Statistical inverse method for train suspensions remote diagnosis using embedded accelerometers
Résumé
Train suspension elements ensure its stability and play a key role in the ride safety and passengers comfort. They undergo damage throughout their lifetime, which may influence the train dynamic behavior. Consequently, they require regular maintenance, usually based on visual inspection or mileage criteria. However, a better knowledge of the actual health state of the suspensions would allow for providing maintenance closer to the real needs.
This work deals with the development of a remote diagnosis method for high-speed train suspensions, which consists in the inverse identification of the suspension mechanical parameters from in-service measurements of the train dynamic behavior by embedded accelerometers.
The excitation source of a rolling train is the track geometric irregularities, which consist of small displacements of the rails relatively to the theoretical track design. Track geometry also undergoes damage because of railway traffic. Consequently, the irregularities evolve through time. Because the train dynamic behavior is very dependent on them, sole acceleration measurements are not sufficient to correctly identify the suspensions mechanical parameters. Measurements of the track irregularities must be taken into account along with the corresponding measurements of the train dynamic behavior. This implies the use of a train dynamics software, in order to simulate the train dynamic behavior on a specific track geometry. For this work, we relied on the commercial multibody code Vampire.
The studied vehicle is a French TGV Réseau. Accelerometers are located at the connections between carbodies, above and on the shared bogie. For each connection, carbody and bogie vertical and lateral accelerations are measured. The various acceleration signals are studied in the frequency domain. Seven mechanical parameters of various suspension types are simultaneously identified: dampers, airsprings, elastomer stiffnesses…
Measurements are performed without interruption during the ride. Consequently, for a single inverse identification, joint measurements of the track geometric irregularities and of the train dynamic behavior on several hundreds of kilometers of track are generally available.
The large quantity of data as well as the uncertain nature of the different physical quantities of interest encourage a statistical approach of the problem. The inverse identification is performed thanks to a Bayesian calibration procedure. The principle of Bayesian calibration is to update the initial knowledge about the system parameters using measurements of the system output. This procedure provides the distribution of probable values of the parameters. Such information allows for estimating of the accuracy of the inverse identification, through the computation of confidence intervals for instance.
Because it requires simulation runs on the hundreds of kilometers of track for numerous values of the parameters, the classical Bayesian calibration procedure would be computationally unaffordable. An adaptation of the procedure relying on the approximation of the expensive likelihood function by a Gaussian process surrogate model has been developed to address this numerical cost issue. The impact of the use of a random surrogate model has been studied, in particular the influence of the surrogate model uncertainty, which represents the error inherent in the approximation of the likelihood function.
The inverse identification procedure has first been validated on a numerical experiment. The principle of a numerical experiment is to generate artificial acceleration signals thanks to simulation, using a vehicle model with known degraded suspension parameters. They can then be used as if they were measurements to perform a mock identification. Since the parameters values are known, the quality of the identification can be measured. In such a case, the inverse identification displayed very satisfying results, with identification errors below 5% of the admissible interval for every parameter.
The inverse identification procedure has then been tested on actual measurements of the train dynamic behavior. A significant evolution can be observed from the parameters nominal value. Since the real value of the suspension parameters remains unknown, no comparison could be performed in this case.
The influence of the surrogate model uncertainty is also emphasized by this study. Indeed, when it is taken into account in the identification procedure, the size of the confidence intervals for the identified parameters significantly increases. This means that the accuracy of the identification tends to be overestimated if the surrogate model uncertainty is ignored.
Transportation systems are nowadays more and more equipped with various kinds of sensors that allow for monitoring its different component. They make remote diagnosis method possible, which can be a precious tool for maintenance optimization. For train suspensions, embedding sensors remains difficult because of the variety and number of suspension elements. The advantage of an approach relying on accelerometers is to provide monitoring with a limited number of sensors. It however requires investing bigger efforts on data processing and on the identification method. Indeed, the expected information, the suspensions state, is not directly accessible in the measurements.
We developed a statistical inverse identification method using measurements of the train dynamic behavior by embedded accelerometers. It involves train dynamics simulations in order to take into account track geometric irregularities measurements. The method shows very promising results on numerical experiments as well as on actual measurements. A subsequent step now consists in developing criteria on the suspension parameters to trigger maintenance operations.
Concerning the mathematical aspects of the method, it is based on a Bayesian calibration procedure, which allow for estimating the identification accuracy. It also uses Gaussian process surrogate modeling in order to reduce computational costs. By applying the identification procedure on measurements performed at different time steps (with a time gap of several months), the evolution of the suspensions parameters with time and thus the gradual degradation of the suspension elements could be studied.