A two-step framework for stochastic dynamic analysis of uncertain vehicle-bridge system subjected to random track irregularity

Abstract This paper presents a two-step probabilistic framework for stochastic dynamic analysis of the coupled vehicle-bridge system (VBS) involving both uncertain parameters and random track irregularity. Firstly, an explicit time-domain method is extended to evaluate the conditional response statistics of the VBS subjected to random irregularity at specific parameter points, and an efficient spectral representation-based formulation is proposed to calculate the excitation correlation matrix required in the analysis. Then, the total response statistics are further evaluated by Gaussian integration of the conditional ones based on the total probability theorem, and an efficient dimension-adaptive algorithm is proposed to collocate the required quadrature points. In the numerical examples, the proposed method is used to study a typical VBS model with both deterministic or random parameters; several other existing methods are employed to illustrate the advantages of the proposed method. The results indicate that the proposed framework is an accurate and efficient method for stochastic dynamic analysis of the vehicle-bridge interaction problem.