Physics-Coupled Factor Graph Disentanglement: An Explainable Physics-Informed Deep Learning Framework for Rotating Machinery Prognostics

Rotating machinery prognostics increasingly relies on deep learning, yet the latent representations learned by conventional models remain opaque and often entangle overlapping fault signatures, which undermines operator trust and limits maintenance decision-making. We propose a physics-coupled factor graph disentanglement framework that integrates a temporal convolutional encoder with a differentiable probabilistic graphical model constrained by the governing equations of rotor dynamics and bearing kinematics. Multivariate sensor measurements, including vibration, rotational speed, and temperature, are mapped by the encoder into a structured latent space whose components correspond explicitly to physical degradation factors such as rotor imbalance, shaft misalignment, bearing defect severity, gear mesh stiffness variation, applied load, and speed deviation. These factors then serve as variable nodes in a factor graph, where each factor computes a residual between the physically predicted response and the observed spectral features; for example, the rotor dynamics factor compares a numerically integrated equation of motion against the reconstructed vibration signal, whereas the bearing kinematics factor evaluates energy mismatches at characteristic defect frequencies. The training objective combines the data-driven prediction error with aggregated physics residuals, a correlation-based disentanglement penalty, and a sparsity constraint on factor activations, so that only relevant physical mechanisms are engaged for a given fault scenario. During inference, the dominant residual pathway yields a physically grounded explanation for the diagnosis and remaining useful life prediction. The main contribution lies in coupling mechanical laws with latent factor learning through a differentiable graph, which enables interpretable separation of concurrent faults. This approach offers a principled route toward trustworthy, physics-consistent prognostics for safety-critical rotating equipment.