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.

本文提出了一个两步概率框架，用于耦合车桥系统 (VBS) 的随机动态分析，包括不确定参数和随机轨道不规则性。首先，将显式时域方法扩展到评估在特定参数点随机不规则的 VBS 的条件响应统计，并提出了一种有效的基于频谱表示的公式来计算分析所需的激励相关矩阵。然后，通过基于总概率定理的条件统计量的高斯积分进一步评估总响应统计量，并提出了一种有效的维数自适应算法来配置所需的正交点。在数值例子中，所提出的方法用于研究具有确定性或随机参数的典型VBS模型；使用其他几种现有方法来说明所提出方法的优点。结果表明，所提出的框架是一种准确有效的车桥相互作用问题随机动力分析方法。