A weighted DJP-MMD based deep transfer metric learning for the fault diagnosis of bearing under variable working conditions

Abstract

The change of working conditions not only makes the data distribution inconsistent, but also increases the diagnosis difficulty of fuzzy samples at the fault boundary. The traditional distance-based deep metric learning cannot effectively classify the fuzzy samples at the fault boundary. In the traditional transfer learning models, the maximum mean discrepancy (MMD) and joint maximum mean discrepancy only increase the transferability of same-class samples, and neglect the discriminability of different-class samples across different domains. The discriminative joint probability MMD (DJP-MMD) increases the transferability of same-class samples and the discriminability of different-class samples across different domains, but it only considers the global transferability of all fault classes, ignoring the different transferability of each same fault class. Therefore, a Yu norm-based deep transfer metric learning based on weighted DJP-MMD is proposed to further improve the diagnosis accuracy of bearings under variable working conditions. The deep transfer metric learning model adopts the Yu norm-based similarity instead of the distance-based similarity to effectively classify the data samples, especially those at the fault boundary, and uses the weighted DJP-MMD to measure the data distribution discrepancy between the source and target domains to increase the transferability of each same-class samples and discriminability of different-class samples across different domains. Through the fault diagnosis analysis on bearings under variable working conditions, the diagnosis results demonstrate that the proposed deep transfer metric learning model can diagnose bearing faults with higher accuracy, stronger generalization and anti-noise capabilities compared with other fault diagnosis methods based on transfer learning.

Graphical abstract

Keywords

Yu norm / weighted DJP-MMD / deep transfer metric learning / fault diagnosis / variable working conditions

References

[1] Jiang H K, Li C L, Li H X. An improved EEMD with multiwavelet packet for rotating machinery multi-fault diagnosis. Mechanical Systems and Signal Processing, 2013, 36(2): 225–239

[2] Qin Y, Qian Q, Wang Y, Zhou J H. Intermediate distribution alignment and its application into mechanical fault transfer diagnosis. IEEE Transactions on Industrial Informatics, 2022, 18(10): 7305–7315

[3] Li S, Ji J C, Feng K, Zhang K, Ni Q, Xu Y D. Neuro-fuzzy system-guided cross-modal zero-sample diagnostic framework using multisource heterogeneous noncontact sensing data. IEEE Transactions on Fuzzy Systems, 2025, 33(1): 302–313

[4] Feng K, Ji J C, Ni Q. A novel gear fatigue monitoring indicator and its application to remaining useful life prediction for spur gear in intelligent manufacturing systems. International Journal of Fatigue, 2023, 168: 107459

[5] Feng K, Ji J C, Zhang Y C, Ni Q, Liu Z, Beer M. Digital twin-driven intelligent assessment of gear surface degradation. Mechanical Systems and Signal Processing, 2023, 186: 109896

[6] Wang J, Shao H D, Peng Y, Liu B. PSparseFormer: enhancing fault feature extraction based on parallel sparse self-attention and multiscale broadcast feed-forward block. IEEE Internet of Things Journal, 2024, 11(13): 22982–22991

[7] Zhang W, Hao H S, Zhang Y W. State of charge prediction of lithium-ion batteries for electric aircraft with swin transformer. IEEE/CAA Journal of Automatica Sinica, 2023, 12(3): 645–647

[8] Yan S, Shao H D, Wang X D, Wang J. Few-shot class-incremental learning for system-level fault diagnosis of wind turbine. IEEE/ASME Transactions on Mechatronics, 2024,

[9] Qin Y, Wu X G, Luo J. Data-model combined driven digital twin of life-cycle rolling bearing. IEEE Transactions on Industrial Informatics, 2022, 3(18): 1530–1540

[10] Li X Q, Jiang H K, Niu M G, Wang R X. An enhanced selective ensemble deep learning method for rolling bearing fault diagnosis with beetle antennae search algorithm. Mechanical Systems and Signal Processing, 2020, 142: 106752

[11] Shao H D, Jiang H K, Zhang H Z, Liang T C. Electric locomotive bearing fault diagnosis using a novel convolutional deep belief network. IEEE Transactions on Industrial Electronics, 2018, 65(3): 2727–2736

[12] Zhao K, Jiang H K, Li X Q, Wang R X. An optimal deep sparse autoencoder with gated recurrent unit for rolling bearing fault diagnosis. Measurement Science & Technology, 2020, 31(1): 015005

[13] Lei Y G, Yang B, Du Z J, Lv N. Deep transfer diagnosis method for machinery in big data era. Journal of Mechanical Engineering, 2019, 55(7): 1–8

[14] Shao H D, Zhang X Y, Cheng J S, Yang Y. Intelligent fault diagnosis of bearing using enhanced deep transfer auto-encoder. Journal of Mechanical Engineering, 2020, 56(9): 84–90

[15] Zhou Y X, Dong Y N, Zhou H K, Tang G. Deep dynamic adaptive transfer network for rolling bearing fault diagnosis with considering cross-machine instance. IEEE Transactions on Instrumentation and Measurement, 2021, 70: 1–11

[16] Wang R X, Jiang H K, Zhu K, Wang Y F, Liu C Q. A deep feature enhanced reinforcement learning method for rolling bearing fault diagnosis. Advanced Engineering Informatics, 2022, 54: 101750

[17] Liu B, Li R L, Feng J F. A brief introduction to deep metric learning. CAAI Transactions on Intelligent Systems, 2019, 14(6): 1064–1072

[18] Li X J, Xu Z B, Xiong W, Wang Z G, Tan J J. Bearing fault diagnosis method based on deep metric learning. Journal of Vibration and Shock, 2020, 39(15): 25–31

[19] Chen K Y, Zhang J Y, Chen S, Zhang S N. Deep metric learning for robust radar signal recognition. Digital Signal Processing, 2023, 137: 104017

[20] Li W Z, Zhou J W, Li X, Cao Y, Jin G. Few-shot object detection on aerial imagery via deep metric learning and knowledge inheritance. International Journal of Applied Earth Observation and Geoinformation, 2023, 122: 103397

[21] Biswas C, Ganguly D, Roy D, Bhattacharya U. Weakly supervised deep metric learning on discrete metric spaces for privacy-preserved clustering. Information Processing & Management, 2023, 60(1): 103109

[22] Xu Z B, Li X J, Lin H, Wang Z G, Peng T. Fault diagnosis of rolling bearing based on modified deep metric learning method. Shock and Vibration, 2021, 2021(1): 6635008

[23] Jia S Y, Deng Y F, Jun L, Du S C, Xie Z Y. Joint distribution adaptation with diverse feature aggregation: a new transfer learning framework for bearing diagnosis across different machines. Measurement, 2022, 187: 110332

[24] Wen H R, Guo W, Li X. A novel deep clustering network using multi-representation autoencoder and adversarial learning for large cross-domain fault diagnosis of rolling bearings. Expert Systems with Applications, 2023, 225: 120066

[25] Li X, Yu S P, Lei Y G, Li N P, Yang B. Dynamic vision-based machinery fault diagnosis with cross-modality feature alignment. IEEE/CAA Journal of Automatica Sinica, 2024, 11(10): 2068–2081

[26] Li X, Zhang W, Li X, Hao H S. Partial domain adaptation in remaining useful life prediction with incomplete target data. IEEE/ASME Transactions on Mechatronics, 2024, 29(3): 1903–1913

[27] Zhu Y Y, Pei Y, Wang A Q, Xie B, Qian Z. A partial domain adaptation scheme based on weighted adversarial nets with improved CBAM for fault diagnosis of wind turbine gearbox. Engineering Applications of Artificial Intelligence, 2023, 125: 106674

[28] Chu L X, Li Q, Yang B R, Chen L, Shen C Q, Wang D. Exploring the essence of compound fault diagnosis: a novel multi-label domain adaptation method and its application to bearings. Heliyon, 2023, 9(3): e14545

[29] Wu Z H, Jiang H K, Wang X, Zhu H X. Knowledge correlation graph-guided multi-source interaction domain adaptation network for rotating machinery fault diagnosis. ISA Transactions, 2023, 142: 663–682

[30] Chen J, Liu H. A multi-gradient hierarchical domain adaptation network for transfer diagnosis of bearing faults. Expert Systems with Applications, 2023, 225: 120139

[31] Li Y, Liu Y F, Zheng D R, Huang Y H, Tang Y L. Discriminable feature enhancement for unsupervised domain adaptation. Image and Vision Computing, 2023, 137: 104755

[32] Weng X X, Huang Y C, Li Y, Yang H, Yu S H. Unsupervised domain adaptation for crack detection. Automation in Construction, 2023, 153: 104939

[33] Wang S D, Rong R C, Gu Z F, Fujimoto J Y, Zhan X W, Xie Y, Xiao G H. Unsupervised domain adaptation for nuclei segmentation: adapting from hematoxylin & eosin stained slides to immunohistochemistry stained slides using a curriculum approach. Computer Methods and Programs in Biomedicine, 2023, 241: 107768

[34] Pereira L A M, da Silva Torres R. Semi-supervised transfer subspace for domain adaptation. Pattern Recognition, 2018, 75: 235–249

[35] Wang P, Li P F, Li Y M, Xu J, Jiang M F. Classification of histopathological whole slide images based on multiple weighted semi-supervised domain adaptation. Biomedical Signal Processing and Control, 2022, 73: 103400

[36] Wang W, Wang H, Zhang Z X, Zhang C, Gao Y. Semi-supervised domain adaptation via Fredholm integral based kernel methods. Pattern Recognition, 2019, 85: 185–197

[37] LongM S, Cao Y, WangJ M, JordanM. Learning transferable features with deep adaptation networks. In: Proceedings of the 32nd International Conference on International Conference on Machine Learning (ICML). JMLR, 2015, 97–105

[38] LongM S, Zhu H, WangJ M, JordanM I. Deep transfer learning with joint adaptation networks. In: Proceedings of the 34th International Conference on Machine Learning. JMLR, 2017, 2208–2217

[39] SunB C, Saenko K. Deep CORAL: correlation alignment for deep domain adaptation. In: Hua G, Jégou H, eds. Computer Vision – ECCV 2016 Workshops. Cham: Springer, 2016, 443–450

[40] Wen L, Gao L, Li X Y. A new deep transfer learning based on sparse auto-encoder for fault diagnosis. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2019, 49(1): 136–144

[41] Guo L, Lei Y G, Xing S B, Yan T, Li N P. Deep convolutional transfer learning network: a new method for intelligent fault diagnosis of machines with unlabeled data. IEEE Transactions on Industrial Electronics, 2019, 66(9): 7316–7325

[42] Han T, Liu C, Yang W G, Jiang D X. Deep transfer network with joint distribution adaptation: a new intelligent fault diagnosis framework for industry application. ISA Transactions, 2020, 97: 269–281

[43] Ma P, Zhang H L, Fan W H, Wang C. A diagnosis framework based on domain adaptation for bearing fault diagnosis across diverse domains. ISA Transactions, 2020, 99: 465–478

[44] ZhangW, Wu D R. Discriminative joint probability maximum mean discrepancy for domain adaptation. In: Proceedings of 2020 International Joint Conference on Neural Networks. Glasgow: IEEE, 2020, 1–8

[45] Yan S C, Xu D, Zhang B Y, Zhang H J, Yang Q, Lin S. Graph embedding and extensions: a general framework for dimensionality reduction. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2007, 29(1): 40–51

[46] Luukka P. Similarity classifier using similarity measure derived from Yu’s norms in classification of medical data sets. Computers in Biology and Medicine, 2007, 37(8): 1133–1140

[47] Daga A P, Fasana A, Marchesiello S, Garibaldi L. The Politecnico di Torino rolling bearing test rig: description and analysis of open access data. Mechanical Systems and Signal Processing, 2019, 120: 252–273

RIGHTS & PERMISSIONS

Higher Education Press