Monotonic Latent Manifold Bayesian Inference for Robust Industrial Predictive Maintenance

Abstract

Industrial predictive maintenance systems require not only accurate fault prediction but also reliable uncertainty estimation and robustness under noisy operational conditions. However, conventional deep learning approaches often produce temporally inconsistent failure trajectories and exhibit poor probabilistic calibration when exposed to stochastic sensor disturbances. This study proposes a Monotonic Latent Manifold Bayesian Neural Network (MM-BNN) framework for robust industrial predictive maintenance. The MM-BNN models degradation progression as a constrained non-decreasing latent probabilistic trajectory, thereby ensuring physically consistent temporal evolution while preserving Bayesian uncertainty quantification. A monotonic latent manifold update mechanism is introduced to enforce structured degradation dynamics across sequential observations. In addition, Bayesian posterior inference is performed using the No-U-Turn Sampler (NUTS) to capture uncertainty in latent degradation states. The proposed MM-BNN framework is evaluated against multiple baseline models, including multilayer perceptron networks, gated recurrent units, random forests, support vector machines, XGBoost, and standard Bayesian neural networks. Experimental results demonstrate that the MM-BNN achieves superior discriminative performance with an average Area Under the Curve (AUC) of 0.772, outperforming competing approaches, most of which remain close to random classification performance. Reliability analysis further demonstrates improved probabilistic calibration, with a low Expected Calibration Error (ECE approx 0.034) and stable reliability behavior under increasing levels of stochastic noise. Ablation studies confirm that the monotonic degradation constraint is the primary factor driving predictive stability and robustness improvements. Furthermore, robustness experiments show that the MM-BNN maintains stable predictive performance even under severe noise perturbations. Overall, the findings indicate that the proposed MM-BNN framework provides a reliable, interpretable, and uncertainty-aware approach for predictive maintenance in safety-critical industrial environments.