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CLC number: TU311.2

On-line Access: 2016-12-06

Received: 2015-09-10

Revision Accepted: 2016-03-06

Crosschecked: 2016-11-11

Cited: 0

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Citations:  Bibtex RefMan EndNote GB/T7714

 ORCID:

Cheng-ming Lan

http://orcid.org/0000-0001-8317-8303

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Journal of Zhejiang University SCIENCE A 2016 Vol.17 No.12 P.961-973

http://doi.org/10.1631/jzus.A1500255


A structural reliability-based sensitivity analysis method using particles swarm optimization: relative convergence rate


Author(s):  Cheng-ming Lan, Hui Li, Jun-Yi Peng, Dong-Bai Sun

Affiliation(s):  for Materials Service Safety, & Technology , 100083,; more

Corresponding email(s):   lanchengming@ustb.edu.cn

Key Words:  Sensitivity analysis (SA), Optimization, Structural reliability, Random variable


Cheng-ming Lan , Hui Li, Jun-Yi Peng , Dong-Bai Sun . A structural reliability-based sensitivity analysis method using particles swarm optimization: relative convergence rate[J]. Journal of Zhejiang University Science A, 2016, 17(12): 961-973.

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author="Cheng-ming Lan , Hui Li, Jun-Yi Peng , Dong-Bai Sun ",
journal="Journal of Zhejiang University Science A",
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%T A structural reliability-based sensitivity analysis method using particles swarm optimization: relative convergence rate
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%A Jun-Yi Peng
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A1 - Cheng-ming Lan
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DOI - 10.1631/jzus.A1500255


Abstract: 
This paper proposes a novel reliability-based sensitivity analysis (SA) method, namely relative convergence rate of random variables using particles swarm optimization (). 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 technique and gradient of limit-state function is the same in the quantitative sense.

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

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。

关键词:敏感性分析;优化;结构可靠度;随机变量

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1]Bjerager, P., Krenk, S., 1989. Parametric sensitivity in first order reliability theory. Journal of Engineering Mechanics, 115(7):1577-1582.

[2]Chakraborty, S., Bhattacharjya, S., Haldar, A., 2012. Sensitivity importance-based robust optimization of structures with incomplete probabilistic information. International Journal for Numerical Methods in Engineering, 90(10):1261-1277.

[3]Cheng, J., Xiao, R.C., 2005. Serviceability reliability analysis of cable-stayed bridges. Structural Engineering and Mechanics, 20(6):609-630.

[4]Du, X., Guo, J., Beeram, H., 2008. Sequential optimization and reliability assessment for multidisciplinary systems design. Structural and Multidisciplinary Optimization, 35(2):117-130.

[5]Eberhart, R.C., Hu, X., 1999. Human tremor analysis using particle swarm optimization. Proceedings of the IEEE Congress on Evolutionary Computation, Washington DC, USA, p.1927-1930.

[6]Eberhart, R.C., Shi, Y., 2000. Comparing inertia weights and constriction factors in particle swarm optimization. Proceedings of the Congress on Evolutionary Computation, La Jolla, CA, USA, p.84-88.

[7]Elegbede, C., 2005. Structural reliability assessment based on particles swarm optimization. Structural Safety, 27(2):171-186.

[8]Elms, D.G., 1999. Achieving structural safety: theoretical considerations. Structural Safety, 21(4):311-333.

[9]Engelbrecht, A.P., Ismail, A., 1999. Training product unit neural networks. Stability and Control: Theory and Applications, 2(1/2):59-74.

[10]Girmscheid, G., 1987. Statische und dynamische Berechnung von Schrägseilbrücken. Bautechnik, 64(10):340-347 (in German).

[11]He, Q., Wang, L., 2007. A hybrid particle swarm optimization with a feasibility-based rule for constrained optimization. Applied Mathematics and Computation, 186(2):1407-1422.

[12]Homma, T., Saltelli, A., 1996. Importance measures in global sensitivity analysis of nonlinear models. Reliability Engineering & System Safety, 52(1):1-17.

[13]Hu, X., Eberhart, R.C., 2002. Solving constrained nonlinear optimization problems with particle swarm optimization. Proceedings of the 6th World Multiconference on Systemics Cybernetics and Informatics, Orlando, FL, USA, p.203-206.

[14]Hu, X., Eberhart, R.C., Shi, Y., 2003. Engineering optimization with particle swarm. IEEE Swarm Intelligence Symposium, Indianapolis, IN, USA, p.193-197.

[15]Jacques, J., Lavergne, C., Devictor, N., 2006. Sensitivity analysis in presence of model uncertainty and correlated inputs. Reliability Engineering & System Safety, 91(10-11):1126-1134.

[16]Jansen, P.W., Perez, R.E., 2011. Constrained structural design optimization via a parallel augmented Lagrangian particle swarm optimization approach. Computers and Structures, 89(13-14):1352-1366.

[17]Karamchandani, A., Cornell, C.A., 1992. Sensitivity estimation within first and second order reliability methods. Structural Safety, 11(2):95-107.

[18]Kennedy, J., Eberhart, R.C., 1995a. A new optimization using particle swarm. Proceedings of the 6th International Symposium on Micro Machine and Human Science, Nagoya, Japan, p.39-43.

[19]Kennedy, J., Eberhart, R.C., 1995b. Particle swarm optimization. Proceedings of the IEEE International Conference on Neural Network, Perth, Australia, p.1942-1948.

[20]Khajehzadeh, M., Taha, M.R., El-Shafie, A., et al., 2011. Modified particle swarm optimization for optimum design of spread footing and retaining wall. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 12(6):415-427.

[21]Madsen, H.O., 1988. Omission sensitivity factors. Structural Safety, 5(1):35-45.

[22]Parsopoulos, K.E., Vrahatis, M.N., 2002. Particle swarm optimization method for constrained optimization problems. Proceeding of the Euro-International Symposium on Computational Intelligence, Košice, Slovakia, p.214-220.

[23]Perez, R.E., Behdinan, K., 2007. Particle swarm approach for structural design optimization. Computers and Structures, 85(19-20):1579-1588.

[24]Ray, T., Liew, K.M., 2001. A swarm with an effective information sharing mechanism for unconstrained and constrained single objective optimization problem. Proceedings of IEEE Congress on Evolutionary Computation, Seoul, Korea, p.75-80.

[25]Shen, H.S., Gao, F., 1994. Reliability analysis of cable-stayed bridge towers. China Journal of Highway and Transport, 7(4):40-43 (in Chinese).

[26]Shi, Y., Eberhart, R.C., 1998. A modified particle swarm optimizer. Proceedings of IEEE International Conference on Evolutionary Computation, Anchorage, Alaska, USA, p.69-73.

[27]Shi, Y., Eberhart, R.C., 1999. Empirical study of particle swarm optimization. Proceedings of Congress on Evolutionary Computation, Washington DC, USA, p.1945-1950.

[28]Sun, C.L., Zeng, J.C., Pan, J.S., 2011. An improved vector particle swarm optimization for constrained optimization problems. Information Science, 181(6):1153-1163.

[29]van den Bergh, F., Engelbrecht, A.P., 2000. Cooperative learning in neural networks using particle swarm optimizers. South African Computer Journal, 26:84-90.

[30]Xiao, N.C., Huang, H.Z., Wang, Z.H., et al., 2011. Reliability sensitivity analysis for structural systems in interval probability form. Structural and Multidisciplinary Optimization, 44(5):691-705.

[31]Xu, C., Gertner, G.Z., 2008. Uncertainty and sensitivity analysis for models with correlated parameters. Reliability Engineering & System Safety, 93(10):1563-1573.

[32]Zahara, E., Hu, C.H., 2008. Solving constrained optimization problems with hybrid particles swarm optimization. Engineering Optimization, 40(11):1031-1049.

[33]Zhang, X., Huang, H.Z., 2010. Sequential optimization and reliability assessment for multidisciplinary design optimization under aleatory and epistemic uncertainties. Structural and Multidisciplinary Optimization, 40(1-6):165-175.

[34]Zhang, X., Huang, H.Z., Xu, H., 2010. Multidisciplinary design optimization with discrete and continuous variables of various uncertainties. Structural and Multidisciplinary Optimization, 42(4):605-618.

[35]Zhao, Y.G., Ono, T., 1999. A general procedure for first/second-order reliability method (/SORM). Structural Safety, 21(2):95-112.

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