{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,11]],"date-time":"2026-06-11T03:16:07Z","timestamp":1781147767005,"version":"3.54.1"},"reference-count":39,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2022,7,29]],"date-time":"2022-07-29T00:00:00Z","timestamp":1659052800000},"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":["U2133202"],"award-info":[{"award-number":["U2133202"]}],"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":["KYCX22_0375"],"award-info":[{"award-number":["KYCX22_0375"]}],"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":["KXKCXJJ202205"],"award-info":[{"award-number":["KXKCXJJ202205"]}],"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":["BK20220687"],"award-info":[{"award-number":["BK20220687"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Postgraduate Research and Practice Innovation Program of Jiangsu Province","award":["U2133202"],"award-info":[{"award-number":["U2133202"]}]},{"name":"Postgraduate Research and Practice Innovation Program of Jiangsu Province","award":["KYCX22_0375"],"award-info":[{"award-number":["KYCX22_0375"]}]},{"name":"Postgraduate Research and Practice Innovation Program of Jiangsu Province","award":["KXKCXJJ202205"],"award-info":[{"award-number":["KXKCXJJ202205"]}]},{"name":"Postgraduate Research and Practice Innovation Program of Jiangsu Province","award":["BK20220687"],"award-info":[{"award-number":["BK20220687"]}]},{"name":"Nanjing University of Aeronautics and Astronautics","award":["U2133202"],"award-info":[{"award-number":["U2133202"]}]},{"name":"Nanjing University of Aeronautics and Astronautics","award":["KYCX22_0375"],"award-info":[{"award-number":["KYCX22_0375"]}]},{"name":"Nanjing University of Aeronautics and Astronautics","award":["KXKCXJJ202205"],"award-info":[{"award-number":["KXKCXJJ202205"]}]},{"name":"Nanjing University of Aeronautics and Astronautics","award":["BK20220687"],"award-info":[{"award-number":["BK20220687"]}]},{"DOI":"10.13039\/501100004608","name":"Natural Science Foundation of Jiangsu Province","doi-asserted-by":"publisher","award":["U2133202"],"award-info":[{"award-number":["U2133202"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004608","name":"Natural Science Foundation of Jiangsu Province","doi-asserted-by":"publisher","award":["KYCX22_0375"],"award-info":[{"award-number":["KYCX22_0375"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004608","name":"Natural Science Foundation of Jiangsu Province","doi-asserted-by":"publisher","award":["KXKCXJJ202205"],"award-info":[{"award-number":["KXKCXJJ202205"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004608","name":"Natural Science Foundation of Jiangsu Province","doi-asserted-by":"publisher","award":["BK20220687"],"award-info":[{"award-number":["BK20220687"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Remaining useful life prediction is one of the essential processes for machine system prognostics and health management. Although there are many new approaches based on deep learning for remaining useful life prediction emerging in recent years, these methods still have the following weaknesses: (1) The correlation between the information collected by each sensor and the remaining useful life of the machinery is not sufficiently considered. (2) The accuracy of deep learning algorithms for remaining useful life prediction is low due to the high noise, over-dimensionality, and non-linear signals generated during the operation of complex systems. To overcome the above weaknesses, a general deep long short memory network-based approach for mechanical remaining useful life prediction is proposed in this paper. Firstly, a two-step maximum information coefficient method was built to calculate the correlation between the sensor data and the remaining useful life. Secondly, the kernel principal component analysis with a simple moving average method was designed to eliminate noise, reduce dimensionality, and extract nonlinear features. Finally, a deep long short memory network-based deep learning method is presented to predict remaining useful life. The efficiency of the proposed method for remaining useful life prediction of a nonlinear degradation process is demonstrated by a test case of NASA\u2019s commercial modular aero-propulsion system simulation data. The experimental results also show that the proposed method has better prediction accuracy than other state-of-the-art methods.<\/jats:p>","DOI":"10.3390\/s22155680","type":"journal-article","created":{"date-parts":[[2022,8,1]],"date-time":"2022-08-01T04:04:00Z","timestamp":1659326640000},"page":"5680","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["A DLSTM-Network-Based Approach for Mechanical Remaining Useful Life Prediction"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6126-6940","authenticated-orcid":false,"given":"Yan","family":"Liu","sequence":"first","affiliation":[{"name":"Civil Aviation Key Laboratory of Aircraft Health Monitoring and Intelligent Maintenance, College of Civil Aviation, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2925-4704","authenticated-orcid":false,"given":"Zhenzhen","family":"Liu","sequence":"additional","affiliation":[{"name":"Civil Aviation Key Laboratory of Aircraft Health Monitoring and Intelligent Maintenance, College of Civil Aviation, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hongfu","family":"Zuo","sequence":"additional","affiliation":[{"name":"Civil Aviation Key Laboratory of Aircraft Health Monitoring and Intelligent Maintenance, College of Civil Aviation, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Heng","family":"Jiang","sequence":"additional","affiliation":[{"name":"Civil Aviation Key Laboratory of Aircraft Health Monitoring and Intelligent Maintenance, College of Civil Aviation, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pengtao","family":"Li","sequence":"additional","affiliation":[{"name":"Civil Aviation Key Laboratory of Aircraft Health Monitoring and Intelligent Maintenance, College of Civil Aviation, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xin","family":"Li","sequence":"additional","affiliation":[{"name":"Civil Aviation Key Laboratory of Aircraft Health Monitoring and Intelligent Maintenance, College of Civil Aviation, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"},{"name":"School of Automotive & Rail Transit, Nanjing Institute of Technology, Nanjing 211167, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/0006-2944(75)90147-7","article-title":"Formate assay in body fluids: Application in methanol poisoning","volume":"13","author":"Makar","year":"1975","journal-title":"Biochem. Med."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1016\/j.ymssp.2017.01.050","article-title":"State of the art and taxonomy of prognostics approaches, trends of prognostics applications and open issues towards maturity at different technology readiness levels","volume":"94","author":"Javed","year":"2017","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_3","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_4","doi-asserted-by":"crossref","unstructured":"Khan, M.M., Tse, P.W., and Trappey, A.J.C. (2021). Development of a Novel Methodology for Remaining Useful Life Prediction of Industrial Slurry Pumps in the Absence of Run to Failure Data. Sensors, 21.","DOI":"10.3390\/s21248420"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"7062","DOI":"10.3390\/s150307062","article-title":"A hybrid PCA-CART-MARS-based prognostic approach of the remaining useful life for aircraft engines","volume":"15","year":"2015","journal-title":"Sensors"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/j.energy.2016.08.039","article-title":"Early fault detection and diagnosis in bearings for more efficient operation of rotating machinery","volume":"136","author":"Brkovic","year":"2017","journal-title":"Energy"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1016\/j.ymssp.2016.07.039","article-title":"An integrated Gaussian process regression for prediction of remaining useful life of slow speed bearings based on acoustic emission","volume":"84","author":"Aye","year":"2017","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"TayebiHaghighi, S., and Koo, I. (2022). Sensor Fault Diagnosis Using a Machine Fuzzy Lyapunov-Based Computed Ratio Algorithm. Sensors, 22.","DOI":"10.3390\/s22082974"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Kim, W.S., Lee, D.H., Kim, Y.J., Kim, Y.S., and Park, S.U. (2021). Estimation of Axle Torque for an Agricultural Tractor Using an Artificial Neural Network. Sensors, 21.","DOI":"10.3390\/s21061989"},{"key":"ref_10","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_11","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_12","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":"IEEE Trans. Neural Netw."},{"key":"ref_13","first-page":"1768","article-title":"Traumatic brain stem lesion. A case with remarkable recovery","volume":"148","author":"Laursen","year":"1986","journal-title":"Ugeskr. Laeger"},{"key":"ref_14","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_15","doi-asserted-by":"crossref","unstructured":"Schroff, F., Kalenichenko, D., and Philbin, J. (2015, January 7\u201312). FaceNet: A Unified Embedding for Face Recognition and Clustering. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Boston, MA, USA.","DOI":"10.1109\/CVPR.2015.7298682"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Graves, A., Mohamed, A.R., and Hinton, G. (2013, January 26\u201331). Speech Recognition with Deep Recurrent Neural Networks. Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Vancouver, BC, Canada.","DOI":"10.1109\/ICASSP.2013.6638947"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1109\/MCI.2018.2840738","article-title":"Recent Trends in Deep Learning Based Natural Language Processing","volume":"13","author":"Young","year":"2018","journal-title":"IEEE Comput. Intell. Mag."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"372","DOI":"10.1016\/j.ress.2019.01.006","article-title":"Gated recurrent unit based recurrent neural network for remaining useful life prediction of nonlinear deterioration process","volume":"185","author":"Chen","year":"2019","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1016\/j.jmsy.2018.05.011","article-title":"Long short-term memory for machine remaining life prediction","volume":"48","author":"Zhang","year":"2018","journal-title":"J. Manuf. Syst."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Wang, B., Lei, Y., Li, N., and Yan, T. (2019). Deep separable convolutional network for remaining useful life prediction of machinery. Mech. Syst. Signal Process., 134.","DOI":"10.1016\/j.ymssp.2019.106330"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Kang, Z., Catal, C., and Tekinerdogan, B. (2021). Remaining Useful Life (RUL) Prediction of Equipment in Production Lines Using Artificial Neural Networks. Sensors, 21.","DOI":"10.3390\/s21030932"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Ji, S., Han, X., Hou, Y., Song, Y., and Du, Q. (2020). Remaining Useful Life Prediction of Airplane Engine Based on PCA-BLSTM. Sensors, 20.","DOI":"10.3390\/s20164537"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"504","DOI":"10.1126\/science.1127647","article-title":"Reducing the dimensionality of data with neural networks","volume":"313","author":"Hinton","year":"2006","journal-title":"Science"},{"key":"ref_24","first-page":"1929","article-title":"Dropout: A Simple Way to Prevent Neural Networks from Overfitting","volume":"15","author":"Srivastava","year":"2014","journal-title":"J. Mach. Learn. Res."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1518","DOI":"10.1126\/science.1205438","article-title":"Detecting novel associations in large data sets","volume":"334","author":"Reshef","year":"2011","journal-title":"Science"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ress.2017.11.021","article-title":"Remaining useful life estimation in prognostics using deep convolution neural networks","volume":"172","author":"Li","year":"2018","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Jolliffe, I.T., and Cadima, J. (2016). Principal component analysis: A review and recent developments. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci., 374.","DOI":"10.1098\/rsta.2015.0202"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1299","DOI":"10.1162\/089976698300017467","article-title":"Nonlinear Component Analysis as a Kernel Eigenvalue Problem","volume":"10","author":"Smola","year":"1998","journal-title":"Neural Comput."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1198\/jbes.2010.09018","article-title":"Forecast Combination Across Estimation Windows","volume":"29","author":"Pesaran","year":"2011","journal-title":"J. Bus. Econ. Stat."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"428","DOI":"10.1016\/j.tics.2007.09.004","article-title":"Learning multiple layers of representation","volume":"11","author":"Hinton","year":"2007","journal-title":"Trends Cogn. Sci."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Al-Dulaimi, A., Zabihi, S., Asif, A., and Mohammed, A. (2020). NBLSTM: Noisy and Hybrid Convolutional Neural Network and BLSTM-Based Deep Architecture for Remaining Useful Life Estimation. J. Comput. Inf. Sci. Eng., 20.","DOI":"10.1115\/1.4045491"},{"key":"ref_32","unstructured":"Kingma, D.P., and Ba, J. (2014). Adam: A method for stochastic optimization. arXiv."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Saxena, A., Goebel, K., Simon, D., and Eklund, N. (2008, January 6\u20139). Damage Propagation Modeling for Aircraft Engine Run-to-Failure Simulation. Proceedings of the 2008 International Conference on Prognostics and Health Management, Denver, CO, USA.","DOI":"10.1109\/PHM.2008.4711414"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Peel, L. (2008, January 6\u20139). Data Driven Prognostics using a Kalman Filter Ensemble of Neural Network Models. Proceedings of the 2008 International Conference on Prognostics and Health Management, Denver, CO, USA.","DOI":"10.1109\/PHM.2008.4711423"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1016\/j.compind.2019.02.004","article-title":"A multimodal and hybrid deep neural network model for Remaining Useful Life estimation","volume":"108","author":"Zabihi","year":"2019","journal-title":"Comput. Ind."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2306","DOI":"10.1109\/TNNLS.2016.2582798","article-title":"Multiobjective 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_37","doi-asserted-by":"crossref","unstructured":"Zheng, S., Ristovski, K., Farahat, A., and Gupta, C. (2017, January 19\u201321). Long Short-Term Memory Network for Remaining Useful Life estimation. Proceedings of the 2017 IEEE International Conference on Prognostics and Health Management (ICPHM), Dallas, TX, USA.","DOI":"10.1109\/ICPHM.2017.7998311"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Wang, J.J., Wen, G.L., Yang, S.P., and Liu, Y.Q. (2018, January 26\u201328). Remaining Useful Life Estimation in Prognostics Using Deep Bidirectional LSTM Neural Network. Proceedings of the Prognostics and System Health Management Conference, Chongqing, China.","DOI":"10.1109\/PHM-Chongqing.2018.00184"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"75464","DOI":"10.1109\/ACCESS.2019.2919566","article-title":"A Directed Acyclic Graph Network Combined with CNN and LSTM for Remaining Useful Life Prediction","volume":"7","author":"Li","year":"2019","journal-title":"IEEE Access"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/15\/5680\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:59:00Z","timestamp":1760140740000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/15\/5680"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,29]]},"references-count":39,"journal-issue":{"issue":"15","published-online":{"date-parts":[[2022,8]]}},"alternative-id":["s22155680"],"URL":"https:\/\/doi.org\/10.3390\/s22155680","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,7,29]]}}}