基于改进CS的混合威布尔分布最优化参数估计
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摘要
混合威布尔分布常用于拟合多失效模式的设备寿命数据,但由于该分布的形式复杂且参数众多,其参数估计较为困难。针对该问题,在对布谷鸟搜索(Cuckoo Search,CS)算法的步长比例和寄主鸟发现概率改进的基础上,提出基于改进CS的混合威布尔分布最优化参数估计方法。该方法以最小化残差平方和为目标,建立参数估计优化模型,并通过改进的CS算法进行参数寻优。案例以飞机挡风玻璃寿命数据为对象,采用CS算法以及3种改进的CS算法分别对两重两参数威布尔分布进行2 000次参数估计,对比分析各算法的寻优结果表明:融合步长比例改进和寄主鸟发现概率改进的CS算法的参数估计精度较高,估计结果较可靠。
The device life data which involve more than one kind of the failure mode are often fitted by the Weibull mixtures. Due to the complex forms and the multiple parameters,the parameter estimation of these distributions is quite difficult. As to this problem above,on the basis of improving the step size scales and the probability of discovery of the Cuckoo Search( CS) algorithm,a parameter estimation of the Weibull mixtures based on the the proposed method is proposed. At first,the method need to build an optimal model for the aim of minimizing the residual sum of squares. Then,the model is solved by the improving algorithm. In the case study,the life data of the craft windshields are regarded as the fitting objects of the two-fold two-parameter Weibull. The Cuckoo Search( CS) algorithm and other three kinds of the improving Cuckoo Search( CS) algorithm are used to search the best solution for 2 000 times simultaneously. The optimization results are compared and the contrast proves that the accuracy and the success rate of the parameter estimation based on the algorithm which mixes the two improved method is the better one.
The device life data which involve more than one kind of the failure mode are often fitted by the Weibull mixtures. Due to the complex forms and the multiple parameters,the parameter estimation of these distributions is quite difficult. As to this problem above,on the basis of improving the step size scales and the probability of discovery of the Cuckoo Search( CS) algorithm,a parameter estimation of the Weibull mixtures based on the the proposed method is proposed. At first,the method need to build an optimal model for the aim of minimizing the residual sum of squares. Then,the model is solved by the improving algorithm. In the case study,the life data of the craft windshields are regarded as the fitting objects of the two-fold two-parameter Weibull. The Cuckoo Search( CS) algorithm and other three kinds of the improving Cuckoo Search( CS) algorithm are used to search the best solution for 2 000 times simultaneously. The optimization results are compared and the contrast proves that the accuracy and the success rate of the parameter estimation based on the algorithm which mixes the two improved method is the better one.
引文
[1]MURTHY D N P,XIE M,JIANG R.Weibull models[M].[S.l.]:John Wiley&Sons,2004.
[2]LING J,PAN J.An optimization method of parameter estimation for mixed Weibull distributions,Reliability and Quality in Design.Proceedings of the fourth ISSAT International Conference[C].Seattle:[s.n.],1998:237-243.
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[4]薛玉霞,申桂香,张英芝,等.基于粒子群优化理论的可靠性分布模型的极大似然参数估计法[J].吉林大学学报(工学版),2009(39):219-221.
[5]毛昭勇,宋保维,李正,等.基于遗传算法的最大似然参数优化估计[J].机械强度,2006,28(1):79-82.
[6]敖长林,郑先哲,谢里阳,等.基于神经网络的拖拉机可靠性模型的参数估计[J].农业机械学报,2004,35(3):31-33.
[7]YANG X S,DEB S.Engineering optimisation by cuckoo search[J].International Journal of Mathematical Modelling and Numerical Optimisation,2010,1(4):330-343.
[8]GANDOMI A H,YANG X S,ALAVI A H.Cuckoo search algorithm:a metaheuristic approach to solve structural optimization problems[J].Engineering with computers,2013,29(1):17-35.
[9]YANG X S,DEB S.Cuckoo search via Lévy flights.2009World Congress on Nature&Biologically Inspired Computing[C].Coimbatore:[s.n.],2009:210-214.
[10]YANG X S,DEB S.Multiobjective cuckoo search for design optimization[J].Computers&Operations Research,2013,40(6):1616-1624.
[11]李国,阮晓青.关于简单遗传算法变异率的理论分析[J].工程数学学报,2006,23(3):468-474.
[12]MURTHY D N P,BULMER M,ECCLESTON J A.Weibull model selection for reliability modelling[J].Reliability Engineering&System Safety,2004,86(3):257-267.
[2]LING J,PAN J.An optimization method of parameter estimation for mixed Weibull distributions,Reliability and Quality in Design.Proceedings of the fourth ISSAT International Conference[C].Seattle:[s.n.],1998:237-243.
[3]ABBASI B,JAHROMI A H E,ARKAT J,et al.Estimating the parameters of Weibull distribution using simulated annealing algorithm[J].Applied Mathematics and Computation,2006,183(1):85-93.
[4]薛玉霞,申桂香,张英芝,等.基于粒子群优化理论的可靠性分布模型的极大似然参数估计法[J].吉林大学学报(工学版),2009(39):219-221.
[5]毛昭勇,宋保维,李正,等.基于遗传算法的最大似然参数优化估计[J].机械强度,2006,28(1):79-82.
[6]敖长林,郑先哲,谢里阳,等.基于神经网络的拖拉机可靠性模型的参数估计[J].农业机械学报,2004,35(3):31-33.
[7]YANG X S,DEB S.Engineering optimisation by cuckoo search[J].International Journal of Mathematical Modelling and Numerical Optimisation,2010,1(4):330-343.
[8]GANDOMI A H,YANG X S,ALAVI A H.Cuckoo search algorithm:a metaheuristic approach to solve structural optimization problems[J].Engineering with computers,2013,29(1):17-35.
[9]YANG X S,DEB S.Cuckoo search via Lévy flights.2009World Congress on Nature&Biologically Inspired Computing[C].Coimbatore:[s.n.],2009:210-214.
[10]YANG X S,DEB S.Multiobjective cuckoo search for design optimization[J].Computers&Operations Research,2013,40(6):1616-1624.
[11]李国,阮晓青.关于简单遗传算法变异率的理论分析[J].工程数学学报,2006,23(3):468-474.
[12]MURTHY D N P,BULMER M,ECCLESTON J A.Weibull model selection for reliability modelling[J].Reliability Engineering&System Safety,2004,86(3):257-267.