Hierarchical Bayesian Multimodal Learning for Probabilistic RUL Pre-diction: An Evidential Framework with Uncertainty-Calibrated Fusion

Abstract

The increasing complexity and interconnectivity of modern industrial machinery, together with persistent demands for operational efficiency, have elevated reliable remaining useful life (RUL) prediction to a cornerstone of industrial intelligence. To this end, multimodal monitoring has been widely adopted, as it provides complementary perspectives on system health. Although numerous studies have exploited multimodal data to enable holistic condition assessment, most existing approaches remain fundamentally deterministic, yielding single-point estimates that are often overconfident and potentially misleading-particularly in safety-critical or cost-sensitive scenarios. To fill this trustworthy gap, a multimodal evidential learning framework is proposed with uncertainty-calibrated fusion. It integrates heterogeneous monitoring modalities by jointly exploiting scarce labeled run-to-failure trajectories and abundant unlabeled operational data. Each modality is modeled using a high-order evidential distribution, which enables an explicit analytical decomposition of predictive uncertainty into aleatory (data-driven) and epistemic (model-driven) components. These modality-specific evidential representations are subsequently fused through an uncertainty-aware mechanism. Experiments on multimodal run-to-failures of robotic harmonic drives validate the proposed framework's performance in both predictive accuracy and uncertainty quantification. Furthermore, ablation studies and comprehensive comparisons with state-of-the-art methods substantiate the contributions of individual modules and confirm the overall framework's suitability as a trustworthy decision-support tool for industrial applications.