In the field of fault diagnosis, most existing research primarily focuses on improving model accuracy and stability, while relatively little attention has been paid to model reliability and the quantification of uncertainty. When exposed to strong noise interference or fault patterns from unknown distributions, models often still produce deterministic diagnostic outputs without indicating the associated level of uncertainty. To address this issue, this paper proposes an adaptive post-hoc calibration method—Input-dependent Temperature Scaling (ITS)—built upon a Bayesian Convolutional Neural Network (B-CNN) to enhance confidence calibration. Unlike conventional global temperature scaling, ITS adaptively learns temperature parameters from input features, thereby enabling more fine-grained confidence adjustment. Within the B-CNN framework, ITS effectively integrates parameter uncertainty with input-dependent post-hoc calibration. Experimental results on the CWRU dataset and a test bench developed by our research group demonstrate that the proposed method can significantly reduce calibration error and improve model reliability, while maintaining stable classification accuracy.
BlundellCCornebiseJKavukcuogluK, et al. (2015) Weight uncertainty in neural networks. ICML'15: Proceedings of the 32nd International Conference on International Conference on Machine Learning37: 1613–1622.
2.
ChenYLiHKCaoSX, et al. (2024) CE-FFGAN: a feature fusion generative adversarial network with deep embedded category information for limited sample fault diagnosis of rotating machinery under speed variation. Advanced Engineering Informatics62: 102605.
3.
GawlikowskiJTassiCRNAliM, et al. (2023) A survey of uncertainty in deep neural networks. Artificial Intelligence Review56(S1): 1513–1589. https://doi.org/10.1007/s10462-023-10562-9
4.
GuoCPleissGSunY, et al. (2017) On calibration of modern neural networks. In: 34th International Conference on Machine Learning (ICML 2017), Sydney, Australia, 6–11 August 2017. https://arxiv.org/abs/1706.04599
5.
HeYLHeDQLaoZP, et al. (2024a) Few-shot fault diagnosis of turnout switch machine based on flexible semi-supervised meta-learning network. Knowledge-Based Systems294: 111746. https://doi.org/10.1016/j.knosys.2024.111746
6.
HeDQZouXYJinZZ, et al. (2024b) Intelligent fault diagnosis of train bearing based on ISTOA-VMD and SE-WDCNN. Journal of Vibration and Control30(15–16): 3572–3583. https://doi.org/10.1177/10775463231196351
7.
HuCQLiYHChenZ, et al. (2023) Research on fault diagnosis of rolling bearing based on multi-sensor bi-layer information fusion under small samples. Review of Scientific Instruments8(9): 115106. https://doi.org/10.1063/5.0174359
8.
JiaFLeiYGLinJ, et al. (2016) Deep neural networks: a promising tool for fault characteristic mining and intelligent diagnosis of rotating machinery with massive data. Mechanical Systems and Signal Processing72–73: 303–315. https://doi.org/10.1016/j.ymssp.2015.10.025
9.
LeiYGLiXWLiX, et al. (2025) Research on large model for general prognostics and health management of machinery. Journal of Mechanical Engineering61(6): 1–13.
10.
LiBXSongPYZhaoCH (2014) Fusing consensus knowledge: a federated learning method for fault diagnosis via privacy-preserving reference under domain shift. Information Fusion106: 102290. https://doi.org/10.1016/j.inffus.2024.102290
11.
LiZXDingXXSongZZ, et al. (2024) Digital twin-assisted dual transfer: a novel information-model adaptation method for rolling bearing fault diagnosis. Information Fusion106: 102271. https://doi.org/10.1016/j.inffus.2024.102271
12.
LiHJiaoJYLiuZY, et al. (2025a) Trustworthy bayesian deep learning framework for uncertainty quantification and confidence calibration: applicationin machinery fault diagnosis. Reliability Engineering and System Safety255: 110657. https://doi.org/10.1016/j.ress.2024.110657
13.
LiXXuYXLeiYG, et al. (2025b) Research on general foundation model for intelligent fault diagnosis for rotating machinery. Journal of Mechanical Engineering7: 1–12.
14.
MenZHHuCQLiYH, et al. (2023) A hybrid intelligent gearbox fault diagnosis method based on EWCEEMD and whale optimization algorithm-optimized SVM. International Journal of Structural Integrity14(2): 322–336. https://doi.org/10.1108/ijsi-12-2022-0145
15.
MenZHLiYHTangWC, et al. (2024) A new multi-modal time series transformation method and multi-scale convolutional attention network for railway wagon bearing fault diagnosis. Journal of Vibration and Control31(17-18): 3675–3690. https://doi.org/10.1177/10775463241276024
16.
MenZHGongDZhouK, et al. (2025a) Unsupervised domain adaptation method for bearing fault diagnosis assisted by twin data under extreme sample scarcity. Mechanical Systems and Signal Processing239: 113359. https://doi.org/10.1016/j.ymssp.2025.113359
17.
MenZHLiYHGaoL, et al. (2025b) Fault diagnosis method for railway wagon bearings under imbalanced dataset based on improved ACWGAN. Nonlinear Dynamics113: 14935–14962. https://doi.org/10.1007/s11071-025-10878-x
18.
MoSLiPWShiJH, et al. (2025) Rolling bearings fault diagnosis under various loads conditions based on GWJO-VMD-MAFCNN. Structural Health Monitoring14759217251334315. Available at: https://doi.org/10.1177/14759217251334315
19.
MukhotiJKulhariaVSanyalA, et al. (2020) Calibrating deep neural networks using focal loss, In: Proceedings of the 34th International Conference on Neural Information Processing Systems, BC Canada, 22–24 December 2020, pp. 15288–15299.
20.
PereyraGTuckerGChorowskiJ, et al. (2017) Regularizing neural networks by penalizing confident output distributions. Neural and Evolutionary Computing. Canada: Curran Associates Inc. Available at: https://doi.org/10.48550/arXiv.1701.0654
21.
QinYLiuHYWangY, et al. (2024) Inverse physics–informed neural networks for digital twin–based bearing fault diagnosis under imbalanced samples. Knowledge-Based Systems292: 111641. https://doi.org/10.1016/j.knosys.2024.111641
22.
ShaoHDYanSXiaoYM, et al. (2023) Semi-supervised bearing fault diagnosis using improved graph attention network under time-varying speeds. Journal of Electronics & Information Technology45(5): 1550–1558.
23.
ShaoHDZhouXDLinJ, et al. (2024) Few-shot cross-domain fault diagnosis of bearing driven by task-supervised ANIL. IEEE Internet of Things Journal11: 22892–22902. https://doi.org/10.1109/jiot.2024.3360432
SmithWARandallRB (2015) Rolling element bearing diagnostics using the case Western reserve university data: a benchmark study. Mechanical Systems and Signal Processing64: 100–131. https://doi.org/10.1016/j.ymssp.2015.04.021
26.
XiaoYQZhouHYZhouXY, et al. (2025) Multilabel transfer learning method with dynamic multimetric for coupling fault diagnosis. IEEE Transactions on Neural Networks and Learning Systems36(10): 18874–18888. Available at: https://doi.org/10.1109/TNNLS.2025.3573090
27.
XuZYuLYLiSB, et al. (2025) An optimized oversampling-based federated transfer learning approach for rotating machinery cluster fault diagnosis. Journal of Computational Design and Engineering12(8): 154–172.
28.
YangBYZhangJYLiuRN, et al. (2025) Point-to-Set metric-gated mixture of experts for multisource domain adaptation fault diagnosis. IEEE Transactions on Neural Networks and Learning Systems36(8): 14893–14907. https://doi.org/10.1109/TNNLS.2025.3548894
YuQXLiQLiLL, et al. (2025) A survey of data-driven fault-diagnosis methods for large-scale industrial production processes. Chinese Journal of Engineering47(4): 780–793.
ZhangCBJiangPTHouQB, et al. (2021) Delving deep into label smoothing. IEEE transactions on Image Processing30(1): 5984–5996. Available at: https://doi.org/10.1109/TIP.2021.3089942
