Phenomena vol 121 no 1-2 pp 75ndash88 1998
[22] J Fan and Q Yao Nonlinear Time Series Nonparametric andParametric Methods Springer Berlin Germany 2002
[23] F Takens Daynamical Systems and Turbulence Lecture Notesin Mathematics Sringer Berlin Germany 1981
[24] L AAguirre ldquoAnonlinear correlation function for selecting thedelay time in dynamical reconstructionsrdquo Physics Letters A vol203 no 2-3 pp 88ndash94 1995
[25] P Grassberger and I Procaccia ldquoMeasuring the strangeness ofstrange attractorsrdquo Physica D Nonlinear Phenomena vol 9 no1-2 pp 189ndash208 1983
[26] G Zhexue and S Zhiqiang Neural Network Theory and ItsApplication Publishing House of Electronics Industry BeijingChina 2008
[27] C Chuang S Su and C Hsiao ldquoThe Annealing Robust Back-propagation (ARBP) learning algorithmrdquo IEEE Transactions onNeural Networks vol 11 no 5 pp 1067ndash1077 2000
[28] H Tsukimoto ldquoExtracting rules from trained neural networksrdquoIEEE Transactions on Neural Networks vol 11 no 2 pp 377ndash389 2000
[29] VN VapnikTheNature of Statistical LearningTheory SpringerBerlin Germany 1998
[30] Z Y Hu Y K Bao and T Xiong ldquoElectricity load forecastingusing support vector regression with memetic algorithmsrdquoTheScientific World Journal vol 2013 Article ID 292575 10 pages2013
[31] R A Johnson Applied Multivariate Statistical Analysis Pren-tice-Hall New York NY USA 1988
[32] L E Kollar M Farzaneh and P van Dyke ldquoModeling iceshedding propagation on transmission lines with or withoutinterphase spacersrdquo IEEE Transactions on Power Delivery vol28 no 1 pp 261ndash267 2013
[33] J A van der Lubbe Information Theory Cambridge UniversityPress Cambridge UK 1997
[34] J Schmidhuber ldquoDeep learning in neural networks anoverviewrdquo Tech Rep University of Lugano amp SUPS I MannoSwitzerland 2014
Submit your manuscripts athttpwwwhindawicom
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Distributed Sensor Networks
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International Journal of
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Navigation and Observation
International Journal of
4 The Scientific World Journal
where the variables are defined as follows 119902119882 icing load
(weight) of transmission line 119879119875 environment temperature
119867 environment humidity 119882119878 wind speed 119882
119863 wind direc-
tion (clockwise angle departure fromnorth)119860119875 air pressure
119878119868 sunlight intensity 119896 sampling time 119892(lowast) mapping
functionThe process of line icing can be regarded as the icing load
at time 119896 which is decided by icing load and micrometeorol-ogy factors at time 119896 minus 1 that is a multivariate time seriesprocess
22 Icing Load Time Series Model Based on Phase-SpaceReconstruction and Machine Learning But as shown inFigure 2 it is evident that the process of transmission lineicing is fitful and complex icing or melting often hap-pens alternately over several months and the increasing ordecreasing of the icing process is nonlinear and nonstation-ary Thus it is difficult to find the mapping function 119892(lowast) in(6)
A chaos time series prediction theory based on phase-space reconstruction has been widely applied in predictionfor multivariable and nonlinear time series [21 22] In thispaper it is the theoretical foundation for modeling the icingprocess
221 Phase-Space Reconstruction of Multivarious Time Seri-ous for Icing Process According to Takensrsquo embedding the-orem [23] for chaos time series modeling a time series canbe defined as 119909
119894119897
119894=1
where 119897 is the length of the time serieswhich can be reconstructed from a 119863-dimensional phasespace described by the following formula
x119894(119905) = [119909
119894(119905) 119909119894(119905 minus 120591) 119909
119894(119905 minus (119898 minus 1) 120591)]
119879
(7)
where 119898 is known as the embedding dimension of recon-structed phase space and 120591 is the delay constant Becausethe power transmission line icing is a multivariate timeseries described by formula (6) according to the phase-spacereconstruction model shown as formula (7) the time seriesprediction model of power transmission line icing can befound as the following formula
119881 (119899) = [119902119882
(119899) 119902119882
(119899 minus 1205911) 119902
119882(119899 minus (119889
1minus 1) 120591
1)
119879119875
(119899) 119879119875
(119899 minus 1205912) 119879
119875(119899 minus (119889
2minus 1) 120591
2)
119867 (119899) 119867 (119899 minus 1205913) 119867 (119899 minus (119889
3minus 1) 120591
3)
119882119878
(119899) 119882119878
(119899 minus 1205914) 119882
119878(119899 minus (119889
4minus 1) 120591
4)
119882119863
(119899) 119882119863
(119899 minus 1205915) 119882
119863(119899 minus (119889
5minus 1) 120591
5)
119860119875
(119899) 119860119875
(119899 minus 1205916) 119860
119875(119899 minus (119889
6minus 1) 120591
6)
119878119871
(119899) 119878119871
(119899 minus 1205917) 119878
119871(119899 minus (119889
7minus 1) 120591
7)]119879
(8)
where 119899 is the total number of sampling for icing processtime series and 120591
119894and 119889
119894are the time delay and embedding
dimension for each variable respectively 119894 = 1 2 7
Table 1 Delay time 120591119894
and embedding dimension 119889119894
Various 119902119908
119879119875
119867 119882119878
119882119863
119860119901
119878119871
120591119894
2 0 0 0 0 0 0119889119894
5 1 1 1 1 1 1
Based on Takensrsquo embedding theorem [23] if 119889 = sum7
119894=1
119889119894is
large enough and 1 le 119896 le 119886 119886 is the most step length forprediction and the mapping function Φ
(119889) is available
119881 (119899 + 119896) = Φ(119889)
(119881 (119899)) (9)
Formula (9) is equal to (10) as follows
119902119882
(119899 + 119896) = Φ1
(119881 (119899))
119879119875
(119899 + 119896) = Φ2
(119881 (119899))
119878119871
(119899 + 119896) = Φ7
(119881 (119899))
(10)
Therefore the mapping for 119902119882
(119899 + 119896) and 119881(119899) can bedescribed as the following formula
119902119882
(119899 + 119896) = Φ1
(119881 (119899)) (11)
As Takensrsquo embedding principle based on chaos theoryindicates selecting 120591
119894and 119889119894is important for (8) because they
decide the degree of approximation for the phase space andthe size of the attractor In this paper the autocorrelationalgorithm [24] was applied to estimate the delay time 120591
119894
and the saturated correlation dimension algorithm (G-Palgorithm) [25] was used to select the embedding dimension119889119894However if there is no noise in this time series then Tak-
ensrsquo embedding principle [23] figures that an unoptimizable120591119894is not influential in its performance for phase space to
describe the dynamic characteristics of a complex processSo owing to decreasing complexity of computing we confirm1205911
= 2 and 120591119894= 0 (119894 = 1)
Values of delay time 120591119894and embedding dimension 119889
119894are
shown in Table 1The mapping between 119902
119882(119899 + 119896) and 119881(119899) is obtained as
the following formula
119902119882
(119899 + 119896) = Φ1
(119902119882
(119899) 119902119882
(119899 minus 2) 119902119882
(119899 minus 4)
119902119882
(119899 minus 10) 119879119875
(119899) 119867 (119899) 119882119878
(119899)
119882119863
(119899) 119860119875
(119899) 119878119871
(119899))
(12)
Function Φ1(sdot) is the optimization mapping which can
be obtained using the following formula
min 119869 =
119873
sum
119899=1
[119902119882
(119899 + 119896) minus Φ1
(119881 (119899))]2
(13)
where Φ1(sdot) is the optimal estimate for Φ
1(sdot)
The Scientific World Journal 5
Adjust related weight or factor
Rated load of tower
Prediction icing load
BPNN or SVM(modeling)
More than the setting training steps or the average of whole
error less than the set point
No
Yes
History meteorological data and icing load
Stop training
BPNN or SVM(established)
Forecast data of meteorological
Results of prediction for
icing threat
(a) Modeling (b) Prediction
Fuzzy reasoning
Pretreatment
Figure 3 The process of modeling and prediction
222 Optimization Mapping Modeling of Icing Process BasedonMachine Learning As Φ
1(sdot) is multivariate and nonlinear
we can obtain it using BPNN (back propagation neuralnetwork) [26ndash28] SVM (support vector machine) [29 30]and other data-driven methods Here Φ
1(sdot) is founded by
BPNN it is a machine learning process as shown in Figure 3After training that is also the prediction model of the icingload time series
As formula (13) shows the output of BPNN is the resultof a prediction at time 119899 which denotes the value of icingload at time 119899 + 119896 119879
119875(119899) 119867(119899) 119882
119878(119899) 119882
119863(119899) 119860
119875(119899) and
119878119871(119899) denote the meteorology factors such as temperature
humidity wind speed wind direction and sunlight whichimpact the process of icing at time 119899
119902119882
(119899) 119902119882
(119899 minus 2) 119902119882
(119899 minus 4) 119902119882
(119899 minus 6) 119902119882
(119899 minus 8) and119902119882
(119899 minus 10) are the history icing loads at time 119899 119899 minus 2 119899 minus 4119899 minus 6 119899 minus 8 and 119899 minus 10 which are achieved by the mechanicalmodel [3 4]
In this method given the ability to approximate anynonlinear mapping using learning in BPNN the functionΦ1(sdot)was found using themodel in Figure 3(a) After training
the BBPN the predictionmodel could be applied as shown inFigure 3(b) Determining the icing prediction values allowsthe relevant departments to assess the threat of inclementweather to the power grid and take some deicing or main-tenance actions in advance
3 Simulation and Analysis
Micrometeorology data including environment temperaturehumidity wind velocity wind direction sunlight intensityand air pressure in addition to the insulatorrsquos mechanicaldata such as pull force wind angle and lean angle wereacquired from an online monitoring system tracking theTao-Luo-Xiong Transmission Line in the northwest area ofYunnan Province China
The data were collected from a variety of sensors andrecorded every 20 minutes from November 2009 to January2010 as shown in Figure 2 which shows the twomost seriousicing processes
For the purposes of this paper in testing the modelrsquosprecision and robustness the simulations were carried outduring the same icing process or different process
However the prediction model in this paper has beenbased on phase-space reconstruction it is a multivariabletime series prediction model which considers multidimen-sional meteorology factors If we take the icing process asa single variable time series and predict it using ARIMA(autoregressive integrated moving average) model [22] thedifferences between the two icing process predictionmethodshave also been analyzed in this paper
As Figure 3(a) shows the first step for finding the icingthreat prediction model based on data-driven methods is to
6 The Scientific World Journal
pretreat the data Because the model is based on methodsincluding BPNN SVM [29] and other machine learningalgorithms the quality of data determines the precision ofthemodel Data pretreatment can reduce uncertain effects formodeling through the use of a filter or smoothing methodsGiven that formula (12) was found without noise datapretreatment is necessary for a prediction model based onphase-space reconstruction
31 Data Pretreatment As shown in Figure 2 wind speedwinddirection sunlight intensity and icing loads are unstablewhen comparing temperature humidity and air pressureThat can result in some disadvantages for modeling asdescribed in the following in which case we only performedpretreatment for those four variations
(1) The sunlight intensity changes periodically Duringthe daytime there is an obvious difference when the weatheris clear or raining but at night regardless whether theweather is clear or raining the sunlight intensity is the sameequaling zero which impacts the learning of BPNN Havingbeen filtered using the wavelets algorithm [31] the curve ofsunlight is displayed in Figure 4 It holds certain relativitywith the icing load the icing begins and increases when thesunlight intensity is close to zero
(2) Owing to uncertain shelling during the icing processthere exist some noise and outliers in the value of the icingload These are determined by the shape and distribution ofice along the transmission line and not only by meteorologyfactors The precision would be influenced if training withthose noise and outliers In Figure 4 the icing load has beensmoothed by using weighted linear least squares model [32]
(3) As shown in the analysis in Section 21 the icingbegins and rises when the wind direction is about 70∘ andwind speed is close to zero Although wind speed and winddirection have some stability over a limited period theychange with the air currentThis also impacts the training forthemodel In Figure 4 thewinddirection and speed have alsobeen smoothed using the weighted linear least squares model[31]
32 Icing Load Prediction in Same Icing Process In this casewe predicted the icing load in the same process whichmeansthe simulation data for training and for prediction exist in thesame icing process In this icing process as shown in Figure 2the number of data is 230 from December 17th to 20th in2009 the frontal 192 data were used as the training inputnot including the shelling (melting) phase The modelingflow chart of the BPNN is shown in Figure 3(a) the maximalsetting of training steps is 1000 the error value of set point is001 and the earning rate parameter is 01
After finding the model the remainder data were availedto prediction As a result we achieved the prediction resultsas Figure 5 when the prediction length 119896 is 1
In Figure 5 the trend of change for the icing process hasbeen predicted accurately the error variance of prediction is1086 kg which is about 14 ofmax icing load in this process
If prediction length 119896 increases the prediction errorvariances will rise rapidly as Table 2 shows But if 119896 le 4
0500
1000Filter result of icing load (kg)
05
1015
Filter result of wind speed (ms)
0100200300
0 500 1000 1500 2000 2500 30000200400600
The first serious icing process The second serious icing process
Filter result of sunlight (Wm2)
Filter result of wind direction (∘)
Figure 4 Filter results of 119902119882
119882119875
119882119863
and 119878119871
0 5 10 15 20 25 30 35 40minus200
0
200
400
600
800
1000
Icin
g lo
ad (k
g)
Prediction valueActual valueError
Figure 5 Results of prediction in the same icing process (119896 = 1) forthe first serious icing process (20091217ndash20091220)
Table 2 The error variances of icing load prediction in sameicing process for the first serious icing process from (12172009sim
12202009)
Prediction length 119896 1 2 3 4 5 6Standard deviation(multivariable predictionbased on BPNN)
1086 1345 1428 1817 2556 2975
Standard deviation (singlevariable prediction basedon ARIMA)
1519 1947 2635 2893 3201 3862
the error variance will be less than 30 of the max icingload This is available prediction information for power griddepartment to use against icing disasters
If we do predict using the ARIMA model it is obviousthat the error variances will be greater than in the model wehave shown in this paperThe results can be found in Table 2
Similarly if we predict the second serious icing process asFigure 2 shows where the number of training data is 109 fromJanuary 10th to 12th in 2010 the number of prediction data is41 on January 12th in 2010 Results are shown in Figure 6 andTable 3
The Scientific World Journal 7
minus200
0
200
400
600
800
1000
Icin
g lo
ad (k
g)
0 5 10 15 20 25 30 35 4540
Prediction valueActual valueError
Figure 6 Results of prediction in same icing process (119896 = 1) for thesecond serious icing process (1102010sim1122010)
Table 3 The error variances of icing load prediction in same icingprocess for the second serious icing process (1102010sim1122010)
Prediction length 119896 1 2 3 4 5 6Standard deviation(multivariable predictionbased on BPNN)
1361 1494 1725 2106 2821 3136
Standard deviation (singlevariable prediction basedon ARIMA)
1452 2049 2887 2936 3684 4074
33 Icing Load Prediction in Different Icing Process As shownin Figure 2 we have selected the full process of the firstserious icing as the training input data which is also shownin Figure 4 The training process involves three phasesincluding inexistence rising and shelling (melting) UnlikeSection 32 the shelling phase is used to train the BPNNThenumber of training data is 310 fromDecember 17th to 20th in2009 the maximal setting steps of training are 1000 the errorvalue of set point is 001 and the earning rate parameter is 01
The second serious icing process is used to make predic-tions The number of predictions is 150 from January 10thto 12th in 2010 which is shown in Figure 2 The results ofsimulation are as shown in Figure 7
In Figure 7 the trend of change for the icing process ispredicted more accurately because the error in the shellingphase is less than found in Figure 6 The error variance ofprediction is 712 kg which is about 10 of max icing loadin this process
This is similar to Section 32 in that the prediction errorvariances will rise rapidly if prediction length 119896 increases asshown in Table 4 If 119896 ge 5 the error variance will be morethan 30 of the max icing load
If we perform a prediction using ARIMA model it isevident that the error variances are greater than found inthe model with the multivariable time series On the otherhand the error variances that were predicted in the different
0 50 100 150minus400
minus200
0
200
400
600
800
1000
Icin
g lo
ad (k
g)
Prediction valueActual valueError
Figure 7 Results of prediction in different icing process (119896 = 1)
Table 4 The error variances of icing load prediction in differenticing process
Prediction length 119896 1 2 3 4 5 6Standard deviation(multivariable predictionbased on BPNN)
712 935 1358 1789 2666 3247
Standard deviation (singlevariable prediction basedon ARIMA)
1263 1333 1711 2299 3172 3568
processes are all less than in the same process and can beobtained if we compare Table 3 to Table 4
34 Analysis and Summary
(1) ThePrecision of the PredictionModel Based on Time SeriesData-Driven Depends on the Integrality and Sufficiency ofHistory Data Machine learning algorithms such as BPNNand SVM are effective methods for utilizing history datato find the prediction model but the modelrsquos precision isdecided by the training data If the data used for the modeldo not include all possible inputs and outputs the model willnot be suitable to describe the mapping relationship betweenthem
In Section 32 the simulation is during the same processof icing it is obvious that the precision is satisfactory beforethe shelling phase and the error is less than 200 kg Howeverin the shelling phase that is unacceptable especially inFigure 6 where the error is greater than 600 kg This isdependent on the training data which does not cover theshelling phase so it is imprecise
When compared with the results of Section 33 thesimulation is performed during different stages in the icingprocess consequently the error variances are less than thoseof Section 32 whether the prediction length is short or longIt is because of this the data for training input involves wholephases of the icing process including inexistence rising andshelling (melting) As the shelling process is very important
8 The Scientific World Journal
for diagnosing the safety of power transmission line [32] theintegrality and sufficiency of history data is very necessary forprediction of it
(2) The Precision of Prediction Model Is Related to the Lengthof Prediction If Prediction Length Were Short the PredictionError Would Be Small According to the information theory[33] that the correlativity would increase if the time distancedecreases This means the value of the icing load at time 119899
is correlative to the value at time 119899 minus 119896 and the correlativitywould decrease if 119896 increased
As the results of Tables 2ndash4 show when 119896 increases theprediction error will also increase If 119896 lt 5 the error variancewill be less than 30 of max icing load That means if theprediction length is less than two hours it will be helpfulfor power grid departments to take actions in advance forpotential icing disasters along the Tao-Luo-Xiong Line But ifthe length of prediction is more than two hours the methodabout deep learning [34] maybe is a good choice
(3) The Precision of the Prediction Model Based on a Data-Driven Multivariable Time Series Is Better Than One Basedon a Single Variable Time Series According to Takensrsquoembedding principle [23] if time delay and embeddingdimensions are suitable the results of a prediction based ona single variable time series would be satisfactory Howeverthere exist some uncertainty and immaturity in the singlevariable time series so we cannot confirm that the phasespace adequately describes the process of a complex dynamicssystem Multivariable time series are comprised of moredynamic information than a single variable
As the analysis of Section 21 shows the icing processalong the transmission line is complex and decided by multi-meteorological factors Therefore if only based on a singlevariable time series such as the ARIMA model it could notdescribe the icing process exactly The results of Tables 2ndash4also indicate the analysis above
4 Conclusions
The transmission line icing is a nonlinear and high dimensionprocess The advantage of using an automatic monitoringsystem for power transmission lines is that a large amountof process data is available to diagnose Because complex lineicing processes cannot be easily represented using accuratemathematical models a data-driven method must be con-sidered After analyzing the Makkonen model of the icingprocess we determined that the line icing is a multivariatetime series process
Consequently in this paper a model based on multi-variable time series has been presented to predict the icingload of the transmission line In this model time effectsof micrometeorology parameters for the icing process wereanalyzed and the phase-space reconstruction theory andmachine learning methods were applied which utilized thehistoric multivariable time series data to establish the modelAs the characteristic of fitfulness in line icing the simulationswere carried out during the same icing process or differentprocess for testing the precision and robustness of the model
According to the results of simulation for the Tao-Luo-Xiong Transmission Line this model has a good accuracyof prediction in different processes if the prediction lengthis less than five That means the maximal prediction time isapproximately two hours which would be helpful for powergrid departments when deciding to take action in advance toaddress potential icing disasters
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This paper was supported by the National High TechnologyResearch and Development Program (ldquo863rdquo Program) ofChina under Grant no 2011AA05A120 the National Natu-ral Science Foundation of China (NSFC) under Grant no61364024 and the 5th Training Program for the Key YoungTeachers of Yunnan University
References
[1] H Hou X Yin Q Chen D You G Tong andD Shao ldquoReviewon the wide area blackout of 500 kV main power grid in someareas of south china in 2008 snow disasterrdquo Automation ofElectric Power Systems vol 32 no 11 pp 12ndash15 2008
[2] K Savadjiev and M Farzaneh ldquoAnalysis and interpretation oficing rate meter and load cell measurements on the MtBelairicing siterdquo in Proceedings of the 9th International Offshore PolarEngineering Conference vol 2 pp 607ndash611 Brest France 1999
[3] X B Huang and Q D Sun ldquoMechanical analysis on transmis-sion line conductor icing and application of online monitoringsystemrdquoAutomation of Electric Power Systems vol 13 no 14 pp98ndash101 2007
[4] L Yang Y Hao W Li et al ldquoA mechanical calculation modelfor on-line icing-monitoring system of overhead transmissionlinesrdquo Proceedings of the Chinese Society of Electrical Engineer-ing vol 30 no 19 pp 100ndash105 2010
[5] Y Xu and R G Bosisio ldquoGoubau ice sensor transitions forelectric power linesrdquo Sensing and Imaging vol 10 no 1-2 pp31ndash40 2009
[6] I Y H Gu U Sistiaga M Sonja et al ldquoAutomatic surveillanceand analysis of snow and ice coverage on electrical insulatorsof power transmission linesrdquo in Proceedings of the InternationalConference (ICCVG rsquo08) vol 5337 of Lecture Notes in ComputerScience pp 368ndash379 Springer 2008
[7] Y Sakamoto ldquoSnow accretion on overhead wiresrdquo PhilosophicalTransactions of the Royal Society A vol 358 no 1776 pp 2941ndash2970 2000
[8] M Farzaneh and K Savadjiev ldquoStatistical analysis of field datafor precipitation icing accretion on overhead power linesrdquo IEEETransactions on Power Delivery vol 20 no 2 pp 1080ndash10872005
[9] L Makkonen ldquoModeling power line icing in freezing precipita-tionrdquo Atmospheric Research vol 46 no 1-2 pp 131ndash142 1998
[10] X Wu L Li and X M Rui ldquoIcing load accretion prognosisfor power transmission linewithmodified hidden semi-Markov
The Scientific World Journal 9
modelrdquo IET Generation Transmission ampDistribution vol 8 no3 pp 480ndash485 2014
[11] S Rajakarunakaran D Devaraj G S Venkatratnam and KSurja Prakasa Rao ldquoArticial neural network approach for faultdetection in LPG transfer systemrdquo Applied Soft Computing vol8 no 1 pp 740ndash748 2008
[12] A Quteishat and C P Lim ldquoA modified fuzzy min-maxneural network with rule extraction and its application to faultdetection and classificationrdquo Applied Soft Computing Journalvol 8 no 2 pp 985ndash995 2008
[13] J Xu and Z Hou ldquoNotes on data-driven system approachesrdquoActa Automatica Sinica vol 35 no 6 pp 668ndash675 2009
[14] E Zio and F Di Maio ldquoA data-driven fuzzy approach forpredicting the remaining useful life in dynamic failure scenariosof a nuclear systemrdquo Reliability Engineering and System Safetyvol 95 no 1 pp 49ndash57 2010
[15] P McComber J De Lafontaine and J Laflamme ldquoA neuralsystem to estimate transmission line icingrdquo in Proceedings of the8th International Workshop on Atmospheric Icing on Structures(IWAIS rsquo98) pp 101ndash106 Reykjavik Iceland 1998
[16] E Larouche J Rouat and G Bouchard ldquoExploration ofstatic and time dependent neural network techniques for thepredicion of ice accertion on overhead line conductorsrdquo inProceedings of the 4th International Workshop on AtmosphericIcing of Structures (IWAIS rsquo00) Chester UK 2000
[17] P Li N Li Q Li M Cao and H Chen ldquoPrediction modelfor power transmission line icing load based on data-drivenrdquoAdvanced Materials Research vol 144 pp 1295ndash1299 2011
[18] P Li Q Li M Cao S Gao and H Huang ldquoTime seriesprediction for icing process of overhead power transmissionline based on BP neural networksrdquo in Proceedings of the 30thChinese Control Conference (CCC rsquo11) pp 5315ndash5318 YantaiChina July 2011
[19] Q Li P Li Q Zhang W Ren M Cao and S Gao ldquoIcingload prediction for overhead power lines based on SVMrdquoin Proceedings of the International Conference on ModellingIdentification and Control (ICMIC rsquo11) vol 6 pp 104ndash108 June2011
[20] L Makkonen ldquoModels for the growth of rime glaze icicles andwet snow on structuresrdquo Philosophical Transactions of the RoyalSociety A Mathematical Physical and Engineering Sciences vol358 no 1776 pp 2913ndash2939 2000
[21] L Cao AMees andK Judd ldquoDynamics frommultivariate timeseriesrdquoPhysicaDNonlinear Phenomena vol 121 no 1-2 pp 75ndash88 1998
[22] J Fan and Q Yao Nonlinear Time Series Nonparametric andParametric Methods Springer Berlin Germany 2002
[23] F Takens Daynamical Systems and Turbulence Lecture Notesin Mathematics Sringer Berlin Germany 1981
[24] L AAguirre ldquoAnonlinear correlation function for selecting thedelay time in dynamical reconstructionsrdquo Physics Letters A vol203 no 2-3 pp 88ndash94 1995
[25] P Grassberger and I Procaccia ldquoMeasuring the strangeness ofstrange attractorsrdquo Physica D Nonlinear Phenomena vol 9 no1-2 pp 189ndash208 1983
[26] G Zhexue and S Zhiqiang Neural Network Theory and ItsApplication Publishing House of Electronics Industry BeijingChina 2008
[27] C Chuang S Su and C Hsiao ldquoThe Annealing Robust Back-propagation (ARBP) learning algorithmrdquo IEEE Transactions onNeural Networks vol 11 no 5 pp 1067ndash1077 2000
[28] H Tsukimoto ldquoExtracting rules from trained neural networksrdquoIEEE Transactions on Neural Networks vol 11 no 2 pp 377ndash389 2000
[29] VN VapnikTheNature of Statistical LearningTheory SpringerBerlin Germany 1998
[30] Z Y Hu Y K Bao and T Xiong ldquoElectricity load forecastingusing support vector regression with memetic algorithmsrdquoTheScientific World Journal vol 2013 Article ID 292575 10 pages2013
[31] R A Johnson Applied Multivariate Statistical Analysis Pren-tice-Hall New York NY USA 1988
[32] L E Kollar M Farzaneh and P van Dyke ldquoModeling iceshedding propagation on transmission lines with or withoutinterphase spacersrdquo IEEE Transactions on Power Delivery vol28 no 1 pp 261ndash267 2013
[33] J A van der Lubbe Information Theory Cambridge UniversityPress Cambridge UK 1997
[34] J Schmidhuber ldquoDeep learning in neural networks anoverviewrdquo Tech Rep University of Lugano amp SUPS I MannoSwitzerland 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
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Shock and Vibration
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Mechanical Engineering
Advances in
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
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Distributed Sensor Networks
International Journal of
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Advances inOptoElectronics
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Chemical EngineeringInternational Journal of
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Control Scienceand Engineering
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Antennas andPropagation
International Journal of
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
The Scientific World Journal 5
Adjust related weight or factor
Rated load of tower
Prediction icing load
BPNN or SVM(modeling)
More than the setting training steps or the average of whole
error less than the set point
No
Yes
History meteorological data and icing load
Stop training
BPNN or SVM(established)
Forecast data of meteorological
Results of prediction for
icing threat
(a) Modeling (b) Prediction
Fuzzy reasoning
Pretreatment
Figure 3 The process of modeling and prediction
222 Optimization Mapping Modeling of Icing Process BasedonMachine Learning As Φ
1(sdot) is multivariate and nonlinear
we can obtain it using BPNN (back propagation neuralnetwork) [26ndash28] SVM (support vector machine) [29 30]and other data-driven methods Here Φ
1(sdot) is founded by
BPNN it is a machine learning process as shown in Figure 3After training that is also the prediction model of the icingload time series
As formula (13) shows the output of BPNN is the resultof a prediction at time 119899 which denotes the value of icingload at time 119899 + 119896 119879
119875(119899) 119867(119899) 119882
119878(119899) 119882
119863(119899) 119860
119875(119899) and
119878119871(119899) denote the meteorology factors such as temperature
humidity wind speed wind direction and sunlight whichimpact the process of icing at time 119899
119902119882
(119899) 119902119882
(119899 minus 2) 119902119882
(119899 minus 4) 119902119882
(119899 minus 6) 119902119882
(119899 minus 8) and119902119882
(119899 minus 10) are the history icing loads at time 119899 119899 minus 2 119899 minus 4119899 minus 6 119899 minus 8 and 119899 minus 10 which are achieved by the mechanicalmodel [3 4]
In this method given the ability to approximate anynonlinear mapping using learning in BPNN the functionΦ1(sdot)was found using themodel in Figure 3(a) After training
the BBPN the predictionmodel could be applied as shown inFigure 3(b) Determining the icing prediction values allowsthe relevant departments to assess the threat of inclementweather to the power grid and take some deicing or main-tenance actions in advance
3 Simulation and Analysis
Micrometeorology data including environment temperaturehumidity wind velocity wind direction sunlight intensityand air pressure in addition to the insulatorrsquos mechanicaldata such as pull force wind angle and lean angle wereacquired from an online monitoring system tracking theTao-Luo-Xiong Transmission Line in the northwest area ofYunnan Province China
The data were collected from a variety of sensors andrecorded every 20 minutes from November 2009 to January2010 as shown in Figure 2 which shows the twomost seriousicing processes
For the purposes of this paper in testing the modelrsquosprecision and robustness the simulations were carried outduring the same icing process or different process
However the prediction model in this paper has beenbased on phase-space reconstruction it is a multivariabletime series prediction model which considers multidimen-sional meteorology factors If we take the icing process asa single variable time series and predict it using ARIMA(autoregressive integrated moving average) model [22] thedifferences between the two icing process predictionmethodshave also been analyzed in this paper
As Figure 3(a) shows the first step for finding the icingthreat prediction model based on data-driven methods is to
6 The Scientific World Journal
pretreat the data Because the model is based on methodsincluding BPNN SVM [29] and other machine learningalgorithms the quality of data determines the precision ofthemodel Data pretreatment can reduce uncertain effects formodeling through the use of a filter or smoothing methodsGiven that formula (12) was found without noise datapretreatment is necessary for a prediction model based onphase-space reconstruction
31 Data Pretreatment As shown in Figure 2 wind speedwinddirection sunlight intensity and icing loads are unstablewhen comparing temperature humidity and air pressureThat can result in some disadvantages for modeling asdescribed in the following in which case we only performedpretreatment for those four variations
(1) The sunlight intensity changes periodically Duringthe daytime there is an obvious difference when the weatheris clear or raining but at night regardless whether theweather is clear or raining the sunlight intensity is the sameequaling zero which impacts the learning of BPNN Havingbeen filtered using the wavelets algorithm [31] the curve ofsunlight is displayed in Figure 4 It holds certain relativitywith the icing load the icing begins and increases when thesunlight intensity is close to zero
(2) Owing to uncertain shelling during the icing processthere exist some noise and outliers in the value of the icingload These are determined by the shape and distribution ofice along the transmission line and not only by meteorologyfactors The precision would be influenced if training withthose noise and outliers In Figure 4 the icing load has beensmoothed by using weighted linear least squares model [32]
(3) As shown in the analysis in Section 21 the icingbegins and rises when the wind direction is about 70∘ andwind speed is close to zero Although wind speed and winddirection have some stability over a limited period theychange with the air currentThis also impacts the training forthemodel In Figure 4 thewinddirection and speed have alsobeen smoothed using the weighted linear least squares model[31]
32 Icing Load Prediction in Same Icing Process In this casewe predicted the icing load in the same process whichmeansthe simulation data for training and for prediction exist in thesame icing process In this icing process as shown in Figure 2the number of data is 230 from December 17th to 20th in2009 the frontal 192 data were used as the training inputnot including the shelling (melting) phase The modelingflow chart of the BPNN is shown in Figure 3(a) the maximalsetting of training steps is 1000 the error value of set point is001 and the earning rate parameter is 01
After finding the model the remainder data were availedto prediction As a result we achieved the prediction resultsas Figure 5 when the prediction length 119896 is 1
In Figure 5 the trend of change for the icing process hasbeen predicted accurately the error variance of prediction is1086 kg which is about 14 ofmax icing load in this process
If prediction length 119896 increases the prediction errorvariances will rise rapidly as Table 2 shows But if 119896 le 4
0500
1000Filter result of icing load (kg)
05
1015
Filter result of wind speed (ms)
0100200300
0 500 1000 1500 2000 2500 30000200400600
The first serious icing process The second serious icing process
Filter result of sunlight (Wm2)
Filter result of wind direction (∘)
Figure 4 Filter results of 119902119882
119882119875
119882119863
and 119878119871
0 5 10 15 20 25 30 35 40minus200
0
200
400
600
800
1000
Icin
g lo
ad (k
g)
Prediction valueActual valueError
Figure 5 Results of prediction in the same icing process (119896 = 1) forthe first serious icing process (20091217ndash20091220)
Table 2 The error variances of icing load prediction in sameicing process for the first serious icing process from (12172009sim
12202009)
Prediction length 119896 1 2 3 4 5 6Standard deviation(multivariable predictionbased on BPNN)
1086 1345 1428 1817 2556 2975
Standard deviation (singlevariable prediction basedon ARIMA)
1519 1947 2635 2893 3201 3862
the error variance will be less than 30 of the max icingload This is available prediction information for power griddepartment to use against icing disasters
If we do predict using the ARIMA model it is obviousthat the error variances will be greater than in the model wehave shown in this paperThe results can be found in Table 2
Similarly if we predict the second serious icing process asFigure 2 shows where the number of training data is 109 fromJanuary 10th to 12th in 2010 the number of prediction data is41 on January 12th in 2010 Results are shown in Figure 6 andTable 3
The Scientific World Journal 7
minus200
0
200
400
600
800
1000
Icin
g lo
ad (k
g)
0 5 10 15 20 25 30 35 4540
Prediction valueActual valueError
Figure 6 Results of prediction in same icing process (119896 = 1) for thesecond serious icing process (1102010sim1122010)
Table 3 The error variances of icing load prediction in same icingprocess for the second serious icing process (1102010sim1122010)
Prediction length 119896 1 2 3 4 5 6Standard deviation(multivariable predictionbased on BPNN)
1361 1494 1725 2106 2821 3136
Standard deviation (singlevariable prediction basedon ARIMA)
1452 2049 2887 2936 3684 4074
33 Icing Load Prediction in Different Icing Process As shownin Figure 2 we have selected the full process of the firstserious icing as the training input data which is also shownin Figure 4 The training process involves three phasesincluding inexistence rising and shelling (melting) UnlikeSection 32 the shelling phase is used to train the BPNNThenumber of training data is 310 fromDecember 17th to 20th in2009 the maximal setting steps of training are 1000 the errorvalue of set point is 001 and the earning rate parameter is 01
The second serious icing process is used to make predic-tions The number of predictions is 150 from January 10thto 12th in 2010 which is shown in Figure 2 The results ofsimulation are as shown in Figure 7
In Figure 7 the trend of change for the icing process ispredicted more accurately because the error in the shellingphase is less than found in Figure 6 The error variance ofprediction is 712 kg which is about 10 of max icing loadin this process
This is similar to Section 32 in that the prediction errorvariances will rise rapidly if prediction length 119896 increases asshown in Table 4 If 119896 ge 5 the error variance will be morethan 30 of the max icing load
If we perform a prediction using ARIMA model it isevident that the error variances are greater than found inthe model with the multivariable time series On the otherhand the error variances that were predicted in the different
0 50 100 150minus400
minus200
0
200
400
600
800
1000
Icin
g lo
ad (k
g)
Prediction valueActual valueError
Figure 7 Results of prediction in different icing process (119896 = 1)
Table 4 The error variances of icing load prediction in differenticing process
Prediction length 119896 1 2 3 4 5 6Standard deviation(multivariable predictionbased on BPNN)
712 935 1358 1789 2666 3247
Standard deviation (singlevariable prediction basedon ARIMA)
1263 1333 1711 2299 3172 3568
processes are all less than in the same process and can beobtained if we compare Table 3 to Table 4
34 Analysis and Summary
(1) ThePrecision of the PredictionModel Based on Time SeriesData-Driven Depends on the Integrality and Sufficiency ofHistory Data Machine learning algorithms such as BPNNand SVM are effective methods for utilizing history datato find the prediction model but the modelrsquos precision isdecided by the training data If the data used for the modeldo not include all possible inputs and outputs the model willnot be suitable to describe the mapping relationship betweenthem
In Section 32 the simulation is during the same processof icing it is obvious that the precision is satisfactory beforethe shelling phase and the error is less than 200 kg Howeverin the shelling phase that is unacceptable especially inFigure 6 where the error is greater than 600 kg This isdependent on the training data which does not cover theshelling phase so it is imprecise
When compared with the results of Section 33 thesimulation is performed during different stages in the icingprocess consequently the error variances are less than thoseof Section 32 whether the prediction length is short or longIt is because of this the data for training input involves wholephases of the icing process including inexistence rising andshelling (melting) As the shelling process is very important
8 The Scientific World Journal
for diagnosing the safety of power transmission line [32] theintegrality and sufficiency of history data is very necessary forprediction of it
(2) The Precision of Prediction Model Is Related to the Lengthof Prediction If Prediction Length Were Short the PredictionError Would Be Small According to the information theory[33] that the correlativity would increase if the time distancedecreases This means the value of the icing load at time 119899
is correlative to the value at time 119899 minus 119896 and the correlativitywould decrease if 119896 increased
As the results of Tables 2ndash4 show when 119896 increases theprediction error will also increase If 119896 lt 5 the error variancewill be less than 30 of max icing load That means if theprediction length is less than two hours it will be helpfulfor power grid departments to take actions in advance forpotential icing disasters along the Tao-Luo-Xiong Line But ifthe length of prediction is more than two hours the methodabout deep learning [34] maybe is a good choice
(3) The Precision of the Prediction Model Based on a Data-Driven Multivariable Time Series Is Better Than One Basedon a Single Variable Time Series According to Takensrsquoembedding principle [23] if time delay and embeddingdimensions are suitable the results of a prediction based ona single variable time series would be satisfactory Howeverthere exist some uncertainty and immaturity in the singlevariable time series so we cannot confirm that the phasespace adequately describes the process of a complex dynamicssystem Multivariable time series are comprised of moredynamic information than a single variable
As the analysis of Section 21 shows the icing processalong the transmission line is complex and decided by multi-meteorological factors Therefore if only based on a singlevariable time series such as the ARIMA model it could notdescribe the icing process exactly The results of Tables 2ndash4also indicate the analysis above
4 Conclusions
The transmission line icing is a nonlinear and high dimensionprocess The advantage of using an automatic monitoringsystem for power transmission lines is that a large amountof process data is available to diagnose Because complex lineicing processes cannot be easily represented using accuratemathematical models a data-driven method must be con-sidered After analyzing the Makkonen model of the icingprocess we determined that the line icing is a multivariatetime series process
Consequently in this paper a model based on multi-variable time series has been presented to predict the icingload of the transmission line In this model time effectsof micrometeorology parameters for the icing process wereanalyzed and the phase-space reconstruction theory andmachine learning methods were applied which utilized thehistoric multivariable time series data to establish the modelAs the characteristic of fitfulness in line icing the simulationswere carried out during the same icing process or differentprocess for testing the precision and robustness of the model
According to the results of simulation for the Tao-Luo-Xiong Transmission Line this model has a good accuracyof prediction in different processes if the prediction lengthis less than five That means the maximal prediction time isapproximately two hours which would be helpful for powergrid departments when deciding to take action in advance toaddress potential icing disasters
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This paper was supported by the National High TechnologyResearch and Development Program (ldquo863rdquo Program) ofChina under Grant no 2011AA05A120 the National Natu-ral Science Foundation of China (NSFC) under Grant no61364024 and the 5th Training Program for the Key YoungTeachers of Yunnan University
References
[1] H Hou X Yin Q Chen D You G Tong andD Shao ldquoReviewon the wide area blackout of 500 kV main power grid in someareas of south china in 2008 snow disasterrdquo Automation ofElectric Power Systems vol 32 no 11 pp 12ndash15 2008
[2] K Savadjiev and M Farzaneh ldquoAnalysis and interpretation oficing rate meter and load cell measurements on the MtBelairicing siterdquo in Proceedings of the 9th International Offshore PolarEngineering Conference vol 2 pp 607ndash611 Brest France 1999
[3] X B Huang and Q D Sun ldquoMechanical analysis on transmis-sion line conductor icing and application of online monitoringsystemrdquoAutomation of Electric Power Systems vol 13 no 14 pp98ndash101 2007
[4] L Yang Y Hao W Li et al ldquoA mechanical calculation modelfor on-line icing-monitoring system of overhead transmissionlinesrdquo Proceedings of the Chinese Society of Electrical Engineer-ing vol 30 no 19 pp 100ndash105 2010
[5] Y Xu and R G Bosisio ldquoGoubau ice sensor transitions forelectric power linesrdquo Sensing and Imaging vol 10 no 1-2 pp31ndash40 2009
[6] I Y H Gu U Sistiaga M Sonja et al ldquoAutomatic surveillanceand analysis of snow and ice coverage on electrical insulatorsof power transmission linesrdquo in Proceedings of the InternationalConference (ICCVG rsquo08) vol 5337 of Lecture Notes in ComputerScience pp 368ndash379 Springer 2008
[7] Y Sakamoto ldquoSnow accretion on overhead wiresrdquo PhilosophicalTransactions of the Royal Society A vol 358 no 1776 pp 2941ndash2970 2000
[8] M Farzaneh and K Savadjiev ldquoStatistical analysis of field datafor precipitation icing accretion on overhead power linesrdquo IEEETransactions on Power Delivery vol 20 no 2 pp 1080ndash10872005
[9] L Makkonen ldquoModeling power line icing in freezing precipita-tionrdquo Atmospheric Research vol 46 no 1-2 pp 131ndash142 1998
[10] X Wu L Li and X M Rui ldquoIcing load accretion prognosisfor power transmission linewithmodified hidden semi-Markov
The Scientific World Journal 9
modelrdquo IET Generation Transmission ampDistribution vol 8 no3 pp 480ndash485 2014
[11] S Rajakarunakaran D Devaraj G S Venkatratnam and KSurja Prakasa Rao ldquoArticial neural network approach for faultdetection in LPG transfer systemrdquo Applied Soft Computing vol8 no 1 pp 740ndash748 2008
[12] A Quteishat and C P Lim ldquoA modified fuzzy min-maxneural network with rule extraction and its application to faultdetection and classificationrdquo Applied Soft Computing Journalvol 8 no 2 pp 985ndash995 2008
[13] J Xu and Z Hou ldquoNotes on data-driven system approachesrdquoActa Automatica Sinica vol 35 no 6 pp 668ndash675 2009
[14] E Zio and F Di Maio ldquoA data-driven fuzzy approach forpredicting the remaining useful life in dynamic failure scenariosof a nuclear systemrdquo Reliability Engineering and System Safetyvol 95 no 1 pp 49ndash57 2010
[15] P McComber J De Lafontaine and J Laflamme ldquoA neuralsystem to estimate transmission line icingrdquo in Proceedings of the8th International Workshop on Atmospheric Icing on Structures(IWAIS rsquo98) pp 101ndash106 Reykjavik Iceland 1998
[16] E Larouche J Rouat and G Bouchard ldquoExploration ofstatic and time dependent neural network techniques for thepredicion of ice accertion on overhead line conductorsrdquo inProceedings of the 4th International Workshop on AtmosphericIcing of Structures (IWAIS rsquo00) Chester UK 2000
[17] P Li N Li Q Li M Cao and H Chen ldquoPrediction modelfor power transmission line icing load based on data-drivenrdquoAdvanced Materials Research vol 144 pp 1295ndash1299 2011
[18] P Li Q Li M Cao S Gao and H Huang ldquoTime seriesprediction for icing process of overhead power transmissionline based on BP neural networksrdquo in Proceedings of the 30thChinese Control Conference (CCC rsquo11) pp 5315ndash5318 YantaiChina July 2011
[19] Q Li P Li Q Zhang W Ren M Cao and S Gao ldquoIcingload prediction for overhead power lines based on SVMrdquoin Proceedings of the International Conference on ModellingIdentification and Control (ICMIC rsquo11) vol 6 pp 104ndash108 June2011
[20] L Makkonen ldquoModels for the growth of rime glaze icicles andwet snow on structuresrdquo Philosophical Transactions of the RoyalSociety A Mathematical Physical and Engineering Sciences vol358 no 1776 pp 2913ndash2939 2000
[21] L Cao AMees andK Judd ldquoDynamics frommultivariate timeseriesrdquoPhysicaDNonlinear Phenomena vol 121 no 1-2 pp 75ndash88 1998
[22] J Fan and Q Yao Nonlinear Time Series Nonparametric andParametric Methods Springer Berlin Germany 2002
[23] F Takens Daynamical Systems and Turbulence Lecture Notesin Mathematics Sringer Berlin Germany 1981
[24] L AAguirre ldquoAnonlinear correlation function for selecting thedelay time in dynamical reconstructionsrdquo Physics Letters A vol203 no 2-3 pp 88ndash94 1995
[25] P Grassberger and I Procaccia ldquoMeasuring the strangeness ofstrange attractorsrdquo Physica D Nonlinear Phenomena vol 9 no1-2 pp 189ndash208 1983
[26] G Zhexue and S Zhiqiang Neural Network Theory and ItsApplication Publishing House of Electronics Industry BeijingChina 2008
[27] C Chuang S Su and C Hsiao ldquoThe Annealing Robust Back-propagation (ARBP) learning algorithmrdquo IEEE Transactions onNeural Networks vol 11 no 5 pp 1067ndash1077 2000
[28] H Tsukimoto ldquoExtracting rules from trained neural networksrdquoIEEE Transactions on Neural Networks vol 11 no 2 pp 377ndash389 2000
[29] VN VapnikTheNature of Statistical LearningTheory SpringerBerlin Germany 1998
[30] Z Y Hu Y K Bao and T Xiong ldquoElectricity load forecastingusing support vector regression with memetic algorithmsrdquoTheScientific World Journal vol 2013 Article ID 292575 10 pages2013
[31] R A Johnson Applied Multivariate Statistical Analysis Pren-tice-Hall New York NY USA 1988
[32] L E Kollar M Farzaneh and P van Dyke ldquoModeling iceshedding propagation on transmission lines with or withoutinterphase spacersrdquo IEEE Transactions on Power Delivery vol28 no 1 pp 261ndash267 2013
[33] J A van der Lubbe Information Theory Cambridge UniversityPress Cambridge UK 1997
[34] J Schmidhuber ldquoDeep learning in neural networks anoverviewrdquo Tech Rep University of Lugano amp SUPS I MannoSwitzerland 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mechanical Engineering
Advances in
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Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Antennas andPropagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
6 The Scientific World Journal
pretreat the data Because the model is based on methodsincluding BPNN SVM [29] and other machine learningalgorithms the quality of data determines the precision ofthemodel Data pretreatment can reduce uncertain effects formodeling through the use of a filter or smoothing methodsGiven that formula (12) was found without noise datapretreatment is necessary for a prediction model based onphase-space reconstruction
31 Data Pretreatment As shown in Figure 2 wind speedwinddirection sunlight intensity and icing loads are unstablewhen comparing temperature humidity and air pressureThat can result in some disadvantages for modeling asdescribed in the following in which case we only performedpretreatment for those four variations
(1) The sunlight intensity changes periodically Duringthe daytime there is an obvious difference when the weatheris clear or raining but at night regardless whether theweather is clear or raining the sunlight intensity is the sameequaling zero which impacts the learning of BPNN Havingbeen filtered using the wavelets algorithm [31] the curve ofsunlight is displayed in Figure 4 It holds certain relativitywith the icing load the icing begins and increases when thesunlight intensity is close to zero
(2) Owing to uncertain shelling during the icing processthere exist some noise and outliers in the value of the icingload These are determined by the shape and distribution ofice along the transmission line and not only by meteorologyfactors The precision would be influenced if training withthose noise and outliers In Figure 4 the icing load has beensmoothed by using weighted linear least squares model [32]
(3) As shown in the analysis in Section 21 the icingbegins and rises when the wind direction is about 70∘ andwind speed is close to zero Although wind speed and winddirection have some stability over a limited period theychange with the air currentThis also impacts the training forthemodel In Figure 4 thewinddirection and speed have alsobeen smoothed using the weighted linear least squares model[31]
32 Icing Load Prediction in Same Icing Process In this casewe predicted the icing load in the same process whichmeansthe simulation data for training and for prediction exist in thesame icing process In this icing process as shown in Figure 2the number of data is 230 from December 17th to 20th in2009 the frontal 192 data were used as the training inputnot including the shelling (melting) phase The modelingflow chart of the BPNN is shown in Figure 3(a) the maximalsetting of training steps is 1000 the error value of set point is001 and the earning rate parameter is 01
After finding the model the remainder data were availedto prediction As a result we achieved the prediction resultsas Figure 5 when the prediction length 119896 is 1
In Figure 5 the trend of change for the icing process hasbeen predicted accurately the error variance of prediction is1086 kg which is about 14 ofmax icing load in this process
If prediction length 119896 increases the prediction errorvariances will rise rapidly as Table 2 shows But if 119896 le 4
0500
1000Filter result of icing load (kg)
05
1015
Filter result of wind speed (ms)
0100200300
0 500 1000 1500 2000 2500 30000200400600
The first serious icing process The second serious icing process
Filter result of sunlight (Wm2)
Filter result of wind direction (∘)
Figure 4 Filter results of 119902119882
119882119875
119882119863
and 119878119871
0 5 10 15 20 25 30 35 40minus200
0
200
400
600
800
1000
Icin
g lo
ad (k
g)
Prediction valueActual valueError
Figure 5 Results of prediction in the same icing process (119896 = 1) forthe first serious icing process (20091217ndash20091220)
Table 2 The error variances of icing load prediction in sameicing process for the first serious icing process from (12172009sim
12202009)
Prediction length 119896 1 2 3 4 5 6Standard deviation(multivariable predictionbased on BPNN)
1086 1345 1428 1817 2556 2975
Standard deviation (singlevariable prediction basedon ARIMA)
1519 1947 2635 2893 3201 3862
the error variance will be less than 30 of the max icingload This is available prediction information for power griddepartment to use against icing disasters
If we do predict using the ARIMA model it is obviousthat the error variances will be greater than in the model wehave shown in this paperThe results can be found in Table 2
Similarly if we predict the second serious icing process asFigure 2 shows where the number of training data is 109 fromJanuary 10th to 12th in 2010 the number of prediction data is41 on January 12th in 2010 Results are shown in Figure 6 andTable 3
The Scientific World Journal 7
minus200
0
200
400
600
800
1000
Icin
g lo
ad (k
g)
0 5 10 15 20 25 30 35 4540
Prediction valueActual valueError
Figure 6 Results of prediction in same icing process (119896 = 1) for thesecond serious icing process (1102010sim1122010)
Table 3 The error variances of icing load prediction in same icingprocess for the second serious icing process (1102010sim1122010)
Prediction length 119896 1 2 3 4 5 6Standard deviation(multivariable predictionbased on BPNN)
1361 1494 1725 2106 2821 3136
Standard deviation (singlevariable prediction basedon ARIMA)
1452 2049 2887 2936 3684 4074
33 Icing Load Prediction in Different Icing Process As shownin Figure 2 we have selected the full process of the firstserious icing as the training input data which is also shownin Figure 4 The training process involves three phasesincluding inexistence rising and shelling (melting) UnlikeSection 32 the shelling phase is used to train the BPNNThenumber of training data is 310 fromDecember 17th to 20th in2009 the maximal setting steps of training are 1000 the errorvalue of set point is 001 and the earning rate parameter is 01
The second serious icing process is used to make predic-tions The number of predictions is 150 from January 10thto 12th in 2010 which is shown in Figure 2 The results ofsimulation are as shown in Figure 7
In Figure 7 the trend of change for the icing process ispredicted more accurately because the error in the shellingphase is less than found in Figure 6 The error variance ofprediction is 712 kg which is about 10 of max icing loadin this process
This is similar to Section 32 in that the prediction errorvariances will rise rapidly if prediction length 119896 increases asshown in Table 4 If 119896 ge 5 the error variance will be morethan 30 of the max icing load
If we perform a prediction using ARIMA model it isevident that the error variances are greater than found inthe model with the multivariable time series On the otherhand the error variances that were predicted in the different
0 50 100 150minus400
minus200
0
200
400
600
800
1000
Icin
g lo
ad (k
g)
Prediction valueActual valueError
Figure 7 Results of prediction in different icing process (119896 = 1)
Table 4 The error variances of icing load prediction in differenticing process
Prediction length 119896 1 2 3 4 5 6Standard deviation(multivariable predictionbased on BPNN)
712 935 1358 1789 2666 3247
Standard deviation (singlevariable prediction basedon ARIMA)
1263 1333 1711 2299 3172 3568
processes are all less than in the same process and can beobtained if we compare Table 3 to Table 4
34 Analysis and Summary
(1) ThePrecision of the PredictionModel Based on Time SeriesData-Driven Depends on the Integrality and Sufficiency ofHistory Data Machine learning algorithms such as BPNNand SVM are effective methods for utilizing history datato find the prediction model but the modelrsquos precision isdecided by the training data If the data used for the modeldo not include all possible inputs and outputs the model willnot be suitable to describe the mapping relationship betweenthem
In Section 32 the simulation is during the same processof icing it is obvious that the precision is satisfactory beforethe shelling phase and the error is less than 200 kg Howeverin the shelling phase that is unacceptable especially inFigure 6 where the error is greater than 600 kg This isdependent on the training data which does not cover theshelling phase so it is imprecise
When compared with the results of Section 33 thesimulation is performed during different stages in the icingprocess consequently the error variances are less than thoseof Section 32 whether the prediction length is short or longIt is because of this the data for training input involves wholephases of the icing process including inexistence rising andshelling (melting) As the shelling process is very important
8 The Scientific World Journal
for diagnosing the safety of power transmission line [32] theintegrality and sufficiency of history data is very necessary forprediction of it
(2) The Precision of Prediction Model Is Related to the Lengthof Prediction If Prediction Length Were Short the PredictionError Would Be Small According to the information theory[33] that the correlativity would increase if the time distancedecreases This means the value of the icing load at time 119899
is correlative to the value at time 119899 minus 119896 and the correlativitywould decrease if 119896 increased
As the results of Tables 2ndash4 show when 119896 increases theprediction error will also increase If 119896 lt 5 the error variancewill be less than 30 of max icing load That means if theprediction length is less than two hours it will be helpfulfor power grid departments to take actions in advance forpotential icing disasters along the Tao-Luo-Xiong Line But ifthe length of prediction is more than two hours the methodabout deep learning [34] maybe is a good choice
(3) The Precision of the Prediction Model Based on a Data-Driven Multivariable Time Series Is Better Than One Basedon a Single Variable Time Series According to Takensrsquoembedding principle [23] if time delay and embeddingdimensions are suitable the results of a prediction based ona single variable time series would be satisfactory Howeverthere exist some uncertainty and immaturity in the singlevariable time series so we cannot confirm that the phasespace adequately describes the process of a complex dynamicssystem Multivariable time series are comprised of moredynamic information than a single variable
As the analysis of Section 21 shows the icing processalong the transmission line is complex and decided by multi-meteorological factors Therefore if only based on a singlevariable time series such as the ARIMA model it could notdescribe the icing process exactly The results of Tables 2ndash4also indicate the analysis above
4 Conclusions
The transmission line icing is a nonlinear and high dimensionprocess The advantage of using an automatic monitoringsystem for power transmission lines is that a large amountof process data is available to diagnose Because complex lineicing processes cannot be easily represented using accuratemathematical models a data-driven method must be con-sidered After analyzing the Makkonen model of the icingprocess we determined that the line icing is a multivariatetime series process
Consequently in this paper a model based on multi-variable time series has been presented to predict the icingload of the transmission line In this model time effectsof micrometeorology parameters for the icing process wereanalyzed and the phase-space reconstruction theory andmachine learning methods were applied which utilized thehistoric multivariable time series data to establish the modelAs the characteristic of fitfulness in line icing the simulationswere carried out during the same icing process or differentprocess for testing the precision and robustness of the model
According to the results of simulation for the Tao-Luo-Xiong Transmission Line this model has a good accuracyof prediction in different processes if the prediction lengthis less than five That means the maximal prediction time isapproximately two hours which would be helpful for powergrid departments when deciding to take action in advance toaddress potential icing disasters
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This paper was supported by the National High TechnologyResearch and Development Program (ldquo863rdquo Program) ofChina under Grant no 2011AA05A120 the National Natu-ral Science Foundation of China (NSFC) under Grant no61364024 and the 5th Training Program for the Key YoungTeachers of Yunnan University
References
[1] H Hou X Yin Q Chen D You G Tong andD Shao ldquoReviewon the wide area blackout of 500 kV main power grid in someareas of south china in 2008 snow disasterrdquo Automation ofElectric Power Systems vol 32 no 11 pp 12ndash15 2008
[2] K Savadjiev and M Farzaneh ldquoAnalysis and interpretation oficing rate meter and load cell measurements on the MtBelairicing siterdquo in Proceedings of the 9th International Offshore PolarEngineering Conference vol 2 pp 607ndash611 Brest France 1999
[3] X B Huang and Q D Sun ldquoMechanical analysis on transmis-sion line conductor icing and application of online monitoringsystemrdquoAutomation of Electric Power Systems vol 13 no 14 pp98ndash101 2007
[4] L Yang Y Hao W Li et al ldquoA mechanical calculation modelfor on-line icing-monitoring system of overhead transmissionlinesrdquo Proceedings of the Chinese Society of Electrical Engineer-ing vol 30 no 19 pp 100ndash105 2010
[5] Y Xu and R G Bosisio ldquoGoubau ice sensor transitions forelectric power linesrdquo Sensing and Imaging vol 10 no 1-2 pp31ndash40 2009
[6] I Y H Gu U Sistiaga M Sonja et al ldquoAutomatic surveillanceand analysis of snow and ice coverage on electrical insulatorsof power transmission linesrdquo in Proceedings of the InternationalConference (ICCVG rsquo08) vol 5337 of Lecture Notes in ComputerScience pp 368ndash379 Springer 2008
[7] Y Sakamoto ldquoSnow accretion on overhead wiresrdquo PhilosophicalTransactions of the Royal Society A vol 358 no 1776 pp 2941ndash2970 2000
[8] M Farzaneh and K Savadjiev ldquoStatistical analysis of field datafor precipitation icing accretion on overhead power linesrdquo IEEETransactions on Power Delivery vol 20 no 2 pp 1080ndash10872005
[9] L Makkonen ldquoModeling power line icing in freezing precipita-tionrdquo Atmospheric Research vol 46 no 1-2 pp 131ndash142 1998
[10] X Wu L Li and X M Rui ldquoIcing load accretion prognosisfor power transmission linewithmodified hidden semi-Markov
The Scientific World Journal 9
modelrdquo IET Generation Transmission ampDistribution vol 8 no3 pp 480ndash485 2014
[11] S Rajakarunakaran D Devaraj G S Venkatratnam and KSurja Prakasa Rao ldquoArticial neural network approach for faultdetection in LPG transfer systemrdquo Applied Soft Computing vol8 no 1 pp 740ndash748 2008
[12] A Quteishat and C P Lim ldquoA modified fuzzy min-maxneural network with rule extraction and its application to faultdetection and classificationrdquo Applied Soft Computing Journalvol 8 no 2 pp 985ndash995 2008
[13] J Xu and Z Hou ldquoNotes on data-driven system approachesrdquoActa Automatica Sinica vol 35 no 6 pp 668ndash675 2009
[14] E Zio and F Di Maio ldquoA data-driven fuzzy approach forpredicting the remaining useful life in dynamic failure scenariosof a nuclear systemrdquo Reliability Engineering and System Safetyvol 95 no 1 pp 49ndash57 2010
[15] P McComber J De Lafontaine and J Laflamme ldquoA neuralsystem to estimate transmission line icingrdquo in Proceedings of the8th International Workshop on Atmospheric Icing on Structures(IWAIS rsquo98) pp 101ndash106 Reykjavik Iceland 1998
[16] E Larouche J Rouat and G Bouchard ldquoExploration ofstatic and time dependent neural network techniques for thepredicion of ice accertion on overhead line conductorsrdquo inProceedings of the 4th International Workshop on AtmosphericIcing of Structures (IWAIS rsquo00) Chester UK 2000
[17] P Li N Li Q Li M Cao and H Chen ldquoPrediction modelfor power transmission line icing load based on data-drivenrdquoAdvanced Materials Research vol 144 pp 1295ndash1299 2011
[18] P Li Q Li M Cao S Gao and H Huang ldquoTime seriesprediction for icing process of overhead power transmissionline based on BP neural networksrdquo in Proceedings of the 30thChinese Control Conference (CCC rsquo11) pp 5315ndash5318 YantaiChina July 2011
[19] Q Li P Li Q Zhang W Ren M Cao and S Gao ldquoIcingload prediction for overhead power lines based on SVMrdquoin Proceedings of the International Conference on ModellingIdentification and Control (ICMIC rsquo11) vol 6 pp 104ndash108 June2011
[20] L Makkonen ldquoModels for the growth of rime glaze icicles andwet snow on structuresrdquo Philosophical Transactions of the RoyalSociety A Mathematical Physical and Engineering Sciences vol358 no 1776 pp 2913ndash2939 2000
[21] L Cao AMees andK Judd ldquoDynamics frommultivariate timeseriesrdquoPhysicaDNonlinear Phenomena vol 121 no 1-2 pp 75ndash88 1998
[22] J Fan and Q Yao Nonlinear Time Series Nonparametric andParametric Methods Springer Berlin Germany 2002
[23] F Takens Daynamical Systems and Turbulence Lecture Notesin Mathematics Sringer Berlin Germany 1981
[24] L AAguirre ldquoAnonlinear correlation function for selecting thedelay time in dynamical reconstructionsrdquo Physics Letters A vol203 no 2-3 pp 88ndash94 1995
[25] P Grassberger and I Procaccia ldquoMeasuring the strangeness ofstrange attractorsrdquo Physica D Nonlinear Phenomena vol 9 no1-2 pp 189ndash208 1983
[26] G Zhexue and S Zhiqiang Neural Network Theory and ItsApplication Publishing House of Electronics Industry BeijingChina 2008
[27] C Chuang S Su and C Hsiao ldquoThe Annealing Robust Back-propagation (ARBP) learning algorithmrdquo IEEE Transactions onNeural Networks vol 11 no 5 pp 1067ndash1077 2000
[28] H Tsukimoto ldquoExtracting rules from trained neural networksrdquoIEEE Transactions on Neural Networks vol 11 no 2 pp 377ndash389 2000
[29] VN VapnikTheNature of Statistical LearningTheory SpringerBerlin Germany 1998
[30] Z Y Hu Y K Bao and T Xiong ldquoElectricity load forecastingusing support vector regression with memetic algorithmsrdquoTheScientific World Journal vol 2013 Article ID 292575 10 pages2013
[31] R A Johnson Applied Multivariate Statistical Analysis Pren-tice-Hall New York NY USA 1988
[32] L E Kollar M Farzaneh and P van Dyke ldquoModeling iceshedding propagation on transmission lines with or withoutinterphase spacersrdquo IEEE Transactions on Power Delivery vol28 no 1 pp 261ndash267 2013
[33] J A van der Lubbe Information Theory Cambridge UniversityPress Cambridge UK 1997
[34] J Schmidhuber ldquoDeep learning in neural networks anoverviewrdquo Tech Rep University of Lugano amp SUPS I MannoSwitzerland 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mechanical Engineering
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Antennas andPropagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
The Scientific World Journal 7
minus200
0
200
400
600
800
1000
Icin
g lo
ad (k
g)
0 5 10 15 20 25 30 35 4540
Prediction valueActual valueError
Figure 6 Results of prediction in same icing process (119896 = 1) for thesecond serious icing process (1102010sim1122010)
Table 3 The error variances of icing load prediction in same icingprocess for the second serious icing process (1102010sim1122010)
Prediction length 119896 1 2 3 4 5 6Standard deviation(multivariable predictionbased on BPNN)
1361 1494 1725 2106 2821 3136
Standard deviation (singlevariable prediction basedon ARIMA)
1452 2049 2887 2936 3684 4074
33 Icing Load Prediction in Different Icing Process As shownin Figure 2 we have selected the full process of the firstserious icing as the training input data which is also shownin Figure 4 The training process involves three phasesincluding inexistence rising and shelling (melting) UnlikeSection 32 the shelling phase is used to train the BPNNThenumber of training data is 310 fromDecember 17th to 20th in2009 the maximal setting steps of training are 1000 the errorvalue of set point is 001 and the earning rate parameter is 01
The second serious icing process is used to make predic-tions The number of predictions is 150 from January 10thto 12th in 2010 which is shown in Figure 2 The results ofsimulation are as shown in Figure 7
In Figure 7 the trend of change for the icing process ispredicted more accurately because the error in the shellingphase is less than found in Figure 6 The error variance ofprediction is 712 kg which is about 10 of max icing loadin this process
This is similar to Section 32 in that the prediction errorvariances will rise rapidly if prediction length 119896 increases asshown in Table 4 If 119896 ge 5 the error variance will be morethan 30 of the max icing load
If we perform a prediction using ARIMA model it isevident that the error variances are greater than found inthe model with the multivariable time series On the otherhand the error variances that were predicted in the different
0 50 100 150minus400
minus200
0
200
400
600
800
1000
Icin
g lo
ad (k
g)
Prediction valueActual valueError
Figure 7 Results of prediction in different icing process (119896 = 1)
Table 4 The error variances of icing load prediction in differenticing process
Prediction length 119896 1 2 3 4 5 6Standard deviation(multivariable predictionbased on BPNN)
712 935 1358 1789 2666 3247
Standard deviation (singlevariable prediction basedon ARIMA)
1263 1333 1711 2299 3172 3568
processes are all less than in the same process and can beobtained if we compare Table 3 to Table 4
34 Analysis and Summary
(1) ThePrecision of the PredictionModel Based on Time SeriesData-Driven Depends on the Integrality and Sufficiency ofHistory Data Machine learning algorithms such as BPNNand SVM are effective methods for utilizing history datato find the prediction model but the modelrsquos precision isdecided by the training data If the data used for the modeldo not include all possible inputs and outputs the model willnot be suitable to describe the mapping relationship betweenthem
In Section 32 the simulation is during the same processof icing it is obvious that the precision is satisfactory beforethe shelling phase and the error is less than 200 kg Howeverin the shelling phase that is unacceptable especially inFigure 6 where the error is greater than 600 kg This isdependent on the training data which does not cover theshelling phase so it is imprecise
When compared with the results of Section 33 thesimulation is performed during different stages in the icingprocess consequently the error variances are less than thoseof Section 32 whether the prediction length is short or longIt is because of this the data for training input involves wholephases of the icing process including inexistence rising andshelling (melting) As the shelling process is very important
8 The Scientific World Journal
for diagnosing the safety of power transmission line [32] theintegrality and sufficiency of history data is very necessary forprediction of it
(2) The Precision of Prediction Model Is Related to the Lengthof Prediction If Prediction Length Were Short the PredictionError Would Be Small According to the information theory[33] that the correlativity would increase if the time distancedecreases This means the value of the icing load at time 119899
is correlative to the value at time 119899 minus 119896 and the correlativitywould decrease if 119896 increased
As the results of Tables 2ndash4 show when 119896 increases theprediction error will also increase If 119896 lt 5 the error variancewill be less than 30 of max icing load That means if theprediction length is less than two hours it will be helpfulfor power grid departments to take actions in advance forpotential icing disasters along the Tao-Luo-Xiong Line But ifthe length of prediction is more than two hours the methodabout deep learning [34] maybe is a good choice
(3) The Precision of the Prediction Model Based on a Data-Driven Multivariable Time Series Is Better Than One Basedon a Single Variable Time Series According to Takensrsquoembedding principle [23] if time delay and embeddingdimensions are suitable the results of a prediction based ona single variable time series would be satisfactory Howeverthere exist some uncertainty and immaturity in the singlevariable time series so we cannot confirm that the phasespace adequately describes the process of a complex dynamicssystem Multivariable time series are comprised of moredynamic information than a single variable
As the analysis of Section 21 shows the icing processalong the transmission line is complex and decided by multi-meteorological factors Therefore if only based on a singlevariable time series such as the ARIMA model it could notdescribe the icing process exactly The results of Tables 2ndash4also indicate the analysis above
4 Conclusions
The transmission line icing is a nonlinear and high dimensionprocess The advantage of using an automatic monitoringsystem for power transmission lines is that a large amountof process data is available to diagnose Because complex lineicing processes cannot be easily represented using accuratemathematical models a data-driven method must be con-sidered After analyzing the Makkonen model of the icingprocess we determined that the line icing is a multivariatetime series process
Consequently in this paper a model based on multi-variable time series has been presented to predict the icingload of the transmission line In this model time effectsof micrometeorology parameters for the icing process wereanalyzed and the phase-space reconstruction theory andmachine learning methods were applied which utilized thehistoric multivariable time series data to establish the modelAs the characteristic of fitfulness in line icing the simulationswere carried out during the same icing process or differentprocess for testing the precision and robustness of the model
According to the results of simulation for the Tao-Luo-Xiong Transmission Line this model has a good accuracyof prediction in different processes if the prediction lengthis less than five That means the maximal prediction time isapproximately two hours which would be helpful for powergrid departments when deciding to take action in advance toaddress potential icing disasters
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This paper was supported by the National High TechnologyResearch and Development Program (ldquo863rdquo Program) ofChina under Grant no 2011AA05A120 the National Natu-ral Science Foundation of China (NSFC) under Grant no61364024 and the 5th Training Program for the Key YoungTeachers of Yunnan University
References
[1] H Hou X Yin Q Chen D You G Tong andD Shao ldquoReviewon the wide area blackout of 500 kV main power grid in someareas of south china in 2008 snow disasterrdquo Automation ofElectric Power Systems vol 32 no 11 pp 12ndash15 2008
[2] K Savadjiev and M Farzaneh ldquoAnalysis and interpretation oficing rate meter and load cell measurements on the MtBelairicing siterdquo in Proceedings of the 9th International Offshore PolarEngineering Conference vol 2 pp 607ndash611 Brest France 1999
[3] X B Huang and Q D Sun ldquoMechanical analysis on transmis-sion line conductor icing and application of online monitoringsystemrdquoAutomation of Electric Power Systems vol 13 no 14 pp98ndash101 2007
[4] L Yang Y Hao W Li et al ldquoA mechanical calculation modelfor on-line icing-monitoring system of overhead transmissionlinesrdquo Proceedings of the Chinese Society of Electrical Engineer-ing vol 30 no 19 pp 100ndash105 2010
[5] Y Xu and R G Bosisio ldquoGoubau ice sensor transitions forelectric power linesrdquo Sensing and Imaging vol 10 no 1-2 pp31ndash40 2009
[6] I Y H Gu U Sistiaga M Sonja et al ldquoAutomatic surveillanceand analysis of snow and ice coverage on electrical insulatorsof power transmission linesrdquo in Proceedings of the InternationalConference (ICCVG rsquo08) vol 5337 of Lecture Notes in ComputerScience pp 368ndash379 Springer 2008
[7] Y Sakamoto ldquoSnow accretion on overhead wiresrdquo PhilosophicalTransactions of the Royal Society A vol 358 no 1776 pp 2941ndash2970 2000
[8] M Farzaneh and K Savadjiev ldquoStatistical analysis of field datafor precipitation icing accretion on overhead power linesrdquo IEEETransactions on Power Delivery vol 20 no 2 pp 1080ndash10872005
[9] L Makkonen ldquoModeling power line icing in freezing precipita-tionrdquo Atmospheric Research vol 46 no 1-2 pp 131ndash142 1998
[10] X Wu L Li and X M Rui ldquoIcing load accretion prognosisfor power transmission linewithmodified hidden semi-Markov
The Scientific World Journal 9
modelrdquo IET Generation Transmission ampDistribution vol 8 no3 pp 480ndash485 2014
[11] S Rajakarunakaran D Devaraj G S Venkatratnam and KSurja Prakasa Rao ldquoArticial neural network approach for faultdetection in LPG transfer systemrdquo Applied Soft Computing vol8 no 1 pp 740ndash748 2008
[12] A Quteishat and C P Lim ldquoA modified fuzzy min-maxneural network with rule extraction and its application to faultdetection and classificationrdquo Applied Soft Computing Journalvol 8 no 2 pp 985ndash995 2008
[13] J Xu and Z Hou ldquoNotes on data-driven system approachesrdquoActa Automatica Sinica vol 35 no 6 pp 668ndash675 2009
[14] E Zio and F Di Maio ldquoA data-driven fuzzy approach forpredicting the remaining useful life in dynamic failure scenariosof a nuclear systemrdquo Reliability Engineering and System Safetyvol 95 no 1 pp 49ndash57 2010
[15] P McComber J De Lafontaine and J Laflamme ldquoA neuralsystem to estimate transmission line icingrdquo in Proceedings of the8th International Workshop on Atmospheric Icing on Structures(IWAIS rsquo98) pp 101ndash106 Reykjavik Iceland 1998
[16] E Larouche J Rouat and G Bouchard ldquoExploration ofstatic and time dependent neural network techniques for thepredicion of ice accertion on overhead line conductorsrdquo inProceedings of the 4th International Workshop on AtmosphericIcing of Structures (IWAIS rsquo00) Chester UK 2000
[17] P Li N Li Q Li M Cao and H Chen ldquoPrediction modelfor power transmission line icing load based on data-drivenrdquoAdvanced Materials Research vol 144 pp 1295ndash1299 2011
[18] P Li Q Li M Cao S Gao and H Huang ldquoTime seriesprediction for icing process of overhead power transmissionline based on BP neural networksrdquo in Proceedings of the 30thChinese Control Conference (CCC rsquo11) pp 5315ndash5318 YantaiChina July 2011
[19] Q Li P Li Q Zhang W Ren M Cao and S Gao ldquoIcingload prediction for overhead power lines based on SVMrdquoin Proceedings of the International Conference on ModellingIdentification and Control (ICMIC rsquo11) vol 6 pp 104ndash108 June2011
[20] L Makkonen ldquoModels for the growth of rime glaze icicles andwet snow on structuresrdquo Philosophical Transactions of the RoyalSociety A Mathematical Physical and Engineering Sciences vol358 no 1776 pp 2913ndash2939 2000
[21] L Cao AMees andK Judd ldquoDynamics frommultivariate timeseriesrdquoPhysicaDNonlinear Phenomena vol 121 no 1-2 pp 75ndash88 1998
[22] J Fan and Q Yao Nonlinear Time Series Nonparametric andParametric Methods Springer Berlin Germany 2002
[23] F Takens Daynamical Systems and Turbulence Lecture Notesin Mathematics Sringer Berlin Germany 1981
[24] L AAguirre ldquoAnonlinear correlation function for selecting thedelay time in dynamical reconstructionsrdquo Physics Letters A vol203 no 2-3 pp 88ndash94 1995
[25] P Grassberger and I Procaccia ldquoMeasuring the strangeness ofstrange attractorsrdquo Physica D Nonlinear Phenomena vol 9 no1-2 pp 189ndash208 1983
[26] G Zhexue and S Zhiqiang Neural Network Theory and ItsApplication Publishing House of Electronics Industry BeijingChina 2008
[27] C Chuang S Su and C Hsiao ldquoThe Annealing Robust Back-propagation (ARBP) learning algorithmrdquo IEEE Transactions onNeural Networks vol 11 no 5 pp 1067ndash1077 2000
[28] H Tsukimoto ldquoExtracting rules from trained neural networksrdquoIEEE Transactions on Neural Networks vol 11 no 2 pp 377ndash389 2000
[29] VN VapnikTheNature of Statistical LearningTheory SpringerBerlin Germany 1998
[30] Z Y Hu Y K Bao and T Xiong ldquoElectricity load forecastingusing support vector regression with memetic algorithmsrdquoTheScientific World Journal vol 2013 Article ID 292575 10 pages2013
[31] R A Johnson Applied Multivariate Statistical Analysis Pren-tice-Hall New York NY USA 1988
[32] L E Kollar M Farzaneh and P van Dyke ldquoModeling iceshedding propagation on transmission lines with or withoutinterphase spacersrdquo IEEE Transactions on Power Delivery vol28 no 1 pp 261ndash267 2013
[33] J A van der Lubbe Information Theory Cambridge UniversityPress Cambridge UK 1997
[34] J Schmidhuber ldquoDeep learning in neural networks anoverviewrdquo Tech Rep University of Lugano amp SUPS I MannoSwitzerland 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mechanical Engineering
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Antennas andPropagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
8 The Scientific World Journal
for diagnosing the safety of power transmission line [32] theintegrality and sufficiency of history data is very necessary forprediction of it
(2) The Precision of Prediction Model Is Related to the Lengthof Prediction If Prediction Length Were Short the PredictionError Would Be Small According to the information theory[33] that the correlativity would increase if the time distancedecreases This means the value of the icing load at time 119899
is correlative to the value at time 119899 minus 119896 and the correlativitywould decrease if 119896 increased
As the results of Tables 2ndash4 show when 119896 increases theprediction error will also increase If 119896 lt 5 the error variancewill be less than 30 of max icing load That means if theprediction length is less than two hours it will be helpfulfor power grid departments to take actions in advance forpotential icing disasters along the Tao-Luo-Xiong Line But ifthe length of prediction is more than two hours the methodabout deep learning [34] maybe is a good choice
(3) The Precision of the Prediction Model Based on a Data-Driven Multivariable Time Series Is Better Than One Basedon a Single Variable Time Series According to Takensrsquoembedding principle [23] if time delay and embeddingdimensions are suitable the results of a prediction based ona single variable time series would be satisfactory Howeverthere exist some uncertainty and immaturity in the singlevariable time series so we cannot confirm that the phasespace adequately describes the process of a complex dynamicssystem Multivariable time series are comprised of moredynamic information than a single variable
As the analysis of Section 21 shows the icing processalong the transmission line is complex and decided by multi-meteorological factors Therefore if only based on a singlevariable time series such as the ARIMA model it could notdescribe the icing process exactly The results of Tables 2ndash4also indicate the analysis above
4 Conclusions
The transmission line icing is a nonlinear and high dimensionprocess The advantage of using an automatic monitoringsystem for power transmission lines is that a large amountof process data is available to diagnose Because complex lineicing processes cannot be easily represented using accuratemathematical models a data-driven method must be con-sidered After analyzing the Makkonen model of the icingprocess we determined that the line icing is a multivariatetime series process
Consequently in this paper a model based on multi-variable time series has been presented to predict the icingload of the transmission line In this model time effectsof micrometeorology parameters for the icing process wereanalyzed and the phase-space reconstruction theory andmachine learning methods were applied which utilized thehistoric multivariable time series data to establish the modelAs the characteristic of fitfulness in line icing the simulationswere carried out during the same icing process or differentprocess for testing the precision and robustness of the model
According to the results of simulation for the Tao-Luo-Xiong Transmission Line this model has a good accuracyof prediction in different processes if the prediction lengthis less than five That means the maximal prediction time isapproximately two hours which would be helpful for powergrid departments when deciding to take action in advance toaddress potential icing disasters
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This paper was supported by the National High TechnologyResearch and Development Program (ldquo863rdquo Program) ofChina under Grant no 2011AA05A120 the National Natu-ral Science Foundation of China (NSFC) under Grant no61364024 and the 5th Training Program for the Key YoungTeachers of Yunnan University
References
[1] H Hou X Yin Q Chen D You G Tong andD Shao ldquoReviewon the wide area blackout of 500 kV main power grid in someareas of south china in 2008 snow disasterrdquo Automation ofElectric Power Systems vol 32 no 11 pp 12ndash15 2008
[2] K Savadjiev and M Farzaneh ldquoAnalysis and interpretation oficing rate meter and load cell measurements on the MtBelairicing siterdquo in Proceedings of the 9th International Offshore PolarEngineering Conference vol 2 pp 607ndash611 Brest France 1999
[3] X B Huang and Q D Sun ldquoMechanical analysis on transmis-sion line conductor icing and application of online monitoringsystemrdquoAutomation of Electric Power Systems vol 13 no 14 pp98ndash101 2007
[4] L Yang Y Hao W Li et al ldquoA mechanical calculation modelfor on-line icing-monitoring system of overhead transmissionlinesrdquo Proceedings of the Chinese Society of Electrical Engineer-ing vol 30 no 19 pp 100ndash105 2010
[5] Y Xu and R G Bosisio ldquoGoubau ice sensor transitions forelectric power linesrdquo Sensing and Imaging vol 10 no 1-2 pp31ndash40 2009
[6] I Y H Gu U Sistiaga M Sonja et al ldquoAutomatic surveillanceand analysis of snow and ice coverage on electrical insulatorsof power transmission linesrdquo in Proceedings of the InternationalConference (ICCVG rsquo08) vol 5337 of Lecture Notes in ComputerScience pp 368ndash379 Springer 2008
[7] Y Sakamoto ldquoSnow accretion on overhead wiresrdquo PhilosophicalTransactions of the Royal Society A vol 358 no 1776 pp 2941ndash2970 2000
[8] M Farzaneh and K Savadjiev ldquoStatistical analysis of field datafor precipitation icing accretion on overhead power linesrdquo IEEETransactions on Power Delivery vol 20 no 2 pp 1080ndash10872005
[9] L Makkonen ldquoModeling power line icing in freezing precipita-tionrdquo Atmospheric Research vol 46 no 1-2 pp 131ndash142 1998
[10] X Wu L Li and X M Rui ldquoIcing load accretion prognosisfor power transmission linewithmodified hidden semi-Markov
The Scientific World Journal 9
modelrdquo IET Generation Transmission ampDistribution vol 8 no3 pp 480ndash485 2014
[11] S Rajakarunakaran D Devaraj G S Venkatratnam and KSurja Prakasa Rao ldquoArticial neural network approach for faultdetection in LPG transfer systemrdquo Applied Soft Computing vol8 no 1 pp 740ndash748 2008
[12] A Quteishat and C P Lim ldquoA modified fuzzy min-maxneural network with rule extraction and its application to faultdetection and classificationrdquo Applied Soft Computing Journalvol 8 no 2 pp 985ndash995 2008
[13] J Xu and Z Hou ldquoNotes on data-driven system approachesrdquoActa Automatica Sinica vol 35 no 6 pp 668ndash675 2009
[14] E Zio and F Di Maio ldquoA data-driven fuzzy approach forpredicting the remaining useful life in dynamic failure scenariosof a nuclear systemrdquo Reliability Engineering and System Safetyvol 95 no 1 pp 49ndash57 2010
[15] P McComber J De Lafontaine and J Laflamme ldquoA neuralsystem to estimate transmission line icingrdquo in Proceedings of the8th International Workshop on Atmospheric Icing on Structures(IWAIS rsquo98) pp 101ndash106 Reykjavik Iceland 1998
[16] E Larouche J Rouat and G Bouchard ldquoExploration ofstatic and time dependent neural network techniques for thepredicion of ice accertion on overhead line conductorsrdquo inProceedings of the 4th International Workshop on AtmosphericIcing of Structures (IWAIS rsquo00) Chester UK 2000
[17] P Li N Li Q Li M Cao and H Chen ldquoPrediction modelfor power transmission line icing load based on data-drivenrdquoAdvanced Materials Research vol 144 pp 1295ndash1299 2011
[18] P Li Q Li M Cao S Gao and H Huang ldquoTime seriesprediction for icing process of overhead power transmissionline based on BP neural networksrdquo in Proceedings of the 30thChinese Control Conference (CCC rsquo11) pp 5315ndash5318 YantaiChina July 2011
[19] Q Li P Li Q Zhang W Ren M Cao and S Gao ldquoIcingload prediction for overhead power lines based on SVMrdquoin Proceedings of the International Conference on ModellingIdentification and Control (ICMIC rsquo11) vol 6 pp 104ndash108 June2011
[20] L Makkonen ldquoModels for the growth of rime glaze icicles andwet snow on structuresrdquo Philosophical Transactions of the RoyalSociety A Mathematical Physical and Engineering Sciences vol358 no 1776 pp 2913ndash2939 2000
[21] L Cao AMees andK Judd ldquoDynamics frommultivariate timeseriesrdquoPhysicaDNonlinear Phenomena vol 121 no 1-2 pp 75ndash88 1998
[22] J Fan and Q Yao Nonlinear Time Series Nonparametric andParametric Methods Springer Berlin Germany 2002
[23] F Takens Daynamical Systems and Turbulence Lecture Notesin Mathematics Sringer Berlin Germany 1981
[24] L AAguirre ldquoAnonlinear correlation function for selecting thedelay time in dynamical reconstructionsrdquo Physics Letters A vol203 no 2-3 pp 88ndash94 1995
[25] P Grassberger and I Procaccia ldquoMeasuring the strangeness ofstrange attractorsrdquo Physica D Nonlinear Phenomena vol 9 no1-2 pp 189ndash208 1983
[26] G Zhexue and S Zhiqiang Neural Network Theory and ItsApplication Publishing House of Electronics Industry BeijingChina 2008
[27] C Chuang S Su and C Hsiao ldquoThe Annealing Robust Back-propagation (ARBP) learning algorithmrdquo IEEE Transactions onNeural Networks vol 11 no 5 pp 1067ndash1077 2000
[28] H Tsukimoto ldquoExtracting rules from trained neural networksrdquoIEEE Transactions on Neural Networks vol 11 no 2 pp 377ndash389 2000
[29] VN VapnikTheNature of Statistical LearningTheory SpringerBerlin Germany 1998
[30] Z Y Hu Y K Bao and T Xiong ldquoElectricity load forecastingusing support vector regression with memetic algorithmsrdquoTheScientific World Journal vol 2013 Article ID 292575 10 pages2013
[31] R A Johnson Applied Multivariate Statistical Analysis Pren-tice-Hall New York NY USA 1988
[32] L E Kollar M Farzaneh and P van Dyke ldquoModeling iceshedding propagation on transmission lines with or withoutinterphase spacersrdquo IEEE Transactions on Power Delivery vol28 no 1 pp 261ndash267 2013
[33] J A van der Lubbe Information Theory Cambridge UniversityPress Cambridge UK 1997
[34] J Schmidhuber ldquoDeep learning in neural networks anoverviewrdquo Tech Rep University of Lugano amp SUPS I MannoSwitzerland 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mechanical Engineering
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Antennas andPropagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
The Scientific World Journal 9
modelrdquo IET Generation Transmission ampDistribution vol 8 no3 pp 480ndash485 2014
[11] S Rajakarunakaran D Devaraj G S Venkatratnam and KSurja Prakasa Rao ldquoArticial neural network approach for faultdetection in LPG transfer systemrdquo Applied Soft Computing vol8 no 1 pp 740ndash748 2008
[12] A Quteishat and C P Lim ldquoA modified fuzzy min-maxneural network with rule extraction and its application to faultdetection and classificationrdquo Applied Soft Computing Journalvol 8 no 2 pp 985ndash995 2008
[13] J Xu and Z Hou ldquoNotes on data-driven system approachesrdquoActa Automatica Sinica vol 35 no 6 pp 668ndash675 2009
[14] E Zio and F Di Maio ldquoA data-driven fuzzy approach forpredicting the remaining useful life in dynamic failure scenariosof a nuclear systemrdquo Reliability Engineering and System Safetyvol 95 no 1 pp 49ndash57 2010
[15] P McComber J De Lafontaine and J Laflamme ldquoA neuralsystem to estimate transmission line icingrdquo in Proceedings of the8th International Workshop on Atmospheric Icing on Structures(IWAIS rsquo98) pp 101ndash106 Reykjavik Iceland 1998
[16] E Larouche J Rouat and G Bouchard ldquoExploration ofstatic and time dependent neural network techniques for thepredicion of ice accertion on overhead line conductorsrdquo inProceedings of the 4th International Workshop on AtmosphericIcing of Structures (IWAIS rsquo00) Chester UK 2000
[17] P Li N Li Q Li M Cao and H Chen ldquoPrediction modelfor power transmission line icing load based on data-drivenrdquoAdvanced Materials Research vol 144 pp 1295ndash1299 2011
[18] P Li Q Li M Cao S Gao and H Huang ldquoTime seriesprediction for icing process of overhead power transmissionline based on BP neural networksrdquo in Proceedings of the 30thChinese Control Conference (CCC rsquo11) pp 5315ndash5318 YantaiChina July 2011
[19] Q Li P Li Q Zhang W Ren M Cao and S Gao ldquoIcingload prediction for overhead power lines based on SVMrdquoin Proceedings of the International Conference on ModellingIdentification and Control (ICMIC rsquo11) vol 6 pp 104ndash108 June2011
[20] L Makkonen ldquoModels for the growth of rime glaze icicles andwet snow on structuresrdquo Philosophical Transactions of the RoyalSociety A Mathematical Physical and Engineering Sciences vol358 no 1776 pp 2913ndash2939 2000
[21] L Cao AMees andK Judd ldquoDynamics frommultivariate timeseriesrdquoPhysicaDNonlinear Phenomena vol 121 no 1-2 pp 75ndash88 1998
[22] J Fan and Q Yao Nonlinear Time Series Nonparametric andParametric Methods Springer Berlin Germany 2002
[23] F Takens Daynamical Systems and Turbulence Lecture Notesin Mathematics Sringer Berlin Germany 1981
[24] L AAguirre ldquoAnonlinear correlation function for selecting thedelay time in dynamical reconstructionsrdquo Physics Letters A vol203 no 2-3 pp 88ndash94 1995
[25] P Grassberger and I Procaccia ldquoMeasuring the strangeness ofstrange attractorsrdquo Physica D Nonlinear Phenomena vol 9 no1-2 pp 189ndash208 1983
[26] G Zhexue and S Zhiqiang Neural Network Theory and ItsApplication Publishing House of Electronics Industry BeijingChina 2008
[27] C Chuang S Su and C Hsiao ldquoThe Annealing Robust Back-propagation (ARBP) learning algorithmrdquo IEEE Transactions onNeural Networks vol 11 no 5 pp 1067ndash1077 2000
[28] H Tsukimoto ldquoExtracting rules from trained neural networksrdquoIEEE Transactions on Neural Networks vol 11 no 2 pp 377ndash389 2000
[29] VN VapnikTheNature of Statistical LearningTheory SpringerBerlin Germany 1998
[30] Z Y Hu Y K Bao and T Xiong ldquoElectricity load forecastingusing support vector regression with memetic algorithmsrdquoTheScientific World Journal vol 2013 Article ID 292575 10 pages2013
[31] R A Johnson Applied Multivariate Statistical Analysis Pren-tice-Hall New York NY USA 1988
[32] L E Kollar M Farzaneh and P van Dyke ldquoModeling iceshedding propagation on transmission lines with or withoutinterphase spacersrdquo IEEE Transactions on Power Delivery vol28 no 1 pp 261ndash267 2013
[33] J A van der Lubbe Information Theory Cambridge UniversityPress Cambridge UK 1997
[34] J Schmidhuber ldquoDeep learning in neural networks anoverviewrdquo Tech Rep University of Lugano amp SUPS I MannoSwitzerland 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mechanical Engineering
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Antennas andPropagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mechanical Engineering
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Antennas andPropagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
