An effective approach for high-dimensional reliability analysis of train-bridge vibration systems via the fractional moment

The safety and stability performance of train-bridge vibration (TBV) systems become seriously concerned with an increasing operation speed of rails. In this regard, many assessment indicators in the railway specification are defined based on the wheel-rail force and vehicle acceleration. However, mathematical modeling of this dynamic system needs the probability theory to account for uncertain damping/stiffness model parameters and stochastic track irregularities, which result in thousands of input random variables for digital simulations of this stochastic TBV model. This extremely high-dimensional (EHD) input uncertainty poses a major challenge for many well-known structural reliability algorithms. To this end, this paper proposes to use the principle of maximum entropy (MaxEnt) and the sample-based fractional moment (ME-SFM) for structural reliability analysis of this TBV system. To implement, the reliability performance functions are first defined via the safety and stability criteria in railway specifications, whereas a small number of low-discrepancy samples are used to estimate the fractional moments of a vehicle response quality, e.g. the maximal wheel-rail force and the Sperling ride comfort index that are considered in numerical examples. This sampling nature can ideally overcome the curse of dimensionality of an ordinary structural reliability algorithm. The fractional exponents and Lagrange multipliers used to recover the response distribution are fully optimized through the MaxEnt procedure. Numerical results are provided to demonstrate potential applications of this ME-SFM approach for structural reliability analysis of stochastic train-bridge vibration systems.