基于阈值因子的结构可靠性解耦优化方法
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摘要
基于结构可靠性理论,引入阈值因子的概念,其物理意义为当前最优解满足可靠性约束需将阈值增减的幅度。随着迭代的进行,对于有效约束,阈值因子收敛于1,能够使得最可能失效点快速向满足可靠性约束的极限状态曲面靠拢,优化效率得以提升。解耦模型中,优化变量可为随机变量也可为非随机变量,当优化变量为随机变量时,采取优化变量拆解方式进行计算。数值算例表明,本文方法对优化变量拆解方式不敏感,对有效约束和非有效约束均能够获得满意的优化结果,且计算效率明显高于经典方法。
A concept of threshold factor is introduced based on the theory of structural reliability in this study.Its physical meaning is the magnitude of the threshold that must be adjusted so that the current optimal solution can satisfy the reliability constraints.The threshold factor approaches 1 for the active constraint with the progress of iterations,which can shift the most possible failure point to the limit state surface that satisfies the reliability constraints,and thus the optimization efficiency is improved.In the proposed method, the design variables can be random variables or non-random variables,and the decomposition method of design variables is used to solve the optimization model when design variables are random variables.Numerical results indicate that the proposed method is not sensitive to the decomposition method,satisfactory results can be obtained for both active and inactive constraints,and the computational efficiency of the proposed method is higher than that of the classical method.
A concept of threshold factor is introduced based on the theory of structural reliability in this study.Its physical meaning is the magnitude of the threshold that must be adjusted so that the current optimal solution can satisfy the reliability constraints.The threshold factor approaches 1 for the active constraint with the progress of iterations,which can shift the most possible failure point to the limit state surface that satisfies the reliability constraints,and thus the optimization efficiency is improved.In the proposed method, the design variables can be random variables or non-random variables,and the decomposition method of design variables is used to solve the optimization model when design variables are random variables.Numerical results indicate that the proposed method is not sensitive to the decomposition method,satisfactory results can be obtained for both active and inactive constraints,and the computational efficiency of the proposed method is higher than that of the classical method.
引文
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[3] Liao K W,Ha C.Application of reliability-based optimization to earth-moving machine:Hydraulic cylinder components design process[J].Structural and Multidisciplinary Optimization,2008,36(5):523-536.
[4] Du X P,Chen W.Sequential optimization and reliabi-lity assessment method for efficient probabilistic design[J].Journal of Mechanical Design,2004,126:225-233.
[5] Dubourg V,Sudret B,Bourinet J M.Reliability-based design optimization using kriging surrogates and subset simulation[J].Structural and Multidisciplinary Optimization,2011,44(5):673-690.
[6] Wu Y T,Shin Y,Sues R,et al.Safety-factor based approach for probability-based design optimization[A].19t h AIAA Applied Aerodynamics Conference[C].Washington,2001.
[7] 赵维涛,刘炜华,杨其蛟.基于可靠性映射函数的结构优化[J].计算力学学报,2016,33(3):405-411.(ZHAO Wei-tao,LIU Wei-hua,YANG Qi-jiao.Structural optimization based on reliability mapping functions[J].Chinese Journal of Computational Mecha-nics,2016,33(3):405-411.(in Chinese))
[8] 赵维涛,王建业,祁武超.结构可靠性优化的三阶段解耦方法[J].计算力学学报,2018,35(1):7-13.(ZHAO Wei-tao,WANG Jian-ye,QI Wu-chao.Three-stage decoupling method of reliability-based design optimization[J].Chinese Journal of Computational Mechanics,2018,35(1):7-13.(in Chinese))
[9] 乔红威,吕震宙,赵新攀.基于随机响应面法的可靠性灵敏度分析及可靠性优化设计[J].计算力学学报,2010,27(2):207-212,237.(QIAO Hong-wei,Lü Zhen-zhou,ZHAO Xin-pan.Reliability sensitivity analysis and reliability-based design optimization based on stochastic response surfaces method[J].Chinese Journal of Computational Mechanics,2010,27(2):207-212,237.(in Chinese))
[10] Chen Z Z,Qiu H B,Gao L,et al.An adaptive decoupling approach for reliability-based design optimization[J].Computers & Structures,2013,117(3):58-66.
[11] 朱海燕,袁修开.基于灵敏度的可靠性优化解耦方法[J].航空学报,2015,36(3):881-888.(ZHU Hai-yan,YUAN Xiu-kai.A decoupling method of reliability optimization based on sensitivity[J].Acta Aeronautica et Astronautica Sinica,2015,36(3):881-888.(in Chinese))
[12] 王红州,蔡恒欲,任桐欣,等.直升机旋翼动力学优化浅析[J].兵器装备工程学报,2018,39(1):25-28.(WANG Hong-zhou,CAI Heng-yu,REN Tong-xin,et al.Analysis of helicopter rotor dynamic optimization[J].Journal of Ordnance Equipment Engineering,2018,39(1):25-28.(in Chinese))
[13] Rahman S,Wei D.Design sensitivity and reliability-based structural optimization by univariate decompo -sition[J].Structural and Multidisciplinary Optimization,2008,35(3):245-261.
[14] Kang S C,Koh H M,Choo J F.An efficient response surface method using moving least squares approximation for structural reliability analysis[J].Probabilistic Engineering Mechanics,2010,25(4):365-371.
[15] Huang Z L,Jiang C,Zhou Y S,et al.An incremental shifting vector approach for reliability-based design optimization[J].Structural and Multidisciplinary Optimization,2016,53(3):523-543.