Christine Funfschilling

IDENTIFICATION OF POLYNOMIAL CHAOS REPRESENTATIONS IN HIGH DIMENSION FROM A SET OF REALIZATIONS

This paper deals with the identification in high dimensions of a polynomial chaos expansion of random vectors from a set of realizations. Due to numerical and memory constraints, the usual polynomial chaos identification methods are based on a series of truncations that induce a numerical bias. This bias becomes very detrimental to the convergence analysis of polynomial chaos identification in high dimensions. This paper therefore proposes a new formulation of the usual polynomial chaos identification algorithms to avoid this numerical bias. After a review of the polynomial chaos identification method, the influence of the numerical bias on the identification accuracy is quantified. The new formulation is then described in detail and illustrated using two examples.

Karhunen-Loève expansion revisited for vector-valued random fields: Scaling, errors and optimal basis.

Due to scaling effects, when dealing with vector-valued random fields, the classical Karhunen-Loeve 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-Loeve 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.

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

The use of reduced basis has spread to many scientific fields for the past 50 years to condense the statistical properties of stochastic processes. Among these bases, the classical Karhunen--Loeve 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--Loeve basis associated with any estimator of the covariance that is not converged to still be optimal. This paper therefore presents an adaptation of the Karhunen--Loeve expansion in order to characterize optimal basis for projection of stochastic processes that are characterized only by a relatively small set of independent realizat...

Propagation of variability in railway dynamic simulations: application to virtual homologation

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.

Virtual testing environment tools for railway vehicle certification

This paper describes the work performed in Work Package 6 of the European project DynoTRAIN. Its task was to investigate the effects that uncertainties present within the track and running conditions have on the simulated behaviour of a railway vehicle. Methodologies and frameworks for using virtual simulation and statistical tools, in order to reduce both the cost and time required for the certification of new or modified railway vehicles, were proposed. In particular, the project developed a virtual test track (VTT) toolkit that is capable of both generating a series of test tracks based on measurements, which can be used in vehicle virtual testing using computer simulation models, and also automatically handling the output results. The toolkit is compliant with prEN14363: 2013. The VTT was used as an experimental tool to analyse cross-correlations between track data (input) and matching vehicle response (output) based on data recorded using a test train. This paper discusses the issues encountered in the process and suggests avenues for future developments and potential use in the context of European cross-acceptance. The VTT offers benefits to the areas of design development and regulatory certification.

Sensitivity of Train Stochastic Dynamics to Long-Term Evolution of Track Irregularities

ABSTRACT The 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 characterisation 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.

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

This 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.

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.

Stochastic representations and statistical inverse identification for uncertainty quantification in computational mechanics

The paper deals with the statistical inverse problem for the identification of a non-Gaussian tensor-valued random field in high stochastic dimension. Such a random field can represent the parameter of a boundary value problem (BVP). The available experimental data, which correspond to observations, can be partial and limited. A general methodology and some algorithms are presented including some adapted stochastic representations for the non-Gaussian tensor-valued random fields and some ensembles of prior algebraic stochastic models for such random fields and the corresponding generators. Three illustrations are presented: (i) the stochastic modeling and the identification of track irregularities for dynamics of high-speed trains, (ii) a stochastic continuum modeling of random interphases from atomistic simulations for a polymer nanocomposite, and (iii) a multiscale experimental identification of the stochastic model of a heterogeneous random medium at mesoscale for mechanical characterization of a human cortical bone.

DYNAMICAL BEHAVIOR OF TRAINS EXCITED BY A NON-GAUSSIAN VECTOR VALUED RANDOM FIELD

The dynamic interaction between the high speed train and the railway track and in particularly, on the contact loads between the wheels and the rail, are very hard to evaluate experimentally. The numerical simulation is bound to play a key role in this context, as it is able to compute these quantities of interest. Nevertheless, 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 lifecycle. In reply to this concern, this paper presents a method to analyze the influence of the track geometry variability on the train behavior, which could be very useful to evaluate and compare the agressiveness of different trains. This method is based on a stochastic modeling of the track geometry, for which parameters have been identified with experimental measurements.