{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,15]],"date-time":"2025-11-15T17:11:24Z","timestamp":1763226684861,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2019,4,22]],"date-time":"2019-04-22T00:00:00Z","timestamp":1555891200000},"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":["61671470"],"award-info":[{"award-number":["61671470"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012165","name":"Key Technologies Research and Development Program","doi-asserted-by":"publisher","award":["2016YFC0802904"],"award-info":[{"award-number":["2016YFC0802904"]}],"id":[{"id":"10.13039\/501100012165","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>With the aim of automatic recognition of weak faults in hydraulic systems, this paper proposes an identification method based on multi-scale permutation entropy feature extraction of fault-sensitive intrinsic mode function (IMF) and deep belief network (DBN). In this method, the leakage fault signal is first decomposed by empirical mode decomposition (EMD), and fault-sensitive IMF components are screened by adopting the correlation analysis method. The multi-scale entropy feature of each screened IMF is then extracted and features closely related to the weak fault information are then obtained. Finally, DBN is used for identification of fault diagnosis. Experimental results prove that this identification method has an ideal recognition effect. It can accurately judge whether there is a leakage fault, determine the degree of severity of the fault, and can diagnose and analyze hydraulic weak faults in general.<\/jats:p>","DOI":"10.3390\/e21040425","type":"journal-article","created":{"date-parts":[[2019,4,22]],"date-time":"2019-04-22T11:02:53Z","timestamp":1555930973000},"page":"425","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["Analysis of Weak Fault in Hydraulic System Based on Multi-scale Permutation Entropy of Fault-Sensitive Intrinsic Mode Function and Deep Belief Network"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2657-2931","authenticated-orcid":false,"given":"Jie","family":"Huang","sequence":"first","affiliation":[{"name":"Urumqi Campus, Engineering University of PAP, Urumqi 830001, China"}]},{"given":"Xinqing","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Field Engineering, Army Engineering University of PLA, Nanjing 210007, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1511-9499","authenticated-orcid":false,"given":"Dong","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Field Engineering, Army Engineering University of PLA, Nanjing 210007, China"},{"name":"Second Institute of Engineering Research and Design, Southern Theatre Command, Kunming 650222, China"}]},{"given":"Zhiwei","family":"Wang","sequence":"additional","affiliation":[{"name":"Urumqi Campus, Engineering University of PAP, Urumqi 830001, China"}]},{"given":"Xia","family":"Hua","sequence":"additional","affiliation":[{"name":"College of Field Engineering, Army Engineering University of PLA, Nanjing 210007, China"}]}],"member":"1968","published-online":{"date-parts":[[2019,4,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Zeng, D., Zhou, D., Tan, C., and Jiang, B. (2018). Research on Model-Based Fault Diagnosis for a Gas Turbine Based on Transient Performance. Appl. Sci., 8.","DOI":"10.3390\/app8010148"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1016\/j.ymssp.2014.09.002","article-title":"Detection of weak transient signals based on wavelet packet transform and manifold learning for rolling element bearing fault diagnosis","volume":"55","author":"Wang","year":"2015","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Bustos, A., Rubio, H., Castej\u00f3n, C., and Garc\u00eda-Prada, J.C. (2018). EMD-Based Methodology for the Identification of a High-Speed Train Running in a Gear Operating State. Sensors, 18.","DOI":"10.3390\/s18030793"},{"key":"ref_4","first-page":"183","article-title":"Hydraulic Pump Fault Diagnosis Method Based on Lyapunov Exponent Analysis","volume":"36","author":"Jiang","year":"2008","journal-title":"Mach. Tool Hydraul."},{"key":"ref_5","first-page":"1","article-title":"Active Fault Diagnosis on a Hydraulic Pitch System Based on Frequency-Domain Identification","volume":"5","author":"Vasquez","year":"2017","journal-title":"IEEE Trans. Contr. Syst. Trans."},{"key":"ref_6","first-page":"119","article-title":"Experimental Research on Sensitive Characteristic Parameter Selection of Hydraulic Cylinder Internal Leakage Fault","volume":"3","author":"Jiang","year":"2014","journal-title":"Chin. Hydraul. Pneum."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Yasir, M.N., and Koh, B.H. (2018). Data Decomposition Techniques with Multi-Scale Permutation Entropy Calculations for Bearing Fault Diagnosis. Sensors, 18.","DOI":"10.3390\/s18041278"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Ju, B., Zhang, H., Liu, Y., Liu, F., Lu, S., and Dai, Z. (2018). A Feature Extraction Method Using Improved Multi-Scale Entropy for Rolling Bearing Fault Diagnosis. Entropy, 20.","DOI":"10.3390\/e20040212"},{"key":"ref_9","first-page":"13","article-title":"Feature extraction of rolling bearing\u2019s weak fault based on POVMD and spectrum auto-correlation analysis","volume":"4","author":"Chen","year":"2018","journal-title":"J. Electron. Meas. Instrum."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/j.ymssp.2014.04.006","article-title":"Feature extraction of rolling bearing\u2019s early weak fault based on EEMD and tunable Q-factor wavelet transform","volume":"48","author":"Wang","year":"2014","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TIM.2018.2801040","article-title":"Sparse Coding Shrinkage in Intrinsic Time-Scale Decomposition for Weak Fault Feature Extraction of Bearings","volume":"67","author":"Yu","year":"2018","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.ymssp.2017.04.006","article-title":"Improving the bearing fault diagnosis efficiency by the adaptive stochastic resonance in a new nonlinear system","volume":"96","author":"Liu","year":"2017","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3148","DOI":"10.1109\/TIM.2017.2751878","article-title":"Weak Fault Feature Extraction of Rolling Bearings Using Local Mean Decomposition-Based Multilayer Hybrid Denoising","volume":"66","author":"Yu","year":"2017","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_14","first-page":"1","article-title":"Weak fault feature extraction for bearings based on an order cepstrum enhanced with Teager energy operator","volume":"34","author":"Yang","year":"2015","journal-title":"J. Vib. Shock"},{"key":"ref_15","first-page":"184","article-title":"Faint Fault Feature Extraction of Hydraulic Pump Based on Adaptive EEMD-Enhancement Factor","volume":"19","author":"Wang","year":"2014","journal-title":"Mach. Tool Hydraul."},{"key":"ref_16","first-page":"1313","article-title":"Fault detection algorithm using DCS method combined with filters bank derived from the wavelet transform","volume":"5","author":"Mustapha","year":"2009","journal-title":"Int. J. Innov. Comput. Inf. Control"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1016\/j.apacoust.2014.08.016","article-title":"Application of empirical mode decomposition and artificial neural network for automatic bearing fault diagnosis based on vibration signals","volume":"89","author":"Ben","year":"2015","journal-title":"Appl. Acoust."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"390","DOI":"10.1016\/j.measurement.2013.12.010","article-title":"Fault diagnosis of hydraulic system in large forging hydraulic press","volume":"49","author":"Fu","year":"2014","journal-title":"Measurement"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.compfluid.2014.09.034","article-title":"Experimental study of hydraulic cylinder leakage and fault feature extraction based on wavelet packet analysis","volume":"106","author":"Zhao","year":"2015","journal-title":"Comput. Fluids"},{"key":"ref_20","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":"2014","journal-title":"Neural Comput."},{"key":"ref_21","first-page":"1","article-title":"A practical guide to training restricted Boltzmann machines","volume":"9","author":"Hinton","year":"2010","journal-title":"Momentum"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"174102","DOI":"10.1103\/PhysRevLett.88.174102","article-title":"Permutation Entropy: A Natural Complexity Measure for Time Series","volume":"88","author":"Bandt","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Aziz, W., and Arif, M. (2005, January 24\u201325). Multiscale Permutation Entropy of Physiological Time Series. Proceedings of the IEEE International Multi-Topic Conference, Karachi, Pakistan.","DOI":"10.1109\/INMIC.2005.334494"},{"key":"ref_24","first-page":"153","article-title":"Greedy layer-wise training of deep networks","volume":"19","author":"Bengio","year":"2007","journal-title":"Adv. Neur. Inform. Process. Syst."},{"key":"ref_25","first-page":"2641","article-title":"Multi-scale permutation entropy and its applications to rolling bearing fault diagnosis","volume":"24","author":"Zheng","year":"2013","journal-title":"China Mech. Eng."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/4\/425\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:46:17Z","timestamp":1760186777000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/4\/425"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,4,22]]},"references-count":25,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2019,4]]}},"alternative-id":["e21040425"],"URL":"https:\/\/doi.org\/10.3390\/e21040425","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2019,4,22]]}}}