Response surface single loop reliability-based design optimization with higher-order reliability assessment

TL;DR

This paper introduces a higher-order response surface single-loop method for reliability-based design optimization, improving accuracy over traditional FORM-based approaches, especially for nonlinear problems, and demonstrating its effectiveness on vehicle crashworthiness design.

Contribution

The paper proposes a novel RSSL method that bypasses the MPP concept, offering higher accuracy and efficiency for RBDO with quadratic response surface models, applicable to industrial problems.

Findings

RSSL method achieves higher accuracy than FORM-based methods.

The method effectively handles problems with varying standard deviations.

Demonstrated success on vehicle crashworthiness design problem.

Abstract

Reliability-based design optimization (RBDO) aims at determination of the optimal design in the presence of uncertainty. The available Single-Loop approaches for RBDO are based on the First-Order Reliability Method (FORM) for the computation of the probability of failure, along with different approximations in order to avoid the expensive inner loop aiming at finding the Most Probable Point (MPP). However, the use of FORM in RBDO may not lead to sufficient accuracy depending on the degree of nonlinearity of the limit-state function. This is demonstrated for an extensively studied reliability-based design for vehicle crashworthiness problem solved in this paper, where all RBDO methods based on FORM strongly violates the probabilistic constraints. The Response Surface Single Loop (RSSL) method for RBDO is proposed based on the higher order probability computation for quadratic models previously presented by the authors. The RSSL-method bypasses the concept of an MPP and has high accuracy and efficiency. The method can solve problems with both constant and varying standard deviation of design variables and is particularly well suited for typical industrial applications where general quadratic response surface models can be used. If the quadratic response surface models of the deterministic constraints are valid in the whole region of interest, the method becomes a true single loop method with accuracy higher than traditional SORM. In other cases, quadratic response surface models are fitted to the deterministic constraints around the deterministic solution and the RBDO problem is solved using the proposed single loop method.