Development of Importance Sampling Method Using Adapted Process with Application to Seismic Reliability Analysis of Nonlinear-hysteretic Structures

The proper assessment of the performance of structures is an important component in a modern performance-based design framework. In the seismic analysis of structures subjected to uncertain earthquake excitations, the reliability analysis of nonlinear-hysteretic structures is an important but challenging problem. The 'first passage probability', i.e., the probability that some response quantities of interest (e.g., interstory drifts) exceed specified threshold levels, is often of concern. Direct Monte Carlo simulation is a versatile method for estimation, but it is not efficient when the failure probability is small, which is often encountered in engineering applications. Importance sampling is a popular variance reduction technique where a change of distribution is applied in order to achieve a higher failure rate in the samples and hence variance reduction. Its success hinges on the proper choice of a user-defined 'importance sampling distribution'. A popular choice makes use of 'design point excitations' that are local most probable points within the failure region in the stochastic load space. Design point excitations participate in the excitation to create large response, leading to a larger failure rate in the samples. Their use has lead to tremendous variance reduction for linear systems. For nonlinear-hysteretic systems, however, recent research shows that the gain in efficiency is much less than their linear counterpart, essentially because plastic excursions cause random phase shifts in the response that de-synchronize it from the design point excitations, undermining their effectiveness in creating large response.This project aims at developing a new importance sampling method for estimating the first passage probability of nonlinear-hysteretic systems subjected to stochastic earthquake excitations. Instead of using fixed design point excitations, the proposed importance sampling distribution is constructed using an 'adapted process' whose future action can be updated based on information up to the present. The updating mechanism improves synchronization and hence effectiveness of the importance sampling distribution for variance reduction. The idea of using adapted process for importance sampling is generally applicable to causal dynamical systems. Theoretical and computational issues related to the proposed importance sampling method shall be investigated. Strategies for designing the adapted process are proposed using energy concepts and control theory. The proposed schemes shall be applied to reliability analysis of non-linear hysteretic structures and their variance reduction capability shall be appraised critically.