Concepedia

TLDR

Reliability‑Based Design Optimization (RBDO) seeks optimal designs under uncertainty, but the conventional double‑loop algorithm is computationally expensive due to nested optimization loops. This study proposes a single‑loop RBDO algorithm applicable to both normal and non‑normal random variables. The method collapses the nested loops by enforcing the KKT optimality conditions of the reliability sub‑problems as deterministic equality constraints, thereby transforming the probabilistic optimization into a single deterministic optimization without repeated MPP evaluations. Numerical tests, including an automotive side‑impact case, confirm that the single‑loop algorithm matches the double‑loop accuracy while achieving superior efficiency comparable to deterministic optimization.

Abstract

Reliability-Based Design Optimization (RBDO) can provide optimum designs in the presence of uncertainty. It can therefore, be a powerful tool for design under uncertainty. The traditional, double-loop RBDO algorithm requires nested optimization loops, where the design optimization (outer) loop, repeatedly calls a series of reliability (inner) loops. Due to the nested optimization loops, the computational effort can be prohibitive for practical problems. A single-loop RBDO algorithm is proposed in this paper for both normal and non-normal random variables. Its accuracy is the same with the double-loop approach and its efficiency is almost equivalent to deterministic optimization. It collapses the nested optimization loops into an equivalent single-loop optimization process by imposing the Karush-Kuhn-Tucker optimality conditions of the reliability loops as equivalent deterministic equality constraints of the design optimization loop. It therefore, converts the probabilistic optimization problem into an equivalent deterministic optimization problem, eliminating the need for calculating the Most Probable Point (MPP) in repeated reliability assessments. Several numerical applications including an automotive vehicle side impact example, demonstrate the accuracy and superior efficiency of the proposed single-loop RBDO algorithm.