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... more
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 Reseau. 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…
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ABSTRACT Railway dynamic simulations are increasingly used to predict and analyse the behaviour of the vehicle and of the track during their whole life cycle. Up to now however, no simulation has been used in the certification procedure... more
ABSTRACT Railway dynamic simulations are increasingly used to predict and analyse the behaviour of the vehicle and of the track during their whole life cycle. Up to now however, no simulation has been used in the certification procedure even if the expected benefits are important: cheaper and shorter procedures, more objectivity, better knowledge of the behaviour around critical situations. Deterministic simulations are nevertheless too poor to represent the whole physical of the track/vehicle system which contains several sources of variability: variability of the mechanical parameters of a train among a class of vehicles (mass, stiffness and damping of different suspensions), variability of the contact parameters (friction coefficient, wheel and rail profiles) and variability of the track design and quality. This variability plays an important role on the safety, on the ride quality, and thus on the certification criteria. When using the simulation for certification purposes, it seems therefore crucial to take into account the variability of the different inputs. The main goal of this article is thus to propose a method to introduce the variability in railway dynamics. A four-step method is described namely the definition of the stochastic problem, the modelling of the inputs variability, the propagation and the analysis of the output. Each step is illustrated with railway examples.
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This paper is concerned with the approximation of a function u u in a given subspace V m V_m of dimension m m from evaluations of the function at n n suitably chosen points. The aim is to construct an approximation of u u in V m V_m which... more
This paper is concerned with the approximation of a function u u in a given subspace V m V_m of dimension m m from evaluations of the function at n n suitably chosen points. The aim is to construct an approximation of u u in V m V_m which yields an error close to the best approximation error in V m V_m and using as few evaluations as possible. Classical least-squares regression, which defines a projection in V m V_m from n n random points, usually requires a large n n to guarantee a stable approximation and an error close to the best approximation error. This is a major drawback for applications where u u is expensive to evaluate. One remedy is to use a weighted least-squares projection using n n samples drawn from a properly selected distribution. In this paper, we introduce a boosted weighted least-squares method which allows to ensure almost surely the stability of the weighted least-squares projection with a sample size close to the interpolation regime n = m n=m . It consists in sampling according to a measure associated with the optimization of a stability criterion over a collection of independent n n -samples, and resampling according to this measure until a stability condition is satisfied. A greedy method is then proposed to remove points from the obtained sample. Quasi-optimality properties in expectation are obtained for the weighted least-squares projection, with or without the greedy procedure. The proposed method is validated on numerical examples and compared to state-of-the-art interpolation and weighted least-squares methods.
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Les nouvelles attentes vis-a-vis des nouveaux trains a grande vitesse sont nombreuses: on les voudrait plus rapides, plus confortables, plus stables, tout en etant moins consommateur d'energie, moins agressif vis-a-vis des voies,... more
Les nouvelles attentes vis-a-vis des nouveaux trains a grande vitesse sont nombreuses: on les voudrait plus rapides, plus confortables, plus stables, tout en etant moins consommateur d'energie, moins agressif vis-a-vis des voies, moins bruyants… Afin d'optimiser la conception de ces trains du futur, il est alors necessaire de pouvoir se baser sur une connaissance precise de l'ensemble des conditions de circulations qu'ils sont susceptibles de rencontrer au cours de leur cycle de vie. Afin de relever ces defis, la simulation a un tres grand role a jouer. Pour que la simulation puisse etre utilisee dans des perspectives de conception, de certification et d'optimisation de la maintenance, elle doit alors etre tout a fait representative de l'ensemble des comportements physiques mis en jeu. Le modele du train, du contact entre les roues et le rail, doivent ainsi etre valides avec attention, et les simulations doivent etre lancees sur des ensembles d'excitation...
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High speed trains are currently meant to run faster and to carry heavier loads, while being less energy consuming and still ensuring the safety and comfort certification criteria. In order to optimize the conception of such innovative... more
High speed trains are currently meant to run faster and to carry heavier loads, while being less energy consuming and still ensuring the safety and comfort certification criteria. In order to optimize the conception of such innovative trains, a precise knowledge of the realm of possibilities of track conditions that the train is likely to be confronted to during its life cycle is necessary. Simulation has therefore a big to play in this context. However, to face these challenges, it has to be very representative of the physical behavior of the system. From a general point of view, a railway simulation can be seen as the dynamic response of a non-linear mechanical system, the train, which is excited by a complex multivariate spatial function, the track geometry. Therefore, the models of the train, of the wheel/rail contact forces have thus to be fully validated and the simulations have to be raised on sets of excitations that are realistic and representative of the track geometry. Ba...
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Thanks to computing power increase, risk quantification relies more and more on computer modeling. Methods of risk quantification based on a fixed computational budget exist, but computer codes are almost always considered as a single... more
Thanks to computing power increase, risk quantification relies more and more on computer modeling. Methods of risk quantification based on a fixed computational budget exist, but computer codes are almost always considered as a single black box. In this paper, we are interested in analyzing the behavior of a complex phenomenon, which consists of two nested computer codes. By two nested computer codes, we mean that some inputs of the second code are outputs of the first code. Each code can be approximated by a parametrized computer model. First we propose methods to calibrate the parameters of the computer models and build a pre-dictor of the nested phenomenon for a given set of observations. The presented methods enable to take into account observations of the first code, the second code and the nested code. Second the choice of the observations is studied. Methods of sequential designs, that means step by step addition of observation points to the observations' set, are examine...
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This paper is concerned with the approximation of a function u u in a given subspace V m V_m of dimension m m from evaluations of the function at n n suitably chosen points. The aim is to construct an approximation of u u in V m V_m which... more
This paper is concerned with the approximation of a function u u in a given subspace V m V_m of dimension m m from evaluations of the function at n n suitably chosen points. The aim is to construct an approximation of u u in V m V_m which yields an error close to the best approximation error in V m V_m and using as few evaluations as possible. Classical least-squares regression, which defines a projection in V m V_m from n n random points, usually requires a large n n to guarantee a stable approximation and an error close to the best approximation error. This is a major drawback for applications where u u is expensive to evaluate. One remedy is to use a weighted least-squares projection using n n samples drawn from a properly selected distribution. In this paper, we introduce a boosted weighted least-squares method which allows to ensure almost surely the stability of the weighted least-squares projection with a sample size close to the interpolation regime n = m n=m . It consists i...
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In this paper we consider two nested computer codes, with the first code output as one of the second code inputs. A predictor of this nested code is obtained by coupling the Gaussian predictors of the two codes. This predictor is non... more
In this paper we consider two nested computer codes, with the first code output as one of the second code inputs. A predictor of this nested code is obtained by coupling the Gaussian predictors of the two codes. This predictor is non Gaussian and computing its statistical moments can be cumbersome. Sequential designs aiming at improving the accuracy of the nested predictor are proposed. One of the criteria allows to choose which code to launch by taking into account the computational costs of the two codes. Finally, two adaptations of the non Gaussian predictor are proposed in order to compute the prediction mean and variance rapidly or exactly.
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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... more
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 ...
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The objective of the work presented here is to perform the Bayesian calibration of parameters describing the mechanical properties of high-speed train suspensions for maintenance purposes. This calibration requires joint measurements of... more
The objective of the work presented here is to perform the Bayesian calibration of parameters describing the mechanical properties of high-speed train suspensions for maintenance purposes. This calibration requires joint measurements of the track geometric irregularities and of the train dynamic response. The calculation of the likelihood function relies on simulation, which makes it computationally expensive. Therefore, the likelihood function is represented by a Kriging metamodel. We present a calibration method that allows for taking into account the uncertainty introduced by the use of this metamodel.
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The work presented here deals with the development of a state health monitoring method for high-speed train suspensions using in-service measurements by embedded accelerometers. Mathematically, it consists in solving a statistical inverse... more
The work presented here deals with the development of a state health monitoring method for high-speed train suspensions using in-service measurements by embedded accelerometers. Mathematically, it consists in solving a statistical inverse problem. A rolling train is a dynamic system excited by the track geometric irregularities. They consist of small displacements of the rails relatively to the theoretical track design. The suspension elements play a key role for the ride safety and comfort. The train dynamic response being dependent on the suspensions mechanical characteristics, information about the suspensions state can be inferred from acceleration measurements in the train. This information would allow for providing a more efficient maintenance. Track geometry is subject to damage caused by railway traffic and to maintenance operations. Consequently, it evolves through time. Because of the high sensitivity of the train dynamic response to the track geometric irregularities, the...
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The identification of the most dangerous combinations of excitations that a non-linear mechanical system can be confronted to is not an easy task. Indeed, in such cases, the link between the maximal values of the inputs and of the outputs... more
The identification of the most dangerous combinations of excitations that a non-linear mechanical system can be confronted to is not an easy task. Indeed, in such cases, the link between the maximal values of the inputs and of the outputs is not direct, as the system can be more sensitive to a problematic succession of excitations of low amplitudes than to high amplitudes for each kind of excitations. This work presents therefore an innovative method to identify the combined shapes of excitations that are the most correlated to problematic responses of the studied mechanical system.
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This presentation deals with an innovative approach to analyze complex and nonlinear systems, which are excited by non-Gaussian and non-stationary random fields, by solving of a statistical inverse problem with experimental measurements.... more
This presentation deals with an innovative approach to analyze complex and nonlinear systems, which are excited by non-Gaussian and non-stationary random fields, by solving of a statistical inverse problem with experimental measurements. The methodology proposed is applied to the case of a railway system: a train is a nonlinear system with many degrees-of-freedom, which is excited by the track geometry and irregularities. These irregularities are of four types (horizontal and vertical alignment irregularities on the first hand, cant and gauge irregularities on the second hand), and vary from one track to another one, from one country to another one. As the track vehicle system is very non-linear, the characterization of the train dynamics cannot be achieved from the analysis of the train response on a single track portion but has to be made on the whole set of track conditions that the train can be confronted to during its lifecycle. In reply to these expectations, the track geometr...