A Physics-Guided Statistical Framework for Bearing Fault Diagnosis Under Unit Variability and Rotational Speed Uncertainty

Abstract

Reliable bearing fault diagnosis must differentiate between defects and normal-operation-condition variation. The predictor must remain accurate when shaft speed is uncertain. Conventional accuracy-driven models often ignore false-positive rates and fail to accurately locate faults on unseen bearings’ data. This study proposes a physics-guided statistical framework that integrates resolution-based order screening, envelope peak-to-floor evidence, search- and collision-matched empirical nulls, and conformal calibration against healthy reference data. A two-stage bearing-level rule detects abnormal operation before localizing the dominant fault order. Evaluation comprised controlled simulations, unit-disjoint Paderborn experiments, and a prospectively frozen external test using the University of Ottawa Rolling-Element Dataset: Vibration and Acoustic Faults under Constant Load and Speed Conditions (UORED-VAFCLS). In simulation, family-wise false-positive rates were 2.58% and 3.12% for the two bearing geometries; detection power reached 83.3–93.8% at −4 dB and 98.3–100% at 0 dB, satisfying all registered criteria. On Paderborn, the overall false-positive rate was 7.08%, but condition-specific false alarms reached 17.5%; inner- and outer-race detection reached only 49.8% and 71.5%, despite high localization accuracy. On UORED-VAFCLS, the healthy false-alarm rate remained 5% (1/20 bearings), while developing-fault detection was 40% for both classes and faulty-state detection was 0% for inner-race and 20% for outer-race bearings. All ten inner-race states were mislocalized to the outer-race order. A post-evaluation diagnostic estimated a median speed of 1784 rpm rather than 1750 rpm. The resulting 1.94% discrepancy exceeded the admissible errors for the ball-pass frequency of the inner race (BPFI) and ball-pass frequency of the outer race (BPFO), 0.61% and 0.98%, respectively, indicating order-probe misalignment. These results show that false-alarm calibration can transfer while diagnostic sensitivity and physical localization fail. The study therefore separates calibration from diagnostic transferability and establishes independent bearing-level validation and explicit speed-uncertainty treatment as requirements for trustworthy physics-guided diagnosis.