{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T13:18:50Z","timestamp":1761743930449,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2014,4,25]],"date-time":"2014-04-25T00:00:00Z","timestamp":1398384000000},"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>This paper investigates one eigenvalue decomposition-based source number estimation method, and three information-based source number estimation methods, namely the Akaike Information Criterion (AIC), Minimum Description Length (MDL) and Bayesian Information Criterion (BIC), and improves BIC as Improved BIC (IBIC) to make it more efficient and easier for calculation. The performances of the abovementioned source number estimation methods are studied comparatively with numerical case studies, which contain a linear superposition case and a both linear superposition and nonlinear modulation mixing case. A test bed with three sound sources is constructed to test the performances of these methods on mechanical systems, and source separation is carried out to validate the effectiveness of the experimental studies. This work can benefit model order selection, complexity analysis of a system, and applications of source separation to mechanical systems for condition monitoring and fault diagnosis purposes.<\/jats:p>","DOI":"10.3390\/s140507625","type":"journal-article","created":{"date-parts":[[2014,4,28]],"date-time":"2014-04-28T05:15:00Z","timestamp":1398662100000},"page":"7625-7646","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["A Comparative Study of Information-Based Source Number Estimation Methods and Experimental Validations on Mechanical Systems"],"prefix":"10.3390","volume":"14","author":[{"given":"Wei","family":"Cheng","sequence":"first","affiliation":[{"name":"State Key Laboratory for Manufacturing Systems Engineering, Xi'an Jiaotong University,  Xi'an 710049, China"}]},{"given":"Zhousuo","family":"Zhang","sequence":"additional","affiliation":[{"name":"State Key Laboratory for Manufacturing Systems Engineering, Xi'an Jiaotong University,  Xi'an 710049, China"}]},{"given":"Hongrui","family":"Cao","sequence":"additional","affiliation":[{"name":"State Key Laboratory for Manufacturing Systems Engineering, Xi'an Jiaotong University,  Xi'an 710049, China"}]},{"given":"Zhengjia","family":"He","sequence":"additional","affiliation":[{"name":"State Key Laboratory for Manufacturing Systems Engineering, Xi'an Jiaotong University,  Xi'an 710049, China"}]},{"given":"Guanwen","family":"Zhu","sequence":"additional","affiliation":[{"name":"State Key Laboratory for Manufacturing Systems Engineering, Xi'an Jiaotong University,  Xi'an 710049, China"}]}],"member":"1968","published-online":{"date-parts":[[2014,4,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"4369","DOI":"10.1109\/TSP.2009.2025806","article-title":"Decomposable Principal Component Analysis","volume":"57","author":"Wiesel","year":"2009","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Cheng, W., Zhang, Z.S., Lee, S., and He, Z.J. (2013). Investigations of denoising source separation technique and its application to source separation and identification of mechanical vibration signals. J. Vib. Control.","DOI":"10.1177\/1077546313483789"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"376","DOI":"10.1109\/TSP.2013.2287683","article-title":"Non-Negative Blind Source Separation Algorithm Based on Minimum Aperture Simplicial Cone","volume":"62","author":"Ouedraogo","year":"2014","journal-title":"IEEE Trans. Signal. Process"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1951","DOI":"10.1166\/asl.2011.1376","article-title":"Enhance the Separation Performance of ICA via Clustering Evaluation and Its Applications","volume":"4","author":"Cheng","year":"2011","journal-title":"Adv. Sci. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Cheng, W., Zhang, Z.S., Lee, S., and He, Z.J. (2012). Source Contribution Evaluation of Mechanical Vibration Signals via Enhanced Independent Component Analysis. J. Manuf. Sci. Eng.","DOI":"10.1115\/1.4005806"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1016\/S0893-6080(00)00026-5","article-title":"Independent Component Analysis: Algorithms and Applications","volume":"13","author":"Hyvarinen","year":"2000","journal-title":"Neural. Netw."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1641","DOI":"10.1162\/089976604774201622","article-title":"Adaptive Blind Separation with an Unknown Number of Sources","volume":"16","author":"Ye","year":"2004","journal-title":"Neural. Comput."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3543","DOI":"10.1109\/TSP.2005.853099","article-title":"Estimation of the Number of Sources in Unbalanced Arrays via Information Theoretic Criteria","volume":"53","author":"Fishler","year":"2005","journal-title":"IEEE Trans. Signal. Process."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1883","DOI":"10.1109\/TBME.2006.876620","article-title":"Estimation of number of independent brain electric sources from the scalp EEGs","volume":"53","author":"Bai","year":"2006","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1007\/s11804-007-6050-4","article-title":"A new source number estimation method based on the beam eigenvalue","volume":"6","author":"Jiang","year":"2007","journal-title":"J. Mar. Sci. Appl."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"4135","DOI":"10.1109\/TSP.2009.2024043","article-title":"MMSE-Based MDL Method for Robust Estimation of Number of Sources Without Eigendecomposition","volume":"57","author":"Huang","year":"2009","journal-title":"IEEE Trans. Signal. Process."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"798","DOI":"10.1109\/LSP.2009.2024785","article-title":"MMSE-Based MDL Method for Accurate Source Number Estimation","volume":"16","author":"Huang","year":"2009","journal-title":"IEEE Signal. Process. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Hu, J.S., and Yang, C.H. (2010). Estimation of Sound Source Number and Directions under a Multisource Reverberant Environment. EURASIP J. Adv. Signal. Process.","DOI":"10.1155\/2010\/870756"},{"key":"ref_14","first-page":"45","article-title":"Estimation Method for the Number of Sources Based on Modified K-means Clustering","volume":"33","author":"Ma","year":"2011","journal-title":"J. Detect. Control."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"5153","DOI":"10.1016\/j.jsv.2012.06.021","article-title":"Independent component analysis based source number estimation and its comparison for mechanical systems","volume":"331","author":"Cheng","year":"2012","journal-title":"J. Sound. Vib."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"6118","DOI":"10.1109\/TSP.2013.2283462","article-title":"Improved Source Number Detection and Direction Estimation with Nested Arrays and ULAs Using Jackknifing","volume":"61","author":"Han","year":"2013","journal-title":"IEEE Trans. Signal. Process."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3574","DOI":"10.1121\/1.4806560","article-title":"Bayesian localization of an unknown number of ocean acoustic sources","volume":"133","author":"Dosso","year":"2013","journal-title":"J. the Acoust. Soc. Am."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"396","DOI":"10.1016\/j.ymssp.2013.06.031","article-title":"Decentralized modal identification of structures using parallel factor decomposition and sparse blind source separation","volume":"41","author":"Sadhu","year":"2013","journal-title":"Mech. Syst. Signal. Process."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"716","DOI":"10.1109\/TAC.1974.1100705","article-title":"A new look at the statistical model identification","volume":"19","author":"Akaike","year":"1974","journal-title":"IEEE Trans. Autom. Control."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3282","DOI":"10.1109\/78.330399","article-title":"Counting the degrees of freedom when using AIC and MDL to detect signals","volume":"42","author":"Williams","year":"1994","journal-title":"IEEE Trans. Signal. Process."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1016\/0005-1098(78)90005-5","article-title":"Modeling by shortest data description","volume":"14","author":"Rissanen","year":"1978","journal-title":"Automatica"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"4806","DOI":"10.1109\/TSP.2013.2273198","article-title":"Source Enumeration via MDL Criterion Based on Linear Shrinkage Estimation of Noise Subspace Covariance Matrix","volume":"61","author":"Huang","year":"2013","journal-title":"IEEE Trans. Signal. Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1959","DOI":"10.1109\/TSP.2011.2108293","article-title":"Inconsistency of the MDL: On the Performance of Model Order Selection Criteria With Increasing Signal-to-Noise Ratio","volume":"59","author":"Quan","year":"2011","journal-title":"IEEE Trans. Signal. Process."},{"key":"ref_24","first-page":"598","article-title":"Automatic choice of dimensionality for PCA","volume":"13","author":"Minka","year":"2001","journal-title":"Adv. Neural. Inf. Process. Syst."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"4956","DOI":"10.1109\/TSP.2012.2203128","article-title":"On the proper forms of BIC for model order selection","volume":"60","author":"Stoica","year":"2012","journal-title":"IEEE Trans. Signal. Process."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2746","DOI":"10.1109\/TSP.2010.2042481","article-title":"Nonparametric detection of signals by information theoretic criteria: Performance analysis and an improved estimator","volume":"58","author":"Nadler","year":"2010","journal-title":"IEEE Trans. Signal. Process."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"5916","DOI":"10.1109\/TSP.2008.929331","article-title":"Source enumeration for high-resolution array processing using improved gerschgorin radii without eigendecomposition","volume":"56","author":"Huang","year":"2008","journal-title":"IEEE Trans. Signal. Process."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"5658","DOI":"10.1109\/TSP.2007.899344","article-title":"Reduced-rank MDL method for source enumeration in high-resolution array processing","volume":"55","author":"Huang","year":"2007","journal-title":"IEEE Trans. Signal. Process."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Cichocki, A., and Amari, S.I. (2002). Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications, John Wiley & Sons.","DOI":"10.1002\/0470845899"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/S0022-460X(86)80159-6","article-title":"Free vibration of a thin cylindrical shell with discrete axial stiffeners","volume":"111","author":"Mead","year":"1986","journal-title":"J. Sound. Vib."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"626","DOI":"10.1109\/72.761722","article-title":"Fast and robust fixed-point algorithms for independent component analysis","volume":"10","author":"Hyvarinen","year":"1999","journal-title":"IEEE Trans. Neural. Netw."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/14\/5\/7625\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:10:45Z","timestamp":1760217045000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/14\/5\/7625"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,4,25]]},"references-count":31,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2014,5]]}},"alternative-id":["s140507625"],"URL":"https:\/\/doi.org\/10.3390\/s140507625","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2014,4,25]]}}}