Empirical Calibration and Conditional-Reliability Diagnostics for Bearing RUL Prediction under Operating-Regime Shift

2026-07-09

AI Summary

This study addresses the challenge of simultaneously achieving accurate point estimates and reliable prediction intervals for bearing remaining useful life (RUL) under varying operating conditions, where conventional evaluation metrics often obscure conditional failure modes. The authors propose a predictive representation model grounded in empirical residual calibration, integrating vibration signals, engineered features, and operational conditions. A bounded reliability assessment protocol is introduced, enabling condition-stratified diagnostics on rigorously partitioned datasets. The analysis reveals substantially degraded coverage—dropping as low as 0.666—under specific conditions such as low load or high rotational speed, and identifies missing raw sensor channels as a critical failure mode. Following residual calibration, the method achieves a 90% prediction interval coverage of 0.941, with a normalized mean absolute error (NMAE) of 0.1477 for the primary model.

Abstract

Remaining useful life (RUL) estimates support reliability and maintenance decisions only if both point accuracy and prediction intervals remain trustworthy when operating conditions change. Convenient mixed splits can hide that failure. This paper studies the question on a documented 10-bearing PHME subset with time-varying load and speed. Derived load-speed regimes define the held-out evaluation units, while models receive only measured load and speed as context. A calibrated predictive-representation model fuses raw vibration windows, engineered descriptors, and operating context, then forms intervals by empirical residual calibration. Under strict train/validation/calibration/test separation, the model reaches normalized MAE 0.1477, empirical 90% coverage 0.900, and retrospective absolute-step MAE 285.26; a 400-tree random forest reaches 0.1538, 0.871, and 294.57. The results do not show uniform dominance: conditional diagnostics expose non-uniform reliability, including 0.666 coverage in a low-load/high-speed cell, and a post-hoc pooled regime-conditioned residual diagnostic raises that cell to 0.941 only as motivation for future pre-specified conditional calibration. Stress tests further identify raw-channel loss as the largest tested reliability failure mode. The contribution is therefore a bounded reliability-evaluation protocol for the processed 10-bearing subset, with conditional undercoverage and raw-channel loss reported explicitly as failure modes rather than deployment guarantees.

Problem

• Remaining Useful Life
• Operating-Regime Shift
• Prediction Reliability
• Conditional Calibration
• Empirical Coverage

Innovation

• empirical calibration
• conditional reliability
• operating-regime shift
• residual diagnostics
• RUL prediction