An enhanced copula-based method for data-driven prognostics considering insufficient training units

Data-driven based prognostics typically requires sufficient run-to-failure training units in order to learn degradation characteristics of engineering components or products without the need of understanding the physics-based degradation mechanisms. With insufficient training units, however, the model form learned from the training units may be inaccurate, which could result in large remaining useful life (RUL) prediction errors for the actual test units. A recently proposed copula-based sampling method does not assume any degradation model form, but builds a set of statistical correlation models for the RUL prediction, which shows high RUL prediction accuracy with sufficient training units. This paper proposes an enhanced copula-based method to address the instability issue of the method when dealing with insufficient training units. In particular, the sampling part for the RUL prediction in the original time domain is replaced by an analytical formulation in the standard uniform space with multiple copulas so that the stability issue can be addressed. Furthermore, a simplified version of the RUL prediction is proposed with extremely high efficiency. Effectiveness of the enhanced method is demonstrated by two case studies: one for resistance degradation of lead-acid batteries and another for capacity degradation of lithium-ion batteries.