Subset Simulation and its Application to Seismic Risk Based on Dynamic Analysis

TLDR

The Subset Simulation approach reformulates rare seismic failure probabilities as products of larger conditional probabilities, converting a rare-event problem into several more frequent conditional simulations. The paper presents a method to efficiently compute small failure probabilities in seismic risk problems involving dynamic analysis. The method employs Markov chain Monte Carlo simulation within an enhanced Subset Simulation framework that incorporates prior reliability information, and is applied to linear and nonlinear hysteretic structures under uncertain earthquake ground motions to generate conditional samples and analyze probable failure scenarios. The approach proves effective for seismic performance assessment of structures under modern performance‑based design, providing detailed probabilistic failure scenarios.

Abstract

A method is presented for efficiently computing small failure probabilities encountered in seismic risk problems involving dynamic analysis. It is based on a procedure recently developed by the writers called Subset Simulation in which the central idea is that a small failure probability can be expressed as a product of larger conditional failure probabilities, thereby turning the problem of simulating a rare failure event into several problems that involve the conditional simulation of more frequent events. Markov chain Monte Carlo simulation is used to efficiently generate the conditional samples, which is otherwise a nontrivial task. The original version of Subset Simulation is improved by allowing greater flexibility for incorporating prior information about the reliability problem so as to increase the efficiency of the method. The method is an effective simulation procedure for seismic performance assessment of structures in the context of modern performance-based design. This application is illustrated by considering the failure of linear and nonlinear hysteretic structures subjected to uncertain earthquake ground motions. Failure analysis is also carried out using the Markov chain samples generated during Subset Simulation to yield information about the probable scenarios that may occur when the structure fails.