ORIGINAL PAPER
Time-ries analysis of GPS monitoring data from a long-span bridge considering the global deformation due to air temperature changes
无犯罪证明介绍信
Hien Van Le 1
•
Mayuko Nishio 1
Received:22October 2014/Revid:21May 2015/Accepted:21May 2015ÓSpringer-Verlag Berlin Heidelberg 2015
Abstract Although the structural health monitoring (SHM)bad on the displacement measurement has been adopted in some cas of long-span bridges and recognized veral advantages,there are some issues required to be considered,such as in acquiring the long-term static dis-placements with high and stable accuracies and in con-verting large amount of data into usable information.The global positioning system (GPS)is expected to solve tho issues.This study aims to analyze the GPS time-ries data acquired in a cable-stayed bridge in Vietnam,and to verify the usable feature for the structural condition asssment.Here,we suggest the u of the global deformations that are due to the periodic air temperature changes.Firstly,we obrved the quality of acquired GPS data,and the missing data was interpolated by applying the least-squares esti-mation.The correlation coefficient analysis was then con-ducted using both the GPS and the air temperature data to understand the global deformation due to temperature changes.It was clarified that the global towers-
girder coupled deformation was dominated by the 1-day periodic temperature change.The autoregressive integrated moving average (ARIMA)model was then applied to the GPS time-ries data,and it was shown that there were high regressions in some AR-MA coefficients plots.It was thus concluded that tho plots could be ud as the ba dis-tributions for the statistical structural condition asssment.
Keywords Global positioning system ÁLong-span bridges ÁTime-ries analysis ÁGlobal deformation ÁTemperature effects ÁARIMA model
1Introduction
Structural health monitoring (SHM)has been considered for the process of implementing structural condition asssment for civil infrastructures as well as for the large-scaled structures,such as long-span bridges.In tho flexible bridges,some structural changes have been con-sidered to relate cloly to deformations [1].A bridge usually has two kinds of individual deformations:long-term and short-term deformations.The long-term defor-mations are irrecoverable or periodic;they are caud by the foundation ttlement,the creep,the temperature ef-fects,and so on.The short-term deformations are caud by dynamic inputs,such as tho induced by wind,tidal cur-rent,earthquake,
and traffic [1–3].The monitoring of tho deformations is thus expected to be appropriate to capture the structural changes.
The SHM system have been applied to the continuous monitoring of civil structures;however,they still have some issues required to be considered,such as how to acquire the long-term static displacements of large-scale structures with stable and high accuracies,and how to convert large amount of data into usable information.In most cas of SHM,the major devices to capture dynamic/static structural respons are the accelerometer and the strain nsor;on the other hand,there are some nsors for measuring the structural displacements,such as the lar interferometer and some electronic distance instruments.Although tho nsors have the advantage of high accu-racies;they also have some disadvantages; e.g.,it is
&Hien Van Le
hienlv84.;le-hien-my@ynu.jp
Mayuko Nishio nishio@ynu.ac.jp
1
Department of Civil Engineering,Yokohama National University,Yokohama,Japan
J Civil Struct Health Monit
DOI 10.1007/s13349-015-0124-9
difficult to capture the measurement points when the dis-placement becomes too large,it is difficult to acquire data in real time,and the data acquisition is limited by climate ,the clear line of sight is one of basic re-quirements[4].
The Global Positioning System(GPS)technology has been successfully ud to measure displacements of oscil-latingflexible civil engineering structures,such as sus-pension bridges and high-ri buildings.There are some advantages of the GPS technology to monitor the dis-placements of the large-scaled civil structures; e.g.,it overcomes the limitation of climate,it can also measure the structural displacements in the three-dimensional direc-tions at centimeter level accuracy[1,4].Actually,there are some cas of the SHM using GPS technology for the monitoring of long-span ,the Tianjin Yonghe cable stayed bridge in Hong Kong[2],the Akashi Kaikyo Bridge in Japan[5].In the ca of the Akashi Kaikyo Bridge which is a suspension bridge with the center span of 1991m,the GPS system has been installed to measure the displacements in three dir
ections at three locations;the center span,the top of one of towers and the anchorage.In the indicated study in[5],possibility to evaluate the con-figuration of a suspension bridge was shown bad on the statistical methods that were applied to the acquired long-term GPS data.Here,the deformations due to an earth-quake and the typhoon were identified.
On the other hand,some papers studied the continuous structural monitoring data,in most of which,the dynamic characteristics were ud to verify the structural changes [6–8].Tho studies pointed out that the long-term monitoring data were greatly affected by the environ-mental and operational effects.Sohn et al.[6]mentioned that tho effects consisted of temperature,humidity,and the changes in operational loads and boundary conditions. The variability of monitoring data due to the environ-mental effects could then mask more subtle structural changes caud by damages.In their study,a linear adaptivefilter model was examined to discriminate the changes of modal parameters due to temperature changes from tho caud by structural damage or other environ-mental effects.The results indicated that a linear adaptive filter to could reproduce the natural variability of the fre-quencies with respect to time of a day.Cornwell et al.[7] studied the variability in modal parameters due to the en-vironmental effects and the operational conditions.In their study,the correlation analysis was conducted using the resonant frequencies and the temperature data measu
red in two data acquisitions,and the high correlation coefficients among them indicated the high influences of the tem-perature changes on the changes of structural properties. Farrar et al.[8]studied quantifying the variability in identified modal parameters caud by some sources,such as variability in testing procedures,in test conditions,and the environmental variability.Most of tho studies then concluded that the consideration of the variability in monitoring data due to the environmental and operational effects was a requirement for effective SHM.
There were then actually some studies that ud the time-ries analysis to asss the structural conditions from the monitoring data that consisted of the environmental and operational effects.Omenzetter et al.[9]ud a asonal autoregressive integrated moving average model with ex-ogenous inputs(SARIMAX)and transfer function to model the relationship between strain data and temperature data. In this study,unusual structural condition changes or damages could be detected by applying the outlier detec-tion and the intervention analysis technique to the esti-mated model.In the other study from the same authors [10],the approach to apply a vector asonal autoregressive integrated moving average(ARIMA)time-ries model was also prented.This study showed that the coefficients of the ARIMA model that were estimated by the adaptive Kalmanfilter could also be ud for detecting the unusual events occurred on the structure.Additionally,the study
by Sohn et al.[11]statistically examined the changes in the autoregressive(AR)model coefficients that estimated from dynamic data.It was shown that the distributions of AR coefficients estimated from data ts,which were from undamaged and damaged systems,could be appropriately classified to exact conditions.
This study aims to analyze the long-term displacement data acquired from a GPS monitoring system in a cable-stayed bridge.We investigated the global deformation patterns mainly due to the temperature effects,and verified whether they can be ud as the structural respon features for the statistical structural condition asssment.The tar-get bridge here is the Can Tho bridge,which is a cable-stayed bridges in Vietnam.The quality of obtained GPS data is discusd and the missing data are handled by ap-plying the least-square approximation to interpolate miss-ing values.Then the correlation coefficient analysis is conducted using the GPS data and the air temperature data to investigate the global deformation modes due to the temperature effects.We then also verify the applicability of one of the time-ries models;the ARIMA model for using the global deformations for the statistical structural con-dition asssment.
2Time-ries GPS data acquired in a target cable-stayed bridge狗牙雨
In general,the GPS system consists of the ba stations,the rover stations,and the communication system.The lec-tions of the reference stations and the remote stations are
J Civil Struct Health Monit
very important to get good-quality data.In the ca of long-span bridges monitoring,the distance between the ba station and each of the rover stations is often t up to satisfy the effects of atmospheric and orbital errors are expected to be very small.However,the missing data are often occurred during the data acquisition due to some reasons,such as the problems in the communication system or in the data logger.Here,the target bridge in this study and the installed GPS system are firstly prented,and the handling of missing data in acquired data is also verified.2.1Target bridge and installed GPS system
The target bridge is the longest cable-stayed bridge in the South East Asia opened in 2010.Figure 1shows the lo-cation and a picture of the target bridge.It is the bridge over the Hau river in the south of Vietnam,with the total length of 2750m,the center span of 550m,and the height of towers are 171m.The bridge has a concrete box-girder with the width of 26m;however,to increa the loading capacity,a part of the center span (middle 210m length)is made by a steel box-girder.The girders con
strained at the towers link to towers by using the elastic rubber bearings.There are two locations of elastic rubber bearings at the towers that are lateral bearings and vertical bearings.Thus,the girders are free to slide longitudinal at the limitation of bearings.The thermal expansion joints are located at the two ends of the main bridge.The SHM system has been installed since 2010,which includes not only the GPS system but also many nsors,such as temperature nsors,anemometers,and accelerometers.
The GPS system installed in the bridge consists of nine nsors as the rover stations and two ba stations as shown in Fig.2.The rover stations were placed on the top of two towers,the center span of the girder (the upstream and downstream sides),the quarter of the center span (the up-stream and downstream sides),and on the top of piers.One of two ba stations was placed on the footing of the North tower,while the other one was placed near the monitoring management office that was located 1-km far away from
the southern side of the bridge.The adopted GPS equip-ments were the products of Leica co.,ltd,GMX 902GG model.The accuracies of the GPS system bad on real time kinematic technique are (±10mm ±1ppm)(part per million)for the horizontal plane and (±20mm ±1ppm)for the vertical direction.The data acquisition system was constructed,in which the GPS signal at each rover
station was acquired in 20Hz,and their 10-min-averaged values were calculated.The averaged three-dimensional coordi-nates from the ba station on the footing of the North tower were then acquired in each 10min;therefore,the data became time-ries data with 10-min interval.Fig-ure 3a–c shows a part of raw GPS data at the center span acquired from February 15th to 22nd in 2013.Here,the x -direction in (a)is the longitudinal direction of the bridge,(b)is the y -direction that is in the lateral direction,and the z -direction in (c)is the vertical direction.2.2Handling of missing parts in GPS data
Actually,many small missing parts,most of which were less than five missing points,were obrved in the raw GPS data.For handling tho missing parts,a simple interpo-lation procedure was adopted for the time-ries analysis.There were actually some previous studies that verified the handling methods of missing data [12,13];when a few data points are missing,it may be possible to interpolate the missing values by the polynomial function estimation on the basis of the least-square method [13].Here,considering a polynomial function with m -th order:y ¼a 0þa 1t þa 2t 2þÁÁÁþa m t m :
ð1Þ
复制起点Equation (1)can be rewritten by a matrix form as:y ¼M :a
ð2Þ
where:the components of y is GPS displacement data y i (i =1-n )around the missing part at time t ;M is a matrix of size n 9(m ?1)that consists of t i and a is a vector of coefficients a j (j =0-m ).Hence,the coefficients of the polynomial can be estimated
by:
Fig.1The target bridge.a The location of bridge.b The Can Tho cable stayed bridge
J Civil Struct Health Monit
a ¼
M T M
À
ÁÀ1
M T y :
ð3Þ
Here,the order of the polynomial m must be determined;the accuracies of the interpolated points basically increa when the higher-order polynomials are ud against the number of missing points.
The performance of interpolation was then verified for interpolating the missing points in acquired GPS data.A part of acquired time-ries without any missing points,which was the data at the top of one of the towers in the vertical z -direction,was taken for the verification,and some missing points;the cas of one to five missing points,were given.The least-squares interpolation was
then applied to examine the accuracy in each ca.Notice that,when the number of missing data points was one or two,the difference between the interpolated and original values became less than 3mm,which was much smaller than the accuracy of the GPS system.Figure 4overlays the plot of the interpolated time-ries and the original one in the cas of three,four,and five missing points.The resi-duals at the missing points are summarized in Table 1.It can be en that the accuracies of interpolated values get lower as the number of missing points increa.In the ca of five missing data points,some of the absolute residuals between the interpolated and original time-ries are more than 10mm,which is the 50%of the
measurement
Fig.2GPS nsors on the Can Tho
bridge
Fig.3Acquired time-ries data by the installed GPS and temperature nsor (blue line :obrved 1-week data,red line :the mean value of 1-week data).a x -direction,b y -direction,c z -direction,d temperature data
J Civil Struct Health Monit
accuracy of installed GPS system in the vertical direction.From the results of the same verification using veral time-histories,it was decided that the three missing points or less were appropriately interpolated by this least-squares bad method in the target GPS data.In addition,it was recognized that the polynomial with the order m =3using three previous and two posterior data points n =5was generally able to obtain accuracies at the interpolated data points,at least better than the measurement accuracy of the GPS system.We thus applied the automatic interpolation process to many missing parts,which were with three missing points or less,in whole acquired GPS data as the pre-processing procedure for the next time-ries analysis.
3Obrvations of time-ries GPS
and temperature data and global deformation modes
业主手册
The GPS time-ries data ud in the time-ries analysis for verification here were the pre-procesd data acquired from February 15th to May 15th,2013.In Fig.3,not only
the GPS time-ries data in (a)–(c),but also the air tem-perature data in the same period of obrvation acquired by using a thermometer placed on the center span is also shown in (d);the mean value of each 1-week data is also indicated by a red line in each figure.In the ca here:the displacement data from the center span,the range of dis-placement around the mean in the z -direction in (c),which is approximately ±0.17m,are much larger than tho in the x -and y -directions in (a)and (b),which are both around ±0.04m.Compared to the time-ries of the air tem-perature in (d),the same periodic behavior,which is almost 144data ,24h,can be obrved especially in the z -direction.It could be en that the daily air temperature changes influenced the global bridge deflection.Therefore,it was considered that the analysis of the correlations be-tween the GPS data and the air temperature could realize the understanding of the global deformations of the target bridge under the temperature changes.
The correlation coefficient analysis was then conducted.The correlation coefficient between two variables X and Y is their covariance normalized by their standard deviations,as a following function:r X ;Y ¼
cov X ;Y ðÞr X r Y ¼
E X Àl X ðÞY Àl Y ðÞ½
r X r Y
ð4Þ
五月天倔强歌词where l X and l Y are the mean values;r X and r Y are the standard deviations of X and Y ,respectively,and E [.]is the expected value operator.Four GPS locations were lected to be analyzed:the top of the north tower:#A,the top of the south tower:#D,the middle of the center span girder:#B,and the quarter of the center span girder:#C,as indi-cated in Fig.2;the locations are the typical positions
亲吻教程to
Fig.4Application of least-square approximation to missing data七星钩
Table 1Difference between the measured values and the estimated value (unit:mm)Sample #3missing 4missing 5missing 4?1.6-1.4-4.55-3.4-7.8-13.46-4.5-9.7-17.57–-11.0-19.88
–
–
-11.3
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