Slow Structural deformation monitoring using Locata a trial at Tumut Pond Dam

Mazher Choudhury, Chris Rizos

ABSTRACT:

Locata Corporations positioning technology Locata is a terrestrial-based RF-ranging

technology that provides high accuracy position solutions using a network (LocataNet) of time

synchronised pseudolite-like transceivers (LocataLites). This technology provides centimetre

level accurate position solutions for static positioning using carrier phase measurement data

which provides an advantage over other technology for monitoring structural movement in many

applications. The Locata network can be deployed in such a configuration around a structure that

optimal network geometry could be ensured despite site constraints. This paper describes the first

deformation trial using Locata technology carried out at Tumut Pond Dam, in the state of New

South Wales, Australia. This trial was run for 22 hours and yielded millimetre-level precision for

horizontal positions, and centimetre-level vertical precision for all observed epochs. The

accuracy of the coordinate solutions was at the few millimetre level with standard deviations of

2.5mm, 2.1mm and 18mm for the east, north and height components respectively. The position

solutions were generated by an iterative least squares estimation process of Locata carrier phase

observations per epoch. Then mean of sixty seconds coordinate solutions was used as input for a

Kalman filter. Standard deformation detection methods were applied. No significant

displacement was observed during this trial.

Keywords: Deformation monitoring, deformation trial, Locata.

INTRODUCTION

Deformation monitoring systems are designed to measure the deflection or distortion of a

structure under normal and extreme conditions. The former is to confirm the normal operations

of that structure, while the latter could enable early detection of structural damage. Dams,

bridges, large and tall buildings are examples of structures that are routinely surveyed and

monitored. Global Navigation Satellites Systems (GNSS) are a very popular technology for

24/7 monitoring of both fast and slow structural deformation. However, the accuracy of

GNSS is dependent on the number as well as geometric distribution of the available satellites,

and it therefore may vary at different observation times. On the other hand, Locata Corporations

positioning technology, known as Locata, potentially provides centimetre-level accurate

position solutions for static positioning using carrier phase measurement data. The Locata

network can be deployed around a structure so as to ensure optimal network geometry under site

constraints. This paper describes the first Locata deformation monitoring trial conducted at the

Tumut Pond Dam near Cabramurra, NSW, Australia.

This paper is organised as follows. In section 2 the Locata positioning system is briefly

described; in section 3 the feasibility of using Locata for slow structural deformation monitoring

is discussed; in section 4 mathematical models of the Locata coordinate solution and the

deformation analysis procedure are presented; in section 5 the Tumut Pond Dam trial is

described, followed by presentation of the results and analyses. Finally, sections 6 and 7 present

concluding remarks and discuss future research and implementation challenges.

2. LOCATA POSITIONING SYSTEM

Locata Corporations technology, Locata, provides positioning solutions with the aid of a

number of time synchronised transceivers known as LocataLites. These LocataLites form a

Locata network (or LocataNet) that transmit Locata signals in the licence-free 2.4GHz

Industry Scientific and Medical band. In any LocataNet there is one master LocataLite and other

LocataLites are time synchronised with that master. Following synchronisation the LocataNet

starts transmitting signals. When a Locata receiver tracks four (or more) signals from four (or

more) different LocataLites, it can perform centimetre-level accurate single point positioning

using phase measurements, without employing a differential technique that requires the

transmission of data corrections. However, following the physical installation of the LocataNet, a

precise survey is required. A detailed description of the Locata technology can be found in, for

example, Barnes et al. (2003).

3. LOCATA IN SUPPORT OF DEFORMATION MONITORING APPLICATIONS

Continuous geodetic deformation monitoring applications typically rely on positioning or

coordinate solutions (provided by GNSS, Total Station or other manual or automatic survey

technology) and a subsequent (or near-real-time) statistical analysis procedure to unambiguously

identify movement of the target or monitoring instrument that is interpreted as structural

deformation. This technology should be highly precise, and able to generate millimetre to

centimetre-level accuracy coordinate solutions. At present there are few systems which can

support 24/7 monitoring (e.g. GPS/GNSS and automated Total Stations). However, the quality

(i.e. accuracy, availability, reliability, and integrity) of GPS-generated positioning solutions

depends on the number, as well as geometric distribution, of the visible satellites. Furthermore,

these position solutions degrade even more when satellites signals are blocked due to

obstructions, as in urban canyons, structural monitoring in valleys, or in deep, open-cut mines, or

in the presence of multipath. Therefore continuous deformation monitoring using GNSS may not

always be feasible. Locata technology can, in principle, overcome these drawbacks as

LocataLites can be placed according to optimal network geometry design. Youjian et al. (2005)

reports that GPS requires more than 20 hours of measurements in order to generate coordinate

precisions which are better than 5mm. In contrast Locata needs less than hour of data (at 2Hz

aggregated data rate) to produce a similar level of precision. On the other hand, deformation

monitoring based on Total Station technology has its own limitations, including: expensive for

24/7 monitoring, requires expert labour resources, line-of-sight constraints, atmospheric effects,

and security issues for the instrumentation.

4. DEFORMATION ANALYSIS

Fundamental to any deformation analysis procedure is the requirement for accurate coordinate

solutions in order to detect statistically significant movement between consecutive epochs of the

coordinate solution time series.

COORDINATE SOLUTION

The Locata coordinate calculation is similar to GNSS position computations. However, there are

differences, principally in the handling of clock effects and tropospheric refraction. The Locata

receiver can make pseudorange as well as carrier phase measurements. For accurate position

calculations the carrier phase measurements are used.

The basic Locata carrier phase observation equation between receiver and LocataLite is:

(1)

where is the carrier phase observation in units of cycles, is the wavelength of the signal,

is the tropospheric delay, is the receiver clock error of the receiver , is the

carrier phase ambiguity and are unmodelled residual errors. Note that there is no transmitter

clock error present in the observation equation due to the time synchronisation of the

LocataLites. Prior experiment (Barnes et al. 2003) has shown that this time synchronisation is

better than 30 picoseconds.

To cancel out the receiver clock error and reduce systematic biases in the measurements, the

carrier phase observations of the same frequency are single-differenced. When is chosen as the

reference signal, and is another signal of the same frequency, the single-difference is:

(2)

The unknown parameters are the receiver coordinates in the single-differenced

range :

(3)

where and are the antenna coordinates of the LocataLites that transmit the

signals and . The tropospheric delays in calculated using a length-based tropospheric

model (Wang et al., 2005) with constants from IAG resolution (1999). The model equation for

the least squares estimation (LSE) process is:

(4)

The observations for equation (4) are and the parameters are ]. The partial

derivatives matrix (needed for the LSE) for observation equation (3) are:

(5)

where n is the number of observations.

The Locata coordinate solution is obtained from an iterative LSE process where

(6)

and where

The estimable parameters are then updated:

(7)

and the precisions of the estimated parameters are given by:

(8)

A is the partial derivative matrix, P is inverse of the input quality of observations matrix and b is

a misclose vector, derived from the difference between the observed distance and the calculated

distance (from initial coordinates x using equation (3)). On the other hand, N (equation 8) is a

full matrix because the number of observations is greater than the number of unknowns in the A

matrix. In other words, in Locata computations, the requirement is for a minimum number of

observations is three/four from three/four different LocataLites for 2D/3D solutions.

However, to achieve higher precision (i.e. millimetre level), as well as to reduce systematic

biases in the measurements, the mean of a predefined time frame coordinate solution is used in

the Kalman filter for subsequent deformation analysis. However, before applying the

deformation analysis procedure, the complete data set needs to be smoothed and outliers

removed. To remove outliers in the position coordinate time series, Grubbs test is used with 95%

significance level (Grubbs, 1969). This test is based on the assumption of a normal distribution.

As this test detects one outlier at a time, the whole process must be repeated over and over again

until there is confidence that there is a complete removal of outliers.

DEFORMATION ANALYSIS PROCEDURE

Deformation of a point can be defined as statistically significant displacement of that point

between two different epochs. For example, at time (t), the position of a point is Pt (Et, Nt, Ht,)

with covariance matrix Qt and at time (t+t), position of the same point is Pt+t (Et+t, Nt+t, Ht+t)

and its covariance matrix is Qt+t. Displacement is obtained by differencing the estimated

coordinates at time (t) and (t+t):

(11)

As a result, the distance (d) between Pt , Pt+t is:

(12)

and in 2D is:

(13)

At the same time, the standard deviation of the coordinates at time (t) and (t+t) are and

respectively which is derived from LSE. For this paper, at time (t) is considered at the

very first epoch where the known point ambiguity resolution process occurred. The combined

(95%) confidence in the horizontal and vertical displacement (USACE, 2002) is:

(14)

(15)

In the deformation analysis the Congruency Test (Caspary, 2000) uses the Student t-distribution,

where the null hypothesis is that there is no displacement between epochs and the alternative

hypothesis claims there is. As a result:

Null hypothesis Ho : d = 0,

Alternative hypothesis Ha : d 0.

The test statistics is:

(16)

Ho is true when satisfies the Student t-distribution, or where is the degree of

freedom, is the significance level and the value of the parameters is derived using equations

(12-15).

If Ha is true, further investigation of the epochs need to be carried out. In this Locata trial case

the deformation calculation is continuous which means the 1st epochs data is used as reference

and all other epochs are compared with the reference epoch. If Ha is true for more than ten

consecutive epochs, then the deformation alert is generated. Although there are other methods

are available for deformation analysis (such as shewhart, CUSUM, EWMA, and other

algorithms), the Congruency Test has been used in these Locata tests.

Further details regarding deformation monitoring methods can be found in such publications as

USACE (2002) and Caspary (2000), and flowcharts of the least squares adjustment as well as the

Locata deformation monitoring solution can be found in Choudhury et al. (2009).

5. TUMUT POND DAM

Tumut Pond Dam (Figure 1), also known as Tumut Pond Reservoir, is located on the upper

reaches of the Tumut River near Cabramurra, in the Snowy Mountains of New South Wales,

Australia. This dam collects the inflow from the Tumut River to form the Tumut Pond Reservoir,

which is diverted through the Tooma-Tumut and the Eucumbene-Tumut tunnels to provide the

head pondage for the Tumut 1 Power Station. The dam is 86.3m high and 217.9m long. The crest

and base width are 3.7m and 29.6m respectively (Snowy Hydro Limited, 2003).

This dam was used for the Locata system test (Figure 2) as it has a long history of deformation

surveys. In this experiment a Total Station was used as the standard technology for movement

detection. Although the surveying prism and the Locata receiver antenna could not be placed at

the same point, Total Station derived coordinates were used as truth data.

Figure 1: Tumut Pond Dam

Figure 2(b): Aerial view of Locata network Figure 2(c): Aerial view of Locata network

GEOMETRY DESCRIPTION

Before running the deformation monitoring trial, a simulated Locata network was designed using

the FIXIT 3 software tool (Harvey, 2006). During this simulation the Locata network was

analysed for redundancy number, error ellipse of the monitoring points and geometric strength of

the Locata network. The points are all nearly in one plane, and analysis confirmed that the

heights of the monitoring point could not be reliably determined. Figure 3 shows the geometry of

the Locata network in 2D view and the error ellipse for the monitoring point with respect to the

fixed LocataLite transmitter sites which have accurate known coordinates computed by an

independent survey. Simulation has shown that the monitoring points standard deviation would

be 1.3mm and 0.8mm for the east and north components respectively. The semi-major, semi-

minor and azimuth of the error ellipse would be 1.3mm, 0.7mm and 89 respectively. For this

simulation it has been assumed that each Locata slope distance observations standard deviation

is 5mm, and that the observations are uncorrelated and not affected by systematic or gross error.

Results from this simulation indicate that millimetre-level precision using Locata is achievable at

the Tumut Pond Dam site.

Figure 3(a): Error ellipse and standard deviation

of the height of the monitored point and the

network plan

Figure 3(b): Error ellipse of the

point(zoomed)

EXPERIMENTAL SETUP

TOTAL STATION

A survey Robotic Total Station (Leica TCRP1201) was used for comparison with the Locata

system. The instrument measured horizontal and vertical angles, and distances to an EDM prism

near the Locata receiver. It was used in "lock" mode from a single setup, recording every minute

interval, measuring a distance of about 176m.

LOCATA SYSTEM

A Locata network, comprising four LocataLites, was established for this trial after analysing the

network geometry LocataLite line-of-sight visibilities. The Locata receiver antenna was mounted

at the top centre of the dam approximately on the middle part of the dam because this point had

the highest probability of movement. The antenna was mounted in such a way that helped to

increase visibility to the LocataLites as well as reduce the effect of multipath. The distances from

the Locata rover receiver to the four LocataLites were approximately 175, 187, 273 and 142

metres (Table 1). The lowest and highest points differed by about 20m in height. The networks

dilution of precision values are listed in Table 2. After deploying the LocataNet, a one hour test

was conducted to ensure there were enough Locata signals for a reliable 3D solution. When the

test run confirmed the desired level of accuracy and precision, a complete trial was conducted for

24 hours.

LocataLite Distance to Rover (m) Elevation angle() Height difference(m)

LL1 174.983 7.9797 24.290

LL2 186.602 2.1979 7.458

LL3 273.349 11.8016 5.168

LL4 141.557 -5.7611 19.957 (below rover)

Table 1: LocataLite configuration

EDOP 0.19

NDOP 0.13

HDOP 0.23

VDOP 1.31

PDOP 1.33

Table 2: Locata position DOP

For this trial experiment, the known point ambiguity resolution method was used for carrier

phase positioning. This monitoring point was also surveyed using the Leica TCRP1201, and

coordinates accurate to 8mm (one standard deviation level) were obtained. Data was logged to

the internal memory card for post processing.

RESULTS

Total Station

Total Station survey was planned for 24 hours. Unfortunately the battery power only lasted for

four hours the time series is shown in Figure 4. It can be observed that maximum apparent

displacement was 9.0mm, 5mm and 10.0mm in east, north and height respectively. Although the

system showed horizontal movement at about the 5mm level, the standard deviation of these

coordinates was +/- 6mm and hence was difficult to compare with Locata due to time

synchronisation with the Locata firmware (version 3.4).

Figure 4: Coordinate variability time series from the Total Station survey

LOCATA SYSTEM

The Locata network at the Tumut Pond Dam was setup to operate for 24 hours. However, battery

power only lasted for 22 hours. To detect point displacement, the data definition for each epoch

was the mean of one minutes worth (i.e. 120 points) of individual Locata coordinate solutions.

The master LocataLites measurements were used for single-differencing in order to remove the

clock error. The other three LocataLites formed a plane that was almost horizontal the lowest

and highest points differed by about 20.61m in height. The Locata rover lies very close to that

plane, preventing the reliable determination of the height of the rover. One possible solution

would be to hold the height of the rover fixed at the known survey coordinates and to carry out

the survey in 2D mode. Alternatively, solving for the height might absorb some distance errors.

Figure 5(a) presents the 2D coordinate differences from the mean value, and Figure 5(b) is the

coordinate solution time series.

Figure 5(a): Position differences from mean

value (averaged solution from each minute)

Figure 5(b): Position solution time series

(averaged solution from each minute)

Figure 6 shows the standard deviations of each minutes epoch-by-epoch coordinate solutions

(mean of 120 individual Locata position solutions) whereas Figure 7 presents the standard

deviations of the mean coordinate solutions. Average standard deviations of the grouped

coordinates (i.e. mean of 120 points) were 4mm and 19mm for the horizontal and vertical

components respectively. This was not unexpected as the vertical geometry (VDOP: 1.31) is

much weaker than the horizontal geometry (VDOP: 0.23) Table 2. Spikes in coordinate

precision may be due to Wi-Fi interference. Nevertheless the average accuracy of the whole

dataset of grouped coordinates was 3mm4mm and 5mm35mm for the horizontal and vertical

components respectively, at the 95% confidence interval.

Figure 6: Locata coordinate standard deviation

per epoch

Figure 7: Standard deviation of mean of Locata

coordinate per epoch

Histogram of standardised residuals (i.e. LSE output of Locata observations residuals divided by

LSE output of Locata observations standard deviation which satisfies the global test) is shown

in Figure 8. Checking the normal distribution of the standardised residuals helps to identify

systematic error, gross error, bias or inappropriate observation quality (Harvey, 2006). Trends of

the standardised residuals are presented in Figure 9. It can be easily observed that this time series

exhibits random scattering, which can be interpreted to mean that there was no systematic effect

in the position solutions. In summary, from both Figures 8 and 9 it can be seen that the

standardised residuals can be approximated by a normal distribution and there is a random

scatter, which implies that the LSE modelling is acceptable (Harvey, 2006).

Figure 8: Histogram of Locata observations

(standardised residuals)

Figure 9: Trend of standardised residuals

DEFORMATION ANALYSIS

In this experiment the vertical geometry was weaker than the horizontal geometry, which was

reflected in the quality of the coordinate solutions average precision of horizontal components

was 4mm, whereas vertical precision was about 20mm. Only the horizontal coordinate variability

was therefore analysed. This experiment, however, was only conducted for one day and hence

the conclusions that can be drawn with regard to detectable coordinate changes are limited.

The grouped coordinates, i.e. mean of 120 points (at the 2Hz data rate, in one minute there are

120 coordinate solutions), were input into a Kalman filter (KF) for smoothing the noisy

coordinate solutions. The KF utilises an iterative prediction-correction model, as described in

Cross(1990):

Prediction:

Correction:

where is the predicted estimate of the state vector at time , is the filtered estimate of the

state vector at time , is the state transition matrix, and is the predicted and

corrected error covariance respectively, K is the Kalman gain, is the measurement vector at

time , H is the measurement matrix, and Q and R denote the covariances of the process noise w

and measurement noise v respectively.

Here, noisy grouped coordinates are and the other parameters are:

With process and the measurement noise statistics defined

by:

Results are shown in Figure 10(a). The first 30 grouped data epochs have not been included due

to the lack of convergence of the Kalman filter at the start.

Apparent horizontal displacement of the monitoring point is shown in Figure 10(b). The

maximum coordinate change detected was 2mm (at 95% confidence interval, it is 4mm). There

was no epoch with higher coordinate change than the statistical threshold (i.e. 7mm) for

deformation detection.

Figure 10(a): Position solution (with Kalman filtered time series)

Figure 10(b): Coordinate change solution (from 2D solution)

6. CONCLUDING REMARKS

This paper describes the first deformation trial using Locata technology carried out at the Tumut

Pond Dam, in the state of New South Wales, Australia. This trial was run for 22 hours and

yielded millimetre-level precision for horizontal positions, and centimetre-level vertical precision

for all observed epochs. The accuracy of the coordinate solutions from the whole 22 hours

dataset is at the few millimetre level with standard deviations of 2.5mm, 2.1mm and 18mm for

the east, north and height components respectively. The position solutions were generated by an

iterative least squares estimation involving Locata carrier phase observations for each

measurement epoch. Then the mean of sixty seconds of coordinate solutions (120 independent

solutions) was used as input for a Kalman filter. Standard deformation detection methods were

then applied. No statistically significant displacement was observed during this trial, although

longer experiments (i.e. weeks, months), when other factors may have an impact on the structure

(e.g. water level in the reservoir, seasonal atmospheric effects, high vehicle movement, etc.),

need to be conducted to verify the utility of the Locata technology for long-term monitoring

applications.

ACKNOWLEDGEMENT

The authors are grateful to Bruce Harvey for his guidance. The authors are also grateful to John

Browne and John Bartell from Snowy Hydro Limited for providing the opportunity to setup and

test the Locata network, for their surveying expertise, as well as their strong support for this

study. Many thanks also to Mr. Nonie Politi and Ms. Aire Olesk from the School of Surveying

and Spatial Information Systems, University of New South Wales, for assisting in this

experiment. The authors wish to also acknowledge the support from the ARC Linkage project

LP0668907 Structural Deformation Monitoring Integrating a New Wireless Positioning

Technology with GPS.

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