Risk-based design optimization under hybrid uncertainties
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ORIGINAL ARTICLE
Risk‑based design optimization under hybrid uncertainties Wei Li1 · Congbo Li1,2 · Liang Gao3 · Mi Xiao3,4,5 Received: 11 September 2020 / Accepted: 6 October 2020 © Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract The rapidly changing requirements of engineering optimization problems require unprecedented levels of compatibility to integrate diverse uncertainty information to search optimum among design region. The sophisticated optimization methods tackling uncertainty involve reliability-based design optimization and robust design optimization. In this paper, a novel alternative approach called risk-based design optimization (RiDO) has been proposed to counterpoise design results and costs under hybrid uncertainties. In this approach, the conditional value at risk (CVaR) is adopted for quantification of the hybrid uncertainties. Then, a CVaR estimation method based on Monte Carlo simulation (MCS) scenario generation approach is derived to measure the risk levels of the objective and constraint functions. The RiDO under hybrid uncertainties is established and leveraged to determine the optimal scheme which satisfies the risk requirement. Three examples with different calculation complexity are provided to verify the developed approach. Keywords Risk analysis · Hybrid uncertainties · Conditional value at risk · Scenario generation approach
1 Introduction Uncertainty generally exists in various practical engineering problems, such as the processing error of the structure size, the actual measurement error, the difference of the material parameter attribute, and the assumption of the real physical system [1–4]. These uncertainties will cause fluctuations in the performance of the actual engineering system, and severe cases can even cause system failure [5–7]. Therefore, in the initial stage of design, it is necessary to consider the various uncertainties that the product may encounter, so as to
* Congbo Li [email protected] 1
College of Mechanical Engineering, Chongqing University, Chongqing 400044, China
2
State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400044, China
3
State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China
4
No. 55 Research Institute of China North Industries Group Corporation, Changchun 130012, China
5
Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan 430074, China
improve the performance level of the product throughout its life cycle. The design optimization under uncertainty method has been recognized as a promising orientation in the field of engineering design optimization [2, 8, 9]. Currently, uncertain design optimization methods are classified into two categories: reliability-based design optimization (RBDO) methods [10, 11] and robust design optimization (RDO) methods [12]. From the perspective of design methodology, RBDO is to ensure the safety of the system, an
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