Karhunen-Loeve expansion revisited for vector-valued random fields: scaling, errors and optimal basis

International audienceDue to scaling effects, when dealing with vector-valued random fields, the classical Karhunen-Loève expansion, which is optimal with respect to the total mean square error, tends to favorize the components of the random field that have the highest signal energy. When these random fields are to be used in mechanical systems, this phenomenon can introduce undesired biases for the results. This paper presents therefore an adaptation of the Karhunen- Loève expansion that allows us to control these biases and to minimize them. This original decomposition is first analyzed from a theoretical point of view, and is then illustrated on a numerical example

Bayesian inference for high-speed train dynamics and speed optimization under uncertainty for energy saving

International audienceThe train is a complex nonlinear system, whose dynamic behavior is difficult to predict accurately because of its environmental sensitivity. Indeed, in spite of a relative fine modeling of the vehicle and its rolling environment (track and wind), the slightest uncontrolled disturbance can modify the dynamic comportment of the train. For this reason, uncertainty must be considered in the physical models. The industrial objective of this work is twofold. Firstly, the construction of a longitudinal dynamic model for high-speed trains able to take into account the fluctuations inherent to the system. Secondly, the optimization under uncertainty of the driver's command with the objective of reducing the energy consumed by the train, under a set of punctuality and physical nonlinear constraints (speed limitation, final speed, and final position constraints)

Modeling and identification of non Gaussian multivariate random fields and application to the excitation of trains by the track irregularities.

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 geometry of the French railway network has been continuously measured since 2007. Based on these measurements, which can be seen as experimental realizations of the track geometry random field, we develop a two steps methodology to analyze the influence of the track geometry variability on the train dynamics. In a first step, a stochastic modeling of the track geometry is proposed. Two decompositions are therefore used to identify the statistical characteristics of this random field. At first, using the Karhunen-Loève expansion, the considered random field is approximated by its truncated projection on a particularly well adapted orthogonal basis. Then, the random vector, which gathers the projection coefficients of the random field on this spatial basis, is characterized using a polynomial chaos expansion approach.The non-Gaussian non-stationary vector-valued random field is identified using the experimental measurements following the methodology presented in and consequently, constitutes a realistic track geometry stochastic modeling. Secondly, the track geometry variability is propagated to the train dynamics by solving a nonlinear stochastic dynamical problem. The results obtained are presented and analysed

High-speed train suspension health monitoring using computational dynamics and acceleration measurements

International audienceThis paper presents a novel method for the state health monitoring of high-speed train suspensions from in-line acceleration measurements by embedded sensors, for maintenance purposes. We propose a model-based method relying on a multibody simulation code. It performs the simultaneous identification of several suspension mechanical parameters. It is adapted to the introduction of uncertainties in the system and to the exploitation of numerous high-dimensional measurements. The novel method consists in a Bayesian calibration approach using a Gaussian process surro-gate model of the likelihood function. The method has been validated on numerical experiments. We demonstrate its ability to detect evolutions of the health state of suspension elements. It has then been tested on actual acceleration measurements to study the time evolution of the suspension parameters

Improved calibration of simulation models in railway dynamics: application of a parameter identification process to the multi-body model of a TGV train

International audienceThis paper aims at estimating the vehicle suspension parameters of a TGV (Train à Grande Vitesse) train from measurement data. A better knowledge of these parameters is required for virtual certification or condition monitoring applications. The estimation of the parameter values is performed by minimising a misfit function describing the distance between the measured and the simulated vehicle response. Due to the unsteady excitation from the real track irregularities and nonlinear effects in the vehicle behaviour, the misfit function is defined in the time domain using a least squares estimation. Then an optimisation algorithm is applied in order to find the best parameter values within the defined constraints. The complexity of the solution surface with many local minima requires the use of global optimisation methods. The results show that the model can be improved by this approach providing a response of the simulation model closer to the measurements

Statistical inverse identification for nonlinear train dynamics using a surrogate model in a Bayesian framework

International audienceThis paper presents a Bayesian calibration method for a simulation-based model with stochastic functional input and output. The originality of the method lies in an adaptation involving the representation of the likelihood function by a Gaussian process surrogate model, to cope with the high computational cost of the simulation, while avoiding the surrogate modeling of the functional output. The adaptation focuses on taking into account the uncertainty introduced by the use of a surrogate model when estimating the parameters posterior probability distribution by MCMC. To this end, trajectories of the random surrogate model of the likelihood function are drawn and injected in the MCMC algorithm. An application on a train suspension monitoring case is presented

Track irregularities stochastic modeling

International audienceA better understanding of the interaction between the dynamics of high speed trains and the track geometry is needed. As during its lifecycle, the train faces a great variability of track conditions, this dynamic behavior has indeed to be characterized on track portions sets that are representative of the whole railway network. This paper is thus devoted to the development of a stochastic modeling of the track geometry and its identification with experimental measurements. Based on a spatial and statistical decomposition, this model allows the spatial and statistical variability and dependency of the track geometry to be taken into account. Moreover, it allows the generation of realistic track geometries that are representative of a whole railway network. First, this paper describes a practical implementation of the proposed method and then applies this method to the modeling of a particular French high speed line, for which experimental data are available

Identification of nonlinear vibrations in railway vehicles including considerations of track defects

International audienceIn this work first results from an ongoing work on parameter identification for a TGV model are presented. The first step of the study is the modeling of the vehicle with a multi-body system code and the comparison of the simulation results with measurements in the time domain. The suspension characteristics are difficult to determine since they can differ from one train to another and are evolving during their life time. Besides, characterization tests on single suspension elements are expensive. The parameter identification based on in- line tests is therefore of particular interest. An adjoint state gradient method is proposed in order to minimize a misfit function describing the difference between measured and modeled response data. The objective of further work is to apply it on a simplified multi-body model of the bogie which is presented in the third part of the proceeding

Robust adaptation of the train speed for energy saving under punctaulity and security constraints

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