基于极大似然估计的数控系统故障分布模型

The Distribution Model of CNC System to Failure Based on Maximum Likelihood Estimation

威布尔分布被广泛用于可靠性工程和寿命数据的分析中。针对两参数威布尔分布,建立基于极大似然法的参数估计模型,采用二阶收敛Newton-Raphson迭代法求解威布尔分布的尺寸参数和形状参数。迭代求解过程中,利用Matlab图形,初步选取似然函数曲线在零值点附近的区域作为初始值的区间,并根据Newton-Raphson迭代法收敛的充分条件进一步确定迭代初值的选取范围。通过matlab绘制迭代趋势三维图,证明与迭代计算结果相符。通过比较,证实本参数估计模型和Newton-Raphson迭代求解法更加精确有效。

Owing to the fact that the Weibull distribution is frequently applied for reliability engineering and lifespan data analysis, the paper established the parameter estimation model using maximum likelihood estimation for the dual-parametric Weibull distribution, it then used second-order convergent Newton- Raphson iteration method to solve the MLE of two-parameter Weibull distribution, which has scale param- eter and shape parameter. In the iteration process, the area around the zero point of likelihood function curve was preliminarily selected as the range of the initial value based on the likelihood function image which was plotted by Matlab, and according to the sufficient conditions for the convergence of Newton- Raphson iteration method to further determine the scope of the iterative initial value. Iteration trend three- dimensional image which was plotted by Matlab proves to be consistent with the results of iterative calcula- tion. Finally, by comparison,this parameter estimation model and the Newton-Raphson iterative solution method were proved to be more accurate and efficient.