{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T22:10:19Z","timestamp":1760220619596,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2011,6,3]],"date-time":"2011-06-03T00:00:00Z","timestamp":1307059200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The sparse decomposition based on matching pursuit is an adaptive sparse expression method for signals. This paper proposes an idea concerning a composite dictionary multi-atom matching decomposition and reconstruction algorithm, and the introduction of threshold de-noising in the reconstruction algorithm. Based on the structural characteristics of gear fault signals, a composite dictionary combining the impulse time-frequency dictionary and the Fourier dictionary was constituted, and a genetic algorithm was applied to search for the best matching atom. The analysis results of gear fault simulation signals indicated the effectiveness of the hard threshold, and the impulse or harmonic characteristic components could be separately extracted. Meanwhile, the robustness of the composite dictionary multi-atom matching algorithm at different noise levels was investigated. Aiming at the effects of data lengths on the calculation efficiency of the algorithm, an improved segmented decomposition and reconstruction algorithm was proposed, and the calculation efficiency of the decomposition algorithm was significantly enhanced. In addition it is shown that the multi-atom matching algorithm was superior to the single-atom matching algorithm in both calculation efficiency and algorithm robustness. Finally, the above algorithm was applied to gear fault engineering signals, and achieved good results.\r\n\t\t\t\t\t\t\t\t\t<\/jats:p>","DOI":"10.3390\/s110605981","type":"journal-article","created":{"date-parts":[[2011,6,3]],"date-time":"2011-06-03T14:58:56Z","timestamp":1307113136000},"page":"5981-6002","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":29,"title":["Application of Composite Dictionary Multi-Atom Matching in Gear Fault Diagnosis"],"prefix":"10.3390","volume":"11","author":[{"given":"Lingli","family":"Cui","sequence":"first","affiliation":[{"name":"Key Laboratory of Advanced Manufacturing Technology, Beijing University of Technology, Chao Yang District, Beijing, 100124, China"}]},{"given":"Chenhui","family":"Kang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Advanced Manufacturing Technology, Beijing University of Technology, Chao Yang District, Beijing, 100124, China"}]},{"given":"Huaqing","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mechanical & Electrical Engineering, Beijing University of Chemical Technology, Chao Yang District, Beijing, 100029, China"}]},{"given":"Peng","family":"Chen","sequence":"additional","affiliation":[{"name":"Graduate School of Bioresources, Mie University, 1577 Kurimamachiya-cho, Tsu, Mie, 514-8507, Japan"}]}],"member":"1968","published-online":{"date-parts":[[2011,6,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1006\/mssp.1999.1260","article-title":"Cyclostationary Processes: Application in Gear Faults Early Diagnosis","volume":"14","author":"Capdessus","year":"2000","journal-title":"Mech. Syst. Sign. Process"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"603","DOI":"10.1006\/mssp.1997.0097","article-title":"Gear Vibration Analysis by B-spline Wavelet-based Linear Wavelet Transform","volume":"1","author":"Lin","year":"1997","journal-title":"Mech. Syst. Sign. Process"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1006\/mssp.1999.1294","article-title":"Effectiveness and Sensitivity of Vibration Processing Techniques for Local Fault Detection in Gears","volume":"14","author":"Dalpiaz","year":"2000","journal-title":"Mech. Syst. Sign. Process"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1006\/mssp.1994.1022","article-title":"Application of the Wavelet Transform to Fault Detection in a Spur Gear","volume":"8","author":"Staszewski","year":"1994","journal-title":"Mech. Syst. Sign. Process"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"823","DOI":"10.1016\/j.measurement.2007.03.004","article-title":"Application of Time-frequency Entropy Method Based on Hilbert-Huang Transform to Gear Fault Diagnosis","volume":"40","author":"Yu","year":"2007","journal-title":"Measurement"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"821","DOI":"10.1016\/j.ymssp.2010.10.002","article-title":"Diagnosis of Gear Faults Based on EMD and Automatic Selection of Intrinsic Mode Functions","volume":"25","author":"Ricci","year":"2011","journal-title":"Mech. Syst. Sign. Process"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1006\/mssp.1995.0038","article-title":"Application of Orthogonal Wavelets to Early Gear Damage Detection","volume":"9","author":"Wang","year":"1995","journal-title":"Mech. Syst. Sign. Process"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3397","DOI":"10.1109\/78.258082","article-title":"Matching Pursuit with Time-Frequency Dictionaries","volume":"41","author":"Mallat","year":"1993","journal-title":"IEEE Trans. Sign. Process"},{"key":"ref_9","unstructured":"Lobo, AP, and Loizou, PC (2003, January 6\u201310). Voiced\/Unvoiced Speech Discrimination in Noise Using Gabor Atomic Decomposition. Hong Kong."},{"key":"ref_10","first-page":"594","article-title":"Low Bit-Rate Video Coding Based on Gabor Dictionary","volume":"27","author":"Liu","year":"2007","journal-title":"Trans. Beijing Instit. Tech"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2912","DOI":"10.1109\/78.650250","article-title":"Matching Pursuits with a Wave-Based Dictionary","volume":"45","author":"McClure","year":"1997","journal-title":"IEEE Trans. Sign. Process"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"994","DOI":"10.1109\/78.917803","article-title":"Fast Matching Pursuit with a Multiscale Dictionary","volume":"49","author":"Gribonval","year":"2001","journal-title":"IEEE Trans. Sign. Process"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1109\/LSP.2003.822904","article-title":"Transient Modeling by Matching Pursuits with a Wavelet Dictionary for Parametric Audio Coding","volume":"11","year":"2004","journal-title":"IEEE Sign. Process. Lett"},{"key":"ref_14","first-page":"26","article-title":"Signal Decomposition with Matching Pursuits and Technology of Extracting Machinery Fault Feature Based on Impulse Time-Frequency Atom","volume":"22","author":"Fei","year":"2003","journal-title":"J. Vib. Shock"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"59","DOI":"10.3901\/JME.2010.15.059","article-title":"Generalized Demodulation Method Based on Multi-scale Chirplet and Sparse Signal Decomposition and Its Application to Gear Fault Diagnosis","volume":"46","author":"Pi","year":"2010","journal-title":"J. Mech. Eng"},{"key":"ref_16","unstructured":"Chu, F, Peng, Z, Feng, Z, and Li, Z (2009). Modern Signal Process Method in Mechanical Fault Diagnosis, Beijing Science Press."},{"key":"ref_17","first-page":"696","article-title":"Extraction of Fault Features in Reciprocating Machinery Based on Matching Pursuits","volume":"35","author":"Meng","year":"2001","journal-title":"J. Xi\u2019an Jiaotong Univ"},{"key":"ref_18","first-page":"910","article-title":"Application of Matching Pursuit in Fault Diagnosis of Gear","volume":"43","author":"Zhao","year":"2009","journal-title":"J. Shanghai Jiaotong Univ"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1016\/j.jsv.2006.11.017","article-title":"Application of Atomic Decomposition to Gear Damage Detection","volume":"302","author":"Feng","year":"2007","journal-title":"J. Sound Vib"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"4311","DOI":"10.1109\/TSP.2006.881199","article-title":"K-SVD: An Algorithm for Designing over Complete Dictionaries for Sparse Representation","volume":"54","author":"Aharon","year":"2006","journal-title":"IEEE Trans. Sign. Process"},{"key":"ref_21","first-page":"390","article-title":"Fault Pattern Recognition of Rolling Bearings Based on Characteristic Waveform Sparse Matching","volume":"32","author":"Wang","year":"2010","journal-title":"J. Univ. Sci. Tech. Beijing"},{"key":"ref_22","first-page":"171","article-title":"Residual Ratio Iteration Termination Condition for MP Method","volume":"44","author":"Liang","year":"2010","journal-title":"J. Shanghai Jiaotong Univ"},{"key":"ref_23","unstructured":"Holland, JH (1975). Adaptation in Natural and Artificial System, University of Michigan Press."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"887","DOI":"10.1006\/mssp.2001.1416","article-title":"Early Detection of Gear Tooth Cracking Using the Resonance Demodulation Technique","volume":"15","author":"Wang","year":"2001","journal-title":"Mech. Syst. Sign. Process"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/11\/6\/5981\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:56:18Z","timestamp":1760219778000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/11\/6\/5981"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,6,3]]},"references-count":24,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2011,6]]}},"alternative-id":["s110605981"],"URL":"https:\/\/doi.org\/10.3390\/s110605981","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2011,6,3]]}}}