Uncertainty Quantification with Applications to Engineering Problems

This paper describes the results of the application of Uncertainty Quantification methods to a railway vehicle dynamical example. Uncertainty Quantification methods take the probability distribution of the system parameters that stems from the parameter tolerances into account in the result. In this paper the methods are applied to a lowdimensional vehicle dynamical model composed by a two-axle bogie, which is connected to a car body by a lateral linear spring, a lateral damper and a torsional spring. Their characteristics are not deterministically defined, but they are defined by probability distributions. The model but with deterministically defined parameters was studied in [1], and this article will focus on the calculation of the critical speed of the model, when the distribution of the parameters is taken into account. Results of the application of the traditional Monte Carlo sampling method will be compared with the results of the application of advanced Uncertainty Quantification methods such as generalized Polynomial Chaos (gPC) [2]. We highlight the computational performance and fast convergence that result from the application of advanced Uncertainty Quantification methods. Generalized Polynomial Chaos will be presented in both the Galerkin and Collocation form with emphasis on the pros and cons of each of those approaches.