基于遗传算法的混合威布尔分布参数最小二乘估计

混合威布尔分布模型常用来分析具有多种失效模式的复杂系统的可靠性数据,由于模型中包含较多参数,与单一威布尔分布相比,混合威布尔分布的参数估计更为复杂。利用遗传算法为优化方法,提出了一种混合威布尔分布参数估计的最小二乘方法。以残差平方和最小为优化目标,以各参数取值范围为约束条件,构建了混合威布尔分布的非线性最小二乘优化模型;通过变换决策变量上下限、引入惩罚因子和保存最优个体等策略改进传统遗传算法以提高算法的性能,进而利用改进后的遗传优化算法对混合威布尔分布的非线性最小二乘优化模型进行求解。实例分析表明本文方法有效,利用本文方法计算得到的可靠度估计值与真实值之间的最大偏差和标准均方根误差,相对于图估计法分别减少了0.028 4与0.032 8,相对于极大似然估计法分别减少了0.000 8与0.003 6。

Least Square Estimation for Mixed Weibull Distribution Based on Genetic Algorithm

Mixed Weibull distributions are widely used in the reliability data analysis of complex systems with multiple failure modes. Since the distribution functions contain much more parameters, the parameter estimation of the mixed Weibull distribution is more complicated than the single Weibull distribution. A least square method for parameter estimations of mixed Weibull distributions is proposed by using a genetic algorithm as the optimization method. The minimum residual sum of square is taken as the optimization objective. The ranges of each parameter are taken as the constraints. And a nonlinear least square model of the mixed Weibull distribution is developed. The traditional genetic algorithm has been improved by altering the upper and lower bounds, introducing the penalty factor and preserving the optimal individual. And the nonlinear least squares model is solved based on the improved genetic algorithm. A case study is presented to illustrate the effectiveness of our proposed method. The maximum deviation and the normalized root mean square error obtained by our method are reduced by 0.028 4 and 0.032 8 compared with those of the graph estimation method, and reduced by 0.000 8 and 0.003 61 compared with those of the maximum likelihood estimation method.