基于HP滤波与非线性维纳过程的退化建模与失效分布研究

Study on degradation modeling and failure distribution based on HP filtering and nonlinear Wiener process

针对退化建模中广泛采用的非线性维纳过程难以得到失效时间分布精确表达式的问题,提出了一种新的非线性维纳过程退化建模与失效分析方法。首先,运用HP（Hodrick-Prescott）滤波提取退化数据的长期趋势;其次,从理论上说明对数变换消除非线性异方差的可行性;然后,提出非线性维纳过程二步估计方法,利用最小二乘法进行确定性漂移趋势的参数估计,利用极大似然估计法进行扩散参数估计,在此基础上给出首达时意义下非线性维纳过程失效时间分布的精确表达式;最后,以焊点为研究对象进行退化建模与失效分析,实测实验数据分析结果表明,非线性维纳过程退化建模方法能够给出焊点失效时间分布,且精度优于线性维纳过程,更优于回归模型。

In degradation modelling based on nonlinear Wiener process,it is difficult to obtain the accurate expression about the failure time distribution. To address this issue,a new nonlinear Wiener process is presented for the degradation modeling and failure analysis.Firstly,Hodrick-Prescott（ HP） filtering is utilized to extract the long-term trend of the degradation data. Secondly,the feasibility about the elimination of nonlinear heteroscedasticity by logarithmic transformation is demonstrated theoretically. Thirdly,a two-step parameter estimation method for nonlinear Wiener process is proposed. The parameters of drift trend are estimated by least squares algorithm,the parameter of diffusion coefficient is estimated by maximum likelihood algorithm. The accurate expression about the failure time distribution under the meaning of first passage time is proposed. Finally,the degradation modeling and failure analysis about the solder joint is illustrated as a case study. Experimental results show that the proposed nonlinear Wiener process degradation model can obtain the failure time distribution of the solder joint,the accuracy is better than the liner wiener process,and much better than the general regression model.