Physics-Informed Multi-Scale Network with Loss-Guided Curriculum Learning for Robust Fault Diagnosis
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Published
Jul 5, 2026
Panfeng Bao
Wenjun Yi
Yue Zhu
Yufeng Shen
Haotian Peng
Abstract
Reliable fault diagnosis of rotating machinery is critical, yet early weak fault impulses are frequently buried in severe compound interference from mechanical harmonics and environmental noise. To address this, a novel Physics-Informed Multi-Scale Network (PI-MSN) is proposed. Variational Mode Decomposition (VMD) is first employed to decouple raw signals into distinct physical frequency bands. Subsequently, a Physics-Informed Channel Attention (PICA) module jointly evaluates the Kurtosis and Root Mean Square of each channel to autonomously highlight fault impulses and suppress harmonic interference. A Multi-Scale Feature Extractor then captures comprehensive fault characteristics. Furthermore, a closed-loop Loss-Guided Smooth Interference Scheduler (LGSIS) dynamically regulates injected interference during training based on real-time loss, fundamentally eradicating catastrophic forgetting. Extensive experiments on the CWRU and HUST datasets demonstrate the framework's exceptional robustness. The highly lightweight PI-MSN achieves state-of-the-art diagnostic accuracy, sustaining over 98\% accuracy even under severe -4 dB compound interference, proving that physical interpretability effectively eliminates the reliance on massive parameter stacking.
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Keywords
Robust fault diagnosis, Physics-informed deep learning, Curriculum learning, Variational mode decomposition, Channel attention
References
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Case Western Reserve University. (2019). Case western reserve university bearing data center. https://engineering.case.edu/bearingdatacenter/downloaddata-file.
Chen, X., Zhang, B., & Gao, D. (2021, April). Bearing fault diagnosis base on multi-scale CNN and LSTM model. Journal of Intelligent Manufacturing, 32(4), 971–987. doi: 10.1007/s10845-020-01600-2
Chen, Z., Hu, B., Chen, Z., & Zhang, J. (2024, October). Progress and thinking on self-supervised learning methods in computer vision: A review. IEEE Sensors Journal, 24(19), 29524–29544. doi: 10.1109/JSEN.2024.3443885
Chen, Z., & Li, W. (2017, July). Multisensor feature fusion for bearing fault diagnosis using sparse autoencoder and deep belief network. IEEE Transactions on Instrumentation and Measurement, 66(7), 1693–1702. doi: 10.1109/TIM.2017.2669947
Chopra, P., Kumar, H., & Yadav, S. (2025, March). PNN: A Novel Progressive Neural Network for Fault Classification in Rotating Machinery under Small Dataset Constraint (No. arXiv:2503.18263). arXiv. doi: 10.48550/arXiv.2503.18263
Dong, Y., Jiang, H., Yao, R., Mu, M., & Yang, Q. (2024, March). Rolling bearing intelligent fault diagnosis towards variable speed and imbalanced samples using multiscale dynamic supervised contrast learning. Reliability Engineering & System Safety, 243, 109805. doi: 10.1016/j.ress.2023.109805
Dragomiretskiy, K., & Zosso, D. (2014, February). Variational mode decomposition. IEEE Transactions on Signal Processing, 62(3), 531–544. doi: 10.1109/TSP.2013.2288675
Hu, J., Shen, L., & Sun, G. (2018). Squeeze-and-Excitation Networks. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (pp. 7132–7141).
Ji, M., & Zhao, G. (2024). DEViT: Deformable convolution-based vision transformer for bearing fault diagnosis. IEEE Transactions on Instrumentation and Measurement, 73, 1–13. doi: 10.1109/TIM.2024.3440383
Jiang, X., Li, X., Wang, Q., Song, Q., Liu, J., & Zhu, Z. (2024, January). Multi-sensor data fusion-enabled semisupervised optimal temperature-guided pcl framework for machinery fault diagnosis. Information Fusion, 101, 102005. doi: 10.1016/j.inffus.2023.102005
Li, G., Atoui, M. A., & Li, X. (2025, April). Attention-Based Multi-Scale Temporal Fusion Network for Uncertain-Mode Fault Diagnosis in Multimode Processes (No. arXiv:2504.05172). arXiv. doi: 10.48550/arXiv.2504.05172
Liao, J.-X., Dong, H.-C., Sun, Z.-Q., Sun, J., Zhang, S., & Fan, F.-L. (2023). Attention-embedded quadratic network (qttention) for effective and interpretable bearing fault diagnosis. IEEE Transactions on Instrumentation and Measurement, 72, 1–13. doi: 10.1109/TIM.2023.3259031
Liu, F., Zhang, T., Zhang, C., Liu, L., Wang, L., & Liu, B. (2023, April). A Review of the Evaluation System for Curriculum Learning. Electronics, 12(7).
Liu, R., Ding, X., Zhang, Y., Zhang, M., & Shao, Y. (2023, February). Variable-scale evolutionary adaptive mode denoising in the application of gearbox early fault diagnosis. Mechanical Systems and Signal Processing, 185, 109773. doi: 10.1016/j.ymssp.2022.109773
Luo, T., Qiu, M., Wu, Z., Zhao, Z., & Zhang, D. (2025, March). Bearing fault diagnosis based on multi-scale spectral images and convolutional neural network (No. arXiv:2503.21566). arXiv. doi: 10.48550/arXiv.2503.21566
Ni, Q., Ji, J., Halkon, B., Feng, K., & Nandi, A. K. (2023, October). Physics-informed residual network (PIResNet) for rolling element bearing fault diagnostics. Mechanical Systems and Signal Processing, 200, 110544. doi: 10.1016/j.ymssp.2023.110544
Niu, G., Liu, E., Wang, X., Ziehl, P., & Zhang, B. (2023, January). Enhanced Discriminate Feature Learning Deep Residual CNN for Multitask Bearing Fault Diagnosis With Information Fusion. IEEE Transactions on Industrial Informatics, 19(1), 762–770. doi: 10.1109/TII.2022.3179011
Pancaldi, F., Dibiase, L., & Cocconcelli, M. (2023, April). Impact of noise model on the performance of algorithms for fault diagnosis in rolling bearings. Mechanical Systems and Signal Processing, 188, 109975. doi: 10.1016/j.ymssp.2022.109975
Peng, D., Wang, H., Desmet, W., & Gryllias, K. (2023, April). RMA-CNN: A residual mixed-domain attention CNN for bearings fault diagnosis and its time-frequency domain interpretability. Journal of Dynamics, Monitoring and Diagnostics, 1–18. doi: 10.37965/jdmd.2023.156
Peng, H., Du, J., Gao, J., Wang, Y., & Wang, W. (2024, May). Adversarial training of multi-scale channel attention network for enhanced robustness in bearing fault diagnosis. Measurement Science and Technology, 35(5), 056204. doi: 10.1088/1361-6501/ad2828
Peng, H., Wang, W., Gao, J., Wang, Y., & Du, J. (2025, September). A lightweight triple-stream network with multisensor fusion for enhanced few-shot learning fault diagnosis. IEEE Transactions on Reliability, 74(3), 4062–4075. doi: 10.1109/TR.2025.3540500
Ruan, D., Wang, J., Yan, J., & G¨uhmann, C. (2023, January). CNN parameter design based on fault signal analysis and its application in bearing fault diagnosis. Advanced Engineering Informatics, 55, 101877. doi: 10.1016/j.aei.2023.101877
Shao, H., Lin, J., Zhang, L., Galar, D., & Kumar, U. (2021, October). A novel approach of multisensory fusion to collaborative fault diagnosis in maintenance. Information Fusion, 74, 65–76. doi: 10.1016/j.inffus.2021.03.008
Song, Q., Jiang, X., Du, G., Liu, J., & Zhu, Z. (2023, April). Smart multichannel mode extraction for enhanced bearing fault diagnosis. Mechanical Systems and Signal Processing, 189, 110107. doi: 10.1016/j.ymssp.2023.110107
Soroush, K., Shirazi, N., & Raji, M. (2025, July). Efficient Triple Modular Redundancy for Reliability Enhancement of DNNs Using Explainable AI (No. arXiv:2507.08829). arXiv. doi: 10.48550/arXiv.2507.08829
Su, Y., Shi, L., Zhou, K., Bai, G., & Wang, Z. (2024, April). Knowledge-informed deep networks for robust fault diagnosis of rolling bearings. Reliability Engineering & System Safety, 244, 109863. doi: 10.1016/j.ress.2023.109863
Sun, W., Yan, R., Jin, R., Zhao, R., & Chen, Z. (2024, December). Curriculum-Based Federated Learning for Machine Fault Diagnosis With Noisy Labels. IEEE Transactions on Industrial Informatics, 20(12), 13820–13830. doi: 10.1109/TII.2024.3435449
Thuan, N. D., & Hong, H. S. (2023, July). HUST bearing: A practical dataset for ball bearing fault diagnosis. BMC Research Notes, 16(1), 138. doi: 10.1186/s13104-023-06400-4
Wang, Y., Gao, J., Wang, W., Yang, X., & Du, J. (2024, April). Curriculum learning-based domain generalization for cross-domain fault diagnosis with category shift. Mechanical Systems and Signal Processing, 212, 111295. doi: 10.1016/j.ymssp.2024.111295
Wei, Q., Tian, X., Cui, L., Zheng, F., & Liu, L. (2023, September). WSAFormer-DFFN: A model for rotating machinery fault diagnosis using 1D window-based multi-head self-attention and deep feature fusion network. Engineering Applications of Artificial Intelligence, 124, 106633. doi: 10.1016/j.engappai.2023.106633
Yan, X., Yan, W.-J., Xu, Y., & Yuen, K.-V. (2023, November). Machinery multi-sensor fault diagnosis based on adaptive multivariate feature mode decomposition and multi-attention fusion residual convolutional neural network. Mechanical Systems and Signal Processing, 202, 110664. doi: 10.1016/j.ymssp.2023.110664
Zhang, G., Kong, X., Ma, H., Wang, Q., Du, J., & Wang, J. (2025, April). Dual disentanglement domain generalization method for rotating Machinery fault diagnosis. Mechanical Systems and Signal Processing, 228, 112460. doi: 10.1016/j.ymssp.2025.112460
Zhang, W., Peng, G., Li, C., Chen, Y., & Zhang, Z. (2017, February). A New Deep Learning Model for Fault Diagnosis with Good Anti-Noise and Domain Adaptation Ability on Raw Vibration Signals. Sensors, 17(2), 425. doi: 10.3390/s17020425
Zhao, C., Zio, E., & Shen, W. (2024, May). Domain generalization for cross-domain fault diagnosis: An application-oriented perspective and a benchmark study. Reliability Engineering & System Safety, 245, 109964. doi: 10.1016/j.ress.2024.109964
Zhao, Y., Zhang, Y., Li, Z., Bu, L., & Han, S. (2023, April). AI-enabled and multimodal data-driven smart health monitoring of wind power systems: A case study. Advanced Engineering Informatics, 56, 102018. doi: 10.1016/j.aei.2023.102018
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