Importance Sampling for Time-Variant Reliability Analysis

Importance sampling methods are extensively used in time-independent reliability analysis. However, the kind of methods is barely studied in the field of time-variant reliability analysis. This article presents an importance sampling method for time-variant reliability analysis. It increases the probability of sampling failure trajectories of a time-variant performance function. To develop the method, the instantaneous performance function at a predefined time instant is regarded as a time-independent one. A time-independent importance sampling is first implemented on the instantaneous performance function in order to obtain instantaneous samples of stochastic processes and random variables. Then, conditional trajectories of stochastic processes are generated on the condition of instantaneous samples achieved above, which utilizes the correlationship among instantaneous uncertainties at different time instants associated with stochastic processes. Subsequently, trajectories of the time-variant performance function are obtained. Validation results show that comparing with crude Monte Carlo simulation, the proposed method remarkably increases the probability of sampling failure trajectories. The efficiency and accuracy of the proposed method are demonstrated.