Health Prognostics of Multivariate Deteriorating Machinery Considering Unit-to-Unit Variability

Multivariable deteriorating machinery (MDM) is commonly encountered in modern industrial environments, where its failure can be attributed to the gradual degradation of multiple health indicators (HIs). More and more researchers have directed their attention toward exploring the dependencies among these HIs and establishing multivariate degradation models. Nevertheless, existing methodologies have disregarded the crucial consideration of unit-to-unit variability in MDM's failure. To address this significant gap, this paper introduces a novel multivariate degradation model. The proposed model effectively incorporates both the dependencies among multiple HIs and the individual differences observed in the degradation process of MDM. The proposed approach employs an online updating algorithm to automatically select the optimal degradation model form and parameters for each HI of MDM, thereby acquiring the marginal failure time distributions. Subsequently, time-varying Copulas are employed here to establish connections between the marginal failure time distributions, and form a joint failure time distribution for MDM. The effectiveness of the proposed method was verified through real degradation data obtained from Stirling refrigerators. The results substantiate the accurate failure time prediction capability of the proposed method while accounting for unit-to-unit variability.