{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,23]],"date-time":"2025-12-23T12:16:49Z","timestamp":1766492209600,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2017,6,29]],"date-time":"2017-06-29T00:00:00Z","timestamp":1498694400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Aiming at the issue of extracting the incipient single-fault and multi-fault of rotating machinery from the nonlinear and non-stationary vibration signals with a strong background noise, a new fault diagnosis method based on improved autoregressive-Minimum entropy deconvolution (improved AR-MED) and variational mode decomposition (VMD) is proposed. Due to the complexity of rotating machinery systems, the periodic transient impulses of single-fault and multiple-faults always emerge in the acquired vibration signals. The improved autoregressive minimum entropy deconvolution (AR-MED) technique can effectively deconvolve the influence of the background noise, which aims to enhance the peak value of the multiple transient impulses. Nevertheless, the envelope spectrum of simulation and experimental in this work shows that there are many interference components exist on both left and right of fault characteristic frequencies when the background noise is strong. To overcome this shortcoming, the VMD is thus applied to adaptively decompose the filtered output vibration signal into a number of quasi-orthogonal intrinsic modes so as to better detect the single- and multiple-faults via those sub-band signals. The experimental and engineering application results demonstrate that the proposed method dramatically sharpens the fault characteristic frequencies (FCFs) from the impacts of bearing outer race and gearbox faults compared to the traditional methods, which show a significant improvement in early incipient faults of rotating machinery.<\/jats:p>","DOI":"10.3390\/e19070317","type":"journal-article","created":{"date-parts":[[2017,6,29]],"date-time":"2017-06-29T10:40:04Z","timestamp":1498732804000},"page":"317","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":35,"title":["Incipient Fault Feature Extraction for Rotating Machinery Based on Improved AR-Minimum Entropy Deconvolution Combined with Variational Mode Decomposition Approach"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7170-4679","authenticated-orcid":false,"given":"Qing","family":"Li","sequence":"first","affiliation":[{"name":"College of Mechanical Engineering, Donghua University, Shanghai 201620, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xia","family":"Ji","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, Donghua University, Shanghai 201620, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Steven Y.","family":"Liang","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, Donghua University, Shanghai 201620, China"},{"name":"George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0405, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,6,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1016\/j.ymssp.2010.07.017","article-title":"Rolling element bearing diagnostics\u2014A tutorial","volume":"25","author":"Randall","year":"2011","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"974","DOI":"10.1016\/j.ymssp.2004.01.006","article-title":"A comparison study of improved Hilbert\u2013Huang transform and wavelet transform: Application to fault diagnosis for rolling bearing","volume":"19","author":"Peng","year":"2005","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1016\/j.ymssp.2016.05.010","article-title":"Bearing diagnostics: A method based on differential geometry","volume":"80","author":"Tian","year":"2016","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1016\/j.triboint.2015.12.037","article-title":"A review on signal processing techniques utilized in the fault diagnosis of rolling element bearings","volume":"96","author":"Rai","year":"2016","journal-title":"Tribol. Int."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1016\/j.measurement.2016.04.036","article-title":"Recent progress on decoupling diagnosis of hybrid failures in gear transmission systems using vibration sensor signal: A review","volume":"90","author":"Li","year":"2016","journal-title":"Measurement"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2763","DOI":"10.1109\/TPEL.2014.2356207","article-title":"High-performance and energy-efficient fault diagnosis using effective envelope analysis and denoising on a general-purpose graphics processing unit","volume":"30","author":"Kang","year":"2015","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_7","first-page":"544","article-title":"Detecting singularities with Harmonic wavelets","volume":"26","author":"Cattani","year":"2009","journal-title":"J. Donghua Univ."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1007\/s11235-009-9208-3","article-title":"Harmonic wavelet approximation of random, fractal and high frequency signals","volume":"43","author":"Cattani","year":"2010","journal-title":"Telecommun. Syst."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2933","DOI":"10.1016\/j.ymssp.2007.02.003","article-title":"Rolling element bearings multi-fault classification based on the wavelet denoising and support vector machine","volume":"21","author":"Abbasion","year":"2007","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1016\/S0888-3270(03)00099-2","article-title":"Application of EMD method and Hilbert spectrum to the fault diagnosis of roller bearings","volume":"19","author":"Yu","year":"2005","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_11","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_12","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1016\/j.triboint.2013.01.001","article-title":"Detection and diagnosis of surface wear failure in a spur geared system using EEMD based vibration signal analysis","volume":"61","author":"Amarnath","year":"2013","journal-title":"Tribol. Int."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/j.measurement.2014.10.026","article-title":"Diagnostics of gear deterioration using EEMD approach and PCA process","volume":"61","author":"Yang","year":"2015","journal-title":"Measurement"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1327","DOI":"10.1016\/j.ymssp.2008.11.005","article-title":"Application of the EEMD method to rotor fault diagnosis of rotating machinery","volume":"23","author":"Lei","year":"2009","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1016\/j.ymssp.2012.12.010","article-title":"An improved EEMD with multiwavelet packet for rotating machinery multi-fault diagnosis","volume":"36","author":"Jiang","year":"2013","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_16","first-page":"11","article-title":"Ensemble empirical mode decomposition: A noise assisted data analysis method","volume":"1","author":"Wu","year":"2009","journal-title":"Adv. Adapt. Data Anal."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1197","DOI":"10.1016\/j.ymssp.2005.09.005","article-title":"Application of support vector regression machines to the processing of end effects of Hilbert\u2013Huang transform","volume":"21","author":"Cheng","year":"2007","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1098\/rsif.2005.0058","article-title":"The local mean decomposition and its application to EEG perception data","volume":"2","author":"Smith","year":"2009","journal-title":"J. R. Soc. Interface"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1016\/j.procir.2016.10.051","article-title":"Revision of bearing fault characteristic spectrum using LMD and interpolation correction algorithm","volume":"56","author":"Li","year":"2016","journal-title":"Procedia CIRP"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/j.isatra.2015.12.009","article-title":"A hybrid fault diagnosis method based on second generation wavelet de-noising and local mean decomposition for rotating machinery","volume":"61","author":"Liu","year":"2016","journal-title":"ISA Trans."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1016\/j.ymssp.2016.08.003","article-title":"Rotating machine fault diagnosis through enhanced stochastic resonance by full-wave signal construction","volume":"85","author":"Lu","year":"2017","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/j.measurement.2014.08.017","article-title":"An improved data fusion technique for faults diagnosis in rotating machines","volume":"58","author":"Kaltungo","year":"2014","journal-title":"Measurement"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/j.measurement.2015.03.041","article-title":"Use of composite higher order spectra for faults diagnosis of rotating machines with different foundation flexibilities","volume":"70","author":"Kaltungo","year":"2015","journal-title":"Measurement"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"604","DOI":"10.1177\/1475921715604388","article-title":"A novel fault diagnosis technique for enhancing maintenance and reliability of rotating machines","volume":"14","author":"Kaltungo","year":"2015","journal-title":"Struct. Health Monit."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1109\/TSP.2013.2288675","article-title":"Variational mode decomposition","volume":"62","author":"Konstantin","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1016\/j.measurement.2016.12.029","article-title":"New methods to estimate the observed noise variance for an ARMA model","volume":"99","author":"Wang","year":"2017","journal-title":"Measurement"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2635","DOI":"10.1016\/j.csda.2005.05.003","article-title":"An improved Akaike information criterion for state-space model selection","volume":"50","author":"Bengtsson","year":"2006","journal-title":"Comput. Stat. Data Anal."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"670","DOI":"10.1016\/j.dsp.2006.08.010","article-title":"ARMA model parameter estimation based on the equivalent MA approach","volume":"16","author":"Kizilkaya","year":"2006","journal-title":"Digit. Signal Process."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"588","DOI":"10.1016\/j.physa.2016.11.037","article-title":"The modified Yule-Walker method for image-stable time series models","volume":"469","author":"Kruczek","year":"2017","journal-title":"Physica A"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/0016-7142(78)90005-4","article-title":"Minimum entropy deconvolution","volume":"16","author":"Wiggins","year":"1978","journal-title":"Geoexplorafion"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"906","DOI":"10.1016\/j.ymssp.2006.02.005","article-title":"Application of a minimum entropy deconvolution filter to enhance autoregressive model based gear tooth fault detection technique","volume":"21","author":"Endo","year":"2007","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1190\/1.1441919","article-title":"Minimum entropy deconvolution and simplicity: A noniterative algorithm","volume":"50","author":"Cabrelli","year":"1985","journal-title":"Geophysics"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"342","DOI":"10.1016\/j.cam.2016.02.001","article-title":"An algorithm twisted from generalized ADMM for multi-block separable convex minimization models","volume":"309","author":"Wang","year":"2017","journal-title":"J. Comput. Appl. Math."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/j.sigpro.2015.11.002","article-title":"Alternating strategies with internal ADMM for low-rank matrix reconstruction","volume":"121","author":"Li","year":"2016","journal-title":"Signal Process."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/j.automatica.2015.07.027","article-title":"Compositional performance certification of interconnected systems using ADMM","volume":"61","author":"Meissen","year":"2015","journal-title":"Automatica"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1066","DOI":"10.1016\/j.jsv.2005.03.007","article-title":"Wavelet filter-based weak signature detection method and its application on roller bearing prognostics","volume":"289","author":"Qiu","year":"2006","journal-title":"J. Sound Vib."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Li, Q., Liang, S.Y., Yang, J.G., and Li, B.Z. (2016). Long range dependence prognostics for bearing vibration intensity chaotic time series. Entropy, 18.","DOI":"10.3390\/e18010023"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/19\/7\/317\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:40:51Z","timestamp":1760208051000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/19\/7\/317"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,6,29]]},"references-count":37,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2017,7]]}},"alternative-id":["e19070317"],"URL":"https:\/\/doi.org\/10.3390\/e19070317","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2017,6,29]]}}}