Sequential Optimization and Reliability Assessment Method for Efficient Probabilistic Design

TLDR

Probabilistic design methods such as reliability‑based and robust design enable reliable decisions under uncertainty, yet their double‑loop optimization is computationally intensive. This study introduces the sequential optimization and reliability assessment (SORA) method to enhance the efficiency of probabilistic optimization. SORA employs a single‑loop framework that alternates deterministic optimization with post‑optimization reliability assessment, shifting low‑reliability constraints toward feasibility using information from the previous cycle. The method yields rapid design improvement across cycles and markedly reduces computational cost, as demonstrated on vehicle crashworthiness and speed‑reducer design cases.

Abstract

Probabilistic design, such as reliability-based design and robust design, offers tools for making reliable decisions with the consideration of uncertainty associated with design variables/parameters and simulation models. Since a probabilistic optimization often involves a double-loop procedure for the overall optimization and iterative probabilistic assessment, the computational demand is extremely high. In this paper, the sequential optimization and reliability assessment (SORA) is developed to improve the efficiency of probabilistic optimization. The SORA method employs a single-loop strategy with a serial of cycles of deterministic optimization and reliability assessment. In each cycle, optimization and reliability assessment are decoupled from each other; the reliability assessment is only conducted after the deterministic optimization to verify constraint feasibility under uncertainty. The key to the proposed method is to shift the boundaries of violated constraints (with low reliability) to the feasible direction based on the reliability information obtained in the previous cycle. The design is quickly improved from cycle to cycle and the computational efficiency is improved significantly. Two engineering applications, the reliability-based design for vehicle crashworthiness of side impact and the integrated reliability and robust design of a speed reducer, are presented to demonstrate the effectiveness of the SORA method.