Making use of long-term transverse vibration monitoring data of DaShengGuan Bridge, the early-warning method of train running safety of the high-speed railway bridge is established by adopting principal component analysis (PCA) method. Firstly, the root mean square (RMS) of the transverse acceleration of the main girder is used as the monitoring parameter for the train running safety. The correlation model between the RMS values measured from different positions is further adopted as the evaluating model for the train running safety. Finally, the effects of the environmental changes on the evaluating model are eliminated using the PCA method and the warning index for the train running safety is further constructed. The analysis results show that the correlation between the RMS values of the accelerations from different measuring positions on the main girder can be analyzed by a quadratic polynomial fitting model. The PCA method can effectively remove the environmental effects on the quadratic polynomial fitting model. The proposed warning method provides a good capability for detecting the abnormal changes of the measured transverse accelerations and hence it is suitable for early-warning of the train running safety.
Nanjing DaShengGuan Bridge, which serves as the shared corridor crossing Yangtze River for both Beijing-Shanghai high-speed railway and Shanghai-Wuhan-Chengdu railway, is the first 6-track high-speed railway bridge with the longest span throughout the world. With its 336 m main span and 6-track railways it ranks itself the largest bridge with heaviest design loading among the high-speed railway bridges by far. Also the design speed of 300 km/h of the bridge is on the advanced level in the world. Due to these remarkable characteristics including long span of the main girder, heavy design loading, and high speed of trains, the considerable transverse vibration of the bridge caused by high-speed trains may threaten the train running safety of DaShengGuan Bridge. Thus the train running safety should be paid special attention during the bridge operation [
To realize the transverse vibration monitoring of the bridge, the structural health monitoring system for the DaShengGuan Bridge has been established by the application of modern techniques in sensing, testing, computing, and network communication. The ideal objective of the bridge health monitoring system is to gather various reliable information that can be used to detect the evolution of the bridge’s condition state and perform reliability-based assessment so as to give the engineer or administrant a great variety of options with respect to maintenance intervention [
Based on the aforementioned motivation, the objective of this paper is to propose an early-warning method of train running safety for high-speed railway bridges. The variability of transverse accelerations of the main girder induced by high-speed trains is quantified and the abnormal changes of the measured transverse accelerations which may threaten the train running safety are detected using the principal component analysis (PCA) method. The paper emphasizes on (i) the choice of monitoring parameter obtained from the transverse accelerations of the main girder; (ii) the establishment of the evaluating model for the train running safety; and (iii) the construction of the warning index using the PCA method. The feasibility of the proposed strategy is demonstrated using 310 days of measured transverse acceleration data on the main girder of Nanjing DaShengGuan Bridge in 2013.
The train running safety is to refer to the safe traveling status of trains without derailment. In particular for high-speed railway bridges, high-speed train derailment incidents may cause heavy casualties and property losses. In the design of high-speed railway bridges, the derailment coefficient and wheel unloading rate are usually used to judge the train running safety. However, Zeng et al. [
The early-warning method of train running safety using transverse vibration monitoring data involves three steps:
(1) to extract the monitoring parameter for the train running safety, that is, to extract the monitoring parameter from the transverse acceleration responses of the main girder, which can indicate the train running safety of high-speed railway bridges: this paper will investigate applicability of two monitoring parameters including the peak value and the RMS value of the transverse acceleration;
(2) to construct the evaluation model for the train running safety; due to the strong stochastic features of the transverse acceleration responses of the train-railway-bridge system with high-speed train traveling by, a deterministic evaluation model should be established to represent the stable condition of the transverse vibration for the whole system based on the extracted monitoring parameter;
(3) to establish an early-warning index for the train running safety; the stability of the transverse vibration of the train-railway-bridge system is a basic rule for the judgment of train running safety; hence, a warning index for the train running safety is further constructed from the constructed evaluation model using a statistical pattern recognition method; the abnormal condition for the train running safety can be alarmed if the monitoring evaluation model disobeys the normal pattern.
The subject of this study is Nanjing DaShengGuan Bridge shown in Figure
View of the Nanjing DaShengGuan Bridge and layout of the transverse vibration monitoring of the main girder.
View of the Nanjing DaShengGuan Bridge
Elevation drawing of the bridge (unit: m)
Locations of the accelerometers in the deck sections
Figure
Transverse acceleration time histories of the main girder induced by a high-speed train.
Accelerometer JSD-11-04
Accelerometer JSD-15-06
In the present study, the acceleration amplitude parameters are utilized as the monitoring parameters to represent the transverse vibration characteristic of the main girder. The acceleration amplitude usually refers to the maximum or effective value of acceleration responses. For this reason, the applicability of the two acceleration amplitude parameters, the peak value and the RMS value, should be studied in this research. It should be noted that, in the calculation of RMS values of the transverse acceleration of the main girder, the filter bandwidth of the transverse accelerations is set to be 0–20 Hz. Figure
Correlations between the amplitude parameters of the transverse accelerations in the middle of the first main span and the speed of the trains.
Correlation between the peak value of transverse accelerations and the speed of trains
Correlation between the RMS value of transverse accelerations and the speed of trains
In the next discussion, the cross-correlation between the amplitude parameters of the transverse accelerations in the middle of two main spans is investigated when the high-speed trains pass through the bridge. Figure
Cross-correlations between the amplitude parameters of the transverse accelerations measured in the middle of two main spans.
Cross-correlation between peak values of transverse accelerations
Cross-correlation between RMS values of transverse accelerations
Fitting effect of cross-correlation between RMS values of transverse accelerations by using quadratic polynomial.
Correlation between the measured RMS values of the transverse accelerations in the middle of the second span and the corresponding fitted values
Computed correlation coefficients of the 310 days in 2013
The analysis results indicate that good cross-correlation exists between the RMS values of the transverse accelerations on the two main spans. This is because the RMS values of the transverse accelerations represent the vibration energy of the train-railway-bridge system, and the cross-correlation between the RMS values of the accelerations at different measuring positions can represent the spatial distribution of the transverse vibration energy which is inputted into the system by the traveling trains. In this case, the randomness of transverse vibration can be transferred into the deterministic feature of the spatial distribution of the transverse vibration energy. Hence, the cross-correlation model of RMS values of transverse accelerations can represent the transverse vibration state of the system when the high-speed train passes through the bridge. According to the theory of random energy analysis for train derailment [
Based on the results in Section
Firstly, there is a need to study the fitted coefficient of the quadratic polynomial for the cross-correlation model based on the long-term monitoring. Figure
Long-term monitoring results of the fitted coefficients of the quadratic polynomial.
Quadratic coefficient
Monomial coefficient
Constant term
Principal component analysis (PCA) method is a statistical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables [
The basic theory of PCA is that a vector
According to the basic theory of PCA as stated above, the key steps of the warning method of train running safety are listed as follows.
(1) Compute the fitted coefficients of the quadratic polynomial for the RMS values of the transverse accelerations each day under the normal running condition. The three coefficients form the 3-dimensional vector
(2) Reduce the dimension of the 3-dimensional vector
(3) The reconstructed value of the RMS of the transverse accelerations is obtained by referring to the 1-dimensional vector
(4) With the help of PCA, the RMS values of the transverse accelerations in an unknown running condition can be reconstructed by using the transform matrix
The analysis of the monitoring data of 310 days in 2013 will be carried out as an example. The first 260-day data of the 310 days will serve as the training samples, the last 50-day data will serve as the test samples. Figure
Training effect of warning idex for train running safety using PCA method.
Measured waring index curve and simulated warning index curve due to the deterioration of the bridge using PCA method.
There is a need to investigate the effectiveness of the proposed method applied to the early-warning of train running safety. The RMS values of the transverse acceleration data (the data of the last 50 days in 2013) in the middle of the second main span are amplified by a factor of 1.05 to simulate the effects of structural deterioration of the bridge on the RMS values of the transverse acceleration. Figure
Daily mean values of the measured data and the simulated data of the RMS values of the transverse acceleration data in the middle of the second main span.
In this paper by referring to the Nanjing DaShengGuan Bridge, the first 6-track high-speed railway bridge with the longest span throughout the world, the early-warning method of train running safety of the high-speed railway bridge is proposed by adopting principal component analysis (PCA) method based on long-term transverse vibration monitoring data. The following are the findings and conclusions.
(1) When high-speed trains passed by, the transverse vibration of the train-railway-bridge system had a strong stochastic feature. The correlation between transverse accelerations from one measuring position on the main girder and the speed of trains cannot represent the transverse vibration condition of the whole system and thus cannot be adopted as the evaluating model for the train running safety.
(2) The correlation between the RMS values of the transverse accelerations from different measuring positions on the main girder represents the spatial distribution feature of transverse vibration energy of the whole system and can be effectively analyzed by a quadratic polynomial fitting model. Thus, the corresponding correlation model can be adopted as the evaluating model for the train running safety.
(3) The PCA method can effectively remove the environmental effects on the measured cross-correlation between the RMS values of transverse accelerations. The proposed warning method provides a good capability for detecting the abnormal changes of the measured transverse accelerations and hence it is suitable for early-warning of the train running safety of DaShengGuan Bridge.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors gratefully acknowledge the National Basic Research Program of China (973 Program) (no. 2015CB060000), the National Science and Technology Support Program of China (no. 2014BAG07B01), the Key Program of National Natural Science Foundation (no. 51438002), the Program of “Six Major Talent Summit” Foundation (no. 1105000268), and the Fundamental Research Funds for the Central Universities and the Innovation Plan Program for Ordinary University Graduates of Jiangsu Province in 2014 (no. KYLX_0156).