{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T01:13:54Z","timestamp":1772500434947,"version":"3.50.1"},"reference-count":53,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T00:00:00Z","timestamp":1698192000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["52121003"],"award-info":[{"award-number":["52121003"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The performance of bearings plays a pivotal role in determining the dependability and security of rotating machinery. In intricate systems demanding exceptional reliability and safety, the ability to accurately forecast fault occurrences during operation holds profound significance. Such predictions serve as invaluable guides for crafting well-considered reliability strategies and executing maintenance practices aimed at enhancing reliability. In the real operational life of bearings, fault information often gets submerged within the noise. Furthermore, employing Long Short-Term Memory (LSTM) neural networks for time series prediction necessitates the configuration of appropriate parameters. Manual parameter selection is often a time-consuming process and demands substantial prior knowledge. In order to ensure the reliability of bearing operation, this article investigates the application of three advanced techniques\u2014Maximum Correlation Kurtosis Deconvolution (MCKD), Multi-Scale Permutation Entropy (MPE), and Long Short-Term Memory (LSTM) recurrent neural networks\u2014for the prediction of the remaining useful life (RUL) of rolling bearings. The improved sparrow search algorithm (ISSA) is employed for configuring parameters in the Long Short-Term Memory (LSTM) network. Each technique\u2019s principles, methodologies, and applications are comprehensively reviewed, offering insights into their respective strengths and limitations. Case studies and experimental evaluations are presented to assess their performance in RUL prediction. Findings reveal that MCKD enhances fault signatures, MPE captures complexity, and LSTM excels in modeling temporal patterns. The root mean square error of the prediction results is 0.007. The fusion of these techniques offers a comprehensive approach to RUL prediction, leveraging their unique attributes for more accurate and reliable predictions.<\/jats:p>","DOI":"10.3390\/e25111477","type":"journal-article","created":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T04:14:47Z","timestamp":1698207287000},"page":"1477","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Remaining Useful Life Prediction of Rolling Bearings Based on Multi-scale Permutation Entropy and ISSA-LSTM"],"prefix":"10.3390","volume":"25","author":[{"given":"Hongju","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mechanical and Electrical Engineering, China University of Mining & Technology (Beijing), Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xi","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mechanical and Electrical Engineering, China University of Mining & Technology (Beijing), Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mingming","family":"Ren","sequence":"additional","affiliation":[{"name":"School of Mechanical and Electrical Engineering, China University of Mining & Technology (Beijing), Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tianhao","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Mechanical and Electrical Engineering, China University of Mining & Technology (Beijing), Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chengkai","family":"Lu","sequence":"additional","affiliation":[{"name":"School of Mechanical and Electrical Engineering, China University of Mining & Technology (Beijing), Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zicheng","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Mechanical and Electrical Engineering, China University of Mining & Technology (Beijing), Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,10,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Shi, R., Wang, B., Wang, Z., Liu, J., Feng, X., and Dong, L. (2022). Research on Fault Diagnosis of Rolling Bearings Based on Variational Mode Decomposition Improved by the Niche Genetic Algorithm. Entropy, 24.","DOI":"10.3390\/e24060825"},{"key":"ref_2","first-page":"243","article-title":"Bearing fault diagnosis and degradation analysis based on improved empirical mode decomposition and maximum correlated kurtosis deconvolution","volume":"17","author":"Zhang","year":"2015","journal-title":"J. Vibroeng."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"107657","DOI":"10.1016\/j.measurement.2020.107657","article-title":"Research on Rolling Bearing State Health Monitoring and Life Prediction Based on PCA and Internet of Things with Multi-sensor","volume":"157","author":"Heng","year":"2020","journal-title":"Measurement"},{"key":"ref_4","unstructured":"Si, X.S., Zhang, Z.X., and Hu, C.H. (2017). Springer Series in Reliability Engineering, National Defense Industry Press and Springer-Verlag GmbH."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1016\/j.jsv.2019.01.042","article-title":"A weighted multi-scale dictionary learning model and its applications on bearing fault diagnosis","volume":"446","author":"Zhao","year":"2019","journal-title":"J. Sound Vib."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"107823","DOI":"10.1016\/j.ymssp.2021.107823","article-title":"Discrete convolution wavelet transform of signal and its application on BEV accident data analysis","volume":"159","author":"Yan","year":"2021","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"104204","DOI":"10.1016\/j.engfailanal.2019.104204","article-title":"Extraction of weak fault transients using variational mode decomposition for fault diagnosis of gearbox under varying speed","volume":"107","author":"Sharma","year":"2020","journal-title":"Eng. Fail. Anal."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"109614","DOI":"10.1016\/j.measurement.2021.109614","article-title":"Rolling bearing fault diagnosis utilizing variational mode decomposition based fractal dimension estimation method","volume":"181","author":"Zhang","year":"2021","journal-title":"Measurement"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"106567.1","DOI":"10.1016\/j.ymssp.2019.106567","article-title":"A quadratic penalty item optimal variational mode decomposition method based on single-objective salp swarm algorithm","volume":"138","author":"Zhao","year":"2020","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"109815","DOI":"10.1016\/j.measurement.2021.109815","article-title":"A Transient Electromagnetic Signal Denoising Method Based on An Improved Variational Mode Decomposition Algorithm","volume":"184","author":"Feng","year":"2021","journal-title":"Measurement"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/j.ymssp.2012.06.010","article-title":"Maximum correlated Kurtosis deconvolution and application on gear tooth chip fault detection","volume":"33","author":"Mcdonald","year":"2012","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/j.measurement.2019.06.022","article-title":"Compound faults diagnosis based on customized balanced multiwavelets and adaptive maximum correlated kurtosis deconvolution","volume":"146","author":"Hong","year":"2019","journal-title":"Measurement"},{"key":"ref_13","first-page":"10","article-title":"Composite fault diagnosis of rolling bearing based on MCKD and teager energy operator","volume":"59","author":"Qi","year":"2019","journal-title":"J. Dalian Univ. Technol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"236","DOI":"10.1016\/j.measurement.2019.02.071","article-title":"Application of improved MCKD method based on QGA in planetary gear compound fault diagnosis","volume":"139","author":"Lyu","year":"2019","journal-title":"Measurement"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/j.ymssp.2017.01.033","article-title":"Application of an improved maximum correlated kurtosis deconvolution method for fault diagnosis of rolling element bearings","volume":"92","author":"Miao","year":"2017","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_16","first-page":"59","article-title":"Application of OPMCKD and ELMD in bearing compound fault diagnosis","volume":"38","author":"Bin","year":"2019","journal-title":"J. Vib. Shock."},{"key":"ref_17","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_18","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_19","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1109\/72.279181","article-title":"Learning long-term dependencies with gradient descent is difficult","volume":"5","author":"Bengio","year":"1994","journal-title":"Neural Netw. IEEE Trans."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2278","DOI":"10.1109\/5.726791","article-title":"Gradient-based learning applied to document recognition","volume":"86","author":"Lecun","year":"1998","journal-title":"Proc. IEEE"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/j.jmsy.2018.04.008","article-title":"Bearing remaining useful life prediction based on deep autoencoder and deep neural networks","volume":"48","author":"Ren","year":"2018","journal-title":"J. Manuf. Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1109\/TSMC.2017.2697842","article-title":"Using Deep Learning-Based Approach to Predict Remaining Useful Life of Rotating Components","volume":"48","author":"Deutsch","year":"2017","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_23","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":"Jun","year":"2019","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"103182","DOI":"10.1016\/j.compind.2019.103182","article-title":"An ensemble framework based on convolutional bi-directional LSTM with multiple time windows for remaining useful life estimation","volume":"115","author":"Xia","year":"2020","journal-title":"Comput. Ind."},{"key":"ref_25","first-page":"119","article-title":"Application of maximum correlated Kurtosis deconvolution on bearing fault detection and degradation analysis","volume":"4","author":"Kang","year":"2014","journal-title":"Vibroeng. Procedia"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1186","DOI":"10.3390\/e14071186","article-title":"Multivariate Multi-Scale Permutation Entropy for Complexity Analysis of Alzheimer\u2019s Disease EEG","volume":"14","author":"Morabito","year":"2012","journal-title":"Entropy"},{"key":"ref_27","unstructured":"Akandeh, A., and Salem, F.M. (2017). Simplified Long Short-term Memory Recurrent Neural Networks: Part III. arXiv."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2418","DOI":"10.1016\/j.egyr.2021.04.045","article-title":"Time\u2013frequency analysis via complementary ensemble adaptive local iterative filtering and enhanced maximum correlation kurtosis deconvolution for wind turbine fault diagnosis","volume":"7","author":"Zhang","year":"2021","journal-title":"Energy Rep."},{"key":"ref_29","first-page":"5","article-title":"Roller Bearing Fault Diagnosis Method Based on Iterative Filtering and Maximum Correlation Kurtosis Deconvolution","volume":"3","author":"Zhang","year":"2019","journal-title":"Modul. Mach. Tool Autom. Manuf. Tech."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.measurement.2020.108138","article-title":"A two-stage method for bearing fault detection using graph similarity evaluation","volume":"165","author":"Sun","year":"2020","journal-title":"Measurement"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"108636","DOI":"10.1016\/j.measurement.2020.108636","article-title":"Rolling bearing fault diagnosis based on composite multiscale permutation entropy and reverse cognitive fruit fly optimization algorithm\u2014Extreme learning machine\u2014ScienceDirect","volume":"173","author":"He","year":"2020","journal-title":"Measurement"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"5432648","DOI":"10.1155\/2016\/5432648","article-title":"A Novel Method of Fault Diagnosis for Rolling Bearing Based on Dual Tree Complex Wavelet Packet Transform and Improved Multiscale Permutation Entropy","volume":"2016","author":"Tang","year":"2016","journal-title":"Math. Probl. Eng."},{"key":"ref_33","first-page":"1","article-title":"Multiscale Permutation Entropy Based Rolling Bearing Fault Diagnosis","volume":"2014","author":"Zheng","year":"2014","journal-title":"Shock. Vib."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"165","DOI":"10.21595\/jve.2017.18502","article-title":"Railway axle box bearing fault identification using LCD-MPE and ELM-AdaBoost","volume":"20","author":"Yao","year":"2018","journal-title":"J. Vibroeng."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1934","DOI":"10.3390\/s18061934","article-title":"A Novel Bearing Multi-Fault Diagnosis Approach Based on Weighted Permutation Entropy and an Improved SVM Ensemble Classifier","volume":"18","author":"Shenghan","year":"2018","journal-title":"Sensors"},{"key":"ref_36","first-page":"7","article-title":"Sequence to Sequence Weather Forecasting with Long Short-Term Memory Recurrent Neural Networks","volume":"143","author":"Zaytar","year":"2016","journal-title":"Int. J. Comput. Appl."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"9a12","DOI":"10.1007\/s00170-019-04349-y","article-title":"Tool remaining useful life prediction method based on LSTM under variable working conditions","volume":"104","author":"Zhou","year":"2019","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_38","first-page":"487","article-title":"A hierarchical scheme for remaining useful life prediction with long short-term memory networks","volume":"28","author":"Song","year":"2022","journal-title":"Neurocomputing"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1177\/1687814018817184","article-title":"Predicting remaining useful life of rolling bearings based on deep feature representation and long short-term memory neural network","volume":"10","author":"Mao","year":"2018","journal-title":"Adv. Mech. Eng."},{"key":"ref_40","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_41","first-page":"494","article-title":"Data-driven predictive maintenance strategy considering the uncertainty in remaining useful life prediction","volume":"14","author":"Chen","year":"2022","journal-title":"Neurocomputing"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1007\/s11633-020-1276-6","article-title":"A Regularized LSTM Method for Predicting Remaining Useful Life of Rolling Bearings","volume":"18","author":"Liu","year":"2021","journal-title":"Int. J. Autom. Comput."},{"key":"ref_43","first-page":"117","article-title":"Prediction for remaining useful life of rolling bearings based on Long Short-Term Memory","volume":"36","author":"Tang","year":"2019","journal-title":"J. Mach. Des."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1080\/17499518.2023.2182889","article-title":"A novel long-short term memory network approach for stress model updating for excavations in high stress environments","volume":"17","author":"Morgenroth","year":"2023","journal-title":"Georisk Assess. Manag. Risk Eng. Syst. Geohazards"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"103587","DOI":"10.1016\/j.engappai.2020.103587","article-title":"Long short-term memory neural network with weight amplification and its application into gear remaining useful life prediction","volume":"91","author":"Xiang","year":"2020","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_46","first-page":"173","article-title":"A Hybrid Prognostics Approach for Estimating Remaining Useful Life of Rolling Element Bearings","volume":"6","author":"Wang","year":"2018","journal-title":"IEEE Trans. Reliab."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"106330","DOI":"10.1016\/j.ymssp.2019.106330","article-title":"Deep separable convolutional network for remaining useful life prediction of machinery","volume":"134","author":"Wang","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"1343","DOI":"10.3390\/e14081343","article-title":"Bearing Fault Diagnosis Based on Multiscale Permutation Entropy and Support Vector Machine","volume":"14","author":"Wu","year":"2012","journal-title":"Entropy"},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Zhang, Y., Lv, Y., and Ge, M. (2021). A Rolling Bearing Fault Classification Scheme Based on k-Optimized Adaptive Local Iterative Filtering and Improved Multiscale Permutation Entropy. Entropy, 23.","DOI":"10.3390\/e23020191"},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Zhang, W., and Zhou, J. (2019). Fault Diagnosis for Rolling Element Bearings Based on Feature Space Reconstruction and Multiscale Permutation Entropy. Entropy, 21.","DOI":"10.3390\/e21050519"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"108707","DOI":"10.1016\/j.measurement.2020.108707","article-title":"A Joint Long Short-Term Memory and AdaBoost regression approach with application to remaining useful life estimation","volume":"170","author":"Zhu","year":"2021","journal-title":"Measurement"},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Zhang, X., Wang, H., Li, X., Gao, S., Guo, K., and Wei, Y. (2022). Fault Diagnosis of Mine Ventilator Bearing Based on Improved Variational Mode Decomposition and Density Peak Clustering. Machines, 11.","DOI":"10.3390\/machines11010027"},{"key":"ref_53","doi-asserted-by":"crossref","unstructured":"Abdelli, K., Griesser, H., and Pachnicke, S. (2022). A Hybrid CNN-LSTM Approach for Laser Remaining Useful Life Prediction. arXiv.","DOI":"10.1364\/OECC.2021.S3D.3"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/11\/1477\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:11:19Z","timestamp":1760130679000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/11\/1477"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,10,25]]},"references-count":53,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2023,11]]}},"alternative-id":["e25111477"],"URL":"https:\/\/doi.org\/10.3390\/e25111477","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,10,25]]}}}