This paper proposes hybrid methods using physics-informed (PI) lightweight Temporal Convolution Neural Network (PITCN) for bearings’ remaining useful life (RUL) prediction under stiffness degradation. It includes three PI hybrid models: a) PI Feature model (PIFM) — constructing physics-informed health indicator (PIHI) to augment the feature space, b) PI Layer model (PILM)—encoding the physics governing equations in a hidden layer, and c) PI Layer Based Loss model (PILLM)—designing PI conflict loss, taking into account the difference before and after integration of the physics input-output relations involved module to the loss function. We simulated 200 different bearing stiffness degradations, using their discrete monitored vibration signals to verify the effectiveness of the proposed method. We also investigate their inference process through feature heat map analysis to interpret how the models melt physics knowledge to assist in capturing the degradation trend. The physics knowledge considered in this paper is the dynamic relationship between vibration amplitude and stiffness in a damped forced vibration model. The results show that all three PITCN models effectively capture degradation-related trend information and perform better than the vanilla lightweight TCN. Furthermore, the visualization of the feature channels highlights the important role of physics information in model training. Channels containing physics information demonstrate higher correlation with results as they significantly dominate the heat map compared to other channels.

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Sparse & noisy monitoring data leads to numerous challenges in prognostic and health management (PHM). Big data volume but poor quality with scarce healthy states information limits the performance of training machine learning (ML) and physics-based failure modeling. To address these challenges, this thesis aims to develop a new hybrid PHM framework with the ability to autonomously discover and exploit incomplete implicit physics knowledge in sparse & noisy monitoring data, providing a solution for deep physics knowledge-ML fusion by physics-informed machine learning algorithms. In addition, the developed hybrid framework also applies the self-supervised learning paradigm to significantly improve the learning performance under uncertain, sparse, and noisy data with lower requirements for specialist area knowledge. The performance of the developed algorithms will be investigated on the sparse and noise data generated by simulation data sets, public benchmark data sets, and the PHM platform to demonstrate its applicability.