Research Article Simplified Building Thermal Model...

Research ArticleSimplified Building Thermal Model Used for Optimal Control ofRadiant Cooling System

Lei He Bo Lei Haiquan Bi and Tao Yu

School of Mechanical Engineering Southwest Jiaotong University Chengdu 610031 China

Correspondence should be addressed to Bo Lei lbswjtu163com

Received 10 November 2015 Accepted 26 January 2016

Academic Editor Hiroyuki Mino

Copyright copy 2016 Lei He 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

MPC has the ability to optimize the system operation parameters for energy conservation Recently it has been used in HVACsystems for saving energy but there are very few applications in radiant cooling systems To implement MPC in buildings withradiant terminals the predictions of cooling load and thermal environment are indispensable In this paper a simplified thermalmodel is proposed for predicting cooling load and thermal environment in buildings with radiant floor In this thermal modelthe black-box model is introduced to derive the incident solar radiation while the genetic algorithm is utilized to identify theparameters of the thermal model In order to further validate this simplified thermal model simulated results from TRNSYS arecompared with those from this model and the deviation is evaluated based on coefficient of variation of root mean square (CV)The results show that the simplified model can predict the operative temperature with a CV lower than 1 and predict coolingloads with a CV lower than 10 For the purpose of supervisory control in HVAC systems this simplified RC thermal model hasan acceptable accuracy and can be used for further MPC in buildings with radiation terminals

1 Introduction

Model predictive control (MPC) is a powerful control tech-nique which can be used in both local and supervisorycontrol in HVAC systems For example it was employed tocontrol the zone air temperature serving as a local controllerof the VAV damper [1] Yuan and Perez [2] employed MPCto regulate the temperature within the limits and supply ade-quate fresh air in aVAV systemMost importantly the superi-ority of MPC lies in saving energy as a supervisory controllerof HVAC systems Henze et al [3] used this technique togenerate the optimal setpoint of zone air temperature and theoptimal charging and discharging profile of thermal storagefor energy saving Siroky et al [4] applied MPC and weatherprediction in a building heating system for energy conserva-tion MPC is an advanced concept for HVAC systems there-fore it has been widely studied in recent years which can befound in a review carried out by Afram and Janabi-Sharifi [5]

MPC uses a system model to predict the future states ofthe system In the model predictive control of the buildingthermal process an accurate building thermal model is aprecondition which is used for the calculation of cooling

load diagnosis of building thermal properties and predictionof indoor thermal comfort Generally the model used forcalculating the building thermal process can be classified intothree categories physical model black-box model and gray-box model Among these three models the physical model ismost widely used and there are various software tools usingthe physical model to simulate the heat transfer process suchas DOE-2 HAPE-20 BLAST TAS HVACSIM+ TRNSYSSPARK and ESP-r [6 7] For improving the accuracy thephysical model is generally solved by the impulse responsemethod or the finite difference method As a result of highorder of the method used physical model has large cal-culation costs but it is a detailed method to represent thephysical process By contrast the black-box model drivenby data cannot reflect the physical thermal process but it isless time-consuming However since the black-box model isdetermined by the sample data formodel training thismodelgets inaccurate results when the predicting data exceeds thescope of sample data Combining the advantages of physicalmodel and black-box model the gray model was developedThis model has the characteristics of fewer calculation costsless time consumption and part revelation of the physical

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2016 Article ID 2976731 15 pageshttpdxdoiorg10115520162976731

2 Mathematical Problems in Engineering

thermal process [8] Since themodels forMPC have to be lesstime-consuming in comparison with the other two modelsthe simplified gray-box model with lower model order ismore suitable for the MPC solution

As a simplified gray-box model the lumped parametermodel always combines with other models to constructthe MPC controller Hazyuk et al [9] adopted this modeland state space model to construct MPC for intermittentheating buildings In their study the results showed thatthe forecasting error was below 10 To maximize the MPCperformance both improving the calculation accuracy andreducing the calculation time of lumped parameter modelare valid approaches For improving the calculation accuracyit is crucial to identify the model parameters Based onthe simplified thermal response model [10] the least squaremethod was used to identify parameters of a solar house [11]They found that the model parameters had the quality ofnonuniqueness and it was unsuitable for evaluating the build-ing thermal performance However the model can adjust theparameters using the sample data so it is suitable for thebuilding energy management system Gouda et al [12] usedthe sequence quadratic programming method to identify themodel parameters of various constructions and to comparedifferent order modelsThe results showed that second-ordermodel balanced the computational accuracy and calculationconsumption moderately The genetic algorithm with datarecorded by building management system was employed toidentify the RC model parameters in frequency-domain [1314] Based on the time domain and frequency-domain analy-sis a method to simplify the RC model was established [15]and this method has higher applicability than the methodbased on electrical analogy [16] Besides the real buildingoperation data the data acquired from the simulation toolscan be used to identify the model parameters as well OrsquoNeillet al [17] adopted EnergyPlus [18] to test the forecast modelconsisting of 3R2C and Extended Kalman Filter Similarlya cost-effective building thermal model was verified byEnergyPlus [19] What is more EnergyPlus and MATLABwere integrated by BCVTB [20] to develop a cooling loadprediction model for optimizing HVAC control and themodel parameters were recognized using the data calculatedby simulation tool [21 22] The above researches show thatthe lumped parameter model has a strong ability to forecastthe indoor temperature and the cooling loadwhich is suitablefor theMPCHowever for the building equippedwith radiantterminals there are some differences from the building withair-based system In the building with radiant terminalsthe long wave radiation between interior surfaces cannot beneglected and the control variable of indoor environmentis usually the operative temperature What is more in thebuilding with all-air system the incident solar radiation onthe interior surfaces firstly warms up the construction Thenthe cooling load is generated by convective heat exchange Bycontrast the incident solar radiation on the radiant coolingsurface is directly absorbed Due to the above differencesthe long wave radiation among the indoor surfaces and theincident solar radiation on the envelope surfaces cannot becalculated by these models and they are incapable of evaluat-ing wall surface temperatures accurately Based on the above

reasons these models in the literature [11ndash13 15 19 21] areinapplicable for theMPC in buildings with radiant terminals

In order to optimize the operation of the air-conditioningsystemwith radiant terminals byMPC technology this paperpresents a prediction model for a building with radiant floorThis model consists of three parts simplified RC modelblack-model and semiempirical model The simplified RCmodel is used to describe the heat transfer process of thebuilding and the black-box model is used to forecast theincident solar radiation on the envelope surfaces while thesemiempirical model is adopted to calculate the long waveradiation between interior surfaces The model parametersare recognized by the genetic algorithm and the samplingdata for the recognition is derived from TRNSYS Finally themodel is used in a case study to predict the indoor operativetemperature and the cooling load of both radiant terminalsand ventilation system

2 Simplified Building Thermal Model

The RC model adopts different model structures to repre-sent building elements with various heat conduction andthermal storage In most studies the optimization methodis employed to simplify the RC model and to determinethe model parameters It is verified that the second-orderRC model can reduce the calculation time without anycompromise of calculation accuracy compared to the higher-order model [11] Similarly Gouda et al [12] proved that theoptimized 2nd-order model could simulate both lightweightand heavyweight buildings with the minimal accuracy lossThus the low-order RCmodel is used to describe the thermalprocess of building envelope in this paper The mean radianttemperature is adopted for calculating the long wave radia-tion between interior wall surfaces and a black-box model isused to predict the solar radiation on the envelope surfaces

21 Lumped ParameterModel of Envelopes Both 3R2Cmodeland 2R1C model are adopted to build the thermal networkmodel of the building as shown in Figure 1 All the enclosurestructures are assumed to be connected to the outdoorenvironment and the thermal mass such as interior wallsand furniture in the room are neglected in the model Dueto the different orientations of the building solar radiationson the different surfaces are distinct leading to the differentsurface temperatures To accurately calculate the operativetemperature heat transmissions from the external walls andthe roof are separately calculated (1)ndash(4) and the heat storageperformance of window (5) is considered by 2R1C modelThe radiant surface is calculated as a surface with a constanttemperature The energy balance for indoor air is shown in(6) The heat gains from internal equipment and occupantsare calculated in (6)

1198921119894119888wall119894

119889119879wall119897119894

119889119905=119879wall119894 minus 119879wall119897119894

1198913119894119877wall119894

minus119879wall119897119894 minus 119879wall119900119894

1198912119894119877wall

(1)

1198922119894119888wall119894

119889119879wall119900119894

119889119905=119879wall119897119894 minus 119879wall119900119894

1198912119894119877wall

minus119879wall119900119894 minus 119879air

1198911119894119877wall

minus 119902wallrad119894 + 119902sol119894

(2)

Mathematical Problems in Engineering 3

Qradfr

TwingwincwinRwin2

Rwin1

Twalloi Twallli

Trf o

Trfl

f3iRwalli

Tair

Qradrfi

Qradwalli

1macpa

1hfrAfr

f2iRwallif1iRwalli

f1rfRrf

f2rfRrf

f3rf Rrf

g2rf crf

g1rf crf

g2icwallig1icwalli

Trf

Tfr

To Twalli

Tout

Figure 1 Schematic of the simplified building thermal model

1198921rf119888rf

119889119879rf 119897

119889119905=119879rf minus 119879rf 119897

1198913rf119877rf

minus119879rf 119897 minus 119879rf 119900

1198912rf119877rf

(3)

1198922rf119888rf

119889119879rf 119900

119889119905=119879rf 119897 minus 119879rf 119900

1198912rf119877rf

minus119879rf 119900 minus 119879air

1198911rf119877rf

minus 119902rf rad119894

+ 119902solrf

(4)

119892win119888win119889119879win119889119905

=119879119900minus 119879win119877win1

minus119879win minus 119879air119877win2

(5)

120588119881119888119901air

119889119879air119889119905

= 119898air119888119901air (119879119904 minus 119879air)

+

119873=4

sum

119894=1

119860wall119894 (119879wall119900119894 minus 119879air

1198911119894119877119894

)

+ 119860 fr (119879rf 119900 minus 119879air

1198911rf119877rf

)

+ 119860win (119879win119900 minus 119879air

119877win1)

+ ℎfr119860 fr (119879fr minus 119879air) + 119878

(6)

22 Long Wave Radiation Model In the building equippedwith radiant terminals on one hand due to the large tem-perature difference between the radiant surface and interiorsurfaces there is long wave radiation heat exchange betweenradiant terminals and interior surfaces On the other handbecause of the solar radiation on different interior surfacesthere are temperature differences between the inside envelopesurfacesTherefore interior surfaces have longwave radiationheat exchange among each other

The radiant heat transfer between interior surfaces iscalculated with the mean radiant temperature based on thebalancemethod ofWalton [23]Themodel calculates the longwave radiation from one surface to the other surfaces witha fictitious surface temperature which is a weighted averagevalue of other surfaces temperatures as shown in (7)ndash(9)The shape factors of every surface to the fictitious surface arecalculated by (10) so the long wave radiation can be derivedin (11) Because of less calculation this model is suitable forthe model predictive controller

119860119898119903119905119894

=

119873

sum

119895=1

119895 =119894

119860119895 (7)

120576119898119903119905119894

=1

119860119898119903119905119894

times

119873

sum

119895=1

119895 =119894

119860119895120576119895 (8)

119879119898119903119905119894

=1

119860119898119903119905119894

120576119898119903119905119894

times

119873

sum

119895=1

119895 =119894

119860119895120576119895119879wall119895 (9)

119865119898119903119905119894

=1

(120576119898119903119905119894

120576119894) + (119860

119894(1 minus 120576

119898119903119905119894) 119860119898119903119905119894

) (10)

119902radwall119894 = 120590120576119898119903119905119894119865119898119903119905119894 (1198794

wall119900119894 minus 1198794

119898119903119905119894) (11)

23 Prediction Model of Solar Radiation Heat Gain Solarradiation on the outside surface of wall or window willincrease the surface temperatures generating the heat fluxthrough the wall or the window This heat flux was not con-sidered in some researches [13 15] and the ambient air tem-perature was used as the boundary condition of outside wallor window But for a building with radiant terminals in orderto forecast the indoor environment and radiant cooling loadit is necessary to take the solar radiation into considerationCooling capacity of the radiant system is primarily affectedby the cooling load type [24] The convective heat transferaccounts for a small proportion of the cooling capacity whenthe mean surface temperature of radiant terminals is closeto the air temperature The long wave radiation and incidentsolar radiation are the dominant heat gains removed byradiant terminals Thus a perfect prediction of the solarradiation (both direct and diffuse radiation) is important forcalculating the cooling load of the radiant terminals Forthis reason both long wave radiation and solar radiation aredemanded to be accurate Thus the integration temperature[25] converted by the sun radiation and ambient temperatureis used as the boundary condition for the exterior wall whichis shown in (12) and can be used for bothwall (119879wall119894) and roof(119879rf ) equations For the window because the transmissivity ofglass is largely greater than absorptivity the outside surfacetemperature of window is unaffected by the incident solarradiation Hence the ambient temperature (119879out) is adoptedas the boundary condition of the window

119879wallrf 119894 = 119879out +120574119894119869119894

ℎ119894

(12)


+

ITt

+

Input Hidden layer Output layer

P

1 1

1 times 1LW12

S1 times 1

S1 times 1

S1 times 1 S2 times 1b1

a1f1

S1

aiS1 times 1

LW23

S2 times S1

b2S2 times S2

a2f2

Ji

qsoli

a1 = f1(LW12P + b1) a2 = f2(LW23P + b2)

Figure 2 Structure chart of BP neural model for incident solar radiation

On the other hand direct solar radiation is one of theaffecting factors for the surface temperatures and the tem-peratures of interior surfaces are the most important factorsfor the indoor long wave radiation load supplied by radiantterminals Therefore it is important to forecast the directsolar radiation on the inside surface for the long waveradiation calculation For the above reasons both incidentsolar radiations on the inside and outside surface of envelopesare significant for the load forecasting model Incident solarradiations on the envelope surfaces (119902sol 119869119894) are influenced bya lot of factors such as solar azimuth solar altitude intensitybuilding orientation and envelope surface absorptivity How-ever for existing buildings with the known orientation andenvelope surface absorptivity solar radiation on the envelopesurface is only a function of the solar azimuth altitude andintensity Solar radiation physical model [26] can predict thesolar radiation on the various orientation building surfacesHowever direct solar radiation on the inside envelope sur-faces is influenced by many factors that are not considered inthe physical model involving the window orientation areaand glass transmissivity Therefore it is difficult to determinethe short wave radiation on the inside envelope surfacesMoreover due to the shading effect of other buildings andshading devices the incidental solar radiation on the blockcannot be accurately calculated Thus it is an effective wayto build a forecast model based on the measurement data topredict the radiation in order to avoid the uncertainties

In this study the black-box model driven by data is usedfor building the prediction models for solar radiation onboth inside and outside envelope surfaces (119902sol 119869119894) Throughanalyzing the sample data the black-box model can expressthe regulation between the input data and output data Thenthe regulation can be used for predicting unknown resultsby the input data [27] As a frequently used black-box model[28] back propagation neural network has a lot of advantagessuch as self-adaptation and powerful ability to deal the noisydata and missing data [28] Hence BP neural network withtwo layers is adopted to identify the regulation betweenthe solar radiation on various envelope surfaces and thehorizontal incident solar radiation as shown in (13)-(14)Theincident solar radiation on the horizontal plane and the timein 24-hour time system are used to calculate the heat gainsof incident solar radiation on the outside surfaces and theshort wave radiation on the inside surfaces The structure ofthe neural network is shown in Figure 2 This mode fromthe input layer to the output layer has the characteristicsof nonlinear mapping and the ability to avoid the localminimum problemThere are 20 neurons in the hidden layer

and the output layer is the weighted sum of hidden layer Thesigmoid function and linear function are used for the hiddenlayer and the output layer respectively

119902sol119894 = 119891 (IT 119905) (13)

119869119894= 119891 (IT 119905) (14)

3 Identification Method of Model Parameters

Themodel identification is amethod to determine amodel todescribe the test system based on the input and output dataIn general the model identification method can be classifiedinto two categories with and without the reference modelSince the model identification method with the referencemodel is intelligible and flexible it is adopted to build theprediction model for the indoor environment and coolingload Meanwhile the hybrid model as shown in Section 2 isemployed as the referencemodelThe referencemodel is usedfor calculating the results of the sample data Then the modelparameters are adjusted to reduce the difference betweenresults of referencemodel and the actual value of sample dataRepeat this process until the difference can be acceptableFinally the parameters getting the acceptable difference canserve as the predicting model parameters As described inSection 2 there are six unknown parameters 119892 119888 119891 119877 120574 ℎin the RC model

The output of the RC model such as the inside envelopesurface temperatures indoor temperature and cooling loadremoved by radiation system and ventilation system areused for building the objection function as shown in (15)It consists of the differences between actual value and theoutput data of the predicting model

fitness =119873

sum

119894=1

(120596119894(119879wall119894 (119905) minus 119879wall119894 (119905))

2

+ 120596rf (119879rf (119905) minus 119879rf (119905))2

+ 120596win (119879win (119905) minus 119879win (119905))2

+ 120596air (119879air (119905) minus 119879air (119905))2

+ 120596119876air

(119876air (119905) minus 119876air (119905))2

+ 120596119876fr(119876fr (119905) minus 119876fr (119905))

2

)

(15)


Start GA identification

Satisfy the constraints

GA population initializing

Calculate the objective function fitness Real value

Stop GA run

GA operation selection

GA operation crossover mutation


Stop GA run

Stop and output

Yes

Yes

No

No

Yes

No

No

D = threshold value

irun = irun + 1

Generating new generation run

irun = max run

(2) Record the elitist and the best fitness fitnessbest

run = 1 g c f R 120574 h

Initializing the values of g c f R 120574 h

Fitness evaluationmdashthe irun generation(1) Calculate the fitness function fitness

g c f R 120574 h

g c f R 120574 h

Figure 3 Identification method for model parameters

120596rf +119873

sum

119894=1

120596wall119894 + 120596air + 120596win + 120596119876air + 120596119876fr = 1 (16)

120596rf 120596wall119894 120596air 120596win 120596119876air 120596119876fr ge 0 (17)

where fitness 119876air(119905) and 119876fr(119905) are the objection functioncooling load of radiation system and ventilation systemrespectively The cooling load of radiation system is definedas the heat transfer (combined radiant and convective) atthe radiant surface The cooling load of ventilation systemis defined as convective heat removed by the ventilation airAccording to the demand of multiobjective optimization allthe weight factors 120596 have to satisfy the conditions in (16) and(17)

To get themodel parameters it is crucial to solve the opti-mization problem in (15) with the specified conditions in (16)and (17) Since the model is complicated and there are manymodel parameters the genetic algorithm independent of thegradient of optimization function is employed to solve theproblem In order to accelerate the calculation and ensure thephysical meaning for the model parameters these unknown

parameters are determined within a range as given in (18)These unknown parameters of the model are compiled intothe individual chromosomes which are used for calculatingthe objection function Through comparing the objectionfunction values these individuals with biggish objectionfunction value are selected to create the new generationthrough the crossover and mutation operation Then theobjection function is evaluated again by the new generationThe GA solver will stop when the relative difference betweenthe objection function values of two generations is acceptableor reaches the maximum generations as shown in Figure 3Finally the individual with the best fitness value is selected asthe model parameter

001 le 119877119894le 20

1 times 104le 119888wall119894 le 1 times 10

7

10 le 119888win le 1 times 103

0 le 120574119894le 1

1 le ℎ119894le 30


Table 1 Construction element properties

Element Layers Thickness [m] Thermal conductivity[W(msdotK)]

Specific heatcapacity [J(kgsdotK)]

Density[kgm3]

External wallBrick 024 089 1000 1800

Insulation 01 004 800 40Plaster 0015 139 1000 2000

Roof Concrete 024 210 800 2400Insulation 016 004 800 40

Window 119880-value 227 119879sol-value 083

3

sum

119894=1

119891119894= 1

2

sum

119894=1

119892119894= 1

(18)

4 Case Study

In the inhabited buildings the occupantsrsquo activity has aninfluence on the accurately measuring of envelope coolingload and the solar radiation Instead of a real building a virtualbuilding is used to test the model identification method inthis paper

41 Testing Case Simulation tools are convenient to get thesample data for model identification Therefore the sim-ulation toolmdashTRNSYSmdashis selected to generate the sampledata for testing the identification method and the followingconditions are assumed

(1) The building thermal performance is stable in theidentification period

(2) The convective heat transfer coefficients of envelopesurfaces are not affected by air velocity and air tem-perature

(3) The radiant floor is assumed to have the uniformand constant temperature Since the purpose of thismodel is to predict the effect of radiant terminaltemperature on the thermal environment and coolingload of system the detailed thermal process of radiantfloor with circulating water is not considered

The simulated case is depicted in Figure 4 and the dimen-sion of this reference room is 49m (length)times 27m (width)times48m (height) One window with a dimension of 20m(width) times 30m (height) is located in the south wall andthe percentage of glazed area compared to the south wallarea is 463 The convective heat transfer coefficients ofsurfaces are determined according to EN ISO 15255 [29]Thermal properties of the constructions are listed in Table 1The internal heat sources involve two occupants and twocomputers with the total power of 580W and the dailyoperation profile is depicted in Figure 5 The indoor thermalenvironment of this building is controlled by both coolingfloor and ventilation system

Ventilation

Incident solar radiationLong wave radiationConvection

20m27m

49m

Figure 4 Geometry of the building for testing case

00

05

10

Daily pattern of internal load

4 8 12 16 20 240Time (h)

Dai

ly p

atte

rn o

f int

erna

l loa

d

Figure 5 Normal patterns of internal load

42 Solar Radiation on Envelop Surfaces In order to identifythe parameters of the model the solar radiation on theenvelope surfaces has to be identified firstly The data calcu-lated by the TRNSYS simulation tool including horizontalsolar radiation time short wave radiation on inside surfacesand incident solar radiation on outside surfaces is usedfor training the black-box model The sample data of solarradiation during one week is shown in Figure 6 Obviouslythe intensities of solar radiation on all surfaces are basicallyproportional to the horizontal solar radiation (IT) The shortwave radiation on the floor is larger than those on the other


Table 2 CV of predicted values for incident solar radiation

South wall North wall West wall East wall Roof FloorInside mdash mdash 966 923 mdash 867Outside 722 979 1323 1216 067 mdash

0

5

10

15

20

25

30

35

40

NSWE

FloorRoof

IT

20 40 60 80 100 120 140 1600Time (h)

Shor

t wav

e rad

iatio

n (W

m2 )

0

200

400

600

800

1000

Tota

l sol

ar ra

diat

ion

(Wm

2 )

(a) Short wave radiation on the inside envelope surfaces

0

200

400

600

800

1000

Inci

dent

sola

r rad

iatio

n (W

m2 )

20 40 60 80 100 120 140 1600Time (h)

NSWE

RoofIT

0

200

400

600

800

1000

Tota

l sol

ar ra

diat

ion

(Wm

2 )

(b) Incident solar radiation on the outside envelope surfaces

Figure 6 Sample data of solar radiation of surfaces and horizontal solar radiation

inside surfaces Because the short wave radiation cannotreach the inside surface of northwall southwall and roof theshort wave radiation of them is zero Moreover the outsidesurface of east wall has the larger solar radiation in theforenoon By contrast the west wall has the larger solar radia-tion in the afternoon Since there is no incident solar radiationin the night the radiation heat fluxes of all surfaces are zero

The data of incident solar radiation and solar heat gainsfor all envelope surfaces within one month are used as thesample data for building the black-box model For improvingthe prediction accuracy of the incident solar and modeltraining speed the sample data is normalized to a range of0 to 1 in the preprocessing The sample data is randomlydivided into two groups training sample and testing sampleThe training sample is used for building the predictionmodelfor the solar heat gains on the envelope while the testingsample is used for validation The predicted values of solarradiation heat gain on the inside surfaces and outside surfacesby themodel and the actual value of sample data are shown inFigure 7 It can be seen that themodel has the samepredictionaccuracy for the training data and testing data Moreovercomparing Figures 7(a) and 7(b) because of the influence ofthe window structure and glass transmissivity it is very clearthat the solar heat gains of inside surfaces are far less thanthose of outside envelope surfaces

The coefficient of variation of root mean square (CV)as given in (19) has the ability to test the average deviationbetween the predicted value and the actual value which isnot affected by the sample data size For this reason the CV

value is adopted to test themodel performance for estimatingthe solar heat gain

CV =

radicsum119899

119894=1(119910119894minus 119894)2

119899

10038161003816100381610038161199101198941003816100381610038161003816

(19)

where 119910119894 119910119894 119894 and 119899 are sample data actual value average

value of sample data predicted value by the model andsample data amount respectively

The CV values of the solar radiation heat gains on bothside surfaces of envelopes are calculated to evaluate theprediction model with the test sample which is presented inTable 2 The prediction model is enough accurate to forecastthe solar radiation heat gain of envelope inside surfaces withall CV values being below 10 But the adaptability of thepredictionmodel for the outside surfaces facing east and westis poor and the CV values are greater than 10 Because thesolar radiation on the outside envelope-surfaces has a smalleffect on the building cooling load the errors of predictionvalue are acceptable So the black-box model is consideredto be reliable for the prediction of solar radiation heat gainsAccordingly it is used in the RC model to forecast the solarradiation heat gains of envelope surfaces (119902sol and 119869119894)

43 Data for Identification The simulation process is influ-enced by the initial conditions and a duration called ldquowarm-uprdquo is needed to eliminate the influence of the initial con-ditions on the simulation results As depicted in Figure 8there are seven cases with different ldquowarm-uprdquo durations


(A) West wall (B) East wall (C) Floor

Pred

icte

d va

lue (

Wm

2 )

0

2

4

6

8

10

2 4 6 8 100Actual value (Wm2)

Pred

icte

d va

lue (

Wm

2 )

0

2

4

6

8

10


Pred

icte

d va

lue (

Wm

2 )

0

10

20

30

40

20 400Actual value (Wm2)

Training dataTesting data



(a) Short wave radiation on the inside surfaces

(A) South wall (B) North wall (C) West wall

(D) East wall (F) Roof


Pred

icte

d va

lue (

Wm

2 )

Pred

icte

d va

lue (

Wm

2 )

0

50

100

150

0

20

40

60

Pred

icte

d va

lue (

Wm

2 )

20 40 600Actual value (Wm2)

0

50

100

150

200

50 100 150 2000Actual value (Wm2)

Pred

icte

d va

lue (

Wm

2 )

Pred

icte

d va

lue (

Wm

2 )

0

50

100

150

200


200 400 600 8000Actual value (Wm2)

0

200

400

600

800



(b) Solar radiation (direct radiation and diffusion radiation) on the outside surfaces

Figure 7 BP model predicted value versus actual value of solar radiation


200204208212216220224228232236240244

Tai

r(∘ C)

24 48 72 96 120 144 168 192 216 240 264 288 312 3360Time (h)

336h288h240h192h

144h96h48h

Figure 8 Schematic diagram for warm-up period of simulationcase

from 2 days to 14 days All cases are started at the same initialconditions with the same ambient environment Due to thedifferent ldquowarm-uprdquo durations it is obvious that the indoortemperatures of different cases are different After the ldquowarm-uprdquo duration the calculation results will not be affected bythe initial conditions According to Figure 8 in the last daythe indoor temperatures have no difference between 12 daysand 14 days It shows that the simulation case can avoid theinfluence of initial conditions through a transitional periodof 14 days In order to ensure the identification accuracy ofmodel parameters the simulation data during the ldquowarm-uprdquoprocess are not included in the sample data After the 14-dayldquowarm-uprdquo process the simulation results within 4 days areused for identifying the simplified model

5 Results and Discussions

For the model predictive control of the ventilation systemcombining radiant terminals and air system accurate fore-casting results of both indoor air temperature and temper-atures of envelope surfaces are crucial In order to applythe model in MPC all the envelope parameters have to beamenable for different ambient conditions and system statusFor this reason the meteorological parameters depicted inFigure 9 are employed to test the reliability of the identifica-tion method and the prediction model

Since the operative temperature as described in (20) canrepresent the effect of air temperature and envelope tempera-ture on the indoor environment it is used for testing themodel in terms of cooling load of air system and radiantcooling floor

119905119900= 119886119903119905119903+ (1 minus 119886

119903) 119905air (20)

119905119903=(008 (119905rf + 119905fr) + 023 (119905119908 + 119905119890) + 035 (119905119904 + 119905119899))

(2 times (008 + 023 + 035)) (21)

Horizontal global solar radiationTout

0

5

10

15

20

25

30

35

40

Out

door

tem

pera

ture

(∘C)

0

200

400

600

800

1000

Hor

izon

tal g

loba

l sol

ar ra

diat

ion

(Wm

2 )

20 40 60 80 100 1200Time (h)

Figure 9 Ambient temperature and horizontal global solar radia-tion

119905119904=119860119904119905wall119904 + 119860win119905win

119860119904+ 119860win

(22)

where 119905119903is themean radiant temperature and 119886

119903is the radiant

fraction 119886119903is a function of relative velocity recommended

by international standard ISO 7730 [30] Because the indoorair velocity is usually below 02ms it is assumed to be05 The mean radiant temperature 119905

119903which is used for

a standing person [31] can be calculated with (21) Sincethere is a window on the south surface of envelope thesouth surface temperature 119905

119904is calculated by the area-weight

average temperature of window surface and wall surface(22) The simplified thermal model for radiant system istested by TRNSYS and the testing results with various floortemperatures air volumes and supply air temperatures areshown in Figures 10ndash12

51 Effect of Floor Temperature Figure 10 shows the effect offloor temperature on the operative temperature and the cool-ing load when the supply air temperature is 18∘C with an airchange rate of 1 hminus1 As seen in Figure 10 with the same otherconditions both operative temperature and cooling load ofair system increase with the floor surface temperature whilethe cooling load supplied by the floor decreasesTheoperativetemperature deviations between the simplified model andTRNSYS are less than 026∘C Meanwhile the floor coolingload deviations are less than 69Wm2 and the cooling loaddeviations of ventilation system are less than 09Wm2

52 Effect of Air Change Rate Similarly Figure 11 presents theeffect of air change rate when the supply air temperature is18∘C and floor temperature is 19∘C As shown in Figure 11with the same other conditions both operative temperatureand cooling load supplied by the floor decrease with theincrease of air change rate while the cooling load of airsystem increases significantly In this case the deviations of


20 40 60 80 100 1200Time (h)

205

210

215

220

225

230

235

240T

op(∘

C)

Simplified modelTRNSYS



Tfr 19∘C

Tfr 20∘C

Tfr 21∘C

(a) Operative temperature

20 40 60 80 100 1200Time (h)

10

20

30

40

50

Coo

ling

load

of fl

oor (

Wm

2 )




Tfr 19∘C

Tfr 20∘C

Tfr 21∘C

(b) Cooling load of floor

20 40 60 80 100 1200Time (h)

5

6

7

8

9

Coo

ling

load

of a

ir sy

stem

(Wm

2 )




Tfr 19∘C

Tfr 20∘C

Tfr 21∘C

(c) Cooling load of ventilation system

Figure 10 Results of simplified model and TRNSYS with various 119879fr (ACH = 1 and 119879119904= 18∘C)

operative temperature floor cooling load and ventilation sys-tem cooling load are less than 025∘C 69Wm2 and 19Wm2 respectively

53 Effect of Supply Air Temperature Figure 12 describes theeffect of various supply air temperature with an air changerate of 1 hminus1 and floor temperature of 19∘C In Figure 12with the same other conditions the operative temperature

increases with the supply air temperature Meanwhile thecooling load supplied by the floor decreases slightly Besidesthe cooling load of air system significantly increases withthe fall of supply air temperature The operative temperaturedeviations between the simplified model and TRNSYS areless than 025∘CMeanwhile the floor cooling load deviationsare less than 69Wm2 and the cooling load deviations ofventilation system are less than 09Wm2


20 40 60 80 100 1200Time (h)

200

205

210

215

220

225T

op(∘

C)




ACH

ACH

ACH1hminus1

2hminus1

3hminus1


10

20

30

40

50

60

70

80

90

100

Coo

ling

load

of fl

oor (

Wm

2 )

20 40 60 80 100 1200Time (h)




ACH 1hminus1

ACH 2hminus1

ACH 3hminus1


20 40 60 80 100 1200Time (h)

4

6

8

10

12

14

16

18

Coo

ling

load

of a

ir sy

stem

(Wm

2 )




ACH

ACH

ACH1hminus1

2hminus1

3hminus1


Figure 11 Results of simplified model and TRNSYS with various ACH (119879fr = 19∘C and 119879119904= 18∘C)

According to Figures 10ndash12 the results of the simplifiedmodel under various conditions are consistent with thosecalculated by TRNSYS It shows that the model parametersderived from the identification method are good for thesimulation case

In order to further investigate the deviation of operativetemperature cooling load of floor and ventilation systemFigure 13 shows the results of these three parameters (inFigure 10) in detail Apparently the deviations of operative

temperature and cooling load of floor and ventilation systemchange with time periodically and the values reach themaximum at noon That is because the black-box model ofincident solar radiation is unfaithful when the solar radiationis too large Therefore the deviation can be reduced throughimproving the incident solar radiation model

The CV values of the results in Figures 10ndash12 are listed inTable 3 and the adaptability of simplified model for variouscontrol parameters can be compared It is very clear that the


205

210

215

220

225

Top

(∘C)

20 40 60 80 100 1200Time (h)




Ts = 16∘C

Ts = 17∘C

Ts = 18∘C


20 40 60 80 100 1200Time (h)

10

20

30

40

50

60

70

80

90

100

Coo

ling

load

of fl

oor (

Wm

2 )




Ts = 16∘C

Ts = 17∘C

Ts = 18∘C


20 40 60 80 100 1200Time (h)

4

5

6

7

8

9

10

Coo

ling

load

of a

ir sy

stem

(Wm

2 )




Ts = 16∘C

Ts = 17∘C

Ts = 18∘C


Figure 12 Results of simplified model and TRNSYS with various 119879119904(119879fr = 19∘C and ACH = 1)

Table 3 CV values of operative temperature and cooling load

Figure 10 Figure 11 Figure 12119879op 063 052 046Cooling load of floor 1193 959 961Cooling load of ventilation system 566 707 535


00

01

02

03

12 24 36 48 60 72 84 96 108 1200Time (h)

Ope

rativ

e tem

pera

ture

dev

iatio

n (∘

C)

(a) Operative temperatureFloorVentilation system

12 24 36 48 60 72 84 96 108 1200Time (h)

0

2

4

6

8

10

12

14

16

Coo

ling

load

dev

iatio

n of

floo

r (W

m2 )

minus12

minus08

minus04

00

04

08

12

Coo

ling

load

dev

iatio

n of

ven

tilat

ion

syste

m (W

m2 )

(b) Cooling load

Figure 13 Deviation of simplified model and TRNSYS

CV values of 119879op under all conditions are smaller than thoseof both floor system cooling load and air system cooling loadAll the CV values of 119879op are below 1 By contrast the CVvalues for floor cooling load (about 12) are larger than thoseof both operative temperature and air system cooling load

The incident solar radiation is the most important factorfor the floor cooling load and the values in the second and thethird days are greater than those in other days (as depictedin Figure 9) Accordingly it is clear that the cooling loadsin the second and the third days are larger than those inother days (Figures 10(b) 11(b) and 12(b)) Since there areprediction errors in the solar radiation heat gains for theenvelope surfaces the error of floor cooling load is largerthan the cooling load of ventilation system Besides an accu-rate prediction of the indoor temperature is beneficial toavoid the condensation which is an important control mis-sion for radiant cooling systems Although there is a largerprediction error in cooling loads the prediction of operativetemperature is accurate Therefore the simplified model issufficient for MPC in buildings with radiant systems

6 Conclusions

In the building with radiant cooling on one hand the radi-ant surface induces long wave radiant heat exchange betweenthe cooling surface and other surfaces On the other handthe incident solar radiation on the cooling surface throughthe window is absorbed directly Both the long wave radi-ation and the incident solar radiation are the dominantinfluencing factors for the cooling capacity of the radiantsurface Therefore it is important to accurately calculate theabove two factors for the prediction model of MPC In thispaper the semiempirical model and black-box model areadopted with RC model to construct the prediction modelfor the building with radiant terminals The RC model isused for modeling the heat transfer of building envelopes

The incident solar radiation is forecasted by the black-boxmodel and the long wave radiant heat exchange is forecastedby the semiempiricalmodel In order to accurately predict theindoor environment and cooling load the genetic algorithmis employed to identify the model parameters

The reference model and identification method are testedwith TRNSYS The testing results show that the referencemodel is suitable for the simulation case The CV values ofoperative temperature are below 1 and the CV values ofcooling load are within 12 The accurate operative temper-ature is beneficial to avoid the cooling surface condensationBut due to the lower accuracy of black-box model for solarradiation heat gains of envelopes the predictive accuracy forcooling load of radiant floor is slightly lower However themaximum error of prediction value is only about 12 sothe model accuracy is considered to be acceptable for thesupervisory control purpose

Compared with other building simulation tools thehybrid model in this paper can integrate with other HVACcomponent models to realize the supervisory control moreconveniently Due to the application of hybrid model themodel complexity has increasedThis may smoothly increasethe calculation time for the parameter identification Butthe model complexity does not have a significant effect onthe application of the hybrid model In the future workit is necessary to improve the accuracy of the model andto increase the model parameter identification efficiencyMoreover the radiant terminal model will be built andcombined with the simplified building thermal model in thispaper to optimize the control of the radiant system

Symbols

119860 Area (m2)119888 Thermal capacity (Jsdotmminus2sdotKminus1)119888119901 Specific heat capacity (Jsdotkgminus1sdotKminus1)


119865 Radiation view factor119891 Proportion of thermal resistancefitness Objection function119892 Proportion of specific heat capacityℎ Convective heat transfer coefficient

(Wsdotmminus2sdotKminus1)IT Incident solar radiation on the horizontal

plane (Wsdotmminus2)119869 Incident solar radiation (Wsdotmminus2)119898 Supply air rate (kgs)119902 Heat flow (Wsdotmminus2)119881 Room volume (m3)119876air Cooling load of ventilation system

(Wsdotmminus2)119876fr Cooling load of radiant system (Wsdotmminus2)119877 Thermal resistance (m2sdotKsdotWminus1)119905 Time (h)119879 Temperature (K)119878 Internal load (W)119879sol Transmissivity of window

Greek Symbols

120576 Emissivity120596 Weight factor120574 Absorption coefficient120588 Air density (kgsdotmminus3)120590 Stefan-Boltzmann constant (Wsdotmminus2sdotKminus4)

Subscripts

rf Rooffr Floorwall Wallwin Window119904 Supply airair Indoor airrad Long wave radiationsol Solar direct radiationout Outside119897 Outside node of 3R2C model119900 Inside node of 3R2C model

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The research work is supported by Sichuan Province YouthScience and Technology Innovation Team of Building Envi-ronment and Energy Efficiency (no 2015TD0015)

References

[1] G Huang ldquoModel predictive control of VAV zone thermalsystems concerning bi-linearity and gain nonlinearityrdquo ControlEngineering Practice vol 19 no 7 pp 700ndash710 2011

[2] S Yuan and R Perez ldquoMultiple-zone ventilation and tempera-ture control of a single-duct VAV systemusingmodel predictivestrategyrdquo Energy and Buildings vol 38 no 10 pp 1248ndash12612006

[3] G P Henze D E Kalz S Liu and C Felsmann ldquoExperimentalanalysis of model-based predictive optimal control for activeand passive building thermal storage inventoryrdquo HVACampRResearch vol 11 no 2 pp 189ndash213 2005

[4] J Siroky F Oldewurtel J I Cigler and S Prıvara ldquoExperimen-tal analysis of model predictive control for an energy efficientbuilding heating systemrdquo Applied Energy vol 88 no 9 pp3079ndash3087 2011

[5] A Afram and F Janabi-Sharifi ldquoTheory and applications ofHVAC control systemsmdasha review of model predictive control(MPC)rdquo Building and Environment vol 72 pp 343ndash355 2014

[6] A J Wright D Bloomfield and T J Wiltshire ldquoReview paperbuilding simulation and building representation overview ofcurrent developmentsrdquo Building Services Engineering Researchamp Technology vol 13 no 1 pp 1ndash11 1992

[7] Z Liao and A L Dexter ldquoA simplified physical model for esti-mating the average air temperature in multi-zone heatingsystemsrdquoBuilding and Environment vol 39 no 9 pp 1013ndash10222004

[8] S Wang and Z Ma ldquoSupervisory and optimal control of build-ing HVAC systems a reviewrdquo HVACampR Research vol 14 no 1pp 3ndash32 2008

[9] I Hazyuk C Ghiaus and D Penhouet ldquoOptimal temperaturecontrol of intermittently heated buildings using Model Pre-dictive Control part Imdashbuilding modelingrdquo Building and Envi-ronment vol 51 pp 379ndash387 2012

[10] J A Crabb N Murdoch and J M Penman ldquoA simplified ther-mal response modelrdquo Building Services Engineering Research ampTechnology vol 1 pp 13ndash19 1987

[11] T Dewson B Day and A D Irving ldquoLeast squares parameterestimation of a reduced order thermalmodel of an experimentalbuildingrdquo Building and Environment vol 28 no 2 pp 127ndash1371993

[12] M M Gouda S Danaher and C P Underwood ldquoBuildingthermal model reduction using nonlinear constrained opti-mizationrdquo Building and Environment vol 37 no 12 pp 1255ndash1265 2002

[13] S Wang and X Xu ldquoSimplified building model for transientthermal performance estimation using GA-based parameteridentificationrdquo International Journal ofThermal Sciences vol 45no 4 pp 419ndash432 2006

[14] X Xu and S Wang ldquoOptimal simplified thermal models ofbuilding envelope based on frequency domain regression usinggenetic algorithmrdquo Energy and Buildings vol 39 no 5 pp 525ndash536 2007

[15] A P Ramallo-Gonzalez M E Eames and D A ColeyldquoLumped parameter models for building thermal modelling ananalytic approach to simplifying complex multi-layered con-structionsrdquo Energy and Buildings vol 60 pp 174ndash184 2013

[16] G Fraisse C Viardot O Lafabrie and G Achard ldquoDevelop-ment of a simplified and accurate buildingmodel based on elec-trical analogyrdquo Energy and Buildings vol 34 no 10 pp 1017ndash1031 2002

[17] Z OrsquoNeill S Narayanan and A R Brahme ldquoModel-basedthermal load estimation in buildingsrdquo in Proceedings of the 4thNational Conference of IBPSA-USA (SimBuild rsquo10) pp 474ndash481New York NY USA August 2010


[18] UIUCLBNL EnergyPlus Engineering ReferenceThe Reference toEnergyPlus Calculations US Department of Energy 2005

[19] A Nassiopoulos R Kuate and F Bourquin ldquoCalibration ofbuilding thermal models using an optimal control approachrdquoEnergy and Buildings vol 76 pp 81ndash91 2014

[20] M Wetter and P Haves ldquoA Modular building controls virtualtest Bed for the Inte-gration of heterogeneous systemsrdquo in Pro-ceedings of the 3rd Nation Conference of IBPSA-USA SimBuildBerkeley Calif USA August 2008

[21] X Li and J Wen ldquoBuilding energy consumption on-line fore-casting using physics based system identificationrdquo Energy andBuildings vol 82 pp 1ndash12 2014

[22] S Royer SThil T Talbert andM Polit ldquoA procedure for mod-eling buildings and their thermal zones using co-simulation andsystem identificationrdquo Energy and Buildings vol 78 pp 231ndash2372014

[23] G NWalton ldquoA new algorithm for radiant interchange in roomload calculationsrdquo ASHRAE Transactions vol 86 pp 190ndash2081980

[24] A Odyjas and A Gorka ldquoSimulations of floor cooling systemcapacityrdquo Applied Thermal Engineering vol 51 no 1-2 pp 84ndash90 2013

[25] Y ZhaoAir Conditioning China Architecture amp Building PressBeijing China 2009 (Chinese)

[26] J A Duffie and W A Beckman Solar Engineering of ThermalProcesses John Wiley amp Sons Hoboken NJ USA 2013

[27] A Kusiak Y Zeng and G Xu ldquoMinimizing energy consump-tion of an air handling unit with a computational intelligenceapproachrdquo Energy and Buildings vol 60 pp 355ndash363 2013

[28] S A Kalogirou ldquoArtificial neural networks and genetic algo-rithms in energy applications in buildingsrdquoAdvances in BuildingEnergy Research vol 3 no 1 pp 83ndash120 2009

[29] CEN ldquoEnergy performance of buildingsmdashsensible room cool-ing load calculationmdashgeneral criteria and validation proce-duresrdquo EN ISO 15255 CEN 2007

[30] J Francis and R E Edwards ldquoSpeedy comfort assessment usingISO 7730rdquo Building Services Engineering Researchamp Technologyvol 16 no 3 pp 165ndash168 1995

[31] ASHRAE ASHRAE Applications Handbook American Societyof Heating Refrigeration and Air-Conditioning EngineeringAtlanta Ga USA 1999

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


thermal process [8] Since themodels forMPC have to be lesstime-consuming in comparison with the other two modelsthe simplified gray-box model with lower model order ismore suitable for the MPC solution

As a simplified gray-box model the lumped parametermodel always combines with other models to constructthe MPC controller Hazyuk et al [9] adopted this modeland state space model to construct MPC for intermittentheating buildings In their study the results showed thatthe forecasting error was below 10 To maximize the MPCperformance both improving the calculation accuracy andreducing the calculation time of lumped parameter modelare valid approaches For improving the calculation accuracyit is crucial to identify the model parameters Based onthe simplified thermal response model [10] the least squaremethod was used to identify parameters of a solar house [11]They found that the model parameters had the quality ofnonuniqueness and it was unsuitable for evaluating the build-ing thermal performance However the model can adjust theparameters using the sample data so it is suitable for thebuilding energy management system Gouda et al [12] usedthe sequence quadratic programming method to identify themodel parameters of various constructions and to comparedifferent order modelsThe results showed that second-ordermodel balanced the computational accuracy and calculationconsumption moderately The genetic algorithm with datarecorded by building management system was employed toidentify the RC model parameters in frequency-domain [1314] Based on the time domain and frequency-domain analy-sis a method to simplify the RC model was established [15]and this method has higher applicability than the methodbased on electrical analogy [16] Besides the real buildingoperation data the data acquired from the simulation toolscan be used to identify the model parameters as well OrsquoNeillet al [17] adopted EnergyPlus [18] to test the forecast modelconsisting of 3R2C and Extended Kalman Filter Similarlya cost-effective building thermal model was verified byEnergyPlus [19] What is more EnergyPlus and MATLABwere integrated by BCVTB [20] to develop a cooling loadprediction model for optimizing HVAC control and themodel parameters were recognized using the data calculatedby simulation tool [21 22] The above researches show thatthe lumped parameter model has a strong ability to forecastthe indoor temperature and the cooling loadwhich is suitablefor theMPCHowever for the building equippedwith radiantterminals there are some differences from the building withair-based system In the building with radiant terminalsthe long wave radiation between interior surfaces cannot beneglected and the control variable of indoor environmentis usually the operative temperature What is more in thebuilding with all-air system the incident solar radiation onthe interior surfaces firstly warms up the construction Thenthe cooling load is generated by convective heat exchange Bycontrast the incident solar radiation on the radiant coolingsurface is directly absorbed Due to the above differencesthe long wave radiation among the indoor surfaces and theincident solar radiation on the envelope surfaces cannot becalculated by these models and they are incapable of evaluat-ing wall surface temperatures accurately Based on the above

reasons these models in the literature [11ndash13 15 19 21] areinapplicable for theMPC in buildings with radiant terminals

In order to optimize the operation of the air-conditioningsystemwith radiant terminals byMPC technology this paperpresents a prediction model for a building with radiant floorThis model consists of three parts simplified RC modelblack-model and semiempirical model The simplified RCmodel is used to describe the heat transfer process of thebuilding and the black-box model is used to forecast theincident solar radiation on the envelope surfaces while thesemiempirical model is adopted to calculate the long waveradiation between interior surfaces The model parametersare recognized by the genetic algorithm and the samplingdata for the recognition is derived from TRNSYS Finally themodel is used in a case study to predict the indoor operativetemperature and the cooling load of both radiant terminalsand ventilation system

2 Simplified Building Thermal Model

The RC model adopts different model structures to repre-sent building elements with various heat conduction andthermal storage In most studies the optimization methodis employed to simplify the RC model and to determinethe model parameters It is verified that the second-orderRC model can reduce the calculation time without anycompromise of calculation accuracy compared to the higher-order model [11] Similarly Gouda et al [12] proved that theoptimized 2nd-order model could simulate both lightweightand heavyweight buildings with the minimal accuracy lossThus the low-order RCmodel is used to describe the thermalprocess of building envelope in this paper The mean radianttemperature is adopted for calculating the long wave radia-tion between interior wall surfaces and a black-box model isused to predict the solar radiation on the envelope surfaces

21 Lumped ParameterModel of Envelopes Both 3R2Cmodeland 2R1C model are adopted to build the thermal networkmodel of the building as shown in Figure 1 All the enclosurestructures are assumed to be connected to the outdoorenvironment and the thermal mass such as interior wallsand furniture in the room are neglected in the model Dueto the different orientations of the building solar radiationson the different surfaces are distinct leading to the differentsurface temperatures To accurately calculate the operativetemperature heat transmissions from the external walls andthe roof are separately calculated (1)ndash(4) and the heat storageperformance of window (5) is considered by 2R1C modelThe radiant surface is calculated as a surface with a constanttemperature The energy balance for indoor air is shown in(6) The heat gains from internal equipment and occupantsare calculated in (6)

1198921119894119888wall119894

119889119879wall119897119894

119889119905=119879wall119894 minus 119879wall119897119894

1198913119894119877wall119894

minus119879wall119897119894 minus 119879wall119900119894

1198912119894119877wall

(1)

1198922119894119888wall119894

119889119879wall119900119894

119889119905=119879wall119897119894 minus 119879wall119900119894

1198912119894119877wall

minus119879wall119900119894 minus 119879air

1198911119894119877wall

minus 119902wallrad119894 + 119902sol119894

(2)


Qradfr

TwingwincwinRwin2

Rwin1

Twalloi Twallli

Trf o

Trfl

f3iRwalli

Tair

Qradrfi

Qradwalli

1macpa

1hfrAfr

f2iRwallif1iRwalli

f1rfRrf

f2rfRrf

f3rf Rrf

g2rf crf

g1rf crf

g2icwallig1icwalli

Trf

Tfr

To Twalli

Tout


1198921rf119888rf

119889119879rf 119897

119889119905=119879rf minus 119879rf 119897

1198913rf119877rf

minus119879rf 119897 minus 119879rf 119900

1198912rf119877rf

(3)

1198922rf119888rf

119889119879rf 119900

119889119905=119879rf 119897 minus 119879rf 119900

1198912rf119877rf


1198911rf119877rf


+ 119902solrf

(4)

119892win119888win119889119879win119889119905

=119879119900minus 119879win119877win1


(5)

120588119881119888119901air

119889119879air119889119905

= 119898air119888119901air (119879119904 minus 119879air)

+

119873=4

sum

119894=1


1198911119894119877119894

)

+ 119860 fr (119879rf 119900 minus 119879air

1198911rf119877rf

)

+ 119860win (119879win119900 minus 119879air

119877win1)


(6)



119860119898119903119905119894

=

119873

sum

119895=1

119895 =119894

119860119895 (7)

120576119898119903119905119894

=1

119860119898119903119905119894

times

119873

sum

119895=1

119895 =119894

119860119895120576119895 (8)

119879119898119903119905119894

=1

119860119898119903119905119894

120576119898119903119905119894

times

119873

sum

119895=1

119895 =119894

119860119895120576119895119879wall119895 (9)

119865119898119903119905119894

=1

(120576119898119903119905119894

120576119894) + (119860

119894(1 minus 120576

119898119903119905119894) 119860119898119903119905119894

) (10)

119902radwall119894 = 120590120576119898119903119905119894119865119898119903119905119894 (1198794

wall119900119894 minus 1198794

119898119903119905119894) (11)


119879wallrf 119894 = 119879out +120574119894119869119894

ℎ119894

(12)


+

ITt

+


P

1 1

1 times 1LW12

S1 times 1

S1 times 1


a1f1

S1

aiS1 times 1

LW23

S2 times S1

b2S2 times S2

a2f2

Ji

qsoli

a1 = f1(LW12P + b1) a2 = f2(LW23P + b2)





119902sol119894 = 119891 (IT 119905) (13)

119869119894= 119891 (IT 119905) (14)




fitness =119873

sum

119894=1

(120596119894(119879wall119894 (119905) minus 119879wall119894 (119905))

2

+ 120596rf (119879rf (119905) minus 119879rf (119905))2

+ 120596win (119879win (119905) minus 119879win (119905))2

+ 120596air (119879air (119905) minus 119879air (119905))2

+ 120596119876air

(119876air (119905) minus 119876air (119905))2

+ 120596119876fr(119876fr (119905) minus 119876fr (119905))

2

)

(15)






Stop GA run




Stop GA run

Stop and output

Yes

Yes

No

No

Yes

No

No

D = threshold value

irun = irun + 1


irun = max run


run = 1 g c f R 120574 h



g c f R 120574 h

g c f R 120574 h


120596rf +119873

sum

119894=1






001 le 119877119894le 20


7


0 le 120574119894le 1

1 le ℎ119894le 30





Density[kgm3]





3

sum

119894=1

119891119894= 1

2

sum

119894=1

119892119894= 1

(18)

4 Case Study







Ventilation


20m27m

49m


00

05

10


4 8 12 16 20 240Time (h)

Dai

ly p

atte

rn o

f int

erna

l loa

d






0

5

10

15

20

25

30

35

40

NSWE

FloorRoof

IT

20 40 60 80 100 120 140 1600Time (h)

Shor

t wav

e rad

iatio

n (W

m2 )

0

200

400

600

800

1000

Tota

l sol

ar ra

diat

ion

(Wm

2 )


0

200

400

600

800

1000

Inci

dent

sola

r rad

iatio

n (W

m2 )

20 40 60 80 100 120 140 1600Time (h)

NSWE

RoofIT

0

200

400

600

800

1000

Tota

l sol

ar ra

diat

ion

(Wm

2 )







CV =

radicsum119899

119894=1(119910119894minus 119894)2

119899

10038161003816100381610038161199101198941003816100381610038161003816

(19)







Pred

icte

d va

lue (

Wm

2 )

0

2

4

6

8

10


Pred

icte

d va

lue (

Wm

2 )

0

2

4

6

8

10


Pred

icte

d va

lue (

Wm

2 )

0

10

20

30

40









Pred

icte

d va

lue (

Wm

2 )

Pred

icte

d va

lue (

Wm

2 )

0

50

100

150

0

20

40

60

Pred

icte

d va

lue (

Wm

2 )


0

50

100

150

200

50 100 150 2000Actual value (Wm2)

Pred

icte

d va

lue (

Wm

2 )

Pred

icte

d va

lue (

Wm

2 )

0

50

100

150

200


200 400 600 8000Actual value (Wm2)

0

200

400

600

800






200204208212216220224228232236240244

Tai

r(∘ C)

24 48 72 96 120 144 168 192 216 240 264 288 312 3360Time (h)

336h288h240h192h

144h96h48h






119905119900= 119886119903119905119903+ (1 minus 119886

119903) 119905air (20)

119905119903=(008 (119905rf + 119905fr) + 023 (119905119908 + 119905119890) + 035 (119905119904 + 119905119899))

(2 times (008 + 023 + 035)) (21)


0

5

10

15

20

25

30

35

40

Out

door

tem

pera

ture

(∘C)

0

200

400

600

800

1000

Hor

izon

tal g

loba

l sol

ar ra

diat

ion

(Wm

2 )

20 40 60 80 100 1200Time (h)


119905119904=119860119904119905wall119904 + 119860win119905win

119860119904+ 119860win

(22)












20 40 60 80 100 1200Time (h)

205

210

215

220

225

230

235

240T

op(∘

C)




Tfr 19∘C

Tfr 20∘C

Tfr 21∘C


20 40 60 80 100 1200Time (h)

10

20

30

40

50

Coo

ling

load

of fl

oor (

Wm

2 )




Tfr 19∘C

Tfr 20∘C

Tfr 21∘C


20 40 60 80 100 1200Time (h)

5

6

7

8

9

Coo

ling

load

of a

ir sy

stem

(Wm

2 )




Tfr 19∘C

Tfr 20∘C

Tfr 21∘C







20 40 60 80 100 1200Time (h)

200

205

210

215

220

225T

op(∘

C)




ACH

ACH

ACH1hminus1

2hminus1

3hminus1


10

20

30

40

50

60

70

80

90

100

Coo

ling

load

of fl

oor (

Wm

2 )

20 40 60 80 100 1200Time (h)




ACH 1hminus1

ACH 2hminus1

ACH 3hminus1


20 40 60 80 100 1200Time (h)

4

6

8

10

12

14

16

18

Coo

ling

load

of a

ir sy

stem

(Wm

2 )




ACH

ACH

ACH1hminus1

2hminus1

3hminus1








205

210

215

220

225

Top

(∘C)

20 40 60 80 100 1200Time (h)




Ts = 16∘C

Ts = 17∘C

Ts = 18∘C


20 40 60 80 100 1200Time (h)

10

20

30

40

50

60

70

80

90

100

Coo

ling

load

of fl

oor (

Wm

2 )




Ts = 16∘C

Ts = 17∘C

Ts = 18∘C


20 40 60 80 100 1200Time (h)

4

5

6

7

8

9

10

Coo

ling

load

of a

ir sy

stem

(Wm

2 )




Ts = 16∘C

Ts = 17∘C

Ts = 18∘C






00

01

02

03

12 24 36 48 60 72 84 96 108 1200Time (h)

Ope

rativ

e tem

pera

ture

dev

iatio

n (∘

C)


12 24 36 48 60 72 84 96 108 1200Time (h)

0

2

4

6

8

10

12

14

16

Coo

ling

load

dev

iatio

n of

floo

r (W

m2 )

minus12

minus08

minus04

00

04

08

12

Coo

ling

load

dev

iatio

n of

ven

tilat

ion

syste

m (W

m2 )

(b) Cooling load




6 Conclusions





Symbols







Greek Symbols


Subscripts




Acknowledgments


References








































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Qradfr

TwingwincwinRwin2

Rwin1

Twalloi Twallli

Trf o

Trfl

f3iRwalli

Tair

Qradrfi

Qradwalli

1macpa

1hfrAfr

f2iRwallif1iRwalli

f1rfRrf

f2rfRrf

f3rf Rrf

g2rf crf

g1rf crf

g2icwallig1icwalli

Trf

Tfr

To Twalli

Tout


1198921rf119888rf

119889119879rf 119897

119889119905=119879rf minus 119879rf 119897

1198913rf119877rf

minus119879rf 119897 minus 119879rf 119900

1198912rf119877rf

(3)

1198922rf119888rf

119889119879rf 119900

119889119905=119879rf 119897 minus 119879rf 119900

1198912rf119877rf


1198911rf119877rf


+ 119902solrf

(4)

119892win119888win119889119879win119889119905

=119879119900minus 119879win119877win1


(5)

120588119881119888119901air

119889119879air119889119905

= 119898air119888119901air (119879119904 minus 119879air)

+

119873=4

sum

119894=1


1198911119894119877119894

)

+ 119860 fr (119879rf 119900 minus 119879air

1198911rf119877rf

)

+ 119860win (119879win119900 minus 119879air

119877win1)


(6)



119860119898119903119905119894

=

119873

sum

119895=1

119895 =119894

119860119895 (7)

120576119898119903119905119894

=1

119860119898119903119905119894

times

119873

sum

119895=1

119895 =119894

119860119895120576119895 (8)

119879119898119903119905119894

=1

119860119898119903119905119894

120576119898119903119905119894

times

119873

sum

119895=1

119895 =119894

119860119895120576119895119879wall119895 (9)

119865119898119903119905119894

=1

(120576119898119903119905119894

120576119894) + (119860

119894(1 minus 120576

119898119903119905119894) 119860119898119903119905119894

) (10)

119902radwall119894 = 120590120576119898119903119905119894119865119898119903119905119894 (1198794

wall119900119894 minus 1198794

119898119903119905119894) (11)


119879wallrf 119894 = 119879out +120574119894119869119894

ℎ119894

(12)


+

ITt

+


P

1 1

1 times 1LW12

S1 times 1

S1 times 1


a1f1

S1

aiS1 times 1

LW23

S2 times S1

b2S2 times S2

a2f2

Ji

qsoli

a1 = f1(LW12P + b1) a2 = f2(LW23P + b2)





119902sol119894 = 119891 (IT 119905) (13)

119869119894= 119891 (IT 119905) (14)




fitness =119873

sum

119894=1

(120596119894(119879wall119894 (119905) minus 119879wall119894 (119905))

2

+ 120596rf (119879rf (119905) minus 119879rf (119905))2

+ 120596win (119879win (119905) minus 119879win (119905))2

+ 120596air (119879air (119905) minus 119879air (119905))2

+ 120596119876air

(119876air (119905) minus 119876air (119905))2

+ 120596119876fr(119876fr (119905) minus 119876fr (119905))

2

)

(15)






Stop GA run




Stop GA run

Stop and output

Yes

Yes

No

No

Yes

No

No

D = threshold value

irun = irun + 1


irun = max run


run = 1 g c f R 120574 h



g c f R 120574 h

g c f R 120574 h


120596rf +119873

sum

119894=1






001 le 119877119894le 20


7


0 le 120574119894le 1

1 le ℎ119894le 30





Density[kgm3]





3

sum

119894=1

119891119894= 1

2

sum

119894=1

119892119894= 1

(18)

4 Case Study







Ventilation


20m27m

49m


00

05

10


4 8 12 16 20 240Time (h)

Dai

ly p

atte

rn o

f int

erna

l loa

d






0

5

10

15

20

25

30

35

40

NSWE

FloorRoof

IT

20 40 60 80 100 120 140 1600Time (h)

Shor

t wav

e rad

iatio

n (W

m2 )

0

200

400

600

800

1000

Tota

l sol

ar ra

diat

ion

(Wm

2 )


0

200

400

600

800

1000

Inci

dent

sola

r rad

iatio

n (W

m2 )

20 40 60 80 100 120 140 1600Time (h)

NSWE

RoofIT

0

200

400

600

800

1000

Tota

l sol

ar ra

diat

ion

(Wm

2 )







CV =

radicsum119899

119894=1(119910119894minus 119894)2

119899

10038161003816100381610038161199101198941003816100381610038161003816

(19)







Pred

icte

d va

lue (

Wm

2 )

0

2

4

6

8

10


Pred

icte

d va

lue (

Wm

2 )

0

2

4

6

8

10


Pred

icte

d va

lue (

Wm

2 )

0

10

20

30

40









Pred

icte

d va

lue (

Wm

2 )

Pred

icte

d va

lue (

Wm

2 )

0

50

100

150

0

20

40

60

Pred

icte

d va

lue (

Wm

2 )


0

50

100

150

200

50 100 150 2000Actual value (Wm2)

Pred

icte

d va

lue (

Wm

2 )

Pred

icte

d va

lue (

Wm

2 )

0

50

100

150

200


200 400 600 8000Actual value (Wm2)

0

200

400

600

800






200204208212216220224228232236240244

Tai

r(∘ C)

24 48 72 96 120 144 168 192 216 240 264 288 312 3360Time (h)

336h288h240h192h

144h96h48h






119905119900= 119886119903119905119903+ (1 minus 119886

119903) 119905air (20)

119905119903=(008 (119905rf + 119905fr) + 023 (119905119908 + 119905119890) + 035 (119905119904 + 119905119899))

(2 times (008 + 023 + 035)) (21)


0

5

10

15

20

25

30

35

40

Out

door

tem

pera

ture

(∘C)

0

200

400

600

800

1000

Hor

izon

tal g

loba

l sol

ar ra

diat

ion

(Wm

2 )

20 40 60 80 100 1200Time (h)


119905119904=119860119904119905wall119904 + 119860win119905win

119860119904+ 119860win

(22)












20 40 60 80 100 1200Time (h)

205

210

215

220

225

230

235

240T

op(∘

C)




Tfr 19∘C

Tfr 20∘C

Tfr 21∘C


20 40 60 80 100 1200Time (h)

10

20

30

40

50

Coo

ling

load

of fl

oor (

Wm

2 )




Tfr 19∘C

Tfr 20∘C

Tfr 21∘C


20 40 60 80 100 1200Time (h)

5

6

7

8

9

Coo

ling

load

of a

ir sy

stem

(Wm

2 )




Tfr 19∘C

Tfr 20∘C

Tfr 21∘C







20 40 60 80 100 1200Time (h)

200

205

210

215

220

225T

op(∘

C)




ACH

ACH

ACH1hminus1

2hminus1

3hminus1


10

20

30

40

50

60

70

80

90

100

Coo

ling

load

of fl

oor (

Wm

2 )

20 40 60 80 100 1200Time (h)




ACH 1hminus1

ACH 2hminus1

ACH 3hminus1


20 40 60 80 100 1200Time (h)

4

6

8

10

12

14

16

18

Coo

ling

load

of a

ir sy

stem

(Wm

2 )




ACH

ACH

ACH1hminus1

2hminus1

3hminus1








205

210

215

220

225

Top

(∘C)

20 40 60 80 100 1200Time (h)




Ts = 16∘C

Ts = 17∘C

Ts = 18∘C


20 40 60 80 100 1200Time (h)

10

20

30

40

50

60

70

80

90

100

Coo

ling

load

of fl

oor (

Wm

2 )




Ts = 16∘C

Ts = 17∘C

Ts = 18∘C


20 40 60 80 100 1200Time (h)

4

5

6

7

8

9

10

Coo

ling

load

of a

ir sy

stem

(Wm

2 )




Ts = 16∘C

Ts = 17∘C

Ts = 18∘C






00

01

02

03

12 24 36 48 60 72 84 96 108 1200Time (h)

Ope

rativ

e tem

pera

ture

dev

iatio

n (∘

C)


12 24 36 48 60 72 84 96 108 1200Time (h)

0

2

4

6

8

10

12

14

16

Coo

ling

load

dev

iatio

n of

floo

r (W

m2 )

minus12

minus08

minus04

00

04

08

12

Coo

ling

load

dev

iatio

n of

ven

tilat

ion

syste

m (W

m2 )

(b) Cooling load




6 Conclusions





Symbols







Greek Symbols


Subscripts




Acknowledgments


References








































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










+

ITt

+


P

1 1

1 times 1LW12

S1 times 1

S1 times 1


a1f1

S1

aiS1 times 1

LW23

S2 times S1

b2S2 times S2

a2f2

Ji

qsoli

a1 = f1(LW12P + b1) a2 = f2(LW23P + b2)





119902sol119894 = 119891 (IT 119905) (13)

119869119894= 119891 (IT 119905) (14)




fitness =119873

sum

119894=1

(120596119894(119879wall119894 (119905) minus 119879wall119894 (119905))

2

+ 120596rf (119879rf (119905) minus 119879rf (119905))2

+ 120596win (119879win (119905) minus 119879win (119905))2

+ 120596air (119879air (119905) minus 119879air (119905))2

+ 120596119876air

(119876air (119905) minus 119876air (119905))2

+ 120596119876fr(119876fr (119905) minus 119876fr (119905))

2

)

(15)






Stop GA run




Stop GA run

Stop and output

Yes

Yes

No

No

Yes

No

No

D = threshold value

irun = irun + 1


irun = max run


run = 1 g c f R 120574 h



g c f R 120574 h

g c f R 120574 h


120596rf +119873

sum

119894=1






001 le 119877119894le 20


7


0 le 120574119894le 1

1 le ℎ119894le 30





Density[kgm3]





3

sum

119894=1

119891119894= 1

2

sum

119894=1

119892119894= 1

(18)

4 Case Study







Ventilation


20m27m

49m


00

05

10


4 8 12 16 20 240Time (h)

Dai

ly p

atte

rn o

f int

erna

l loa

d






0

5

10

15

20

25

30

35

40

NSWE

FloorRoof

IT

20 40 60 80 100 120 140 1600Time (h)

Shor

t wav

e rad

iatio

n (W

m2 )

0

200

400

600

800

1000

Tota

l sol

ar ra

diat

ion

(Wm

2 )


0

200

400

600

800

1000

Inci

dent

sola

r rad

iatio

n (W

m2 )

20 40 60 80 100 120 140 1600Time (h)

NSWE

RoofIT

0

200

400

600

800

1000

Tota

l sol

ar ra

diat

ion

(Wm

2 )







CV =

radicsum119899

119894=1(119910119894minus 119894)2

119899

10038161003816100381610038161199101198941003816100381610038161003816

(19)







Pred

icte

d va

lue (

Wm

2 )

0

2

4

6

8

10


Pred

icte

d va

lue (

Wm

2 )

0

2

4

6

8

10


Pred

icte

d va

lue (

Wm

2 )

0

10

20

30

40









Pred

icte

d va

lue (

Wm

2 )

Pred

icte

d va

lue (

Wm

2 )

0

50

100

150

0

20

40

60

Pred

icte

d va

lue (

Wm

2 )


0

50

100

150

200

50 100 150 2000Actual value (Wm2)

Pred

icte

d va

lue (

Wm

2 )

Pred

icte

d va

lue (

Wm

2 )

0

50

100

150

200


200 400 600 8000Actual value (Wm2)

0

200

400

600

800






200204208212216220224228232236240244

Tai

r(∘ C)

24 48 72 96 120 144 168 192 216 240 264 288 312 3360Time (h)

336h288h240h192h

144h96h48h






119905119900= 119886119903119905119903+ (1 minus 119886

119903) 119905air (20)

119905119903=(008 (119905rf + 119905fr) + 023 (119905119908 + 119905119890) + 035 (119905119904 + 119905119899))

(2 times (008 + 023 + 035)) (21)


0

5

10

15

20

25

30

35

40

Out

door

tem

pera

ture

(∘C)

0

200

400

600

800

1000

Hor

izon

tal g

loba

l sol

ar ra

diat

ion

(Wm

2 )

20 40 60 80 100 1200Time (h)


119905119904=119860119904119905wall119904 + 119860win119905win

119860119904+ 119860win

(22)












20 40 60 80 100 1200Time (h)

205

210

215

220

225

230

235

240T

op(∘

C)




Tfr 19∘C

Tfr 20∘C

Tfr 21∘C


20 40 60 80 100 1200Time (h)

10

20

30

40

50

Coo

ling

load

of fl

oor (

Wm

2 )




Tfr 19∘C

Tfr 20∘C

Tfr 21∘C


20 40 60 80 100 1200Time (h)

5

6

7

8

9

Coo

ling

load

of a

ir sy

stem

(Wm

2 )




Tfr 19∘C

Tfr 20∘C

Tfr 21∘C







20 40 60 80 100 1200Time (h)

200

205

210

215

220

225T

op(∘

C)




ACH

ACH

ACH1hminus1

2hminus1

3hminus1


10

20

30

40

50

60

70

80

90

100

Coo

ling

load

of fl

oor (

Wm

2 )

20 40 60 80 100 1200Time (h)




ACH 1hminus1

ACH 2hminus1

ACH 3hminus1


20 40 60 80 100 1200Time (h)

4

6

8

10

12

14

16

18

Coo

ling

load

of a

ir sy

stem

(Wm

2 )




ACH

ACH

ACH1hminus1

2hminus1

3hminus1








205

210

215

220

225

Top

(∘C)

20 40 60 80 100 1200Time (h)




Ts = 16∘C

Ts = 17∘C

Ts = 18∘C


20 40 60 80 100 1200Time (h)

10

20

30

40

50

60

70

80

90

100

Coo

ling

load

of fl

oor (

Wm

2 )




Ts = 16∘C

Ts = 17∘C

Ts = 18∘C


20 40 60 80 100 1200Time (h)

4

5

6

7

8

9

10

Coo

ling

load

of a

ir sy

stem

(Wm

2 )




Ts = 16∘C

Ts = 17∘C

Ts = 18∘C






00

01

02

03

12 24 36 48 60 72 84 96 108 1200Time (h)

Ope

rativ

e tem

pera

ture

dev

iatio

n (∘

C)


12 24 36 48 60 72 84 96 108 1200Time (h)

0

2

4

6

8

10

12

14

16

Coo

ling

load

dev

iatio

n of

floo

r (W

m2 )

minus12

minus08

minus04

00

04

08

12

Coo

ling

load

dev

iatio

n of

ven

tilat

ion

syste

m (W

m2 )

(b) Cooling load




6 Conclusions





Symbols







Greek Symbols


Subscripts




Acknowledgments


References








































Volume 2014




Journal of











Journal of


Function Spaces






Algebra














Stop GA run




Stop GA run

Stop and output

Yes

Yes

No

No

Yes

No

No

D = threshold value

irun = irun + 1


irun = max run


run = 1 g c f R 120574 h



g c f R 120574 h

g c f R 120574 h


120596rf +119873

sum

119894=1






001 le 119877119894le 20


7


0 le 120574119894le 1

1 le ℎ119894le 30





Density[kgm3]





3

sum

119894=1

119891119894= 1

2

sum

119894=1

119892119894= 1

(18)

4 Case Study







Ventilation


20m27m

49m


00

05

10


4 8 12 16 20 240Time (h)

Dai

ly p

atte

rn o

f int

erna

l loa

d






0

5

10

15

20

25

30

35

40

NSWE

FloorRoof

IT

20 40 60 80 100 120 140 1600Time (h)

Shor

t wav

e rad

iatio

n (W

m2 )

0

200

400

600

800

1000

Tota

l sol

ar ra

diat

ion

(Wm

2 )


0

200

400

600

800

1000

Inci

dent

sola

r rad

iatio

n (W

m2 )

20 40 60 80 100 120 140 1600Time (h)

NSWE

RoofIT

0

200

400

600

800

1000

Tota

l sol

ar ra

diat

ion

(Wm

2 )







CV =

radicsum119899

119894=1(119910119894minus 119894)2

119899

10038161003816100381610038161199101198941003816100381610038161003816

(19)







Pred

icte

d va

lue (

Wm

2 )

0

2

4

6

8

10


Pred

icte

d va

lue (

Wm

2 )

0

2

4

6

8

10


Pred

icte

d va

lue (

Wm

2 )

0

10

20

30

40









Pred

icte

d va

lue (

Wm

2 )

Pred

icte

d va

lue (

Wm

2 )

0

50

100

150

0

20

40

60

Pred

icte

d va

lue (

Wm

2 )


0

50

100

150

200

50 100 150 2000Actual value (Wm2)

Pred

icte

d va

lue (

Wm

2 )

Pred

icte

d va

lue (

Wm

2 )

0

50

100

150

200


200 400 600 8000Actual value (Wm2)

0

200

400

600

800






200204208212216220224228232236240244

Tai

r(∘ C)

24 48 72 96 120 144 168 192 216 240 264 288 312 3360Time (h)

336h288h240h192h

144h96h48h






119905119900= 119886119903119905119903+ (1 minus 119886

119903) 119905air (20)

119905119903=(008 (119905rf + 119905fr) + 023 (119905119908 + 119905119890) + 035 (119905119904 + 119905119899))

(2 times (008 + 023 + 035)) (21)


0

5

10

15

20

25

30

35

40

Out

door

tem

pera

ture

(∘C)

0

200

400

600

800

1000

Hor

izon

tal g

loba

l sol

ar ra

diat

ion

(Wm

2 )

20 40 60 80 100 1200Time (h)


119905119904=119860119904119905wall119904 + 119860win119905win

119860119904+ 119860win

(22)












20 40 60 80 100 1200Time (h)

205

210

215

220

225

230

235

240T

op(∘

C)




Tfr 19∘C

Tfr 20∘C

Tfr 21∘C


20 40 60 80 100 1200Time (h)

10

20

30

40

50

Coo

ling

load

of fl

oor (

Wm

2 )




Tfr 19∘C

Tfr 20∘C

Tfr 21∘C


20 40 60 80 100 1200Time (h)

5

6

7

8

9

Coo

ling

load

of a

ir sy

stem

(Wm

2 )




Tfr 19∘C

Tfr 20∘C

Tfr 21∘C







20 40 60 80 100 1200Time (h)

200

205

210

215

220

225T

op(∘

C)




ACH

ACH

ACH1hminus1

2hminus1

3hminus1


10

20

30

40

50

60

70

80

90

100

Coo

ling

load

of fl

oor (

Wm

2 )

20 40 60 80 100 1200Time (h)




ACH 1hminus1

ACH 2hminus1

ACH 3hminus1


20 40 60 80 100 1200Time (h)

4

6

8

10

12

14

16

18

Coo

ling

load

of a

ir sy

stem

(Wm

2 )




ACH

ACH

ACH1hminus1

2hminus1

3hminus1








205

210

215

220

225

Top

(∘C)

20 40 60 80 100 1200Time (h)




Ts = 16∘C

Ts = 17∘C

Ts = 18∘C


20 40 60 80 100 1200Time (h)

10

20

30

40

50

60

70

80

90

100

Coo

ling

load

of fl

oor (

Wm

2 )




Ts = 16∘C

Ts = 17∘C

Ts = 18∘C


20 40 60 80 100 1200Time (h)

4

5

6

7

8

9

10

Coo

ling

load

of a

ir sy

stem

(Wm

2 )




Ts = 16∘C

Ts = 17∘C

Ts = 18∘C






00

01

02

03

12 24 36 48 60 72 84 96 108 1200Time (h)

Ope

rativ

e tem

pera

ture

dev

iatio

n (∘

C)


12 24 36 48 60 72 84 96 108 1200Time (h)

0

2

4

6

8

10

12

14

16

Coo

ling

load

dev

iatio

n of

floo

r (W

m2 )

minus12

minus08

minus04

00

04

08

12

Coo

ling

load

dev

iatio

n of

ven

tilat

ion

syste

m (W

m2 )

(b) Cooling load




6 Conclusions





Symbols







Greek Symbols


Subscripts




Acknowledgments


References








































Volume 2014




Journal of











Journal of


Function Spaces






Algebra













Density[kgm3]





3

sum

119894=1

119891119894= 1

2

sum

119894=1

119892119894= 1

(18)

4 Case Study







Ventilation


20m27m

49m


00

05

10


4 8 12 16 20 240Time (h)

Dai

ly p

atte

rn o

f int

erna

l loa

d






0

5

10

15

20

25

30

35

40

NSWE

FloorRoof

IT

20 40 60 80 100 120 140 1600Time (h)

Shor

t wav

e rad

iatio

n (W

m2 )

0

200

400

600

800

1000

Tota

l sol

ar ra

diat

ion

(Wm

2 )


0

200

400

600

800

1000

Inci

dent

sola

r rad

iatio

n (W

m2 )

20 40 60 80 100 120 140 1600Time (h)

NSWE

RoofIT

0

200

400

600

800

1000

Tota

l sol

ar ra

diat

ion

(Wm

2 )







CV =

radicsum119899

119894=1(119910119894minus 119894)2

119899

10038161003816100381610038161199101198941003816100381610038161003816

(19)







Pred

icte

d va

lue (

Wm

2 )

0

2

4

6

8

10


Pred

icte

d va

lue (

Wm

2 )

0

2

4

6

8

10


Pred

icte

d va

lue (

Wm

2 )

0

10

20

30

40









Pred

icte

d va

lue (

Wm

2 )

Pred

icte

d va

lue (

Wm

2 )

0

50

100

150

0

20

40

60

Pred

icte

d va

lue (

Wm

2 )


0

50

100

150

200

50 100 150 2000Actual value (Wm2)

Pred

icte

d va

lue (

Wm

2 )

Pred

icte

d va

lue (

Wm

2 )

0

50

100

150

200


200 400 600 8000Actual value (Wm2)

0

200

400

600

800






200204208212216220224228232236240244

Tai

r(∘ C)

24 48 72 96 120 144 168 192 216 240 264 288 312 3360Time (h)

336h288h240h192h

144h96h48h






119905119900= 119886119903119905119903+ (1 minus 119886

119903) 119905air (20)

119905119903=(008 (119905rf + 119905fr) + 023 (119905119908 + 119905119890) + 035 (119905119904 + 119905119899))

(2 times (008 + 023 + 035)) (21)


0

5

10

15

20

25

30

35

40

Out

door

tem

pera

ture

(∘C)

0

200

400

600

800

1000

Hor

izon

tal g

loba

l sol

ar ra

diat

ion

(Wm

2 )

20 40 60 80 100 1200Time (h)


119905119904=119860119904119905wall119904 + 119860win119905win

119860119904+ 119860win

(22)












20 40 60 80 100 1200Time (h)

205

210

215

220

225

230

235

240T

op(∘

C)




Tfr 19∘C

Tfr 20∘C

Tfr 21∘C


20 40 60 80 100 1200Time (h)

10

20

30

40

50

Coo

ling

load

of fl

oor (

Wm

2 )




Tfr 19∘C

Tfr 20∘C

Tfr 21∘C


20 40 60 80 100 1200Time (h)

5

6

7

8

9

Coo

ling

load

of a

ir sy

stem

(Wm

2 )




Tfr 19∘C

Tfr 20∘C

Tfr 21∘C







20 40 60 80 100 1200Time (h)

200

205

210

215

220

225T

op(∘

C)




ACH

ACH

ACH1hminus1

2hminus1

3hminus1


10

20

30

40

50

60

70

80

90

100

Coo

ling

load

of fl

oor (

Wm

2 )

20 40 60 80 100 1200Time (h)




ACH 1hminus1

ACH 2hminus1

ACH 3hminus1


20 40 60 80 100 1200Time (h)

4

6

8

10

12

14

16

18

Coo

ling

load

of a

ir sy

stem

(Wm

2 )




ACH

ACH

ACH1hminus1

2hminus1

3hminus1








205

210

215

220

225

Top

(∘C)

20 40 60 80 100 1200Time (h)




Ts = 16∘C

Ts = 17∘C

Ts = 18∘C


20 40 60 80 100 1200Time (h)

10

20

30

40

50

60

70

80

90

100

Coo

ling

load

of fl

oor (

Wm

2 )




Ts = 16∘C

Ts = 17∘C

Ts = 18∘C


20 40 60 80 100 1200Time (h)

4

5

6

7

8

9

10

Coo

ling

load

of a

ir sy

stem

(Wm

2 )




Ts = 16∘C

Ts = 17∘C

Ts = 18∘C






00

01

02

03

12 24 36 48 60 72 84 96 108 1200Time (h)

Ope

rativ

e tem

pera

ture

dev

iatio

n (∘

C)


12 24 36 48 60 72 84 96 108 1200Time (h)

0

2

4

6

8

10

12

14

16

Coo

ling

load

dev

iatio

n of

floo

r (W

m2 )

minus12

minus08

minus04

00

04

08

12

Coo

ling

load

dev

iatio

n of

ven

tilat

ion

syste

m (W

m2 )

(b) Cooling load




6 Conclusions





Symbols







Greek Symbols


Subscripts




Acknowledgments


References








































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












0

5

10

15

20

25

30

35

40

NSWE

FloorRoof

IT

20 40 60 80 100 120 140 1600Time (h)

Shor

t wav

e rad

iatio

n (W

m2 )

0

200

400

600

800

1000

Tota

l sol

ar ra

diat

ion

(Wm

2 )


0

200

400

600

800

1000

Inci

dent

sola

r rad

iatio

n (W

m2 )

20 40 60 80 100 120 140 1600Time (h)

NSWE

RoofIT

0

200

400

600

800

1000

Tota

l sol

ar ra

diat

ion

(Wm

2 )







CV =

radicsum119899

119894=1(119910119894minus 119894)2

119899

10038161003816100381610038161199101198941003816100381610038161003816

(19)







Pred

icte

d va

lue (

Wm

2 )

0

2

4

6

8

10


Pred

icte

d va

lue (

Wm

2 )

0

2

4

6

8

10


Pred

icte

d va

lue (

Wm

2 )

0

10

20

30

40









Pred

icte

d va

lue (

Wm

2 )

Pred

icte

d va

lue (

Wm

2 )

0

50

100

150

0

20

40

60

Pred

icte

d va

lue (

Wm

2 )


0

50

100

150

200

50 100 150 2000Actual value (Wm2)

Pred

icte

d va

lue (

Wm

2 )

Pred

icte

d va

lue (

Wm

2 )

0

50

100

150

200


200 400 600 8000Actual value (Wm2)

0

200

400

600

800






200204208212216220224228232236240244

Tai

r(∘ C)

24 48 72 96 120 144 168 192 216 240 264 288 312 3360Time (h)

336h288h240h192h

144h96h48h






119905119900= 119886119903119905119903+ (1 minus 119886

119903) 119905air (20)

119905119903=(008 (119905rf + 119905fr) + 023 (119905119908 + 119905119890) + 035 (119905119904 + 119905119899))

(2 times (008 + 023 + 035)) (21)


0

5

10

15

20

25

30

35

40

Out

door

tem

pera

ture

(∘C)

0

200

400

600

800

1000

Hor

izon

tal g

loba

l sol

ar ra

diat

ion

(Wm

2 )

20 40 60 80 100 1200Time (h)


119905119904=119860119904119905wall119904 + 119860win119905win

119860119904+ 119860win

(22)












20 40 60 80 100 1200Time (h)

205

210

215

220

225

230

235

240T

op(∘

C)




Tfr 19∘C

Tfr 20∘C

Tfr 21∘C


20 40 60 80 100 1200Time (h)

10

20

30

40

50

Coo

ling

load

of fl

oor (

Wm

2 )




Tfr 19∘C

Tfr 20∘C

Tfr 21∘C


20 40 60 80 100 1200Time (h)

5

6

7

8

9

Coo

ling

load

of a

ir sy

stem

(Wm

2 )




Tfr 19∘C

Tfr 20∘C

Tfr 21∘C







20 40 60 80 100 1200Time (h)

200

205

210

215

220

225T

op(∘

C)




ACH

ACH

ACH1hminus1

2hminus1

3hminus1


10

20

30

40

50

60

70

80

90

100

Coo

ling

load

of fl

oor (

Wm

2 )

20 40 60 80 100 1200Time (h)




ACH 1hminus1

ACH 2hminus1

ACH 3hminus1


20 40 60 80 100 1200Time (h)

4

6

8

10

12

14

16

18

Coo

ling

load

of a

ir sy

stem

(Wm

2 )




ACH

ACH

ACH1hminus1

2hminus1

3hminus1








205

210

215

220

225

Top

(∘C)

20 40 60 80 100 1200Time (h)




Ts = 16∘C

Ts = 17∘C

Ts = 18∘C


20 40 60 80 100 1200Time (h)

10

20

30

40

50

60

70

80

90

100

Coo

ling

load

of fl

oor (

Wm

2 )




Ts = 16∘C

Ts = 17∘C

Ts = 18∘C


20 40 60 80 100 1200Time (h)

4

5

6

7

8

9

10

Coo

ling

load

of a

ir sy

stem

(Wm

2 )




Ts = 16∘C

Ts = 17∘C

Ts = 18∘C






00

01

02

03

12 24 36 48 60 72 84 96 108 1200Time (h)

Ope

rativ

e tem

pera

ture

dev

iatio

n (∘

C)


12 24 36 48 60 72 84 96 108 1200Time (h)

0

2

4

6

8

10

12

14

16

Coo

ling

load

dev

iatio

n of

floo

r (W

m2 )

minus12

minus08

minus04

00

04

08

12

Coo

ling

load

dev

iatio

n of

ven

tilat

ion

syste

m (W

m2 )

(b) Cooling load




6 Conclusions





Symbols







Greek Symbols


Subscripts




Acknowledgments


References








































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Pred

icte

d va

lue (

Wm

2 )

0

2

4

6

8

10


Pred

icte

d va

lue (

Wm

2 )

0

2

4

6

8

10


Pred

icte

d va

lue (

Wm

2 )

0

10

20

30

40









Pred

icte

d va

lue (

Wm

2 )

Pred

icte

d va

lue (

Wm

2 )

0

50

100

150

0

20

40

60

Pred

icte

d va

lue (

Wm

2 )


0

50

100

150

200

50 100 150 2000Actual value (Wm2)

Pred

icte

d va

lue (

Wm

2 )

Pred

icte

d va

lue (

Wm

2 )

0

50

100

150

200


200 400 600 8000Actual value (Wm2)

0

200

400

600

800






200204208212216220224228232236240244

Tai

r(∘ C)

24 48 72 96 120 144 168 192 216 240 264 288 312 3360Time (h)

336h288h240h192h

144h96h48h






119905119900= 119886119903119905119903+ (1 minus 119886

119903) 119905air (20)

119905119903=(008 (119905rf + 119905fr) + 023 (119905119908 + 119905119890) + 035 (119905119904 + 119905119899))

(2 times (008 + 023 + 035)) (21)


0

5

10

15

20

25

30

35

40

Out

door

tem

pera

ture

(∘C)

0

200

400

600

800

1000

Hor

izon

tal g

loba

l sol

ar ra

diat

ion

(Wm

2 )

20 40 60 80 100 1200Time (h)


119905119904=119860119904119905wall119904 + 119860win119905win

119860119904+ 119860win

(22)












20 40 60 80 100 1200Time (h)

205

210

215

220

225

230

235

240T

op(∘

C)




Tfr 19∘C

Tfr 20∘C

Tfr 21∘C


20 40 60 80 100 1200Time (h)

10

20

30

40

50

Coo

ling

load

of fl

oor (

Wm

2 )




Tfr 19∘C

Tfr 20∘C

Tfr 21∘C


20 40 60 80 100 1200Time (h)

5

6

7

8

9

Coo

ling

load

of a

ir sy

stem

(Wm

2 )




Tfr 19∘C

Tfr 20∘C

Tfr 21∘C







20 40 60 80 100 1200Time (h)

200

205

210

215

220

225T

op(∘

C)




ACH

ACH

ACH1hminus1

2hminus1

3hminus1


10

20

30

40

50

60

70

80

90

100

Coo

ling

load

of fl

oor (

Wm

2 )

20 40 60 80 100 1200Time (h)




ACH 1hminus1

ACH 2hminus1

ACH 3hminus1


20 40 60 80 100 1200Time (h)

4

6

8

10

12

14

16

18

Coo

ling

load

of a

ir sy

stem

(Wm

2 )




ACH

ACH

ACH1hminus1

2hminus1

3hminus1








205

210

215

220

225

Top

(∘C)

20 40 60 80 100 1200Time (h)




Ts = 16∘C

Ts = 17∘C

Ts = 18∘C


20 40 60 80 100 1200Time (h)

10

20

30

40

50

60

70

80

90

100

Coo

ling

load

of fl

oor (

Wm

2 )




Ts = 16∘C

Ts = 17∘C

Ts = 18∘C


20 40 60 80 100 1200Time (h)

4

5

6

7

8

9

10

Coo

ling

load

of a

ir sy

stem

(Wm

2 )




Ts = 16∘C

Ts = 17∘C

Ts = 18∘C






00

01

02

03

12 24 36 48 60 72 84 96 108 1200Time (h)

Ope

rativ

e tem

pera

ture

dev

iatio

n (∘

C)


12 24 36 48 60 72 84 96 108 1200Time (h)

0

2

4

6

8

10

12

14

16

Coo

ling

load

dev

iatio

n of

floo

r (W

m2 )

minus12

minus08

minus04

00

04

08

12

Coo

ling

load

dev

iatio

n of

ven

tilat

ion

syste

m (W

m2 )

(b) Cooling load




6 Conclusions





Symbols







Greek Symbols


Subscripts




Acknowledgments


References








































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










200204208212216220224228232236240244

Tai

r(∘ C)

24 48 72 96 120 144 168 192 216 240 264 288 312 3360Time (h)

336h288h240h192h

144h96h48h






119905119900= 119886119903119905119903+ (1 minus 119886

119903) 119905air (20)

119905119903=(008 (119905rf + 119905fr) + 023 (119905119908 + 119905119890) + 035 (119905119904 + 119905119899))

(2 times (008 + 023 + 035)) (21)


0

5

10

15

20

25

30

35

40

Out

door

tem

pera

ture

(∘C)

0

200

400

600

800

1000

Hor

izon

tal g

loba

l sol

ar ra

diat

ion

(Wm

2 )

20 40 60 80 100 1200Time (h)


119905119904=119860119904119905wall119904 + 119860win119905win

119860119904+ 119860win

(22)












20 40 60 80 100 1200Time (h)

205

210

215

220

225

230

235

240T

op(∘

C)




Tfr 19∘C

Tfr 20∘C

Tfr 21∘C


20 40 60 80 100 1200Time (h)

10

20

30

40

50

Coo

ling

load

of fl

oor (

Wm

2 )




Tfr 19∘C

Tfr 20∘C

Tfr 21∘C


20 40 60 80 100 1200Time (h)

5

6

7

8

9

Coo

ling

load

of a

ir sy

stem

(Wm

2 )




Tfr 19∘C

Tfr 20∘C

Tfr 21∘C







20 40 60 80 100 1200Time (h)

200

205

210

215

220

225T

op(∘

C)




ACH

ACH

ACH1hminus1

2hminus1

3hminus1


10

20

30

40

50

60

70

80

90

100

Coo

ling

load

of fl

oor (

Wm

2 )

20 40 60 80 100 1200Time (h)




ACH 1hminus1

ACH 2hminus1

ACH 3hminus1


20 40 60 80 100 1200Time (h)

4

6

8

10

12

14

16

18

Coo

ling

load

of a

ir sy

stem

(Wm

2 )




ACH

ACH

ACH1hminus1

2hminus1

3hminus1








205

210

215

220

225

Top

(∘C)

20 40 60 80 100 1200Time (h)




Ts = 16∘C

Ts = 17∘C

Ts = 18∘C


20 40 60 80 100 1200Time (h)

10

20

30

40

50

60

70

80

90

100

Coo

ling

load

of fl

oor (

Wm

2 )




Ts = 16∘C

Ts = 17∘C

Ts = 18∘C


20 40 60 80 100 1200Time (h)

4

5

6

7

8

9

10

Coo

ling

load

of a

ir sy

stem

(Wm

2 )




Ts = 16∘C

Ts = 17∘C

Ts = 18∘C






00

01

02

03

12 24 36 48 60 72 84 96 108 1200Time (h)

Ope

rativ

e tem

pera

ture

dev

iatio

n (∘

C)


12 24 36 48 60 72 84 96 108 1200Time (h)

0

2

4

6

8

10

12

14

16

Coo

ling

load

dev

iatio

n of

floo

r (W

m2 )

minus12

minus08

minus04

00

04

08

12

Coo

ling

load

dev

iatio

n of

ven

tilat

ion

syste

m (W

m2 )

(b) Cooling load




6 Conclusions





Symbols







Greek Symbols


Subscripts




Acknowledgments


References








































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










20 40 60 80 100 1200Time (h)

205

210

215

220

225

230

235

240T

op(∘

C)




Tfr 19∘C

Tfr 20∘C

Tfr 21∘C


20 40 60 80 100 1200Time (h)

10

20

30

40

50

Coo

ling

load

of fl

oor (

Wm

2 )




Tfr 19∘C

Tfr 20∘C

Tfr 21∘C


20 40 60 80 100 1200Time (h)

5

6

7

8

9

Coo

ling

load

of a

ir sy

stem

(Wm

2 )




Tfr 19∘C

Tfr 20∘C

Tfr 21∘C







20 40 60 80 100 1200Time (h)

200

205

210

215

220

225T

op(∘

C)




ACH

ACH

ACH1hminus1

2hminus1

3hminus1


10

20

30

40

50

60

70

80

90

100

Coo

ling

load

of fl

oor (

Wm

2 )

20 40 60 80 100 1200Time (h)




ACH 1hminus1

ACH 2hminus1

ACH 3hminus1


20 40 60 80 100 1200Time (h)

4

6

8

10

12

14

16

18

Coo

ling

load

of a

ir sy

stem

(Wm

2 )




ACH

ACH

ACH1hminus1

2hminus1

3hminus1








205

210

215

220

225

Top

(∘C)

20 40 60 80 100 1200Time (h)




Ts = 16∘C

Ts = 17∘C

Ts = 18∘C


20 40 60 80 100 1200Time (h)

10

20

30

40

50

60

70

80

90

100

Coo

ling

load

of fl

oor (

Wm

2 )




Ts = 16∘C

Ts = 17∘C

Ts = 18∘C


20 40 60 80 100 1200Time (h)

4

5

6

7

8

9

10

Coo

ling

load

of a

ir sy

stem

(Wm

2 )




Ts = 16∘C

Ts = 17∘C

Ts = 18∘C






00

01

02

03

12 24 36 48 60 72 84 96 108 1200Time (h)

Ope

rativ

e tem

pera

ture

dev

iatio

n (∘

C)


12 24 36 48 60 72 84 96 108 1200Time (h)

0

2

4

6

8

10

12

14

16

Coo

ling

load

dev

iatio

n of

floo

r (W

m2 )

minus12

minus08

minus04

00

04

08

12

Coo

ling

load

dev

iatio

n of

ven

tilat

ion

syste

m (W

m2 )

(b) Cooling load




6 Conclusions





Symbols







Greek Symbols


Subscripts




Acknowledgments


References








































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










20 40 60 80 100 1200Time (h)

200

205

210

215

220

225T

op(∘

C)




ACH

ACH

ACH1hminus1

2hminus1

3hminus1


10

20

30

40

50

60

70

80

90

100

Coo

ling

load

of fl

oor (

Wm

2 )

20 40 60 80 100 1200Time (h)




ACH 1hminus1

ACH 2hminus1

ACH 3hminus1


20 40 60 80 100 1200Time (h)

4

6

8

10

12

14

16

18

Coo

ling

load

of a

ir sy

stem

(Wm

2 )




ACH

ACH

ACH1hminus1

2hminus1

3hminus1








205

210

215

220

225

Top

(∘C)

20 40 60 80 100 1200Time (h)




Ts = 16∘C

Ts = 17∘C

Ts = 18∘C


20 40 60 80 100 1200Time (h)

10

20

30

40

50

60

70

80

90

100

Coo

ling

load

of fl

oor (

Wm

2 )




Ts = 16∘C

Ts = 17∘C

Ts = 18∘C


20 40 60 80 100 1200Time (h)

4

5

6

7

8

9

10

Coo

ling

load

of a

ir sy

stem

(Wm

2 )




Ts = 16∘C

Ts = 17∘C

Ts = 18∘C






00

01

02

03

12 24 36 48 60 72 84 96 108 1200Time (h)

Ope

rativ

e tem

pera

ture

dev

iatio

n (∘

C)


12 24 36 48 60 72 84 96 108 1200Time (h)

0

2

4

6

8

10

12

14

16

Coo

ling

load

dev

iatio

n of

floo

r (W

m2 )

minus12

minus08

minus04

00

04

08

12

Coo

ling

load

dev

iatio

n of

ven

tilat

ion

syste

m (W

m2 )

(b) Cooling load




6 Conclusions





Symbols







Greek Symbols


Subscripts




Acknowledgments


References








































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










205

210

215

220

225

Top

(∘C)

20 40 60 80 100 1200Time (h)




Ts = 16∘C

Ts = 17∘C

Ts = 18∘C


20 40 60 80 100 1200Time (h)

10

20

30

40

50

60

70

80

90

100

Coo

ling

load

of fl

oor (

Wm

2 )




Ts = 16∘C

Ts = 17∘C

Ts = 18∘C


20 40 60 80 100 1200Time (h)

4

5

6

7

8

9

10

Coo

ling

load

of a

ir sy

stem

(Wm

2 )




Ts = 16∘C

Ts = 17∘C

Ts = 18∘C






00

01

02

03

12 24 36 48 60 72 84 96 108 1200Time (h)

Ope

rativ

e tem

pera

ture

dev

iatio

n (∘

C)


12 24 36 48 60 72 84 96 108 1200Time (h)

0

2

4

6

8

10

12

14

16

Coo

ling

load

dev

iatio

n of

floo

r (W

m2 )

minus12

minus08

minus04

00

04

08

12

Coo

ling

load

dev

iatio

n of

ven

tilat

ion

syste

m (W

m2 )

(b) Cooling load




6 Conclusions





Symbols







Greek Symbols


Subscripts




Acknowledgments


References








































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










00

01

02

03

12 24 36 48 60 72 84 96 108 1200Time (h)

Ope

rativ

e tem

pera

ture

dev

iatio

n (∘

C)


12 24 36 48 60 72 84 96 108 1200Time (h)

0

2

4

6

8

10

12

14

16

Coo

ling

load

dev

iatio

n of

floo

r (W

m2 )

minus12

minus08

minus04

00

04

08

12

Coo

ling

load

dev

iatio

n of

ven

tilat

ion

syste

m (W

m2 )

(b) Cooling load




6 Conclusions





Symbols







Greek Symbols


Subscripts




Acknowledgments


References








































Volume 2014




Journal of











Journal of


Function Spaces






Algebra














Greek Symbols


Subscripts




Acknowledgments


References








































Volume 2014




Journal of











Journal of


Function Spaces






Algebra































Volume 2014




Journal of











Journal of


Function Spaces






Algebra









Research Article Simplified Building Thermal Model...

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