Efficient time-dependent reliability analysis for a railway bridge model

This paper proposes a framework for efficient time-dependent reliability analysis for a parametrized stochastic dynamic system, namely a train bridge load model with uncertain design properties. The Probability Density Evolution Method is utilized to explore the multidimensional random space, identify specific failure paths contributing to the failure region, and provide a full probabilistic output of the desired target quantity. The framework is tested on an uncertain railway bridge subjected to train transit (moving loads). The peak acceleration as a function of the train speed in a certain interval is analysed and utilised as performance criteria. The main sources of uncertainties are the damping and the bridge's moment of inertia. The full evolutionary Probability Density Function of the bridge's maximum deck acceleration is obtained, the reliability is assessed and a probability of failure estimated. The results show that in the considered speed intervals, the velocities contributing to the failure region are depending on the underlying sampling method. The Probability Density Evolution Method offers additional insight on the evolution of the critical peak accelerations while at the same time performing a reasonable amount of full model evaluations. The study concludes that further discussion is needed to determine the appropriate prediction of the train speeds that may or may not significantly contribute to the probability of failure in this bridge train model.