Predicting bearing remaining useful life (RUL) under unseen operating condi-tions remains a major challenge for data-driven prognostics. We evaluate whether Early Warning Signal (EWS) features—rooted in statistical physics—enable deep learning models to learn physically meaningful representations. Six LSTM variants (simple unidirectional, bidirectional, attention-augmented, and domain-adversarial) are compared across three leave-one-condition-out splits of the XJTU-SY dataset (15 bearings, three speeds/loads). Rigorous multi-seed valida-tion (15 independent random seeds per split) and Bayesian posterior estimation establish stable performance. Optimal architecture is context-dependent: simple unidirectional LSTM excels on the lowest-speed test condition (MAE 0<Emphasis Type="BoldItalic">.</Emphasis>275 <Emphasis Type="BoldItalic">±</Emphasis> 0<Emphasis Type="BoldItalic">.</Emphasis>020 min, <Emphasis Type="BoldItalic">R</Emphasis>2 = 0<Emphasis Type="BoldItalic">.</Emphasis>556), domain-adaptation LSTM on the intermediate con-dition (MAE 0<Emphasis Type="BoldItalic">.</Emphasis>712 <Emphasis Type="BoldItalic">±</Emphasis> 0<Emphasis Type="BoldItalic">.</Emphasis>038 min, <Emphasis Type="BoldItalic">R</Emphasis>2 = 0<Emphasis Type="BoldItalic">.</Emphasis>184), and bidirectional LSTM with attention on the highest-speed condition (MAE 2<Emphasis Type="BoldItalic">.</Emphasis>36 <Emphasis Type="BoldItalic">±</Emphasis> 0<Emphasis Type="BoldItalic">.</Emphasis>12 min, <Emphasis Type="BoldItalic">R</Emphasis>2 = 0<Emphasis Type="BoldItalic">.</Emphasis>412). SHAP analysis reveals a pattern consistent with bearing fault physics: at the lowest test speed (35 Hz) the model relies predominantly on the low-frequency approximation band (0–800 Hz, cA4/other ratio 1<Emphasis Type="BoldItalic">.</Emphasis>50, 95% CI [1<Emphasis Type="BoldItalic">.</Emphasis>29<Emphasis Type="BoldItalic">,</Emphasis> 1<Emphasis Type="BoldItalic">.</Emphasis>75]), at intermediate speed (37.5 Hz) low-frequency importance increases (ratio 1<Emphasis Type="BoldItalic">.</Emphasis>83, [1<Emphasis Type="BoldItalic">.</Emphasis>68<Emphasis Type="BoldItalic">,</Emphasis> 1<Emphasis Type="BoldItalic">.</Emphasis>95]), and at the highest speed (40 Hz) the mid-frequency detail band (800–1600 Hz) becomes dominant (ratio 0<Emphasis Type="BoldItalic">.</Emphasis>752, [0<Emphasis Type="BoldItalic">.</Emphasis>686<Emphasis Type="BoldItalic">,</Emphasis> 0<Emphasis Type="BoldItalic">.</Emphasis>831]). This speed-dependent shift aligns with bearing fault physics, where characteristic frequencies and their harmonics move upward with rotational speed. An ablation study demonstrates that raw vibration input yields strongly negative <Emphasis Type="BoldItalic">R</Emphasis>2 (<Emphasis Type="BoldItalic">−</Emphasis>0<Emphasis Type="BoldItalic">.</Emphasis>58), con-firming that wavelet-based EWS features are indispensable for cross-condition generalisation. These findings establish that while attention improves temporal modelling, robust transfer and interpretability emerge from SHAP-based spectral attribution on physics-inspired EWS features. While validation on addi-tional datasets is needed, this work provides both a practical baseline and a validation framework for transparent AI in industrial prognostics.

Cross-Condition Bearing Prognostics Using Early Warning Signal Features: A Comparative Study of Attention Mechanisms and SHAP-Based Spectral Attribution

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发表日期：

2026年5月30日

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Thuraya Shaheen,
Elena Gebel

摘要

Predicting bearing remaining useful life (RUL) under unseen operating condi-tions remains a major challenge for data-driven prognostics. We evaluate whether Early Warning Signal (EWS) features—rooted in statistical physics—enable deep learning models to learn physically meaningful representations. Six LSTM variants (simple unidirectional, bidirectional, attention-augmented, and domain-adversarial) are compared across three leave-one-condition-out splits of the XJTU-SY dataset (15 bearings, three speeds/loads). Rigorous multi-seed valida-tion (15 independent random seeds per split) and Bayesian posterior estimation establish stable performance. Optimal architecture is context-dependent: simple unidirectional LSTM excels on the lowest-speed test condition (MAE 0.275 ± 0.020 min, R² = 0.556), domain-adaptation LSTM on the intermediate con-dition (MAE 0.712 ± 0.038 min, R² = 0.184), and bidirectional LSTM with attention on the highest-speed condition (MAE 2.36 ± 0.12 min, R² = 0.412). SHAP analysis reveals a pattern consistent with bearing fault physics: at the lowest test speed (35 Hz) the model relies predominantly on the low-frequency approximation band (0–800 Hz, cA4/other ratio 1.50, 95% CI [1.29, 1.75]), at intermediate speed (37.5 Hz) low-frequency importance increases (ratio 1.83, [1.68, 1.95]), and at the highest speed (40 Hz) the mid-frequency detail band (800–1600 Hz) becomes dominant (ratio 0.752, [0.686, 0.831]). This speed-dependent shift aligns with bearing fault physics, where characteristic frequencies and their harmonics move upward with rotational speed. An ablation study demonstrates that raw vibration input yields strongly negative R² (−0.58), con-firming that wavelet-based EWS features are indispensable for cross-condition generalisation. These findings establish that while attention improves temporal modelling, robust transfer and interpretability emerge from SHAP-based spectral attribution on physics-inspired EWS features. While validation on addi-tional datasets is needed, this work provides both a practical baseline and a validation framework for transparent AI in industrial prognostics.