{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T14:57:05Z","timestamp":1773327425989,"version":"3.50.1"},"reference-count":30,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2022,3,21]],"date-time":"2022-03-21T00:00:00Z","timestamp":1647820800000},"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":["52075001, 52105082, 52105040, 52075002"],"award-info":[{"award-number":["52075001, 52105082, 52105040, 52075002"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Key Basic Research Project","award":["MKF20210008"],"award-info":[{"award-number":["MKF20210008"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Predicting the degradation of mechanical components, such as rolling bearings is critical to the proper monitoring of the condition of mechanical equipment. A new method, based on a long short-term memory network (LSTM) algorithm, has been developed to improve the accuracy of degradation prediction. The model parameters are optimized via improved particle swarm optimization (IPSO). Regarding how this applies to the rolling bearings, firstly, multi-dimension feature parameters are extracted from the bearing\u2019s vibration signals and fused into responsive features by using the kernel joint approximate diagonalization of eigen-matrices (KJADE) method. Then, the between-class and within-class scatter (SS) are calculated to develop performance degradation indicators. Since network model parameters influence the predictive accuracy of the LSTM model, an IPSO algorithm is used to obtain the optimal prediction model via the LSTM model parameters\u2019 optimization. Finally, the LSTM model, with said optimal parameters, was used to predict the degradation trend of the bearing\u2019s performance. The experiment\u2019s results show that the proposed method can effectively identify the trends of degradation and performance. Moreover, the predictive accuracy of this proposed method is greater than that of the extreme learning machine (ELM) and support vector regression (SVR), which are the algorithms conventionally used in degradation modeling.<\/jats:p>","DOI":"10.3390\/s22062407","type":"journal-article","created":{"date-parts":[[2022,3,21]],"date-time":"2022-03-21T21:48:42Z","timestamp":1647899322000},"page":"2407","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["Performance Degradation Prediction Using LSTM with Optimized Parameters"],"prefix":"10.3390","volume":"22","author":[{"given":"Yawei","family":"Hu","sequence":"first","affiliation":[{"name":"College of Electrical Engineering and Automation, Anhui University, Hefei 230601, China"}]},{"given":"Ran","family":"Wei","sequence":"additional","affiliation":[{"name":"Anhui NARI Jiyuan Electric Co., Ltd., Hefei 230601, China"}]},{"given":"Yang","family":"Yang","sequence":"additional","affiliation":[{"name":"China North Vehicle Research Institute, Beijing 100071, China"}]},{"given":"Xuanlin","family":"Li","sequence":"additional","affiliation":[{"name":"College of Electrical Engineering and Automation, Anhui University, Hefei 230601, China"}]},{"given":"Zhifu","family":"Huang","sequence":"additional","affiliation":[{"name":"College of Electrical Engineering and Automation, Anhui University, Hefei 230601, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3420-3784","authenticated-orcid":false,"given":"Yongbin","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Electrical Engineering and Automation, Anhui University, Hefei 230601, China"}]},{"given":"Changbo","family":"He","sequence":"additional","affiliation":[{"name":"College of Electrical Engineering and Automation, Anhui University, Hefei 230601, China"}]},{"given":"Huitian","family":"Lu","sequence":"additional","affiliation":[{"name":"JJL College of Engineering, South Dakota State University, Brookings, SD 57007, USA"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1016\/j.measurement.2017.07.030","article-title":"The use of MD-CUMSUM and NARX neural network for anticipating the remaining useful life of bearings","volume":"111","author":"Rai","year":"2017","journal-title":"Measurement"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Nohal, L., Vaculka, M., and Iop (2017, January 9\u201311). Experimental and computational evaluation of rolling bearing steel durability. Proceedings of the 4th International Conference Recent Trends in Structural Materials (COMAT), Pilsen, Czech Republic.","DOI":"10.1088\/1757-899X\/179\/1\/012054"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"4168","DOI":"10.1016\/j.eswa.2009.11.006","article-title":"Incipient gear box fault diagnosis using discrete wavelet transform (DWT) for feature extraction and classification using artificial neural network (ANN)","volume":"37","author":"Saravanan","year":"2010","journal-title":"Expert Syst. Appl."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1016\/j.cja.2019.07.011","article-title":"A new bearing fault diagnosis method based on modified convolutional neural networks","volume":"33","author":"Zhang","year":"2020","journal-title":"Chin. J. Aeronaut."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"3208","DOI":"10.1109\/TIE.2018.2844856","article-title":"Estimation of Bearing Remaining Useful Life Based on Multiscale Convolutional Neural Network","volume":"66","author":"Zhu","year":"2019","journal-title":"Ieee Trans. Ind. Electron."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1007\/s10845-009-0356-9","article-title":"An artificial neural network method for remaining useful life prediction of equipment subject to condition monitoring","volume":"23","author":"Tian","year":"2012","journal-title":"J. Intell. Manuf."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"746","DOI":"10.1016\/j.ymssp.2016.09.010","article-title":"Rolling bearing fault detection and diagnosis based on composite multiscale fuzzy entropy and ensemble support vector machines","volume":"85","author":"Zheng","year":"2017","journal-title":"Mech. Syst. Signal Processing"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/j.compind.2018.12.016","article-title":"Bearing performance degradation assessment using long short-term memory recurrent network","volume":"106","author":"Zhang","year":"2019","journal-title":"Comput. Ind."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Li, X., Jiang, H., Wang, R., and Niu, M. (2021). Rolling bearing fault diagnosis using optimal ensemble deep transfer network. Knowl.-Based Syst., 213.","DOI":"10.1016\/j.knosys.2020.106695"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Hu, M., Wang, G., Ma, K., Cao, Z., and Yang, S. (2021). Bearing performance degradation assessment based on optimized EWT and CNN. Measurement, 172.","DOI":"10.1016\/j.measurement.2020.108868"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1109\/TIM.2011.2169182","article-title":"Prediction of Machine Health Condition Using Neuro-Fuzzy and Bayesian Algorithms","volume":"61","author":"Chen","year":"2012","journal-title":"Ieee Trans. Instrum. Meas."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"13041","DOI":"10.1109\/ACCESS.2018.2804930","article-title":"Prediction of Bearing Remaining Useful Life With Deep Convolution Neural Network","volume":"6","author":"Ren","year":"2018","journal-title":"IEEE Access"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1038\/nature14539","article-title":"Deep learning","volume":"521","author":"LeCun","year":"2015","journal-title":"Nature"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"703","DOI":"10.1109\/TIM.2010.2078296","article-title":"Prognosis of Defect Propagation Based on Recurrent Neural Networks","volume":"60","author":"Malhi","year":"2011","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1539","DOI":"10.1109\/TIE.2017.2733438","article-title":"Machine Health Monitoring Using Local Feature-Based Gated Recurrent Unit Networks","volume":"65","author":"Zhao","year":"2018","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_16","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_17","doi-asserted-by":"crossref","first-page":"1658","DOI":"10.1109\/TII.2020.2991796","article-title":"Deep-Convolution-Based LSTM Network for Remaining Useful Life Prediction","volume":"17","author":"Ma","year":"2021","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Liu, G., Zhao, J., and Zhang, X. (2019). Bearing degradation trend prediction under different operational conditions based on CNN-LSTM. IOP Conf. Ser. Mater. Sci. Eng., 612.","DOI":"10.1088\/1757-899X\/612\/3\/032042"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1016\/j.neucom.2018.09.076","article-title":"Bidirectional handshaking LSTM for remaining useful life prediction","volume":"323","author":"Elsheikh","year":"2019","journal-title":"Neurocomputing"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Tang, G., Zhou, Y., Wang, H., and Li, G. (2018, January 14\u201317). Prediction of bearing performance degradation with bottleneck feature based on LSTM network. Proceedings of the 2018 IEEE International Instrumentation and Measurement Technology Conference, I2MTC 2018, Houston, TX, USA,.","DOI":"10.1109\/I2MTC.2018.8409564"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1186\/s10033-021-00570-7","article-title":"Challenges and Opportunities of AI-Enabled Monitoring, Diagnosis & Prognosis: A Review","volume":"34","author":"Zhao","year":"2021","journal-title":"Chin. J. Mech. Eng."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Ding, N., Li, H., Yin, Z., Zhong, N., and Zhang, L. (2020). Journal bearing seizure degradation assessment and remaining useful life prediction based on long short-term memory neural network. Measurement, 166.","DOI":"10.1016\/j.measurement.2020.108215"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Rathore, M.S., and Harsha, S.P. (2022). Prognostics Analysis of Rolling Bearing Based on Bi-Directional LSTM and Attention Mechanism. J. Fail. Anal. Prev., 1\u201320.","DOI":"10.1007\/s11668-022-01357-1"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/j.neucom.2019.10.064","article-title":"Recurrent convolutional neural network: A new framework for remaining useful life prediction of machinery","volume":"379","author":"Wang","year":"2020","journal-title":"Neurocomputing"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/j.chemolab.2015.08.020","article-title":"Particle swarm optimization (PSO). A tutorial","volume":"149","author":"Marini","year":"2015","journal-title":"Chemom. Intell. Lab. Syst."},{"key":"ref_26","first-page":"8","article-title":"Robot Path Planning and Experiment with an Improved PSO Algorith","volume":"42","author":"Kang","year":"2020","journal-title":"Robot"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1016\/j.jsv.2016.09.018","article-title":"Feature fusion using kernel joint approximate diagonalization of eigen-matrices for rolling bearing fault identification","volume":"385","author":"Liu","year":"2016","journal-title":"J. Sound Vib."},{"key":"ref_28","unstructured":"Gousseau, W., Antoni, J., Girardin, F., and Griffaton, J. (2016, January 10). Analysis of the Rolling Element Bearing data set of the Center for Intelligent Maintenance Systems of the University of Cincinnati. Proceedings of the CM 2016, Charenton, France."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1699","DOI":"10.1177\/0954406215621585","article-title":"Residual life prediction for ball bearings based on joint approximate diagonalization of eigen matrices and extreme learning machine","volume":"231","author":"Fang","year":"2017","journal-title":"Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Liu, F., Li, L., Liu, Y., Cao, Z., and Lu, S. (2020). HKF-SVR Optimized by Krill Herd Algorithm for Coaxial Bearings Performance Degradation Prediction. Sensors, 20.","DOI":"10.3390\/s20030660"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/6\/2407\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:40:16Z","timestamp":1760136016000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/6\/2407"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,21]]},"references-count":30,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2022,3]]}},"alternative-id":["s22062407"],"URL":"https:\/\/doi.org\/10.3390\/s22062407","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,3,21]]}}}