Importance Sampling for Time-Variant Reliability Analysis

Abstract

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 paper 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.

An Efficient Self-Tuning Proposal Distribution for Random Variate Generation With Complex Density Representation

“…So it is not necessary to pay attention to the CDF or the inverse CDF, but only require that the probability density of the target distribution can be calculated. For the importance sampling [18], [19], the sampled data are not be rejected during sampling, but each data is assigned a weight related to the target distribution, which also only requires that the probability density can be calculated. In terms of functions, the problems to be solved by rejection sampling and importance sampling are slightly different.…”

A Time-Variant Reliability Analysis Method Based on the Stochastic Process Discretization under Random and Interval Variables

“…Although many first-passage methods [10,12,13] aimed at accuracy and efficiency have been developed for two decades, it is generally hard to achieve the first-time out-crossing rate due to complicated mathematical characteristics. Different numerical simulation methods have been developed including Monte Carlo methods [14] and their improved versions, namely important sampling methods [15,16] and subset methods [17][18][19]. Although the numerical simulation method is accurate, it demands huge computational cost.…”