基于逆高斯过程的二元退化可靠性建模与评估  

A bivariate degradation model for reliability analysis based on inverse Gaussian process

作　　者：安绮梦 闫在在[1] 孙立君 AN Qi-meng;YAN Zai-zai;SUN Li-jun(College of Science,Inner Mongolia University of Technology,Hohhot 010051,China)

机构地区：[1]内蒙古工业大学理学院,呼和浩特010051

出　　处：《控制与决策》2024年第11期3727-3735,共9页Control and Decision

基　　金：国家自然科学基金项目(12361058,11861049);内蒙古2023研究生创新项目(ZTY2023015);内蒙古自治区自然科学基金项目(2022MS01006);内蒙古自治区直属高校基本科研业务费项目(JY20220083)。

摘　　要：为了实现单个产品的可靠度估计和剩余使用寿命预测,在综合利用产品总体和个体退化信息的基础上,提出一种考虑个体差异性的二元逆高斯退化模型.首先,基于Copula函数建立二元逆高斯过程退化模型,并从性能退化速率与性能间相关关系两方面对个体差异性进行描述;然后,利用两阶段期望最大化算法,先后对单性能模型和Copula函数中参数值进行估计;接着,基于个体退化特性和Bayes理论,分别提出个体缺失观测值估计和退化值预测的模拟方法,并利用退化量预测值对个体的剩余使用寿命进行预测;最后,通过重型机床的实例数据验证所提出模型和统计推断方法的有效性,并对产品后续预防性维修和健康管理提出建议.In order to get the reliability estimation and remaining useful lifetime(RUL)prediction of a product,a bivariate inverse Gaussian(IG)degradation model is proposed based on the degradation information of the population and units.The bivariate degradation model is established based on Copula function,and the model can capture heterogeneities of degradation rates and correlation between two performance characteristics within the population.Then,the two-stage expectation maximization(EM)algorithm is used to estimate parameters of marginal distributions and Copula function successively.In addition,based on the degradation characteristics of individuals and Bayes’theorem,we propose simulation studies to estimate the missing observations and future observations,and get unit-specific RUL using future observations.To verify the feasibility of the proposed model and inference methods,a numerical example about heavy machine tools is proposed,and suggestions are put forward for the preventive maintenance and health management of products.

关 键 词：逆高斯过程 两阶段期望最大化算法 COPULA函数 缺失观测值 剩余使用寿命预测 

分 类 号：TB114.3[理学—概率论与数理统计]