{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T05:17:47Z","timestamp":1779340667607,"version":"3.51.4"},"reference-count":46,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2023,8,4]],"date-time":"2023-08-04T00:00:00Z","timestamp":1691107200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Guangdong Province Key Construction Discipline Scientific Research Capacity Improvement Project","award":["2022ZDJS114"],"award-info":[{"award-number":["2022ZDJS114"]}]},{"name":"Guangdong Province Key Construction Discipline Scientific Research Capacity Improvement Project","award":["2022SA-07-18"],"award-info":[{"award-number":["2022SA-07-18"]}]},{"name":"Guangdong Province Key Construction Discipline Scientific Research Capacity Improvement Project","award":["JSZZ202301013"],"award-info":[{"award-number":["JSZZ202301013"]}]},{"name":"Guangdong Province Key Construction Discipline Scientific Research Capacity Improvement Project","award":["2021YJ0371"],"award-info":[{"award-number":["2021YJ0371"]}]},{"name":"Key Laboratory of Robot Intelligence Technology for 3C Machinery Industry","award":["2022ZDJS114"],"award-info":[{"award-number":["2022ZDJS114"]}]},{"name":"Key Laboratory of Robot Intelligence Technology for 3C Machinery Industry","award":["2022SA-07-18"],"award-info":[{"award-number":["2022SA-07-18"]}]},{"name":"Key Laboratory of Robot Intelligence Technology for 3C Machinery Industry","award":["JSZZ202301013"],"award-info":[{"award-number":["JSZZ202301013"]}]},{"name":"Key Laboratory of Robot Intelligence Technology for 3C Machinery Industry","award":["2021YJ0371"],"award-info":[{"award-number":["2021YJ0371"]}]},{"name":"Self-made Experimental Instruments and Equipment Project of Shenzhen Technology University","award":["2022ZDJS114"],"award-info":[{"award-number":["2022ZDJS114"]}]},{"name":"Self-made Experimental Instruments and Equipment Project of Shenzhen Technology University","award":["2022SA-07-18"],"award-info":[{"award-number":["2022SA-07-18"]}]},{"name":"Self-made Experimental Instruments and Equipment Project of Shenzhen Technology University","award":["JSZZ202301013"],"award-info":[{"award-number":["JSZZ202301013"]}]},{"name":"Self-made Experimental Instruments and Equipment Project of Shenzhen Technology University","award":["2021YJ0371"],"award-info":[{"award-number":["2021YJ0371"]}]},{"name":"Sichuan Science and technology planning project","award":["2022ZDJS114"],"award-info":[{"award-number":["2022ZDJS114"]}]},{"name":"Sichuan Science and technology planning project","award":["2022SA-07-18"],"award-info":[{"award-number":["2022SA-07-18"]}]},{"name":"Sichuan Science and technology planning project","award":["JSZZ202301013"],"award-info":[{"award-number":["JSZZ202301013"]}]},{"name":"Sichuan Science and technology planning project","award":["2021YJ0371"],"award-info":[{"award-number":["2021YJ0371"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The lack of labeled data and variable working conditions brings challenges to the application of intelligent fault diagnosis. Given this, extracting labeled information and learning distribution-invariant representation provides a feasible and promising way. Enlightened by metric learning and semi-supervised architecture, a triplet-guided path-interaction ladder network (Tri-CLAN) is proposed based on the aspects of algorithm structure and feature space. An encoder\u2013decoder structure with path interaction is built to utilize the unlabeled data with fewer parameters, and the network structure is simplified by CNN and an element additive combination activation function. Metric learning is introduced to the feature space of the established algorithm structure, which enables the mining of hard samples from extremely limited labeled data and the learning of working condition-independent representations. The generalization and applicability of Tri-CLAN are proved by experiments, and the contribution of the algorithm structure and the metric learning in the feature space are discussed.<\/jats:p>","DOI":"10.3390\/s23156951","type":"journal-article","created":{"date-parts":[[2023,8,5]],"date-time":"2023-08-05T10:25:36Z","timestamp":1691231136000},"page":"6951","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Metric Learning-Guided Semi-Supervised Path-Interaction Fault Diagnosis Method for Extremely Limited Labeled Samples under Variable Working Conditions"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6733-7893","authenticated-orcid":false,"given":"Zheng","family":"Yang","sequence":"first","affiliation":[{"name":"School of Mechanical and Aerospace Engineering, Jilin University, Changchun 130025, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fei","family":"Chen","sequence":"additional","affiliation":[{"name":"Sino-German College of Intelligent Manufacturing, Shenzhen Technology University, Shenzhen 518118, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Binbin","family":"Xu","sequence":"additional","affiliation":[{"name":"Sino-German College of Intelligent Manufacturing, Shenzhen Technology University, Shenzhen 518118, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Boquan","family":"Ma","sequence":"additional","affiliation":[{"name":"Sino-German College of Intelligent Manufacturing, Shenzhen Technology University, Shenzhen 518118, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zege","family":"Qu","sequence":"additional","affiliation":[{"name":"Sino-German College of Intelligent Manufacturing, Shenzhen Technology University, Shenzhen 518118, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xin","family":"Zhou","sequence":"additional","affiliation":[{"name":"Sino-German College of Intelligent Manufacturing, Shenzhen Technology University, Shenzhen 518118, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"106587","DOI":"10.1016\/j.ymssp.2019.106587","article-title":"Applications of machine learning to machine fault diagnosis: A review and roadmap","volume":"138","author":"Lei","year":"2020","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"110460","DOI":"10.1016\/j.measurement.2021.110460","article-title":"Autoencoder-based representation learning and its application in intelligent fault diagnosis: A review","volume":"189","author":"Yang","year":"2022","journal-title":"Measurement"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2617","DOI":"10.1109\/TIE.2020.2972461","article-title":"Distribution-invariant deep belief network for intelligent fault diagnosis of machines under new working conditions","volume":"68","author":"Xing","year":"2021","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"110511","DOI":"10.1016\/j.measurement.2021.110511","article-title":"Multiscale inverted residual convolutional neural network for intelligent diagnosis of bearings under variable load condition","volume":"188","author":"Zhao","year":"2022","journal-title":"Measurement"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/j.isatra.2019.11.010","article-title":"A novel bearing intelligent fault diagnosis framework under time-varying working conditions using recurrent neural network","volume":"100","author":"An","year":"2020","journal-title":"ISA Trans."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"108639","DOI":"10.1016\/j.knosys.2022.108639","article-title":"Deep multiple auto-encoder with attention mechanism network: A dynamic domain adaptation method for rotary machine fault diagnosis under different working conditions","volume":"249","author":"Yang","year":"2022","journal-title":"Knowl. Based Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1016\/j.isatra.2022.04.026","article-title":"Intelligent fault diagnosis of rolling bearings under varying operating conditions based on domain-adversarial neural network and attention mechanism","volume":"130","author":"Wu","year":"2022","journal-title":"ISA Trans."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1016\/j.isatra.2021.02.042","article-title":"Intelligent fault diagnosis of machines with small & imbalanced data: A state-of-the-art review and possible extensions","volume":"119","author":"Zhang","year":"2022","journal-title":"ISA Trans."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"105313","DOI":"10.1016\/j.knosys.2019.105313","article-title":"Deep transfer multi-wavelet auto-encoder for intelligent fault diagnosis of gearbox with few target training samples","volume":"191","author":"He","year":"2020","journal-title":"Knowl. Based Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"107570","DOI":"10.1016\/j.measurement.2020.107570","article-title":"Deep balanced domain adaptation neural networks for fault diagnosis of planetary gearboxes with limited labeled data","volume":"156","author":"Li","year":"2020","journal-title":"Measurement"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"7471","DOI":"10.1109\/ACCESS.2021.3049193","article-title":"An effective induction motor fault diagnosis approach using graph-based semi-supervised learning","volume":"9","author":"Zaman","year":"2021","journal-title":"IEEE Access"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1016\/j.chemolab.2015.10.019","article-title":"Fault detection and classification for complex processes using semi-supervised learning algorithm","volume":"149","author":"Wang","year":"2015","journal-title":"Chemom. Intell. Lab. Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"104445","DOI":"10.1016\/j.mechmachtheory.2021.104445","article-title":"Semi-supervised hierarchical attribute representation learning via multi-layer matrix factorization for machinery fault diagnosis","volume":"167","author":"Wang","year":"2022","journal-title":"Mech. Mach. Theory"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"107327","DOI":"10.1016\/j.ymssp.2020.107327","article-title":"A hybrid classification autoencoder for semi-supervised fault diagnosis in rotating machinery","volume":"149","author":"Wu","year":"2021","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"106843","DOI":"10.1016\/j.compchemeng.2020.106843","article-title":"Semi-supervised process fault classification based on convolutional ladder network with local and global feature fusion","volume":"140","author":"Li","year":"2020","journal-title":"Comput. Chem. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1007\/s40544-021-0584-3","article-title":"Long short-term memory based semi-supervised encoder-decoder for early prediction of failures in self-lubricating bearings","volume":"11","author":"Pandiyan","year":"2022","journal-title":"Friction"},{"key":"ref_17","unstructured":"Rasmus, A., Valpola, H., Honkala, M., Berglund, M., and Raiko, T. (2015, January 7\u201312). Semi-supervised learning with ladder networks. Proceedings of the Advances in Neural Information Processing Systems, Montreal, QC, Canada."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"117467","DOI":"10.1016\/j.ces.2022.117467","article-title":"Semi-supervised LSTM ladder autoencoder for chemical process fault diagnosis and localization","volume":"251","author":"Zhang","year":"2022","journal-title":"Chem. Eng. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"6476","DOI":"10.1109\/JSEN.2020.3040696","article-title":"Semi-supervised bearing fault diagnosis and classification using variational autoencoder-based deep generative models","volume":"21","author":"Zhang","year":"2021","journal-title":"IEEE Sens. J."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1016\/j.ymssp.2019.05.049","article-title":"Fault diagnosis of planetary gearbox using a novel semi-supervised method of multiple association layers networks","volume":"131","author":"Zhang","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"6331","DOI":"10.1109\/TIE.2018.2873546","article-title":"Information fusion and semi-supervised deep learning scheme for diagnosing gear faults in induction machine systems","volume":"66","author":"Hallaji","year":"2019","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"107043","DOI":"10.1016\/j.ymssp.2020.107043","article-title":"A multi-stage semi-supervised learning approach for intelligent fault diagnosis of rolling bearing using data augmentation and metric learning","volume":"146","author":"Yu","year":"2021","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"168781402097774","DOI":"10.1177\/1687814020977748","article-title":"Rolling bearing fault diagnosis based on probabilistic mixture model and semi-supervised ladder network","volume":"12","author":"Ding","year":"2020","journal-title":"Adv. Mech. Eng."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1016\/j.isatra.2020.10.033","article-title":"Bearing defect diagnosis based on semi-supervised kernel local fisher discriminant analysis using pseudo labels","volume":"110","author":"Tao","year":"2021","journal-title":"ISA Trans."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"27736","DOI":"10.1109\/ACCESS.2021.3058334","article-title":"An imbalanced fault diagnosis method for rolling bearing based on semi-supervised conditional generative adversarial network with spectral normalization","volume":"9","author":"Xu","year":"2021","journal-title":"IEEE Access"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"10787","DOI":"10.1007\/s00521-022-07011-z","article-title":"A novel semi-supervised generative adversarial network based on the actor-critic algorithm for compound fault recognition","volume":"34","author":"Wang","year":"2022","journal-title":"Neural Comput. Appl."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.isatra.2021.11.040","article-title":"Generative adversarial network in mechanical fault diagnosis under small sample: A systematic review on applications and future perspectives","volume":"128","author":"Pan","year":"2021","journal-title":"ISA Trans."},{"key":"ref_28","first-page":"1","article-title":"Toward small sample challenge in intelligent fault diagnosis: Attention-weighted multidepth feature fusion net with signals augmentation","volume":"71","author":"Zhang","year":"2022","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"106333","DOI":"10.1016\/j.asoc.2020.106333","article-title":"Imbalanced sample fault diagnosis of rotating machinery using conditional variational auto-encoder generative adversarial network","volume":"92","author":"Wang","year":"2020","journal-title":"Appl. Soft Comput. J."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"108371","DOI":"10.1016\/j.measurement.2020.108371","article-title":"Rolling bearing fault diagnosis using variational autoencoding generative adversarial networks with deep regret analysis","volume":"168","author":"Liu","year":"2021","journal-title":"Measurement"},{"key":"ref_31","unstructured":"Yi, S., Wang, X., and Tang, X. (2014). Deep learning face representation by joint identification-verification. arXiv."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Schroff, F., Kalenichenko, D., and Philbin, J. (2015). FaceNet: A unified embedding for face recognition and clustering. arXiv, pp. 815\u2013823.","DOI":"10.1109\/CVPR.2015.7298682"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"109050","DOI":"10.1016\/j.ymssp.2022.109050","article-title":"Convolution enabled transformer via random contrastive regularization for rotating machinery diagnosis under time-varying working conditions","volume":"173","author":"Zhou","year":"2022","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TIM.2022.3154000","article-title":"Conditional contrastive domain generalization for fault diagnosis","volume":"71","author":"Ragab","year":"2022","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2463","DOI":"10.1109\/TII.2022.3149935","article-title":"Open-set fault diagnosis via supervised contrastive learning with negative out-of-distribution data augmentation","volume":"19","author":"Peng","year":"2022","journal-title":"IEEE Trans. Ind. Inf."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Rombach, K., Michau, G., and Fink, O. (2021). Contrastive learning for fault detection and diagnostics in the context of changing operating conditions and novel fault types. Sensors, 21.","DOI":"10.3390\/s21103550"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1109\/TSTE.2020.2985217","article-title":"A multi-fault detection method with improved triplet loss based on hard sample mining","volume":"12","author":"Qu","year":"2021","journal-title":"IEEE Trans. Sustain. Energy"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Wang, X., and Liu, F. (2020). Triplet loss guided adversarial domain adaptation for bearing fault diagnosis. Sensors, 20.","DOI":"10.3390\/s20010320"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1527","DOI":"10.1162\/neco.2006.18.7.1527","article-title":"A fast learning algorithm for deep belief nets","volume":"18","author":"Hinton","year":"2006","journal-title":"Neural Comput."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Vincent, P., Larochelle, H., Bengio, Y., and Manzagol, P.-A. (2008, January 5\u20139). Extracting and composing robust features with denoising autoencoders. Proceedings of the 25th International Conference on Machine Learning, Helsinki, Finland.","DOI":"10.1145\/1390156.1390294"},{"key":"ref_41","unstructured":"Kingma, D., and Ba, J. (2014). Adam: A method for stochastic optimization. arXiv."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"110084","DOI":"10.1016\/j.measurement.2021.110084","article-title":"Semi-supervised graph convolutional network and its application in intelligent fault diagnosis of rotating machinery","volume":"186","author":"Gao","year":"2021","journal-title":"Measurement"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"107510","DOI":"10.1016\/j.ymssp.2020.107510","article-title":"Metric-based meta-learning model for few-shot fault diagnosis under multiple limited data conditions","volume":"155","author":"Wang","year":"2021","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"92743","DOI":"10.1109\/ACCESS.2020.2995198","article-title":"A novel method of bearing fault diagnosis in time-frequency graphs using InceptionResnet and deformable convolution networks","volume":"8","author":"Li","year":"2020","journal-title":"IEEE Access"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1016\/j.ymssp.2015.04.021","article-title":"Rolling element bearing diagnostics using the Case Western Reserve University data: A benchmark study","volume":"64\u201365","author":"Smith","year":"2015","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"6637335","DOI":"10.1155\/2021\/6637335","article-title":"Reliability test rig of the motorized spindle and improvements on its ability for high-speed and long-term tests","volume":"2021","author":"Yang","year":"2021","journal-title":"Shock Vib."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/15\/6951\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:26:08Z","timestamp":1760127968000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/15\/6951"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,4]]},"references-count":46,"journal-issue":{"issue":"15","published-online":{"date-parts":[[2023,8]]}},"alternative-id":["s23156951"],"URL":"https:\/\/doi.org\/10.3390\/s23156951","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,8,4]]}}}