非正态变量情况下基于杂交SAPSO-SFLA的多目标稳健协同优化  

MULTI-OBJECTIVES ROBUST COLLABORATIVE OPTIMIZATION BASED ON HYBRID SAPSO-SFLA FOR STRUCTURE WITH NON-NORMAL VARIABLES

作　　者：张干清[1] 龚宪生[1,2] 

机构地区：[1]重庆大学机械传动国家重点实验室,重庆400044 [2]重庆大学机械工程学院,重庆400044

出　　处：《工程力学》2013年第5期24-35,共12页Engineering Mechanics

基　　金：国家自然科学基金项目(51175525);重庆市科技攻关计划项目(2007AC3015);重庆大学机械传动国家重点实验室自主研究基金项目(0301002109137)

摘　　要：为解决非正态变量空间中复杂多变的隐式非线性功能函数的可靠性及灵敏度的问题,融合鞍点估计与线抽样法的优点,结合二分法的特点与黄金分割法的求解效率,提出基于黄金分割二分法的鞍点线抽样法,即可沿重要线抽样方向利用黄金分割点的二分法快速找到各样本点对应于功能函数的零点,将结构失效概率转化为一系列线性功能函数失效概率的平均值,求出相关变量的可靠性灵敏度,从而导出失效概率对变量均值与方差的可靠性灵敏度及结构轻量化的多目标优化问题,并阐明了多目标协同优化的思想。同时,针对可靠性灵敏度作为目标函数因误差导致多目标协同优化难以收敛的问题,提出了利用误差的思想与方法;为提高算法的收敛性,对粒子群优化(Particle Swarm Optimization,PSO)算法与混合蛙跳算法(Shuffled Frog-Leaping Algorithm,SFLA)进行改进以后,再将两者进行杂交,提出杂交自适应粒子群优化-混合蛙跳算法(Self-Adaptive PSO-SFLA,SAPSO-SFLA),并用来求解上述多目标优化问题。算例表明:1)基于黄金分割二分法的鞍点线抽样法在求解复杂非线性功能函数的可靠性及灵敏度时精度高,速度快;2)与粒子群优化和混合蛙跳算法相比,所提杂交SAPSO-SFLA不仅具有更快的收敛速度,其鲁棒性还能使盾构行星减速器箱体体积减小8.42%。To solve the reliability and its sensitivity for structural system whose implicit nonlinear performance function （PF） are complicated, changeable and of non-normal variables, the advantages of the saddlepoint approximation （SA） and line sampling （LS） are merged while the merits of dichotomy and the solution efficiency of the golden section method are combined to propose the saddlepoint approximation-line sampling method （SA-LS） based on the dichotomy of the golden section point. It is quick to find the zeropoint in PF corresponding to each sample along the important line sampling direction by the dichotomy above so that the structural failure probability can be transformed into the mean of a series linear PF failure probability, by which reliability sensitivity can be solved, thus the multi-objectives are inferred about the reliability sensitivity of failure probability with respect to the variables mean and variance and optimal economic indicator, such as volume. The collaborative optimization idea for multi-objectives is proposed to overcome the problem that it is difficult to converge for multi-objectives to be collaboratively optimized because of the errors when the RS is used as an objective function. To increase the convergence of the algorithm, the particle swarm optimization （PSO） algorithm and shuffled frog-leaping algorithm （SFLA） are hybridized after they are modified, and then the hybrid algorithm is applied to answer the foregoing multi-objectives. Examples show that： 1） the SPLSM based on the dichotomy of the golden section point is of high precision and fast velocity; 2） the convergence velocity of the proposed hybrid SAPSO-SFLA is superior to that of the modified PSO and SFLA, and its robustness can reduce the volume of the planet reducer gearbox in shield turning machine by 8.42%.

关 键 词：粒子群优化算法 混合蛙跳算法 鞍点估计 线抽样法 二分法 可靠性灵敏度 协同优化 

分 类 号：O302[理学—力学]