摘要
目的:采用粒子群优化算法(PSO)提高可靠指标计算效率,探讨PSO求解过程中粒子群在不同维上统计特性及其收敛速率表征的物理含义,研究优化过程中粒子收敛速率与随机变量敏感性的关系,提出可靠度敏感性分析新方法。创新点:1.根据PSO寻优过程中粒子在不同维上收敛速率不同,提出采用收敛速率表征随机变量的敏感性;2.建立最优化策略组避免粒子群收敛过程中产生波动,保证最优化策略组内粒子在不同维上连续收敛,定义相对收敛率表征随机变量敏感性。方法:1.根据Hasofer-Lind可靠指标的几何意义,建立可靠指标的优化模型,提出采用改进的PSO求解可靠指标与验算点,采用可行策略方法处理约束条件;2.通过理论推导,构造PSO迭代过程的最优评价函数集(公式(18)),建立最优化策略组保证粒子在不同维上连续收敛,提出表征随机变量敏感性的相对收敛率计算公式(公式(19));3.通过数值模拟并与传统基于梯度的敏感性分析计算结果比较,验证本文所提方法的可行性和有效性。结论:1.相对收敛率可以表征随机变量的敏感性;2.最优化策略组避免相对收敛率的波动,保证候选粒子变异系数曲线在解空间内连续收敛;3.最优化策略组内随机变量候选解的变异系数越小则其表征的随机变量越敏感;4.基于PSO的可靠度及敏感性分析对复杂问题更有效。
This paper proposes a novel reliability-based sensitivity analysis（SA） method, namely relative convergence rate of random variables using particles swarm optimization（PSO）. The convergence rate of a random variable during the optimum evolution process reflects the sensitivity of the objective function with respect to the random variables. An optimized group strategy is proposed to consider the fluctuation of the convergence rate of a variable during the optimum process. The coefficient of variation（COV） for candidate particles and the relative convergence rate of a random variable can be calculated using the particles in the optimized group. The smaller the COV for candidate particles, i.e., the larger the relative convergence rate, the more sensitive the objective function with respect to the variable. Three examples are available for the application of this method, and the results indicate that the sensitivity of the reliability index with respect to the variable obtained using the PSO technique and gradient of limit-state function is the same in the quantitative sense.
基金
Project supported by the National Natural Science Foundation of China(No.51478039)
the Fundamental Research Funds for the Central Universities of China(Nos.FRF-TP-14-063A2 and FRF-TP-15-001C1)
the Beijing Nova Program(No.Z151100000315053)
the 111 Project(No.B12012)
the Ningbo Science and Technology Project(No.2015C110020),China
关键词
敏感性分析
优化
结构可靠度
随机变量
Sensitivity analysis（SA）
Optimization
Structural reliability
Random variable
