State health monitoring of high-speed train suspensions by bayesian calibration based on gaussian surrogate modeling

International audienceThe 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, their evolution must be taken into account through the use of train dynamics simulation.Because the system input (the track geometric irregularities) and output (the train dynamic response) are stochastic quantities, the inverse problem is solved in the Bayesian framework. The monitoring method thus consists in performing a Bayesian calibration of a simulation-based model using joint measurements of the system input and output. Its objective is to identify the posterior distribution of the model parameters describing the suspensions mechanical characteristics.Classical Bayesian calibration implies the computation of a likelihood function using a stochastic model and experimental data. This likelihood function is then used to estimate the posterior distribution of the model parameters. This step can be performed by Markov Chain Monte Carlo (MCMC) algorithms, which require numerous calls to the likelihood function. If the latter is expensive to compute, it may result in unaffordable computational costs, which is the case here. To address this issue, we propose to rely on surrogate models. They are usually used to provide an algebraic approximation of the system output. However, in the present case, the output is functional, which makes a surrogate model difficult to build. Instead, we propose a calibration method based on a Gaussian surrogate model of the scalar likelihood function. We present how such a random surrogate model can be used to estimate the model parameters distribution, how the new uncertainty it introduces can be taken into account to correctly evaluate the calibration accuracy, and the results of the method applied to our railway monitoring case