Optimization of the detection of train wheel defects. SNCF Innovation and Research Department Paris, FRANCE 1

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1 Optimization of the detection of train wheel defects 1 R. Ziani SNCF Innovation and Research Department Paris, FRANCE 1 Abstract This paper describes how statistical models and learning algorithms could help to improve the efficiency of train wheel defect detection. The objective is to optimize maintenance operations through better prognostics of train wheel defects. The early detection of wheel defect is a crucial issue for SNCF because it can help to prevent accelerated deterioration of rail and degradation of wheels. The development of wheel defects induces periodic vibrations which can affect passenger s comfort and safety. In this study, we present in one part a methodology based on learning algorithms and statistical tests which could be used to identify the wheel defect s appearance from operational data and in second part statistical models to predict the development of a defect. 1. Introduction Friction between rail and train wheel leads to deformation of wheel running surface. Wheel deformations contribute to accelerate deterioration of train axle boxes and deterioration of rail. When a defect develops on a wheel, it continues to grow damaging rail by producing unusual vibrations. Train s passengers can sometimes hear and feel these vibrations, which can make the travel unpleasant. In addition to degrading the passenger s comfort, the wheel defects are very expensive in maintenance. Indeed, the axles whose wheel is failing must be withdrawn in order to carry out a reshaping. The reshaping consists in removing the sufficient quantity of metal to correct the deformation of the wheel. The more the wheel is deformed, the more the quantity of metal to be removed must be significant. A great quantity of metal removed from the wheel will result in changing the axle earlier. The early detection of a defect thus becomes an important question for the SNCF in order to improve the lifespan of the axles. With the aim of improving the effectiveness of maintenance and the quality of service to its customers, SNCF developed a system of detection of wheel defects. This monitoring system made of accelerometer sensors is mainly installed on the high speed lines. It is possible to measure with the passage of each train the vibration of the rail generated by the contact of the wheels on the rail. The wheels whose vibrations on the rail are abnormal are identified. This monitoring system allows to follow each wheel and to remove failing wheels before affecting rails. SNCF set up a plan of conditional maintenance based on measures provided by the system. The purpose of the study is to use measurements resulting from the system for each wheel in order to detect the appearance of a possible defect as soon as possible and to predict its evolution. Earlier the defect is detected, earlier the wheel is sent to maintenance centre. In this paper, we briefly describe the system of measure. Then we detail the algorithms of rupture detection which allow identifying the appearance of a defect. Three approaches are tested to detect the appearance of a defect: the Bi-model approach, the detection by CUSUM algorithm and the detection by One-Class SVM. Finally, we present the statistical models used to forecast evolution of defects: the linear model and the autoregressive model. We finish this paper by the conclusion. 2. The measurement system of wheel defects The measurement system: The measurement system of wheel defect is composed of several accelerometer sensors located on the tracks: some sensors positioned on the right side of the rail and some sensors positioned on the left side.

2 The accelerometer sensors are fixed on the rail and are spaced at equal distance so that distance between the first one and the last one is equal to the circumference of a wheel. When trains passing, measurements of accelerometers corresponding to the response of the rail to wheel contact are recorded and processed by a computer located at the edge of the track. Processed measurements are sent to a supervision centre where they are analysed. The following figure presents the system of measurement: Accelerometer sensors Hot Box detector Accelerometer sensors On the railway Recording and data processing Analyse of indicators of wheel defects Supervision centre Indicators of wheel defects Transmission of the data to supervision centre Figure 1: illustration of the measurement system of wheel defects Wheel flats, out of rounds, wheel spalling, tread defects are wheel defects with particular characteristics. Their particularities result in their appearance, formation and development. The reasons why a wheel become out-of-round are complex and the goal of this is document is not to explain it. However, this document aims at explaining the methods that could be used to detect these defects and to predict their evolution. The maintenance rules The maintenance agents of the supervision centre receive for each wheel an indicator of defect when train running over the measuring site. The indicator of defect is a value calculated from several transformations of the signal emitted by the accelerometer sensors. Several check tests showed us that these indicators were highly correlated with the level of deformation of the running surface. These tests were carried out while making pass a test train over the measuring sites. A test train is a train with wheel defects whose level of deformation of running surface is measured in a maintenance centre with a specific device. We can then compare the indicators of defect provided by the supervision centre and the level of deformation of the running surface measured. According to these tests, an alert threshold concerning the indicator of defect was fixed. It is always difficult to have to fix such a threshold for maintenance because a too weak threshold would result in removing wheels which do not have a significant defect, whereas a too high threshold would result in letting wheels with significant defects evolve and possibly cause important damage. Moreover some defects evolve quickly and the maintenance threshold is quickly reached whereas other defects evolve more slowly. This thresholding can lead to quickly carry out a maintenance action for the wheels whose defect evolves quickly. In order to plan maintenance actions, we propose to detect the appearance of the defect as soon as possible and to model its development. The objective

3 is to predict the remaining time before reaching this threshold. Thus, we can firstly deal with the most serious defects and those which quickly evolve in order to minimize the damage caused. Correction of the sensors drift Maintenance experts must trust in the system detection. Or in the course of time, as any electronic equipment, the sensitivity of the accelerometer sensors could change. Accelerometer sensors could give incorrect signal and so incorrect indicators. Wheels without any defect could be detected by the system as defected wheels and sent to maintenance, whereas defective wheels could be considered as good ones. The maintenance policy could be inefficient and costly because of sensor s failures. The reliability and stability of the accelerometer sensors is so crucial. To prevent the detection system from this type of failure, trains with benchmark axles (axles with identified defects) often pass over measurement sites. Provided indicators and the measure of the wheel deformation (maintenance data) are compared to detect any difference of sensitivity of sensors. If the parameters of the regression model making the relation between the indicators and the measured deformation significantly change, the accelerometers sensors have to be checked. The data The following table indicates the structure of the data for a high speed train TGV with 26 axles: Attribute Description Date Date of measurement Time Time of measurement Num_train Number of train Num_trainset Number of trainset Pos_trainset Position of trainset (head or queue) for coupled trainset Num_head Number of the head car in the trainset (one or eight) Vmean Mean of speed Num_site Number of measurement site Val_L1 Value of defect indicator of left wheel of axle 1 Val_R1 Value of defect indicator of right wheel of axle 1 Val_L2 Value of defect indicator of left wheel of axle 2 Val_R2 Value of defect indicator of right wheel of axle 2 Val_L26 Value of defect indicator of left wheel of axle 26 Val_R26 Value of defect indicator of right wheel of axle 26 Table 1: defect indicators for a TGV with 26 axles. The data we used to perform this study comes from a measurement site installed near Paris on the high speed line 1 between Paris and Lyon. This data relates to the state of the wheels of 30 TGV trainsets over a period of 45 days. The observed TGV trainsets contain 26 axles. When a TGV trainset passes over a measurement site, we get 56 values of defect indicator. The parity of the number of the measurement site enables us to know the direction of the train (from Paris to Lyon or from Lyon to Paris). The number of the trainset and the number of the head car allow us identifying a wheel by a single number whatever the direction of the train and the position of the trainset are. With some simple transformations, we are thus able to follow a wheel during a period as presented in figure 2.

4 Figure 2: Evolution of the defect indicator of a safe wheel during 45 days The figure 2 shows that the defect indicator of the observed wheel moves around 1. Given that the threshold of intervention is fixed to 5, this wheel does not require an intervention. We can notice that the behaviour of the wheel defect indicator is stationary which means that no defect is developing. However, the formation of a defect generally creates an abrupt change of trend of the wheel defect indicator. The next section presents change detection algorithms used to identify abrupt changes which could indicate the appearance of a defect. 3. The statistical methods to optimize detection and to predict development of wheel defects 3.1 Detection of abrupt changes: Our study is based on the idea that degradation is a continuous phenomenon which can be identified before reaching a maintenance threshold. Each wheel is defined as a time series of wheel defect indicator. The abrupt change of the trend of the time series for a wheel could indicate the formation of a defect. So, we have to focus on the methods which allow detecting abrupt changes of a time series. In this section, we present the various methods we used to detect abrupt changes. We also present some results. The bi-model approach An interesting step consists in dividing the time series in two parts in order to compare the statistical characteristics of each part (mean, standard deviation, distribution function). For a given wheel at each time of observation, we have two observation windows, one corresponding to the values of the defect indicator before time t, the other corresponding to the values after time t. We used two different ways to construct the observation windows as shown in the figure 3. Model 1 Model 1 Model 2 Model 1 Case a) Case b) Figure 3: illustration of the bi-model approach In the case a, the size of the first window equal to t-l is variable whereas the size of the second moving window is fixed to L.

5 In the case b, the size of the first window is increasing with the whole number of observations and the second window is still moving with a size equal to L. Our problematic is equivalent to perform the following test: H0 (null hypothesis): there are no abrupt changes in the signal between the first observation window (model 1) and the second observation window (model 2). H1 (alternative hypothesis): There is an abrupt change between the first observation window (model 1) and the second observation window (model 2). Detection of a jump in the average In order to compare the means of each observations window, we considered the case a) illustrated in the figure 3. The signal in each window is represented by its mean value. The estimation of the means and the standard deviations are given by the next formulas: (1) Under the assumption of Gaussian distribution of the data, the difference between the estimation of the means follows a Gaussian distribution. Under the null hypothesis that the means of observations between the two windows are equal, the next formula follows a khi2 (1) test: (2) As the Gaussian hypothesis of the data is not always confirmed because we do not have a sufficient quantity of data (the observation window is too small), we decide not to use this statistical test. However, we choose to compare the formula (2) to a threshold whose adjustment will depend on the desired sensitivity and the observed results both. If we used the statistical test, we would compare the formula (2) to a quantile of the khi2 distribution determined by the level significance of the test. The detection procedure becomes: - At each observation time t, calculate the estimation of the standard deviation and the mean corresponding to the two windows, - If the formula (2) is greater than a threshold h to be defined, we conclude that there is an abrupt change of mean. If the abrupt change is detected at time ta, a rough estimate of the change moment is equal to k=ta-l. The size of the first window influences the delay of detection. The parameters of the detection procedure are the threshold h and the size of the window L. Test on mean and standard deviation of the residuals (test based on the CUSUM algorithm) We considered the case b illustrated in the figure 3 to make two observation windows. This test consists in comparing the statistical characteristics of the residuals of the two windows to detect any change. This method is inspired by the algorithm CUSUM of Page-Hinkley [4]. The detection procedure is described by the following steps: - calculate the residuals and the variances :

6 (3) - We consider an abrupt change if the quantity gt defined below is greater than a threshold h: (4) The parameters of this test are the threshold h and the size L of the second observation window. An estimate of the abrupt change moment is given by the last time k before the detection time verifying the equality gk=0. Other estimation is k=ta-l. Detection by One-Class SVM (Support Vector Machines): Support Vector Machines have received some attention over the recent years. This is not only due to their superior statistical properties but also because of their numerous successful applications. SVM is a supervised classification algorithm used in two class classification problems. Considering the data provided by our monitoring system, our problematic is a one class classification problem because we do not know which wheel is failing and which one is safe. Our problem differs from conventional classification problems in the manner of how the classifier is trained. It is only trained by one class of data which is the target. The One Class SVM algorithm is an algorithm based on the SVM approach which estimates the support of a distribution or the contour of data belonging to a single group. It is possible to obtain a change detection method from One Class SVM by constructing a dissimilarity measure. The dissimilarity measure is then applied to compare two time series of wheel indicators one before time t and one after time t. If the dissimilarity between the time series exceeds a threshold (to be defined), the algorithm indicates an abrupt change at time t. The figure 4 illustrates the windowing we have used: Figure 4: Example of windowing used Description of the One Class SVM algorithm For introducing to the key concept and parameters used, we give a brief description. Consider the kernel space H defined such as: (5) We will suppose that k(.,.) is such as k(x,x)=1. (6)

7 A function f belonging to the kernel space H could be written as: (7) The figure 5 illustrates the principle of the One Class SVM: Figure 5: illustration of the principle of One Class SVM The Kernel maps the data onto the surface of a hypershere in the feature space as showed in the figure 5 (the hypersphere is a circle centered around the origin) The objective of the One Class SVM algorithm is to separate the data from the origin by using a hyperplane (the hyperplane is the line W). The problem is therefore to find the hyperplane that maximize the margin of separation from the origin, ie maximize the following distance: In the kernel space, a hyperplane is written as: (8) Thus, the algorithm aims at making the majority of the data to be located on the side of the hyperplane furthest away from the origin. The majority of the data must satisfy the condition: In the figure 5, the data satisfying this condition is written Non-SVs. We accept that some data supposed to be extreme do not satisfy this condition. This extreme data is written in the figure 5 Non-Margin SV. Finally, the maximum margin of separation from the origin is found by solving [5]: (9) (10) Subject to Construction of dissimilarity measure From One Class SVM, an algorithm of boundary estimation, it becomes possible to construct a change detection method. Considering the times series illustrated in figure 4, one time series corresponding to the series of defect indicator before time t, other after time t:

8 Figure 6: One Class SVM applied to two time series allows obtaining two hyperplanes The dissimilarity measure proposed by Desobry [4] is: (11) where all the points are described in the figure 6. The procedure of change detection becomes: Calculate the two hyperplanes by One Class SVM for each time t, 3.2 Results of abrupt change detection and prediction of defect evolution For each wheel, since an abrupt change of the defect indicator due to a possible defect is confirmed by the above algorithms, it is important to know how the defect will grow. Statistical models try to give the predictive remaining time or the predictive remaining kilometres before the defect indicator will reach a defined threshold. Autoregressive models and linear regression models are experimented to do so. Some results are presented in figure 8 and figure 9:

9 Date of rupture Figure 8: change detection using One Class SVM and linear prediction model Date of rupture detection We can observe that we detect a change ten days after it appears. This result depends on the size of the observation window used. We can notice that a simple linear model is sufficient to have good predictions. Although, we do not have enough data, we decide to try an autoregressive model for prediction (figure 9). Date of rupture Date of rupture detection Figure 9: Change detection using CUSUM approach and AR(2) prediction model The CUSUM approach detects at the day numbered 36 that a rupture occurred at the day numbered 26. The autoregressive model needs many points to give good estimate. With the few data that we have, it is better to use the linear model regression. 4. Conclusion The change detection algorithms seem to give good results, but parameters like the size of the window must be adjusted with care. It can seriously affect the accuracy of the algorithms. To adjust those parameters and to test the real efficiency of those algorithms, it is necessary to gather maintenance data in order to identify wheel with real defect and wheel with no defect. The adjustment of those parameters depends on the desired rate of good detection and the rate of false detection. The research study is attempted to improve the system by giving prognostic of wheel defects. Learning algorithms detect the first occurrence of a defect as soon as possible and predictive models propose a predictive development of the defect.

10 The design of a preventive maintenance schedules is always a difficult task, but a monitoring system supplemented by statistical analysis can allow huge cost savings both in terms of safety and productivity. Acknowledgments We acknowledge A. Rakotomamonjy and G. Gasso [4] professors at the National Institute for Applied Sciences (INSA Rouen) for their large contribution to this study. References [1] A. Bousquet. Introduction aux «Support Vector Machines», Ecole Polytechnique (2001) [2] O. Bernard. Recalage des mesures dans le cadre de la détection de défauts de roue de TGV, training course (2003) [3] S. Létourneau, C. Yang. Learning to predict train wheel failures, National Research Council of Canada [4] A. Rakotomamonjy, G. Gasso. Détection de rupture et de défauts de roue de TGV, INSA Rouen (2006) [5] R. Unnporsson. Model selection in One-Class SVMs using RBF Kernel, sigillum universitatis islandiae (Iceland April 2003)