Reliability optimization using probabilistic sufficiency factor and correction response surface

Abstract

Reliability-based design optimization for low failure probability often requires millions of function analyses. Response surface approximation of the response functions (analysis response surface(ARS)) is often used to reduce the cost of failure probability calculations. Failure probabilities obtained from numerical sampling schemes are noisy and unsuitable for gradient-based optimization. To overcome this, response surfaces have been fitted to the failure probability of the designs (design response surface (DRS)) as a function of the design variables and used in optimization. Two shortcomings of the approach are that (i) the ARS fitting is extremely expensive for a large number of variables, especially for the high accuracy required to obtain very accurate reliability estimates, and (ii) DRS introduces fitting errors which affect the tails of the distributions which are significant for low failure probabilities. An approach to obtaining high-accuracy reliability estimates using the probabilistic sufficiency factor and correction response surface is investigated in this article. The method is demonstrated using a thin-walled box beam structure designed for minimum weight with failure probability constraints. The design is subjected to buckling, strength, and displacement constraints. Two methods of correcting low-fidelity analyses are compared for accuracy and efficiency. It is shown that correction to the response function is more accurate than the correction fitted to the probabilistic sufficiency factor.