Bivariate-dependent remaining useful life prediction based on copulas and Tweedie exponential dispersion process

In complex engineering systems, operational safety and effective predictive maintenance both rely on the accuracy of remaining useful life (RUL) predictions. The existing methods face significant challenges caused by the presence of dependent failure modes or degradation indicators compounded by inherent uncertainties, including temporal variation, unit-to-unit (UtU) variability, measurement error, and model uncertainty. In addition, there is also lack of an effective algorithm for simultaneously updating all the unknown parameters. All these issues limit the accuracy of RUL prediction. To solve the aforementioned problems, this paper proposes a novel generalized RUL prediction framework, which combines Tweedie exponential dispersion (TED) processes with copula functions. Firstly, the TED process, as a general stochastic process, is used to model the degradation process, capturing dynamic stochasticity while reducing model uncertainty. Copulas are used to characterize the time-varying dependencies between multiple indicators. Secondly, a state-space bivariate degradation model is developed by incorporating multiple uncertainties. Afterwards, an adaptive parameter estimation algorithm based on particle filter and expectation-maximization algorithm is proposed. It enables simultaneous online updating of all the parameters and hidden variables of the model, and to conduct real-time RUL calculation through weighted particles. Finally, a numerical and a case study are provided. The obtained results show the high performance in accurately predicting the RUL of systems exhibiting complex multi-mode dependency and multiple uncertainty sources.