A new look at the response surface approach for reliability analysis

Abstract

Closed-form mechanical models to predict the behaviour of complex structural systems often are unavailable. Although reliability analysis of such systems can be carried out by Monte Carlo simulations, the large number of structural analyses required results in prohibitively high computational costs. By using polynomial approximations of actual limit states in the reliability analysis, the number of analyses required can be minimized. Such approximations are referred to as Response Surfaces. This paper briefly describes the response surface methodology and critically evaluates existing approaches for choosing the experimental points at which the structural analyses must be performed. Methods are investigated to incorporate information on probability distributions of random variables in selecting the experimental points and to ensure that the response surface fits the actual limit state in the region of maximum likelihood. A criterion for reduction in the number of experiments after the first iteration is suggested. Two numerical examples show the application of the approach.