Remaining useful life prediction for multivariate stochastic degradation systems under functionally dependent failure modes

Multivariate stochastic degradation systems are widely encountered in complex industrial equipment, where performance deterioration exhibits coupling characteristics among multiple indicators. However, functionally dependent failure may still occur even when no single indicator exceeds its individual threshold, leading to unexpected system breakdowns. Compared with the extensive research on competing failure modes, the problem of remaining useful life (RUL) prediction under functionally dependent failure scenarios has not received sufficient attention. In this paper, a nonlinear Wiener process framework is established to model the degradation process of multivariate systems. A Copula-based model is employed to describe nonlinear dependencies among degradation variables, and a vector envelope plane method is developed to approximate complex functionally dependent failure boundaries. Bayesian MCMC (Markov chain Monte Carlo) is used for offline parameter estimation, while sequential Monte Carlo (SMC) is adopted for online updating. Furthermore, analytical and semi-analytical RUL distributions are derived for linear and nonlinear associations, respectively, based on first passage time theory. The linear case is handled through equivalent transformation of multivariate degradation processes, while the nonlinear case is addressed using a Copula-based dependence representation combined with the vector envelope plane approximation. Finally, numerical simulations and two engineering case studies involving gearboxes and gyroscopes are conducted to evaluate the prediction performance of the proposed method.