Reliability-Based Robust Design Optimization of Structures Considering Uncertainty in Design Variables

Shujuan Wang,Gordon J Savage,Qiuyang Li

doi:10.1155/2015/280940

Abstract

This paper investigates the structural design optimization to cover both the reliability and robustness under uncertainty in design variables. The main objective is to improve the efficiency of the optimization process. To address this problem, a hybrid reliability-based robust design optimization (RRDO) method is proposed. Prior to the design optimization, the Sobol sensitivity analysis is used for selecting key design variables and providing response variance as well, resulting in significantly reduced computational complexity. The single-loop algorithm is employed to guarantee the structural reliability, allowing fast optimization process. In the case of robust design, the weighting factor balances the response performance and variance with respect to the uncertainty in design variables. The main contribution of this paper is that the proposed method applies the RRDO strategy with the usage of global approximation and the Sobol sensitivity analysis, leading to the reduced computational cost. A structural example is given to illustrate the performance of the proposed method.

Highlights

The deterministic models do not account for parameter variation, which is poorly identified and provides an inaccurate picture of the problem in question
This paper investigates the structural design optimization to cover both the reliability and robustness under uncertainty in design variables
Nondeterministic methods can be classified into two approaches, namely, reliability-based design optimization (RBDO) and robust design optimization (RDO) [3]

Summary

Introduction

The deterministic models do not account for parameter variation, which is poorly identified and provides an inaccurate picture of the problem in question. Nondeterministic methods can be classified into two approaches, namely, reliability-based design optimization (RBDO) and robust design optimization (RDO) [3]. RBDO concentrates on finding an optimal design with low probability of failure, while RDO aims to reduce the variability of the system performance. Reliability methods reduce the sampling sets and simulation cost, they make the optimization structure more complex with double loops (the outer loop is the optimization loop and reliability analysis is performed in the inner loop), even triple loops (including robustness evaluation loop) as presented in [9]. The main purpose of this paper is to improve the optimization efficiency for both the reliability design and the robust design under uncertainty To address this problem, a hybrid RRDO method is proposed combining the single-loop RBDO algorithm and monoobjective RDO formulation to improve efficiency. The results are compared with those from other methods in the literature, leading to a reduced computational cost

Design Optimization under Uncertainty

Methodology Used in RRDO

Case Study

Objective

Findings

Conclusions