基于粒子群优化算法的结构可靠度敏感性分析方法:相对收敛率（英文）

发布时间：2018-10-17 20:04

【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。
[Abstract]:Aim: to improve the efficiency of reliability index calculation by using particle swarm optimization (PSO) algorithm, and to study the statistical characteristics of particle swarm in different dimensions and the physical meaning of convergence rate in the process of PSO solution. The relationship between particle convergence rate and the sensitivity of random variables in the optimization process is studied. A new method for reliability sensitivity analysis is proposed. Innovation: 1. According to the different convergence rates of particles in different dimensions in the process of PSO optimization, the sensitivity of the random variables is represented by the convergence rate. 2. An optimization strategy group is established to avoid fluctuations in the process of particle swarm convergence, to ensure the continuous convergence of particles in different dimensions within the optimization strategy group, and to define the relative convergence rate to characterize the sensitivity of random variables. Methods: 1. According to the geometric meaning of Hasofer-Lind reliability index, the optimization model of reliability index is established, and the improved PSO is used to solve the reliability index and check point, and the feasible strategy method is adopted to deal with the constraint condition. 2. By theoretical derivation, the optimal evaluation function set of PSO iterative process is constructed. (18), sets of optimization strategies are established to ensure the continuous convergence of particles in different dimensions, and the relative convergence rate formula (19); 3), which represents the sensitivity of random variables, is proposed. The feasibility and effectiveness of the proposed method are verified by numerical simulation and comparison with the traditional sensitivity analysis results based on gradient. Conclusion: 1. The relative convergence rate can characterize the sensitivity of random variables. 2. The optimization strategy group avoids the fluctuation of relative convergence rate and ensures the continuous convergence of candidate particle variation coefficient curve in the solution space. 3. The smaller the coefficient of variation of the candidate solutions of random variables in the optimization strategy group, the more sensitive the random variables represented. 4. Reliability and sensitivity analysis based on PSO is more effective for complex problems.
【作者单位】： National
【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
【分类号】：TU311.2

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