Probabilistic simulation for the certification of railway vehicles

The present dynamic certification process that is based on experiments has been essentially built on the basis of experience. The introduction of simulation techniques into this process would be of great interest. However, an accurate simulation of complex, nonlinear systems is a difficult task, in particular when rare events (for example, unstable behaviour) are considered. After analysing the system and the currently utilized procedure, this paper proposes a method to achieve, in some particular cases, a simulation-based certification. It focuses on the need for precise and representative excitations (running conditions) and on their variable nature. A probabilistic approach is therefore proposed and illustrated using an example. First, this paper presents a short description of the vehicle / track system and of the experimental procedure. The proposed simulation process is then described. The requirement to analyse a set of running conditions that is at least as large as the one tested experimentally is explained. In the third section, a sensitivity analysis to determine the most influential parameters of the system is reported. Finally, the proposed method is summarized and an application is presented

Predictive track maintenance: how statistics models and vehicle-track interaction open new prospects: Maintenance prédictive des voies : comment les modèles statistiques et l'interaction véhicule-voie ouvrent de nouvelles perspectives

National audienceLa thèse présentée dans cet article a été menée dans le cadre de recherches d'outils de maintenance prédictive de la voie. A partir du calcul de la réponse dynamique d'un train à grande vitesse sur la voie, d'un modèle statistique des défauts de géométrie d'une portion de voie et d'outils mathématiques, elle a pour objet de prévoir statistiquement l'évolution, à une échéance de temps donnée, de la réponse dynamique du train sur la portion de voie étudiée. Le modèle de prévision développé permet ainsi l'atteinte de valeurs seuils déclenchant une opération de maintenance de la voie

Stochastic prediction of high-speed train dynamics to long-term evolution of track irregularities

International audienceThere is a great interest to predict the long-term evolution of the track irregularities for a given track stretch of the high-speed train network, in order to be able to anticipate the start off of the maintenance operations. In this paper, a stochastic predictive model, based on big data made up of a lot of experimental measurements performed on the French high-speed train network, is proposed for predicting the statistical quantities of a vector-valued random indicator related to the nonlinear dynamic responses of the high-speed train excited by stochastic track irregularities. The long-term evolution of the vector-valued random indicator is modeled by a discrete non-Gaussian nonstationary stochas-tic model (ARMA type model), for which the coefficients are time-dependent. These coefficients are identified by a least-squares method and fitted on long time, using experimental measurements. The quality assessment of the stochas-tic predictive model is presented, which validates the proposed stochastic model

Sensitivity of train stochastic dynamics to long-time evolution of track irregularities

International audienceThe influence of the track geometry on the dynamic response of the train is of great concern for the railway companies, because they have to guarantee the safety of the train passengers in ensuring the stability of the train. In this paper, the long-term evolution of the dynamic response of the train on a stretch of the railway track is studied with respect to the long-term evolution of the track geometry. The characterization of the long-term evolution of the train response allows the railway companies to start off maintenance operations of the track at the best moment. The study is performed using measurements of the track geometry, which are carried out very regularly by a measuring train. A stochastic model of the studied stretch of track is created in order to take into account the measurement uncertainties in the track geometry. The dynamic response of the train is simulated with a multibody software. A noise is added in output of the simulation to consider the uncertainties in the computational model of the train dynamics. Indicators on the dynamic response of the train are defined, allowing to visualize the long-term evolution of the stability and the comfort of the train, when the track geometry deteriorates

Characterization of the evolution of the train dynamic response under the effect of track irregularities

International audienceThere is a great interest to predict the long-time evolution of the track irregularities for a given track portion of the high-speed train network, in order to be able to anticipate the start off of the maintenance operations. In this paper, a stochastic predictive model is proposed for predicting the long-time evolution of a vector-valued random dynamic indicator related to the nonlinear dynamic responses of the high-speed train excited by the stochastic track irregularities. The long-time evolution of the vector-valued random indicator is modeled by a discrete non-Gaussian nonstationary stochastic model (ARMA type model), for which the coefficients are time-dependent. The quality assessment of the stochastic predictive model is presented, which validates the proposed stochastic model

Quantification of the influence of the track geometry variability on the train dynamics

International audienceIn a context of increasing interoperability, several high speed trains, such as ICE, TGV, ETR 500, are likely to run on the same tracks, whereas they have been originally designed for specific and different railway networks. Due to different mechanical properties and structures, the dynamic behaviors, the aggressiveness of the vehicle on the track and the probabilities of exceeding security and comfort thresholds will be very different from one train to an other. These maintenance, certification and comfort criteria depend on the dynamic interaction between the vehicle and the railway track and in particularly on the contact loads between the wheels and the rail, which are very hard to evaluate experimentally. Moreover, the track-vehicle system being strongly non-linear, this dynamic interaction has to be analyzed not only on a few track portions but on the whole realm of possibilities of running conditions that the train is bound to be confronted to during its life cycle. The idea of this paper is therefore to show to what extent this influence of the track geometry variability on the train dynamics can be analyzed from the coupling of a deter-ministic multibody modeling of the train with a track geometry stochastic modeling, which has been identified and validated from experimental data

A Posteriori Error and Optimal Reduced Basis for Stochastic Processes Defined by a Finite Set of Realizations

International audienceThe use of reduced basis has spread to many scientific fields for the last fifty years to condense the statistical properties of stochastic processes. Among these basis, the classical Karhunen-Loève basis corresponds to the Hilbertian basis that is constructed as the eigenfunctions of the covariance operator of the stochastic process of interest. The importance of this basis stems from its optimality in the sense that it minimizes the total mean square error. When the available information about this stochastic process is characterized by a limited set of independent realizations, the covariance operator is not perfectly known. In this case, there is no reason for the Karhunen-Loève basis associated with any estimator of the covariance that are not converged to be still optimal. This paper presents therefore an adaptation of the Karhunen-Loève expansion in order to characterize optimal basis for projection of stochastic processes that are only characterized by a relatively small set of independent realizations

Statistical inverse method for train suspensions remote diagnosis using embedded accelerometers

International audienceTrain 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

Identification expérimentale des paramètres de suspensions des trains à grande vitesse par méthode statistique inverse

International audienceL’objectif du travail présenté ici est l’identification statistique inverse de paramètres décrivant les caractéristiques mécaniques de suspensions de train à grande vitesse à des fins de maintenance. Cette identification se fait par la comparaison de mesures accélérométriques en circulation et de résultats de simulation de dynamique ferroviaire du train. Elle implique la définition d’une distance entre mesures et simulations par une fonction coût, l’introduction des incertitudes de mesure et du modèle de train et la définition d’un problème d’optimisation robuste

Bayesian calibration of mechanical parameters of high-speed train suspensions

International audienceThe objective of the work presented here is a bayesian calibration of parameters describing the mechanical characteristics of high-speed train suspensions for maintenance purposes. This calibration is achieved by comparing simulation results to on-track accelerometric measurements. It requires the estimation on the multidimensionnal admissible set of the parameters of the likelihood function of the train dynamic response. This estimation is achieved thanks to the identification of a kriging metamodel of this likelihood function to reduce the numerical cost. From this metamodel, the posterior probability density function of the parameters is estimated using an MCMC algorithm