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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。
OBJECTIVE: To improve the computational efficiency of reliable index by particle swarm optimization (PSO), to explore the physical meanings of statistical properties and convergence rate of particle swarm in different dimensions in solving PSO, and to study the relationship between particle convergence rate and random variable sensitivity in optimization process The relationship between the reliability of sensitivity analysis proposed a new method. Innovative points: 1. According to the different convergence rates of particles in different dimensions in the process of PSO optimization, the sensitivity of the convergence rate to characterize random variables is proposed. 2. The optimization strategy is set up to avoid the fluctuations in the process of particle swarm convergence and ensure the optimization The particles in the strategy group converge continuously on different dimensions, and the relative convergence rate is defined to characterize the sensitivity of random variables. According to the geometric meaning of Hasofer-Lind’s reliable indicator, an optimization model of reliable indicator is established. The improved PSO is used to solve the reliability index and check point and the feasible strategy method is used to deal with the constraint condition.2. Through the theoretical derivation, the PSO iteration The optimal evaluation function set (formula (18)) of the process is established, and an optimal strategy group is established to ensure that the particles continuously converge on different dimensions. The formula for calculating the relative convergence rate that characterizes the sensitivity of random variables (formula (19) The numerical simulation is compared with the traditional gradient-based sensitivity analysis to verify the feasibility and effectiveness of the proposed method. The relative convergence rate can characterize the sensitivity of random variables.2. The optimization strategy avoids the fluctuation of the relative convergence rate and ensures the continuous convergence of the CV curve of the candidate particles in the solution space. 3. The smaller the coefficient of variation of the candidate solution is, the more sensitive the random variables it represents. 4. The PSO-based reliability and sensitivity analysis is more effective for complex problems.