A novel non-Markovian degradation model with global state dependency for prognostics

Timely prognostics of remaining useful life (RUL) are increasingly critical for engineering systems, especially as long-life components face complex and evolving degradation risks. Nevertheless, conventional degradation models are frequently inadequate in capturing the memory effects and latent global state dependencies inherent in practical degradation processes. These limitations hinder the generalizability of existing methods. To overcome these challenges, this paper proposes a class of nonlinear degradation models that explicitly incorporate generalized spatiotemporal dependencies and memory effects among multiple similar components. The models are formulated using continuous stochastic differential equations and discretized via two numerical schemes to enable efficient parameter estimation through maximum likelihood (ML) methods. Subsequently, RUL predictions are derived using Monte Carlo simulation, with point estimates extracted from the resulting frequency histograms. The proposed method is validated through a numerical example and a blast furnace case study.