Reliability Analysis of Single-Degree-of-Freedom Elastoplastic Systems. I: Critical Excitations

This paper investigates the application of importance sampling method to estimating the first passage probability of single-degree-of-freedom elastoplastic systems subjected to white noise excitations. The importance sampling density is constructed using a conventional choice as a weighted sum of Gaussian distributions centered among design points. It is well known that the design points, or equivalently the critical excitations in the function space, are difficult to obtain for nonlinear hysteretic systems. An efficient method has been developed recently for finding the critical excitations, on which this paper is based. Characteristics of the critical excitation for elastoplastic systems are explored and the efficiency of the resulting importance sampling strategy is critically assessed. It is found that some efficiency is gained by importance sampling over direct Monte Carlo method but to a lesser extent compared to its linear-elastic counterparts. The cause of this drop in efficiency will be investigated. The study calls for revisiting a basic assumption of importance sampling densities constructed using design points, where they are expected to generate samples lying frequently in the failure region, but in reality their capability should not be taken for granted. A companion paper investigates the approximation of the critical excitation that allows its simple determination.