A physical knowledge-guided and data-driven framework for remaining useful life prediction (The case of turbofan engines)

Abstract

Accurate prediction of the remaining useful life (RUL) of turbofan engines is crucial for predictive maintenance and operational reliability. Although data-driven methods have shown strong potential in capturing degradation patterns, several practical challenges remain, including the limited integration of physical domain knowledge and the insufficient characterization of prediction uncertainty. To address these issues, this paper proposes a hybrid RUL prediction and uncertainty quantification framework (PhyMix-UQ-RUL) that combines physical knowledge with data-driven approaches. Specifically, a multi-scale dilated convolutional neural network (MsDCNN) is incorporated to extend the WTTE-RNN framework. By introducing a learnable channel-attention weighting mechanism, the model dynamically adjusts the importance of features across different temporal scales, thereby enhancing its ability to extract local features at multiple resolutions. Furthermore, a gated degradation stage regularization (GDSR) module is designed based on the bathtub curve theory, which dynamically constrains the β parameter of the Weibull distribution to ensure consistency with physical laws. In addition, a global stability constraint is applied to suppress abrupt fluctuations in the β parameter, while a stage-adaptive constraint is introduced to further improve the physical rationality of the model’s predictions. Finally, the proposed method is comprehensively validated on the NASA C-MAPSS turbofan engine dataset, and its generalization capability is further evaluated on selected subsets of the N-CMAPSS dataset. Experimental results demonstrate that PhyMix-UQ-RUL delivers competitive prediction accuracy and effectively quantifies prediction uncertainty. Moreover, the proposed framework features a concise architecture and high interpretability, offering valuable support for equipment health assessment and risk management.