Enriched single-loop approach for reliability-based design optimization of complex nonlinear problems
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ORIGINAL ARTICLE
Enriched single‑loop approach for reliability‑based design optimization of complex nonlinear problems Meide Yang1,2 · Dequan Zhang1 · Xu Han1,2 Received: 13 July 2020 / Accepted: 6 October 2020 © Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract Single-loop approach (SLA) is an efficient reliability-based design optimization (RBDO) method, where the current most probable point (MPP) is located through the gradient information of previous MPP. However, the MPP obtained by SLA may not be accurate for complex nonlinear RBDO problems, which probably causes SLA to be inefficient, converge to the wrong optimal solution or even difficulty in convergence. In this study, an enriched single-loop approach based on enhanced advanced mean value (ESLA-EAMV) is proposed to improve convergence performance of the original SLA for complex nonlinear RBDO problems. First, an enhanced advanced mean value (EAMV) method is developed to find the MPP, where the negative gradient vector of the previous MPP in AMV is replaced by a vector with adaptive step size in EAMV. Then, the proposed EAMV method is integrated into the original SLA to improve the convergence ability of the original SLA. Finally, seven benchmark nonlinear problems are presented to verify the accuracy, efficiency and robustness of the proposed ESLA-MAMV compared with other existing RBDO methods. Comparison results show that the proposed ESLA-MAMV can improve the convergence performance of the original SLA. Keywords Reliability-based design optimization · Enhanced advanced mean value method · Enriched single-loop approach · Adaptive step-size update strategy
1 Introduction Uncertainty is widespread in the real physical world [1, 2], e.g., link dimension, joint rotation angle and link torsion angle in industrial robots are uncertain quantities due to machining and assembly errors [3–5]. If the uncertainty is neglected, low reliability or even disastrous failure may occur. Therefore, it is essential to take uncertainty into account in engineering design. Due to the consideration of the effect of uncertainty on engineering structures, * Dequan Zhang [email protected] * Xu Han [email protected] 1
State Key Laboratory of Reliability and Intelligence of Electrical Equipment, School of Mechanical Engineering, Hebei University of Technology, Tianjin 300401, China
State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China
2
reliability-based design optimization (RBDO) has been extensively studied, whose mathematical model is typically described as [6]
find 𝐝, 𝛍𝐗 ( ) min f 𝐝, 𝛍𝐗 , 𝛍𝐏 ( ) s.t. Prob gi (𝐝, 𝐗, 𝐏) ≤ 0 ≥ Ri , 𝐝L ≤ 𝐝 ≤ 𝐝U ,
i = 1, 2, … , m
(1)
𝛍L𝐗 ≤ 𝛍𝐗 ≤ 𝛍U , 𝐗
where f refers to objective function; 𝐝 expresses the deterministic design vector; 𝐗 and 𝐏 are the vectors of random design variables and random parameter, respectively; 𝛍𝐗 represents the mean vector of 𝐗 and 𝛍𝐏 is the mean vector of 𝐏 ; Prob(⋅) means t
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