Empirical Likelihood Stacking for Remaining Useful Life Estimation

Paper in proceeding, 2026

Predictive maintenance (PdM) plays an important role in the transition toward Industry 4.0, offering the potential to increase operational efficiency and reduce unexpected downtime. A central application of PdM involves the estimation of a system component’s remaining useful life (RUL) to enable informed maintenance decisions. Deep learning (DL) models have demonstrated strong performance in RUL prediction tasks. However, these models often lack the capability to reliably quantify predictive uncertainty, which is essential for risk-aware decision-making in industrial applications. Bayesian approximation models, like Stochastic Weight Averaging Bayesian and Variational Inference, can yield a distribution of predictions while avoiding the prohibitively costly process of true Bayesian inference. This distribution can be used to reason about the uncertainty of the model, but often shows the model being overconfident. We propose empirical likelihood stacking, a method for improving uncertainty quantification for DL models. By applying stacking and deep ensembles to estimate the RUL of turbofan engines, we show the trade-offs between these two methods when applied to DL models. We find that the stacked model has a better calibrated uncertainty at a small cost to point prediction accuracy, when compared to the ensemble.