Advanced simulation methods for reliability analysis and updating of stochastic dynamic systems with applications to structural dynamics, seismic risk and loss assessment

Abstract

Given the fact that often low-probability extreme events can lead to disastrous consequences, the simulation and prior assessment of the civil engineering systems and critical infrastructure systems in such events are very important. To assess the system performance subjected to dynamic excitations realistically, stochastic system analyses considering all the important uncertainties including both aleatory and epistemic uncertainties, and modeling errors, which require a huge number of random variables, need to be performed. In this thesis, the focus is on the development of new stochastic simulation algorithms for Bayesian model updating, robust reliability (or its compliment probability) updating, extreme-event simulation and probability computation, conditional failure sample simulation, and their applications to the evaluation of reliability, seismic risk and loss assessment of civil engineering structures. A new stochastic simulation based Bayesian model updating technique is developed to update a stochastic dynamic system model based on measured system response data. The technique is extended and a new stochastic simulation approach is proposed using system response data for computing the updated robust reliability of a stochastic dynamic system when it is subjected to uncertain future stochastic excitations. Next, a new fully probabilistic algorithm is developed for a comprehensive seismic risk and loss analysis and investigation. The newly developed computational method to update the robust stochastic dynamic system reliability based on system response data is integrated with the newly developed fully probabilistic loss estimation formulation to evaluate the updated tail probability distribution of risk and loss. In addition, a new stochastic simulation approach is proposed to evaluate the failure probabilities with multiple performance objectives as a function of various combinations of thresholds with each threshold corresponding to one performance objective. The proposed approaches are robust to the number of random variables involved and are much more efficient than standard Monte Carlo Simulation. Although the illustrative examples mostly involve structural dynamic systems, the proposed methods developed are general enough to be applied or extended to handle problems involving other types of engineering dynamic systems and critical infrastructure systems. Theorems and mathematical proofs are also developed in this work for proving the correctness and evaluating the accuracy and computational efficiency of all the algorithms developed.