Structural Reliability Estimation Using Markov Chain Splitting and Girsanov’s Transformation Based Methods

Abstract

The work reported in this thesis is in the area of Monte Carlo simulation based methods for structural reliability estimation with special focus on strategies to reduce sampling variance of the estimator for the probability of failure. The thesis aims to improve upon two existing methods of reliability assessment, namely, the Markov chain Monte Carlo based subset simulation, and the Girsanov transformation based importance sampling methods for dynamical systems. Specifically, three issues have been addressed in this thesis: (a) strategies to quantify and reduce sampling variance in the subset simulation based methods by modifying a few intermediate steps in the existing subset simulation algorithm, (b) development of closed loop Girsanov controls in the study of structural dynamical systems governed by stochastic differential equations, and (c) combining the Markov chain particle splitting methods and the closed loop Girsanov transformation based method to assess reliability of dynamical systems with uncertain parameters. A wide range of illustrations covering static/dynamic/thermo-mechanical behaviour of linear/non-linear systems are presented. The results from variance reduction based estimation are compared with pertinent results from large-scale Monte Carlo simulation.