{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T22:24:28Z","timestamp":1775082268633,"version":"3.50.1"},"reference-count":32,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2020,4,20]],"date-time":"2020-04-20T00:00:00Z","timestamp":1587340800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Key Science and Technology Research Project of Chongqing","award":["cstc2018jszx-cyztzxX0032."],"award-info":[{"award-number":["cstc2018jszx-cyztzxX0032."]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The gearbox is one of the most fragile parts of a wind turbine (WT). Fault diagnosis of the WT gearbox is of great importance to reduce operation and maintenance (O&amp;M) costs and improve cost-effectiveness. At present, intelligent fault diagnosis methods based on long short-term memory (LSTM) networks have been widely adopted. As the traditional softmax loss of an LSTM network usually lacks the power of discrimination, this paper proposes a fault diagnosis method for wind turbine gearboxes based on optimized LSTM neural networks with cosine loss (Cos-LSTM). The loss can be converted from Euclid space to angular space by cosine loss, thus eliminating the effect of signal strength and improve the diagnosis accuracy. The energy sequence features and the wavelet energy entropy of the vibration signals are used to evaluate the Cos-LSTM networks. The effectiveness of the proposed method is verified with the fault vibration data collected on a gearbox fault diagnosis experimental platform. In addition, the Cos-LSTM method is also compared with other classic fault diagnosis techniques. The results demonstrate that the Cos-LSTM has better performance for gearbox fault diagnosis.<\/jats:p>","DOI":"10.3390\/s20082339","type":"journal-article","created":{"date-parts":[[2020,4,21]],"date-time":"2020-04-21T04:49:38Z","timestamp":1587444578000},"page":"2339","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":95,"title":["Fault Diagnosis of Wind Turbine Gearbox Based on the Optimized LSTM Neural Network with Cosine Loss"],"prefix":"10.3390","volume":"20","author":[{"given":"Aijun","family":"Yin","sequence":"first","affiliation":[{"name":"State Key Laboratory of Mechanical Transmissions, Chongqing University, Chongqing 400044, China"},{"name":"College of Mechanical Engineering, Chongqing University, Chongqing 400044, China"}]},{"given":"Yinghua","family":"Yan","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Mechanical Transmissions, Chongqing University, Chongqing 400044, China"},{"name":"College of Mechanical Engineering, Chongqing University, Chongqing 400044, China"}]},{"given":"Zhiyu","family":"Zhang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Mechanical Transmissions, Chongqing University, Chongqing 400044, China"},{"name":"College of Mechanical Engineering, Chongqing University, Chongqing 400044, China"}]},{"given":"Chuan","family":"Li","sequence":"additional","affiliation":[{"name":"Research Center of System Health Maintenance, Chongqing Technology and Business University, Chongqing 400067, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0395-9228","authenticated-orcid":false,"given":"Ren\u00e9-Vinicio","family":"S\u00e1nchez","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Universidad Polit\u00e9cnica Salesiana, Cuenca 010105, Ecuador"}]}],"member":"1968","published-online":{"date-parts":[[2020,4,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"8634","DOI":"10.1109\/ACCESS.2016.2631505","article-title":"A Wind-Wave Farm System with Self-Energy Storage and Smoothed Power Output","volume":"4","author":"Zhao","year":"2016","journal-title":"IEEE Access"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"767","DOI":"10.1016\/j.renene.2015.04.063","article-title":"A new wind turbine fault diagnosis method based on ensemble intrinsic time-scale decomposition and WPT-fractal dimension","volume":"83","author":"Hu","year":"2015","journal-title":"Renew. Energy"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Walford, C.A. (2006). Wind Turbine Reliability: Understanding and Minimizing Wind Turbine Operation and Maintenance Costs.","DOI":"10.2172\/882048"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"3196","DOI":"10.1109\/TIE.2018.2844805","article-title":"Multiscale Convolutional Neural Networks for Fault Diagnosis of Wind Turbine Gearbox","volume":"66","author":"Jiang","year":"2019","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/j.renene.2015.06.041","article-title":"Time-frequency analysis based on Vold-Kalman filter and higher order energy separation for fault diagnosis of wind turbine planetary gearbox under nonstationary conditions","volume":"85","author":"Feng","year":"2016","journal-title":"Renew. Energy"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1016\/j.renene.2017.03.035","article-title":"Planet gear fault localization for wind turbine gearbox using acoustic emission signals","volume":"109","author":"Zhang","year":"2017","journal-title":"Renew. Energy"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1080\/20464177.2018.1492361","article-title":"Utilising elastic waves of acoustic emission to assess the condition of spray nozzles in a marine diesel engine","volume":"17","author":"Bejger","year":"2018","journal-title":"J. Mar. Eng. Technol."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Bejger, A., and Drzewieniecki, J.B. (2019). The Use of Acoustic Emission to Diagnosis of Fuel Injection Pumps of Marine Diesel Engines. Energies, 12.","DOI":"10.3390\/en12244661"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1016\/j.ymssp.2015.10.025","article-title":"Deep neural networks: A promising tool for fault characteristic mining and intelligent diagnosis of rotating machinery with massive data","volume":"72\u201373","author":"Jia","year":"2016","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"3137","DOI":"10.1109\/TIE.2016.2519325","article-title":"An Intelligent Fault Diagnosis Method Using Unsupervised Feature Learning Towards Mechanical Big Data","volume":"63","author":"Lei","year":"2016","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2280","DOI":"10.1016\/j.ymssp.2006.11.003","article-title":"Fault diagnosis of rotating machinery based on multiple ANFIS combination with GAS","volume":"21","author":"Lei","year":"2007","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Wang, D., Tse, P.W., Guo, W., and Miao, Q. (2011). Support vector data description for fusion of multiple health indicators for enhancing gearbox fault diagnosis and prognosis. Meas. Sci. Technol., 22.","DOI":"10.1088\/0957-0233\/22\/2\/025102"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/j.renene.2017.09.061","article-title":"A novel wind turbine fault diagnosis method based on intergral extension load mean decomposition multiscale entropy and least squares support vector machine","volume":"116","author":"Gao","year":"2018","journal-title":"Renew. Energy"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"5627","DOI":"10.3390\/s150305627","article-title":"An SVM-Based Solution for Fault Detection in Wind Turbines","volume":"15","author":"Santos","year":"2015","journal-title":"Sensors"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2933","DOI":"10.1016\/j.ymssp.2007.02.003","article-title":"Rolling element bearings multi-fault classification based on the wavelet denoising and support vector machine","volume":"21","author":"Abbasion","year":"2007","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1016\/j.measurement.2015.06.005","article-title":"A novel wind turbine bearing fault diagnosis method based on Integral Extension LMD","volume":"74","author":"Liu","year":"2015","journal-title":"Measurement"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Lei, Y. (2017). Intelligent Fault Diagnosis and Remaining Useful Life Prediction of Rotating Machinery, Xi\u2019an Jiaotong University Press.","DOI":"10.1016\/B978-0-12-811534-3.00006-8"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Li, C., Sanchez, R.-V., Zurita, G., Cerrada, M., and Cabrera, D. (2016). Fault Diagnosis for Rotating Machinery Using Vibration Measurement Deep Statistical Feature Learning. Sensors, 16.","DOI":"10.3390\/s16060895"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Chen, Z., Li, C., and Sanchez, R.-V. (2015). Gearbox Fault Identification and Classification with Convolutional Neural Networks. Shock Vib.","DOI":"10.1155\/2015\/390134"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"An, Z., Li, S., Wang, J., and Jiang, X. (2019). A novel bearing intelligent fault diagnosis framework under time-varying working conditions using recurrent neural network. ISA Trans.","DOI":"10.1016\/j.isatra.2019.11.010"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Cao, L., Zhang, J., Wang, J., and Qian, Z. (2019, January 12\u201314). Intelligent fault diagnosis of wind turbine gearbox based on Long short-term memory networks. Proceedings of the 2019 IEEE 28th International Symposium on Industrial Electronics, Vancouver, BC, Canada.","DOI":"10.1109\/ISIE.2019.8781108"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Medina, R., Cerrada, M., Cabrera, D., Sanchez, R.-V., Li, C., and de Oliveira, J.V. (2019, January 2\u20135). Deep Learning-Based Gear Pitting Severity Assessment using Acoustic Emission, Vibration and Currents signals. Proceedings of the 2019 Prognostics and System Health Management Conference, Paris, France.","DOI":"10.1109\/PHM-Paris.2019.00042"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Wang, H., Wang, Y., Zhou, Z., Ji, X., Gong, D., Zhou, J., Li, Z., and Liu, W. (2018, January 18\u201323). CosFace: Large Margin Cosine Loss for Deep Face Recognition. Proceedings of the 2018 IEEE\/Cvf Conference on Computer Vision and Pattern Recognition, Salt Lake City, UT, USA.","DOI":"10.1109\/CVPR.2018.00552"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1735","DOI":"10.1162\/neco.1997.9.8.1735","article-title":"Long short-term memory","volume":"9","author":"Hochreiter","year":"1997","journal-title":"Neural Comput."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Graves, A. (2012). Supervised sequence labelling. Supervised Sequence Labelling with Recurrent Neural Networks, Springer.","DOI":"10.1007\/978-3-642-24797-2"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Wen, Y., Zhang, K., Li, Z., and Qiao, Y. (2016, January 8\u201316). A discriminative feature learning approach for deep face recognition. Proceedings of European Conference on Computer Vision, Amsterdam, The Netherlands.","DOI":"10.1007\/978-3-319-46478-7_31"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Liu, W., Wen, Y., Yu, Z., Li, M., Raj, B., and Song, L. (2017, January 21\u201326). SphereFace: Deep Hypersphere Embedding for Face Recognition. Proceedings of the 30th IEEE Conference on Computer Vision and Pattern Recognition, Honolulu, HI, USA.","DOI":"10.1109\/CVPR.2017.713"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Shao, Y., Ge, L., and Fang, J. (2008, January 14\u201317). Fault diagnosis system based on smart bearing. Proceedings of the 2008 International Conference on Control, Automation and Systems, Seoul, Korea.","DOI":"10.1109\/ICCAS.2008.4694313"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"4186","DOI":"10.1177\/0954406216663782","article-title":"Fault feature extraction and classification based on WPT and SVD: Application to element bearings with artificially created faults under variable conditions","volume":"231","author":"Kedadouche","year":"2017","journal-title":"Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci."},{"key":"ref_30","first-page":"148","article-title":"A fault diagnosis method for gearbox based on neutrosophic K-Nearest Neighbor","volume":"38","author":"Wang","year":"2019","journal-title":"Shock Vib."},{"key":"ref_31","unstructured":"Wang, W.Q., and Yang, S. (2009). A method for choosing the wavelet decomposition level in structural fault analysis. Struct. Environ. Eng."},{"key":"ref_32","first-page":"51","article-title":"Gearbox Faults diagnosis method for gearboxes based on 1-D convolutional neural network","volume":"37","author":"Wu","year":"2018","journal-title":"Shock Vib."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/8\/2339\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T14:09:05Z","timestamp":1760364545000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/8\/2339"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,4,20]]},"references-count":32,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2020,4]]}},"alternative-id":["s20082339"],"URL":"https:\/\/doi.org\/10.3390\/s20082339","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,4,20]]}}}