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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: [email protected]
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.