{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:38:39Z","timestamp":1760150319038,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2023,11,13]],"date-time":"2023-11-13T00:00:00Z","timestamp":1699833600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004735","name":"Natural Science Foundation of Hunan Province","doi-asserted-by":"publisher","award":["2023JJ50200","22A0390"],"award-info":[{"award-number":["2023JJ50200","22A0390"]}],"id":[{"id":"10.13039\/501100004735","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Key project of Hunan Provincial Education Department","award":["2023JJ50200","22A0390"],"award-info":[{"award-number":["2023JJ50200","22A0390"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Currently, the research on the predictions of remaining useful life (RUL) of rotating machinery mainly focuses on the process of health indicator (HI) construction and the determination of the first prediction time (FPT). In complex industrial environments, the influence of environmental factors such as noise may affect the accuracy of RUL predictions. Accurately estimating the remaining useful life of bearings plays a vital role in reducing costly unscheduled maintenance and increasing machine reliability. To overcome these problems, a health indicator construction and prediction method based on multi-featured factor analysis are proposed. Compared with the existing methods, the advantages of this method are the use of factor analysis, to mine hidden common factors from multiple features, and the construction of health indicators based on the maximization of variance contribution after rotation. A dynamic window rectification method is designed to reduce and weaken the stochastic fluctuations in the health indicators. The first prediction time was determined by the cumulative gradient change in the trajectory of the HI. A regression-based adaptive prediction model is used to learn the evolutionary trend of the HI and estimate the RUL of the bearings. The experimental results of two publicly available bearing datasets show the advantages of the method.<\/jats:p>","DOI":"10.3390\/e25111539","type":"journal-article","created":{"date-parts":[[2023,11,13]],"date-time":"2023-11-13T08:35:52Z","timestamp":1699864552000},"page":"1539","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Multi-Featured Factor Analysis and Dynamic Window Rectification Method for Remaining Useful Life Prognosis of Rolling Bearings"],"prefix":"10.3390","volume":"25","author":[{"given":"Cheng","family":"Peng","sequence":"first","affiliation":[{"name":"School of Computer, Hunan University of Technology, Zhuzhou 412007, China"},{"name":"School of Automation, Central South University, Changsha 410083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuanyuan","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Computer, Hunan University of Technology, Zhuzhou 412007, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Changyun","family":"Li","sequence":"additional","affiliation":[{"name":"School of Computer, Hunan University of Technology, Zhuzhou 412007, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhaohui","family":"Tang","sequence":"additional","affiliation":[{"name":"School of Automation, Central South University, Changsha 410083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weihua","family":"Gui","sequence":"additional","affiliation":[{"name":"School of Automation, Central South University, Changsha 410083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"799","DOI":"10.1016\/j.ymssp.2017.11.016","article-title":"Machinery health prognostics: A systematic review from data acquisition to RUL prediction","volume":"104","author":"Lei","year":"2018","journal-title":"Mech. Syst. Signal Proc."},{"key":"ref_2","first-page":"3151169","article-title":"Bearing Remaining Useful Life Prediction Based on Regression Shapalet and Graph Neural Network","volume":"71","author":"Yang","year":"2022","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/j.jmsy.2020.11.016","article-title":"A joint classification-regression method for multi-stage remaining useful life prediction","volume":"58","author":"Wu","year":"2021","journal-title":"J. Manuf. Syst."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1016\/j.isatra.2019.08.058","article-title":"Bearing remaining useful life prediction using support vector machine and hybrid degradation tracking model","volume":"98","author":"Yan","year":"2020","journal-title":"ISA Trans."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"106899","DOI":"10.1016\/j.ymssp.2020.106899","article-title":"A two-stage method based on extreme learning machine for predicting the remaining useful life of rolling-element bearings","volume":"144","author":"Pan","year":"2020","journal-title":"Mech. Syst. Signal Proc."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"109706","DOI":"10.1016\/j.measurement.2021.109706","article-title":"Wiener-based remaining useful life prediction of rolling bearings using improved Kalman filtering and adaptive modification","volume":"182","author":"Li","year":"2021","journal-title":"Measurement"},{"key":"ref_7","first-page":"3511910","article-title":"Feature extraction for data-driven remaining useful life prediction of rolling bearings","volume":"70","author":"Zhao","year":"2021","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"110393","DOI":"10.1016\/j.measurement.2021.110393","article-title":"A method for predicting the remaining useful life of rolling bearings under different working conditions based on multi-domain adversarial networks","volume":"188","author":"Zou","year":"2022","journal-title":"Measurement"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/j.ress.2018.02.003","article-title":"A reliable technique for remaining useful life estimation of rolling element bearings using dynamic regression models","volume":"184","author":"Ahmad","year":"2019","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"12041","DOI":"10.1021\/acs.iecr.9b00524","article-title":"Process fault prognosis using hidden Markov model\u2013bayesian networks hybrid model","volume":"58","author":"Khan","year":"2019","journal-title":"Ind. Eng. Chem. Res."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"108286","DOI":"10.1016\/j.measurement.2020.108286","article-title":"Transferable convolutional neural network based remaining useful life prediction of bearing under multiple failure behaviors","volume":"168","author":"Cheng","year":"2021","journal-title":"Measurement"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1076","DOI":"10.1007\/s10489-021-02503-2","article-title":"Convolutional neural network based on attention mechanism and Bi-LSTM for bearing remaining life prediction","volume":"52","author":"Luo","year":"2022","journal-title":"Appl. Intell."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Civera, M., and Surace, C. (2022). An application of instantaneous spectral entropy for the condition monitoring of wind turbines. Appl. Sci., 12.","DOI":"10.3390\/app12031059"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1301","DOI":"10.1109\/TII.2022.3169465","article-title":"Data-driven prognostic scheme for bearings based on a novel health indicator and gated recurrent unit network","volume":"19","author":"Ni","year":"2022","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"3104414","DOI":"10.1109\/TIM.2021.3104414","article-title":"A Health Index Construction Framework for Prognostics Based on Feature Fusion and Constrained Optimization","volume":"70","author":"Chen","year":"2021","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1314","DOI":"10.1109\/TR.2016.2570568","article-title":"A model-based method for remaining useful life prediction of machinery","volume":"65","author":"Lei","year":"2016","journal-title":"IEEE Trans. Reliab."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Lei, Y., Niu, S., Guo, L., and Li, N. (2017, January 16\u201318). A distance metric learning based health indicator for health prognostics of bearings. Proceedings of the 2017 International Conference on Sensing, Diagnostics, Prognostics, and Control (SDPC), Shanghai, China.","DOI":"10.1109\/SDPC.2017.19"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1577","DOI":"10.1109\/TIE.2017.2733487","article-title":"A hybrid prognostics technique for rolling element bearings using adaptive predictive models","volume":"65","author":"Ahmad","year":"2017","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"290","DOI":"10.1016\/j.isatra.2021.10.031","article-title":"An effective method for remaining useful life estimation of bearings with elbow point detection and adaptive regression models","volume":"128","author":"Yan","year":"2021","journal-title":"ISA Trans."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2633","DOI":"10.1109\/TIE.2016.2515054","article-title":"Health index-based prognostics for remaining useful life predictions in electrical machines","volume":"63","author":"Yang","year":"2016","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"3210933","DOI":"10.1109\/TIM.2022.3210933","article-title":"Dual-Attention-Based Multiscale Convolutional Neural Network with Stage Division for Remaining Useful Life Prediction of Rolling Bearings","volume":"71","author":"Jiang","year":"2022","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"117415","DOI":"10.1016\/j.eswa.2022.117415","article-title":"Joint training of a predictor network and a generative adversarial network for time series forecasting: A case study of bearing prognostics","volume":"203","author":"Lu","year":"2022","journal-title":"Expert Syst. Appl."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"21","DOI":"10.4173\/mic.2022.1.3","article-title":"RMS Based Health Indicators for Remaining Useful Lifetime Estimation of Bearings","volume":"43","author":"Klausen","year":"2022","journal-title":"MIC J. Model. Identif. Control"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Rigamonti, M., Baraldi, P., Zio, E., Roychoudhury, I., Goebel, K., and Poll, S. (2016, January 5\u20138). Echo state network for the remaining useful life prediction of a turbofan engine. Proceedings of the PHM Society European Conference, Bilbao, Spain.","DOI":"10.36001\/phme.2016.v3i1.1623"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"106987","DOI":"10.1016\/j.ymssp.2020.106987","article-title":"More effective prognostics with elbow point detection and deep learning","volume":"146","author":"Baptista","year":"2021","journal-title":"Mech. Syst. Signal Proc."},{"key":"ref_26","unstructured":"Saha, B., and Goebel, K. (2007). Battery Data Set, NASA Ames Prognostics Data Repository."},{"key":"ref_27","unstructured":"Hui, H., Lenczner, M., Cogan, S., Meister, A., Favre, M., Overstolz, T., Couturier, R., and Domas, S. (2013). FEMTO-ST, Time Frequency Department, University of Franche-Comte."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"108064","DOI":"10.1016\/j.measurement.2020.108064","article-title":"Degradation assessment of bearings with trend-reconstruct-based features selection and gated recurrent unit network","volume":"165","author":"Xiao","year":"2020","journal-title":"Measurement"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Saxena, A., Celaya, J., Balaban, E., Goebel, K., Saha, B., Saha, S., and Schwabacher, M. (2008, January 6\u20139). Metrics for evaluating performance of prognostic techniques. Proceedings of the 2008 International Conference on Prognostics and Health Management, Denver, CO, USA.","DOI":"10.1109\/PHM.2008.4711436"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Hu, Y., Palm\u00e9, T., and Fink, O. (2016, January 3\u20136). Deep health indicator extraction: A method based on auto-encoders and extreme learning machines. Proceedings of the Annual Conference of the PHM Society, Denver, CO, USA.","DOI":"10.36001\/phmconf.2016.v8i1.2587"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Jin, X., Sun, Y., Shan, J., Wang, Y., and Xu, Z. (2014, January 24\u201327). Health monitoring and fault detection using wavelet packet technique and multivariate process control method. Proceedings of the 2014 Prognostics and System Health Management Conference (PHM-2014 Hunan), Zhangjiajie, China.","DOI":"10.1109\/PHM.2014.6988174"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1781","DOI":"10.1109\/TIE.2014.2336616","article-title":"Extended Kalman filtering for remaining-useful-life estimation of bearings","volume":"62","author":"Singleton","year":"2014","journal-title":"IEEE Trans. Ind. Electron."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/11\/1539\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:22:09Z","timestamp":1760131329000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/11\/1539"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,11,13]]},"references-count":32,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2023,11]]}},"alternative-id":["e25111539"],"URL":"https:\/\/doi.org\/10.3390\/e25111539","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2023,11,13]]}}}