基于混沌模拟退火PSO算法的威布尔分布参数估计应用研究

PDF(1119 KB)

振动与冲击 ›› 2017, Vol. 36 ›› Issue (12) : 134-139.

论文

许伟，程刚，黄林，位秀雷，瓮雷

作者信息 +

Chaotic simulated PSO algorithm application research for Weibull distribution parameter estimation

XU Wei，CHENG Gang，HUANG Lin,WEI Xiu Lei,WENG Lei

Author information +

文章历史 +

摘要

针对三参数威布尔分布模型采用精确解法直接求解的不足，提出基于混沌模拟退火粒子群优化方法进行参数估计，引入Logistic混沌因子调整粒子群优化算法的更新策略以充分释放其遍历搜索能力，并采用模拟退火方法依据Tsallis接受准则以一定概率接受新状态，使算法避免陷入“早熟”进而实现全局最优搜索。同时为降低算法在迭代计算上的时间开销，运用图解法获得的初始解为其提供搜索范围。将该方法运用到轴承转子可靠度威布尔分布参数估计中，实验分析表明该方法具有可行性和有效性，与遗传算法、模拟退火粒子群优化算法相比具有更好的寻优能力。

Abstract

Aiming at the deficiency of three parameter Weibull distribution model in directly solving by means of accurate solution, the parameter estimation based on chaotic simulated annealing particle swarm optimization algorithm is proposed, and the Logistic chaos factor is introduced to adjust the update strategy of particle swarm optimization algorithm so as to fully release its ergodic search ability. The simulated annealing method is used to accept the new state with a certain probability according to the acceptance criteria of Tsallis, so that the algorithm can avoid premature convergence and realize the global optimal search. At the same time, in order to reduce the time of iterative calculation, the initial solution obtained by the graphic method is used to provide the search scope. The method is applied to the reliable Weibull distribution parameter estimation of bearing rotor. Experimental results show that the method is feasible and effective and has better optimization performance compared with genetic algorithm and simulated particle swarm optimization algorithm.

导出引用

许伟，程刚，黄林，位秀雷，瓮雷. 基于混沌模拟退火PSO算法的威布尔分布参数估计应用研究[J]. 振动与冲击, 2017, 36(12): 134-139

XU Wei，CHENG Gang，HUANG Lin,WEI Xiu Lei,WENG Lei. Chaotic simulated PSO algorithm application research for Weibull distribution parameter estimation[J]. Journal of Vibration and Shock, 2017, 36(12): 134-139

参考文献

[1] Shimizua S. P-S-N/P-F-L curve approach using three-parameter Weibull distribution for life and fatigue analysis of structural and rolling contact components [J]. Tribology Transactions, 2005, 48(4): 576-582.
[2] Ling D. Research on Weibull Distribution and Its Applications in Mechanical Reliability Engineering [D].Chengdu: University of electronic science and technology, 2010.
凌丹.威布尔分布模型及其在机械可靠性中的应用研究 [D]. 成都: 电子科技大学, 2010.
[3] Zhang L F, Xie M, Tangga L C. A study of two estimation approaches for parameters of Weibull distribution based on WPP [J]. Reliability Engineering & System Safety,2007, 92(3):360-368.
[4] Touw A E. Bayesian estimation of mixed Weibull distributions[J]. Reliability Engineering & System Safety, 2009, 94(2): 463-473.
[5] Dong S, Han Y, Tao S S, et al. Parameters Estimation for Weibull Distribution with Particle Swarm Optimization[J].Ocean University of China, 2012, 42(6): 120-125.
董胜，韩意，陶山山，等. Weibull分布参数的粒子群算法估计[J]. 中国海洋大学学报, 2012, 42(6): 120-125.
[6] Yang Z Z, Liu R Y. Improved Methods of the Parameter Estimating of Three-parameter Weibull Distribution[J]. Journal of engineering mathematics, 2004, 21(2): 281-284.
杨志忠，刘瑞元. 三参数Weibull分布参数估计求法改[J]. 工程数学学报, 2004, 21(2): 281-284.
[7] Yang M C, Nie H. Advanced Algorithm for Maximum Likelihood Estimation of Three Parameter Weibull Distribution[J]. Journal of Nanjing University of Aeronautics & Astronautics，2007, 39(1): 22-24.
杨谋存，聂宏. 三参数Weibull分布参数的极大似然估计数值解法[J]. 南京航空航天大学学报，2007, 39(1): 22-24.
[8] Pan X C. Low-order probability-weighted moments method for wind speed probability distribution parameter estimation[J]. Proceeding of the CSEE, 2012, 32(5): 132-136.
潘晓春. 风速概率分布参数估计的低阶概率权重矩法[J]. 中国电机工程学报, 2012, 32(5): 132-136.
[9] Clerc M. Discrete particle swarm optimization illustrated by the traveling salesman problem [M].Heidelberg：Springer，2004：200-223.
[10] Liang J J, Cai Q, Chu Z L. Bayesian network structure learning algorithm using particle swarm optimization[J].Huazhong Univ. of Sci & Tech(Natural science edition), 2012, 40(12): 44-48.
梁洁，蔡琦，初珠立. 基于微粒群优化的贝叶斯网络结构学习方法[J]. 华中科技大学学报（自然科学版）, 2012, 40(12): 44-48.
[11] Luo H, Wang H J, Huang J G et al. Method of united estimation to the parameter of three-parameter Weibull distribution based on PSO[J]. Chinese Journal of scientific Instrument, 2009, 30(8): 1605-1612.
罗航，王后军，黄建国，等. 基于PSO的三参数威布尔分布参数的联合估计方法[J]. 仪器仪表学报, 2009, 30(8): 1605-1612.
[12] Wang Q, Wang L, Ren W J. Research on estimating parameters of Weibull distribution Model Based on FPSO-SA[J].Journal of Jilin University(Information science Edition) , 2014, 32(5): 476-483.
王琼，王磊，任伟建.基于FPSO-SA算法的威布尔分布参数估计研究[J]. 吉林大学学报（信息科学版）, 2014, 32(5): 476-483.
[13] Liu A J, Yang Y, Li P. Chaotic simulated annealing particle swarm optimization algorithm research and its application[J]. Journal of Zhejiang University(Engineering Science) , 2013, 47(10),: 1722-1730.
刘爱军，杨育，李斐. 混沌模拟退火粒子群优化算法研究及应用[J]. 浙江大学学报（工学版）, 2013, 47(10),: 1722-1730.
[14] Huang P. Improved Particle Swarm algorithm and its application in power system[D]. Guang Zhou：South China University of Technology，2012.
黄平.粒子群算法改进及其在电力系统的应用[D].广州：华南理工大学, 2012.
[15] Pang F. The Principle of SA Algorithm and Algorithm,s Application on Optimization Problem[D]. Chang Chun: Ji Lin University,2006.
庞峰. 模拟退火算法的原理及算法在优化问题上的应用[D]. 长春：吉林大学，2006.
[16] 郑锐.三参数威布尔分布参数估计及在可靠性分析中的应用[J].振动与冲击,2015,34(5):78-81.
ZHENG Rui.Parameter estimation of three-parameter Weibull distribution and its application in reliability analysis[J].Journal of Vibration and Shock,2015,34(5):78-81.
[17] Nelson E W. Applied Life Data Analysis [M].New York，1982.