Benchmark study of numerical methods for reliability-based design optimization

• Published in: Structural and multidisciplinary optimization Vol. 41; no. 2; pp. 277 - 294
• Main Authors: Aoues, Younes, Chateauneuf, Alaa
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01-03-2010; Springer Nature B.V
• Subjects: Benchmark Case Studies; Benchmarks; Comparative studies; Computational Mathematics and Numerical Analysis; Design optimization; Engineering; Engineering Design; Finite element method; Mathematical analysis; Numerical methods; Reliability; Robustness (mathematics); Theoretical and Applied Mechanics; Performance measure; Numerical efficiency; Reliability; Reliability index; Optimization
• ISSN: 1615-147X; 1615-1488
• DOI: 10.1007/s00158-009-0412-2

The reliability-based design optimization (RBDO) seeks for the best compromise between cost and safety, by considering system uncertainties. In order to overcome computational difficulties, many formulations have been recently developed, leading to confusion about what method should be selected for a given application, due to the lack of full-scale comparative studies. In this context, the present paper aims at giving an overview of various RBDO approaches which are tested on a benchmark constituted of four examples using mathematical and finite element models, with different levels of difficulties. The study is focused on the three main approaches, namely the
two-level approach
, the
single loop approach
and the
decoupled approach
; for each category, two RBDO formulations are discussed, implemented and tested for numerical examples. The benchmark study allows us to give comprehensive overview of various approaches, to give clear ideas about their capabilities and limitations, and to draw useful conclusions regarding robustness and numerical performance.