摘要
为解答实际工程中变量相关情况下的高维小概率失效问题,将子集模拟与重要抽样法结合起来,根据重要抽样的概率密度函数获取的相关变量的样本点来构造中间失效事件,从而将小失效概率问题转化为一条由一系列易于求解的较大条件失效概率的连乘积组成的马尔可夫链(Markov chain,MC),并直接抽取相关样本点来高效模拟结构的可靠性灵敏度。由此创建失效概率对各变量均值、方差(包含相关系数)的可靠性灵敏度最低以及体积最小的多目标优化问题,并提出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,提出利用误差的思想与方法;为加速遗传算法(Genetic algorithm,GA)与粒子群优化(Particle swarm optimization,PSO)算法的收敛,提出克隆与进化同时并举的精英策略及相似交配的思想,并用此GA得到的个体与PSO算法杂交,以进一步提高其收敛性;最后,以盾构三级行星减速器的三个行星架为例,运用上述算法对所建数学模型进行求解,结果表明:①所提直接抽取相关样本的MC能很好地模拟出相关变量的可靠性及灵敏度,免除了变量独立化过程反复转换的繁琐;②提出的杂交GA-PSO协同算法较GA与PSO算法有更快的收敛速度,当相关系数为0.7时,可使该行星架的总体积减小7.06%;③证实将可靠性灵敏度作为目标函数时所提利用误差的思想与方法的可行性与正确性。
To answer the small failure probabilities with high-dimensional correlated variables in the practical engineering, the subset simulation（SS） is combined together with importance sampling（IS） method. The samples from the probability density functions（PDF） of the importance sampling are used to construct the intermediate failure events, by which the small failure probabilities are turned into a Markov chain, which is a product of a series large failure probabilities or conditional failure probabilities（CFP） which are easily answered, on which the structural reliability sensitivity（RS） can be efficiently simulated by directly obtaining the correlated samples. Multi-objectives optimization models are established on minimizing the RS of failure probability with respect to the variable mean, variance（including the correlated coefficient between them） respectively and volume, and the collaborative optimization idea for multi-objectives is put forward, in the meantime, in view of 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, the idea and method that utilize the errors are proposed. To accelerate the convergence of genetic algorithm（GA） and particle swarm optimization（PSO）, the elite strategy that have elitist cloned and to take part in evolution simultaneously and the idea of similar mating are put forward. And the individuals from the modified GA are hybridized with those individuals from PSO to further improve their convergence. Finally, the 3 planet carriers of three-stage planetary reducers in shield machine are as illustrative examples to answer the mathematical models according to the algorithm above, the results show that ① the SS of the IS with correlated variables can highly simulate failure probability and its sensitivity. ②the convergent velocity of the collaborative algorithm of hybrid GA-PSO is superior to that of the GA and PSO, it can reduce the total v
出处
《机械工程学报》
EI
CAS
CSCD
北大核心
2012年第15期113-125,共13页
Journal of Mechanical Engineering
基金
国家自然科学基金(51175525)
机械传动国家重点实验室自主研究基金(0301002109137)
重庆市科技攻关计划(CSTC
2007AC3015)资助项目
关键词
马尔可夫链
杂交遗传粒子群算法
相关变量
协同优化
可靠性灵敏度
子集模拟
重要抽样
Hybrid Markov chain ,Hybrid genetic particle swarm optimization, Correlated variables ,Collaborative optimization, Reliability sensitivity ,Subset simulation ,Importance sampling
