基于Wiener过程的多阶段非线性复杂退化产品可靠性分析模型  

Nonlinear Wiener process multi-stage complex degradation model and reliability analysis

作　　者：周子韩 唐家银[1,2] ZHOU Zihan;TANG Jiayin(School of Mathematics,Southwest Jiaotong University,Chengdu 611756,China;National Engineering Laboratory of Integrated Transportation Big Data Application Technology,Chengdu 611756,China)

机构地区：[1]西南交通大学数学学院,四川成都611756 [2]西南交通大学综合交通大数据应用技术国家工程实验室,四川成都611756

出　　处：《湖北大学学报（自然科学版）》2024年第3期433-444,共12页Journal of Hubei University：Natural Science

基　　金：教育部人文社会科学研究规划基金项目(20XJAZH009);四川省2021—2023年高等教育人才培养质量和教学改革项目(JG2021-394);西南交通大学2020年度研究生研究类教育改革项目(YJG4-2020-Y035);中央高校基础研究培育专题2021年度项目(2682021ZTPY018)资助。

摘　　要：为提高非线性退化轨迹拟合的精度,针对多阶段退化中的非线性规律建立Wiener过程模型,考虑变点的连续性与部件个体的差异性,给出基于非线性复杂退化的可靠性评估方法。结合幂律函数推导出非线性多阶段Wiener过程模型,得到模型参数的极大似然估计量;通过最小均方误差原则给出变点以及幂参数的初值确定方法;根据SIC(schwarz information criterion)方法得到模型变点的精确值,并检验其准确性;结合不同部件之间的差异性,得到变点的连续分布;推导出非线性Wiener过程连续时段内的可靠度函数估计;利用本模型对高压脉冲电容器电容相对变化量的退化数据建模,与线性建模结果对比,验证多阶段Wiener过程模型在可靠性评估方面的有效性与可行性,估计结果更接近真实值。In order to improve the accuracy of nonlinear degradation fitting,a Wiener process model was established for multi-stage degradation.Considering the continuity of change points and the differences of individual components,a reliability method based on nonlinear complex degradation was proposed.The nonlinear multi-stage Wiener process model was derived by Wiener process combined with power-law function,and the maximum likelihood estimators of the model parameters were obtained.The method of determining the initial value of change point and power parameter was given by the principle of least mean square error.The exact value of the change point of the model was obtained by schwarz information criterion method,and its correctness was verified.Combined with the differences between different components,the distribution estimation of change points was obtained.The reliability function estimation of linear Wiener process in nonlinear continuous period was derived.This model was used to model the degradation data of the relative capacitance variation of high-voltage pulse capacitors.Compared with the linear modeling results,the effectiveness and feasibility of the multi-stage Wiener process model in reliability evaluation were verified,and the estimated results were closer to the real value.

关 键 词：多阶段退化 WIENER过程 变点识别 非线性退化 可靠性 

分 类 号：O212.3[理学—概率论与数理统计] TB114.3[理学—数学]