基于粒子群優(yōu)化算法的結(jié)構(gòu)可靠度敏感性分析方法:相對收斂率（英文）
發(fā)布時間：2018-10-17 20:04
【摘要】：目的:采用粒子群優(yōu)化算法(PSO)提高可靠指標(biāo)計算效率,探討PSO求解過程中粒子群在不同維上統(tǒng)計特性及其收斂速率表征的物理含義,研究優(yōu)化過程中粒子收斂速率與隨機(jī)變量敏感性的關(guān)系,提出可靠度敏感性分析新方法。創(chuàng)新點:1.根據(jù)PSO尋優(yōu)過程中粒子在不同維上收斂速率不同,提出采用收斂速率表征隨機(jī)變量的敏感性;2.建立最優(yōu)化策略組避免粒子群收斂過程中產(chǎn)生波動,保證最優(yōu)化策略組內(nèi)粒子在不同維上連續(xù)收斂,定義相對收斂率表征隨機(jī)變量敏感性。方法:1.根據(jù)Hasofer-Lind可靠指標(biāo)的幾何意義,建立可靠指標(biāo)的優(yōu)化模型,提出采用改進(jìn)的PSO求解可靠指標(biāo)與驗算點,采用可行策略方法處理約束條件;2.通過理論推導(dǎo),構(gòu)造PSO迭代過程的最優(yōu)評價函數(shù)集(公式(18)),建立最優(yōu)化策略組保證粒子在不同維上連續(xù)收斂,提出表征隨機(jī)變量敏感性的相對收斂率計算公式(公式(19));3.通過數(shù)值模擬并與傳統(tǒng)基于梯度的敏感性分析計算結(jié)果比較,驗證本文所提方法的可行性和有效性。結(jié)論:1.相對收斂率可以表征隨機(jī)變量的敏感性;2.最優(yōu)化策略組避免相對收斂率的波動,保證候選粒子變異系數(shù)曲線在解空間內(nèi)連續(xù)收斂;3.最優(yōu)化策略組內(nèi)隨機(jī)變量候選解的變異系數(shù)越小則其表征的隨機(jī)變量越敏感;4.基于PSO的可靠度及敏感性分析對復(fù)雜問題更有效。
[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.
【作者單位】： 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
【分類號】：TU311.2
本文編號：2277806
[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.
【作者單位】： 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
【分類號】：TU311.2
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