HYBRID RELIABILITY MODELLING FOR ROTATING EQUIPMENT: PHYSICS‑INFORMED LEARNING WITH SPARSE FAILURE DATA

Abstract

Accurate reliability estimation for rotating equipment is severely challenged by the chronic scarcity of failure data in industrial settings — assets with mean times between failures measured in thousands of hours routinely accumulate fewer than ten observed failures across their entire operational life. Classical Weibull maximum-likelihood estimation (MLE) under such sparse-data regimes produces wide confidence intervals that are operationally uninformative, while purely data-driven machine learning models lack the physical grounding to generalise reliably beyond the observed failure regime. The present paper proposes a Physics-Informed Machine Learning (PIML) hybrid framework that embeds differential-equation-based degradation physics directly into the prior structure of a Bayesian Weibull model, combining the explanatory power of first-principles mechanics with the uncertainty-quantification capabilities of Bayesian inference. Degradation physics — encompassing Lundberg-Palmgren contact fatigue, Archard tribological wear, and rotor-dynamic stress accumulation — constrain the Weibull shape and scale parameters through a physics-derived likelihood structure, regularising inference even when observed failure counts are as low as n = 3 to 5. The framework also assimilates continuous ISO 13374-compliant condition-monitoring sensor streams through a sensor-informed likelihood update, enabling real-time posterior revision without requiring new observed failures. Validation is performed on six rotating equipment types (centrifugal pump, reciprocating compressor, axial gas turbine, high-speed gearbox, rolling-element bearing, and centrifugal compressor) at a heavy petrochemical facility over a 48-month period, demonstrating a 66% mean reduction in B10 life RMSE relative to classical MLE, 91.7% empirical coverage of 90% posterior predictive intervals, and a prognostic warning horizon of 400–800 hours ahead of failure compared to 50–150 hours for threshold-based alarms. The proposed methodology is directly compatible with CMMS environments and ISO 13374 data architectures.