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

Jul 16, 2026

Remaining useful life (RUL) estimates support maintenance decisions only when both point accuracy and prediction-interval reliability remain credible after operating conditions change. The study analyzes a documented 10-bearing PHME subset with time-varying load and speed, using derived load–speed regimes to define held-out evaluation units and providing models only measured load and speed as context. A calibrated predictive-representation model fuses vibration windows, engineered descriptors, and context, then builds intervals via empirical residual calibration. Results report normalized MAE, empirical coverage, and regime-conditioned undercoverage, plus stress tests identifying raw-channel loss as a major reliability failure mode.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages36

Reading Time1 h 31 min

AccessFree to download

Abstract

Introduction

Problem: trust under operating-regime shift

Prior work and gap

Proposed approach and evaluation focus

arXiv :2607 .08273v 1 [ cs .CE] 9 Jul 2026 Empirical Calibration and Conditional-Reliability Diagnostics for Bearing RUL Prediction under Operating-Regime Shift Shaoliang Yang 1 , Jun Wang∗1, and Yunsheng Wang 1 1 Department of Mechanical Engineering, Santa Clara University, Santa Clara, CA 95053, USA July 9, 2026 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 ina 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. Keywords: reliability; prognostics; remaining useful life; calibration; conformal prediction; operating-regime shift; bearing 1 Introduction Rolling bearings rarely fail under a single fixed load and speed. In service they see changing duty cycles, and those changes reshape both vibration signatures and degradation rates. Remaining useful life (RUL) prediction is meant to turn condition-monitoring signals into time-to-failure estimates that can support inspection and replacement decisions [19, 24, 51] . For bearings, public accelerated-degradation experiments have made vibration-based RUL a mature research setting [35, 45] . The open question is no longer whether a model can fit a convenient split; it is whether accuracy and uncertainty remain trustworthy when operating conditions shift. ∗ Corresponding author. E-mail: [jwang22@scu.edu](jwang22@scu.edu) That shift is the practical bottleneck. A model trained under one load–speed mixture can degrade under another because the signal distribution and the remaining-life mapping both move. Reliability modeling has treated time-varying operating conditions with state-space degradation formulations [26], while data-driven work has pursued cross-condition transfer and domain adaptation [7, 9, 49] . The PHME time-varying operating-condition bearing archive makes the issue concrete: run-to-failure experiments with measured load and speed variation [1, 21] . Methodologically, the surrounding literature is already dense. Deep encoders, recurrent and convolutional predictors, graph fusion models, and PHM surveys establish learned RUL representations as standard tools rather than novelty claims [10, 27, 30, 31, 44, 48] . Digital-twin and physics-informed studies cover much of the language that can otherwise sound new [6, 13, 25, 32, 33] . This paper therefore does not present a new digital twin, a new fatigue theory, or a full-PHME leaderboard result. The gap we address is narrower and more reliability-facing. Under time-varying bearing regimes, point error alone is not enough. Useful evaluation should ask whether a model still works when the test regi

FAQs

What reliability requirement must hold for bearing RUL predictions when operating conditions shift?

Both point accuracy and the trustworthiness of prediction intervals must remain credible after operating conditions change.

How are evaluation splits and reporting units constructed in the study?

Derived load–speed regimes define held-out evaluation units, and models receive only measured load and speed as context.

What main failure modes are highlighted by conditional diagnostics and stress tests?

Conditional diagnostics reveal non-uniform reliability and undercoverage in specific low-load/high-speed cells, and stress tests identify raw-channel loss as the largest tested reliability failure mode.

Jul 16, 2026

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