253

TS 6 – GNSS

INGEO 2011 – 5th International Conference on Engineering Surveying

Brijuni, Croatia, September 22-24, 2011

Investigation of Viaduct Movements during Train Pass

Using GPS Technique

Rzepecka, Z., Cellmer, S. and Rapi ski, J.

Institute of Geodesy, University of Warmia and Mazury in Olsztyn, Poland

E-mail: jacek.rapinski@gmail.com

Abstract

In this paper we study the possibility of a railway viaduct behavior determination using

GPS receivers. In the survey we took advantage of a 20 Hz GNSS receivers, providing

possibility of 20 times per second position determinations. For elaboration of positioning

results a GPS software developed by the authors was used. For further analysis some tools for

signal processing were admitted: those enabled within the Signal Analysis Software

SIGVIEW v. 2.2.5 by Goran Obradovic and SignalLab as well as those designed by the

authors themselves. Studies of how much important information is lost when using 1Hz data

were also performed.

Key words: GNSS, signal processing

1 INTRODUCTION

Modern GPS receivers allow to perform precise and almost continuous surveys. Advanced

data processing techniques along with high sampling rates encourages to use GPS receivers in

more and more precise applications. The use of GPS is no longer limited to standard

navigation or surveying tasks like map making. It is gaining a lot of attention in the field of

survey engineering for example deformation monitoring. The survey of a bridge span

deflection under the load of a passing train is presented as an example of such application.

The deformation of the bridge span under the dynamic load is an important aspect of the

bridge safety monitoring. The maximum deflection of the bridge in all axes must be

monitored along with it's dynamics.

2 EQUIPEMENT

For the purpose of the survey we used Javad Triumph GNSS receivers. It is a 216

channels, GPS L1/L2/L2C/L5 receiver with GLONASS L1/L2 and Galileo E1/E5A options

with L1/L2 C/A and P code and carrier tracking ability. The receiver uses internal battery and

internal memory. The nominal performance of the receiver in post processing mode is 0.3 cm

+ 0.5ppm horizontal and 0.5 cm + 0.5 ppm vertical [1]. The raw data recording interval was

set to 20Hz. The same type of receiver was used on a reference station located on the roof of

254 INGEO 2011

the building in the University of Warmia and Mazury Campus. The distance between base

station and the bridge was about 2 km. Since there was no room on the viaduct to safely place

the receiver, it was firmly mounted to the safety rail.

Figure 1 Javad Triumph GNSS receiver mounted on the bridge.

3 SURVEY OBJECT ENVIRONMENT

For the experiment we chose a railway viaduct located over the Shuman avenue. It is a one

span, steel construction with one support in the middle of the span. The length of the span is

about 90 m. The overall view of the viaduct is presented in Figure 2 while Figure 3 shows the

moment of train passing the receiver. The receiver was located in the middle of the distance

between the abutment and a support. The approximate weight of a train was 20 tons per one

of four locomotive axle and about 10 tons per each of carriage axles (six carriages). Since the

viaduct is only about 300 m from the railway station the speed of the train was about 20 km/h.

Figure 2 Overall view of the viaduct

Figure 3 Train passing the receiver on the viaduct

Rzepecka, Z. et al.: Investigation of Viaduct Movements during Train … 255

The viaduct is directed almost in east-west direction. To track as many satellites as

possible, the receiver was placed on the south side of the bridge. The low elevation satellite

signals from the north were obstructed by the train (Figure 4).

Figure 4 Distribution of satellites during survey (Ashtech online mission planning tool).

Figure 5 The outline of survey configuration.

4 POSITIONING ALGORITHM

Ambiguities were resolved on the basis of the first 200 epochs, when the viaduct was

empty. For further evaluation the Kalman filter algorithm was used. The so called position-

velocity (p-v) model was admitted (Kai Borre, 2005; Brown and Hwang, 1992).

The stochastic model for the Kalman filter requires definition of preliminary estimate of

the system parameters 1x and its covariance matrix 1P for the first epoch to be processed,

of observations for each epoch kR and of the assumed dynamics model. The dynamics

model is expressed with the transition matrix k and the so called process noise matrix kQ .

Both 1P and kR are diagonal, with variances of the preliminary estimate of the parameters

(it was assumed 5 m2 for X, Y, Z and 1 m

2/s2 for respective components of the velocity in

1P ) and (0.01 m)2 for phase observations in kR . Matrix kQ is of 2 by 2 block diagonal

256 INGEO 2011

form – it follows from assuming two states for each direction X, Y, Z. Its explicit form reads

(Hofmann - Wellenhof et al., 1997; Strang and Borre, 1997):

,

00

00

00

,

,

,

Zk

Yk

Xk

k

Q

Q

Q

Q where

tStS

tStS

QQQ

p

p

pp

ZkYkXk

2

232

23

,,, (1)

where: pS is the spectral amplitude of the noise in position (it is introduced by random

accelerations that have not been taken into account in the two-state p-v model). Since the state

is almost static, the pS is set to a very small value and equals to 0.001.

Also the state transition matrix is of block diagonal form:

,

00

00

00

,

,

,

Zk

Yk

Xk

k where 10

1,,,

tZkYkXk (2)

where t is sampling interval, 0.05 sec in our case.

5 EVALUATION OF RESULTS

The GPS survey results are in the Easting – Northing and Height coordinate system. For

the purpose of deformation monitoring, these coordinates must be transformed to the axis

parallel and perpendicular to the span. To complete this task a rotation matrix was applied to

the results. The well known form of rotation matrix was used:

[x 'y ']=[cos sin

sin cos ][xy] (3)

where is the rotation angle.

Figure 6 depicts obtained results. Green line depicts the displacement along the span, red –

perpendicular to the span and blue line is a vertical displacement. There is almost no

displacement in the direction perpendicular to the viaduct. About 18 mm displacement is seen

along the span. As expected the biggest displacement is in the vertical direction.

Figure 6 Raw data results at 20Hz.

Rzepecka, Z. et al.: Investigation of Viaduct Movements during Train … 257

At first the span at the receiver position uplifted by about 15 mm then sediment by 50 mm

and uplifted again by 15 mm.

To see if there is a necessity to use a sampling rate of 20Hz the calculations were repeated

with 1 s interval. The results are depicted in Figure 7.

Figure 6 Raw data results at 1Hz

The Figures 6 and 7 indicates noisy data. Such noisy data may be attributed to sources

such as multipath error resulting from the surrounding structures environment and movements

of train during pass [2]. To smooth the data the low pass filter was applied with 0.1Hz cutoff

frequency. It is depicted with a black line for 1Hz data and with red line for 20 Hz data in

Figure 8. The offset of about 1 mm is visible in the maximum deflection. Also the plot is

much smoother with less detail visible for 1Hz data.

Figure 8 Vertical displacement after filtering.

Figures 9 and 10 represents the spectrogram for 20Hz and 1Hz respectively. It is clear that

1Hz data contains much less information about the bridge vibration frequencies.

258 INGEO 2011

Figure 9 Spectrogram of 20Hz signal.

Figure 10 Spectrogram of 1Hz signal.

6 CONCLUSIONS

The use of modern precise GNSS techniques allows to monitor engineering structures

like bridges or viaducts.

The results obtained from the Kalman filter processing are rather noisy. The noise

amplitude is of the order of 1-2 mm. Such noisy data may result from multipath error

following surrounding metal structures. But also further investigations are needed to check if

the values admitted into the Kalman filter model are optimal to describe the phenomena.

Also, in the experiment performed, the reference station was set over 2 km from the

viaduct. In the next experiment, the reference will be as near from the viaduct as possible. It is

hoped it will improve the results and diminish the noise.

The noise in the data causes inability to discover what information is lost when the

recording interval is set to 1 second.

REFERENCES

BROWN R.G. - HWANG P.Y.C. (1992): Introduction to Random Signals and Applied

Kalman Filtering – second edition, John Wiley & Sons, Inc., New York.

HOFMANN-WELLENHOF, B. - LICHTENEGGER H. - COLLINS J. 1997. GPS. Theory

and Practice. Fourth edition. ISBN 3-211-82591-6, Springer-Verlag, Wien, New York.

Javad Triumph-1 data sheet, available at

http://javad.com/downloads/javadgnss/sheets/TRIUMPH-1_Datasheet.pdf

BARAKA M.A. - EL-SHAZLY A.H. 2005 Monitoring Bridge Deformations during Static

Loading Tests Using GPS, proceedings of the FIG Working Week and GSDI-8 Cairo, Egypt

April 16-21, 2005

STRANG G. - BORRE K. 1997. Linear Algebra, Geodesy and GPS, Wellesley – Cambridge

Press, ISBN 0-9624088-6-3

XINHUA QIN, 1992 Very Precise Differential GPS – Development Status and Test Results.