Reliability-Based Design Using Saddlepoint Approximation

Abstract

Reliability-based design optimization is much more computationally expensive than deterministic design optimization. To alleviate the computational demand, the First Order Reliability Method (FORM) is usually used in reliability-based design. Since FORM requires a nonlinear transformation from non-normal random variables to normal random variables, the nonlinearity of a constraint function may increase. As a result, the transformation may lead to a large error in reliability calculation. In order to improve accuracy, a new reliability-based design method with Saddlepoint Approximation is proposed in this work. The strategy of sequential optimization and reliability assessment is employed where the reliability analysis is decoupled from deterministic optimization. The accurate First Order Saddlepoint method is used for reliability analysis in the original random space without any transformation, and the chance of increasing nonlinearity of a constraint function is therefore eliminated. The overall reliability-based design is conducted in a sequence of cycles of deterministic optimization and reliability analysis. In each cycle, the percentile value of the constraint function corresponding to the required reliability is calculated with the Saddlepoint Approximation at the optimal point of the deterministic optimization. Then the reliability analysis results are used to formulate a new deterministic optimization model for the next cycle. The solution process converges within a few cycles. The demonstrative examples show that the proposed method is more accurate and efficient than the reliability-based design with FORM.