{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,7]],"date-time":"2026-02-07T11:35:17Z","timestamp":1770464117584,"version":"3.49.0"},"reference-count":42,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,1,28]],"date-time":"2023-01-28T00:00:00Z","timestamp":1674864000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62073213"],"award-info":[{"award-number":["62073213"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52205111"],"award-info":[{"award-number":["52205111"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China Youth Fund","doi-asserted-by":"publisher","award":["62073213"],"award-info":[{"award-number":["62073213"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China Youth Fund","doi-asserted-by":"publisher","award":["52205111"],"award-info":[{"award-number":["52205111"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Deep learning can be applied in the field of fault diagnosis without an accurate mechanism model. However, the accurate diagnosis of minor faults using deep learning is limited by the training sample size. In the case that only a small number of noise-polluted samples is available, it is crucial to design a new learning mechanism for the training of deep neural networks to make it more powerful in feature representation. The new learning mechanism for deep neural networks model is accomplished by designing a new loss function such that accurate feature representation driven by consistency of trend features and accurate fault classification driven by consistency of fault direction both can be secured. In such a way, a more robust and more reliable fault diagnosis model using deep neural networks can be established to effectively discriminate those faults with equal or similar membership values of fault classifiers, which is unavailable for traditional methods. Validation for gearbox fault diagnosis shows that 100 training samples polluted with strong noise are adequate for the proposed method to successfully train deep neural networks to achieve satisfactory fault diagnosis accuracy, while more than 1500 training samples are required for traditional methods to achieve comparative fault diagnosis accuracy.<\/jats:p>","DOI":"10.3390\/e25020242","type":"journal-article","created":{"date-parts":[[2023,1,30]],"date-time":"2023-01-30T04:31:27Z","timestamp":1675053087000},"page":"242","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Trend Feature Consistency Guided Deep Learning Method for Minor Fault Diagnosis"],"prefix":"10.3390","volume":"25","author":[{"given":"Pengpeng","family":"Jia","sequence":"first","affiliation":[{"name":"School of Logistic Engineering, Shanghai Maritime University, Shanghai 201306, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chaoge","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Logistic Engineering, Shanghai Maritime University, Shanghai 201306, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Funa","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Logistic Engineering, Shanghai Maritime University, Shanghai 201306, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiong","family":"Hu","sequence":"additional","affiliation":[{"name":"School of Logistic Engineering, Shanghai Maritime University, Shanghai 201306, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.ymssp.2018.02.016","article-title":"Artificial intelligence for fault diagnosis of rotating machinery: A review","volume":"108","author":"Liu","year":"2018","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"4931","DOI":"10.1016\/j.matpr.2020.12.050","article-title":"Machine learning algorithms for rotating machinery bearing fault diagnostics","volume":"44","author":"Adamsab","year":"2021","journal-title":"Mater. Today Proc."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.knosys.2012.05.013","article-title":"A rule-based intelligent method for fault diagnosis of rotating machinery","volume":"36","author":"Dou","year":"2012","journal-title":"Knowl. Based Syst."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1016\/j.ifacol.2019.09.140","article-title":"Bearing Fault Diagnosis Based on Optimal Time-Frequency Representation Method","volume":"52","author":"Quinde","year":"2019","journal-title":"IFAC-PapersOnLine"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"108587","DOI":"10.1016\/j.apacoust.2021.108587","article-title":"Incipient fault diagnosis of planetary gearboxes based on an adaptive parameter-induced stochastic resonance method","volume":"188","author":"Xu","year":"2022","journal-title":"Appl. Acoust."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1016\/j.measurement.2013.11.012","article-title":"Condition monitoring and fault diagnosis of planetary gearboxes: A review","volume":"48","author":"Lei","year":"2014","journal-title":"Measurement"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1016\/j.sigpro.2015.09.008","article-title":"An optimal fault detection threshold for early detection using Kullback\u2013Leibler Divergence for unknown distribution data","volume":"120","author":"Youssef","year":"2016","journal-title":"Signal Process."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1109\/TIM.2009.2023814","article-title":"An Enhanced Diagnostic Scheme for Bearing Condition Monitoring","volume":"59","author":"Liu","year":"2010","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2102","DOI":"10.1109\/JSEN.2010.2093879","article-title":"Single-sensor incipient fault detection","volume":"11","author":"Ren","year":"2011","journal-title":"IEEE Sens. J."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1557","DOI":"10.1007\/s11265-022-01761-8","article-title":"Degradation Pattern of High Speed Roller Bearings Using a Data-Driven Deep Learning Approach","volume":"94","author":"Rathore","year":"2022","journal-title":"J. Signal Process. Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2477","DOI":"10.1109\/TNNLS.2014.2387439","article-title":"Deep and shallow architecture of multilayer neural networks","volume":"26","author":"Chang","year":"2015","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2306","DOI":"10.1109\/TNNLS.2016.2582798","article-title":"Multi-objective deep belief networks ensemble for remaining useful life estimation in prognostics","volume":"28","author":"Zhang","year":"2017","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_13","first-page":"390134","article-title":"Gearbox fault identification and classification with convolutional neural networks","volume":"2015","author":"Chen","year":"2015","journal-title":"Shock Vib."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1016\/j.neucom.2017.02.045","article-title":"A recurrent neural network based health indicator for remaining useful life prediction of bearings","volume":"240","author":"Guo","year":"2017","journal-title":"Neurocomputing"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1016\/j.neucom.2017.07.032","article-title":"A neural network constructed by deep learning technique and its application to intelligent fault diagnosis of machines","volume":"272","author":"Jia","year":"2018","journal-title":"Neurocomputing"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1016\/j.microrel.2017.03.006","article-title":"Deep neural networks-based rolling bearing fault diagnosis","volume":"75","author":"Chen","year":"2017","journal-title":"Minor. Reliab."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1016\/j.measurement.2018.08.002","article-title":"Study on planetary gear fault diagnosis based on variational mode decomposition and deep neural networks","volume":"130","author":"Li","year":"2018","journal-title":"Measurement"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"12727","DOI":"10.1016\/j.egyr.2022.09.113","article-title":"A wind turbine bearing fault diagnosis method based on fused depth features in time\u2013frequency domain","volume":"8","author":"Tang","year":"2022","journal-title":"Energy Rep."},{"key":"ref_19","first-page":"196","article-title":"Planetary gearboxes fault diagnosis based on multiple feature extraction and information fusion combined with deep learning","volume":"30","author":"Jin","year":"2019","journal-title":"China Mech. Eng."},{"key":"ref_20","first-page":"59","article-title":"Fault Diagnosis Methods of Rolling Bearings Based on Decision Fusion of Multiple Deep Learning Models","volume":"8","author":"Zhang","year":"2019","journal-title":"Modul. Mach. Tool Automatic Manuf. Tech."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1016\/j.sigpro.2016.07.028","article-title":"Fault diagnosis of rotary machinery components using a stacked denoising autoencoder-based health state identification","volume":"130","author":"Lu","year":"2017","journal-title":"Signal Process."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1469","DOI":"10.1016\/j.renene.2019.09.041","article-title":"Anomaly detection for wind turbines based on the reconstruction of condition parameters using stacked denoising autoencoders","volume":"147","author":"Chen","year":"2020","journal-title":"Renew. Energy"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"108898","DOI":"10.1016\/j.asoc.2022.108898","article-title":"Output-related fault detection in non-stationary processes using constructive correlative-SAE and demoting correlative-DNN","volume":"123","author":"Rashidi","year":"2022","journal-title":"Appl. Soft Comput."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"106060","DOI":"10.1016\/j.asoc.2019.106060","article-title":"Stacked pruning sparse denoising autoencoder based intelligent fault diagnosis of rolling bearings","volume":"88","author":"Zhu","year":"2020","journal-title":"Appl. Soft Comput."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1889","DOI":"10.1007\/s11760-021-01939-w","article-title":"A sparse denoising deep neural network for improving fault diagnosis performance","volume":"15","author":"Zhou","year":"2021","journal-title":"Signal Image Video Process."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"278","DOI":"10.1016\/j.ymssp.2017.09.026","article-title":"A novel method for intelligent fault diagnosis of rolling bearings using ensemble deep auto-encoders","volume":"102","author":"Shao","year":"2018","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"107132","DOI":"10.1016\/j.measurement.2019.107132","article-title":"A multi-ensemble method based on deep auto-encoders for fault diagnosis of rolling bearings","volume":"151","author":"Kong","year":"2020","journal-title":"Measurement"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"3794","DOI":"10.1109\/TIE.2018.2856193","article-title":"Using Multiple-Feature-Spaces-Based Deep Learning for Tool Condition Monitoring in Ultraprecision on Manufacturing","volume":"66","author":"Shi","year":"2019","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Zhou, F.N., Zhang, Z.Q., and Chen, D.M. (2020, January 16\u201318). Bearing fault diagnosis based on DNN using multi-scale feature fusion. Proceedings of the 2020 35th Youth Academic Annual Conference of Chinese Association of Automation (YAC), Zhanjiang, China.","DOI":"10.1109\/YAC51587.2020.9337689"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Zhou, F.N., He, Y.F., and Han, H.T. (2019, January 24\u201327). Fault Diagnosis of Multi-source Heterogeneous Information Fusion Based on Deep Learning. Proceedings of the 2019 IEEE 8th Data Driven Control and Learning Systems Conference (DDCLS), Dali, China.","DOI":"10.1109\/DDCLS.2019.8909017"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"110099","DOI":"10.1016\/j.measurement.2021.110099","article-title":"Gearbox fault diagnosis based on Multi-Scale deep residual learning and stacked LSTM model","volume":"186","author":"Ravikumar","year":"2021","journal-title":"Measurement"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"109399","DOI":"10.1016\/j.knosys.2022.109399","article-title":"Health indicator construction for degradation assessment by embedded LSTM-CNN autoencoder and growing self-organized map","volume":"252","author":"Chen","year":"2022","journal-title":"Knowl. Based Syst."},{"key":"ref_33","first-page":"1873","article-title":"Real-time fault diagnosis using deep fusion of features extracted by parallel long short-term memory with peephole and convolutional neural network","volume":"235","author":"Zhou","year":"2021","journal-title":"Proc. Inst. Mech. Eng. Part I J. Syst. Control Eng."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"177","DOI":"10.2478\/msr-2022-0022","article-title":"Stacked Auto-encoder Based Feature Transfer Learning and Optimized LSSVM-PSO Classifier in Bearing Fault Diagnosis","volume":"22","author":"Nguyen","year":"2022","journal-title":"Meas. Sci. Rev."},{"key":"ref_35","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_36","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1016\/j.neucom.2018.06.078","article-title":"A survey on Deep Learning based bearing fault diagnosis","volume":"335","author":"Hoang","year":"2019","journal-title":"Neurocomputing"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"504","DOI":"10.1016\/j.physa.2017.08.045","article-title":"Cross-correlations and influence in world gold markets","volume":"490","author":"Lin","year":"2018","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1016\/j.cja.2022.01.004","article-title":"A novel imprecise stochastic process model for time-variant or dynamic uncertainty quantification","volume":"35","author":"Li","year":"2022","journal-title":"Chin. J. Aeronaut."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"108745","DOI":"10.1016\/j.knosys.2022.108754","article-title":"Multi-view 3D object retrieval leveraging the aggregation of view and instance attentive features","volume":"247","author":"Lin","year":"2022","journal-title":"Knowl. Based Syst."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/j.ymssp.2017.03.034","article-title":"A novel deep autoencoder feature learning method for rotating machinery fault diagnosis","volume":"95","author":"Shao","year":"2017","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_41","unstructured":"(2022, June 21). Gearbox Data Set [DB\/OL]. Available online: http:\/\/www.pudn.com\/Download\/item\/id\/3205015.html."},{"key":"ref_42","unstructured":"(2022, August 24). Case Western Reserve University Bearing Data Center Website. Available online: http:\/\/www.eecs.case.edu\/laboratory\/bearing."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/2\/242\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:18:21Z","timestamp":1760120301000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/2\/242"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1,28]]},"references-count":42,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2023,2]]}},"alternative-id":["e25020242"],"URL":"https:\/\/doi.org\/10.3390\/e25020242","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,1,28]]}}}