Importance Sampling in the Evaluation and Optimization of Buffered Failure Probability

Abstract

Engineering design is a process in which a system’s parameters are selected such that the system meets certain criteria. These criteria vary in nature and may involve such matters as structural strength, implementation cost, architectural considerations, etc. When random variables are part of a system model, an added criterion is usually the failure probability. In this paper, we examine the buffered failure probability as an attractive alternative to the failure probability in design optimization problems. The buffered failure probability is more conservative and possesses properties that make it more convenient to compute and optimize. Since a failure event usually occurs with small probability in structural systems, Monte-Carlo sampling methods require large sample sizes for high accuracy estimates of failure and buffered failure probabilities. We examine importance sampling techniques for efficient evaluation of buffered failure probabilities, and illustrate their use in structural design of two multi-story frames subject to ground motion. We formulate a problem of design optimization as a cost minimization problem subject to buffered failure probability constraints. The problem is solved using importance sampling and a nonlinear optimization algorithm.