{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,16]],"date-time":"2026-02-16T08:22:13Z","timestamp":1771230133713,"version":"3.50.1"},"reference-count":53,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2014,5,23]],"date-time":"2014-05-23T00:00:00Z","timestamp":1400803200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Honeycomb sandwich structures are used in a wide variety of applications. Nevertheless, due to manufacturing defects or impact loads, these structures can be subject to imperfect bonding or debonding between the skin and the honeycomb core. The presence of debonding reduces the bending stiffness of the composite panel, which causes detectable changes in its vibration characteristics. This article presents a new supervised learning algorithm to identify debonded regions in aluminum honeycomb panels. The algorithm uses a linear approximation method handled by a statistical inference model based on the maximum-entropy principle. The merits of this new approach are twofold: training is avoided and data is processed in a period of time that is comparable to the one of neural networks. The honeycomb panels are modeled with finite elements using a simplified three-layer shell model. The adhesive layer between the skin and core is modeled using linear springs, the rigidities of which are reduced in debonded sectors. The algorithm is validated using experimental data of an aluminum honeycomb panel under different damage scenarios.<\/jats:p>","DOI":"10.3390\/e16052869","type":"journal-article","created":{"date-parts":[[2014,5,23]],"date-time":"2014-05-23T12:46:27Z","timestamp":1400849187000},"page":"2869-2889","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["A Maximum Entropy Approach to Assess Debonding in Honeycomb aluminum Plates"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6692-2687","authenticated-orcid":false,"given":"Viviana","family":"Meruane","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, Universidad de Chile, Beauchef 850, Santiago, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Valentina","family":"Fierro","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Universidad de Chile, Beauchef 850, Santiago, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alejandro","family":"Ortiz-Bernardin","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Universidad de Chile, Beauchef 850, Santiago, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2014,5,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Vinson, J.R. (2005). Sandwich Structures 7: Advancing with Sandwich Structures and Materials, Springer.","DOI":"10.1177\/1099636205049810"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1177\/1475921704047500","article-title":"Vibration Based Condition Monitoring: A Review","volume":"3","author":"Carden","year":"2004","journal-title":"Struct. Health Monit"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1006\/jsvi.1999.2624","article-title":"Vibration-based model-dependent damage (delamination) identification and health monitoring for composite structures-a review","volume":"230","author":"Zou","year":"2000","journal-title":"J. Sound Vib"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1177\/0583102406065898","article-title":"Review of Vibration-based Structural Health Monitoring with Special Emphasis on Composite Materials","volume":"38","author":"Montalvao","year":"2006","journal-title":"Shock Vib. Digest"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"773","DOI":"10.1016\/0045-7949(94)00428-6","article-title":"Vibratory behaviour of delaminated honeycomb structures: A 3-D finite element modelling","volume":"55","author":"Jiang","year":"1995","journal-title":"Comput. Struct"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/S0263-8223(01)00136-2","article-title":"Effect of debonding on natural frequencies and frequency response functions of honeycomb sandwich beams","volume":"55","author":"Kim","year":"2002","journal-title":"Compos. Struct"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1263","DOI":"10.1016\/j.commatsci.2010.08.005","article-title":"Dynamic behaviour of sandwich plates containing single\/multiple debonding","volume":"50","author":"Burlayenko","year":"2011","journal-title":"Comput. Mater. Sci"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"959","DOI":"10.1016\/j.ijnonlinmec.2009.07.002","article-title":"Influence of skin\/core debonding on free vibration behavior of foam and honeycomb cored sandwich plates","volume":"45","author":"Burlayenko","year":"2010","journal-title":"Int. J. Non-Lin. Mech"},{"key":"ref_9","first-page":"174","article-title":"Performance Assessment of Sandwich Structures with Debonds and Dents","volume":"4","author":"Mohanan","year":"2013","journal-title":"Int. J. Sci. Eng. Res"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"566","DOI":"10.1016\/j.jsv.2009.09.029","article-title":"Damage monitoring in sandwich beams by modal parameter shifts: A comparative study of burst random and sine dwell vibration testing","volume":"329","author":"Shahdin","year":"2010","journal-title":"J. Sound Vib"},{"key":"ref_11","first-page":"623","article-title":"Damage prognosis: the future of structural health monitoring","volume":"365","author":"Farrar","year":"2007","journal-title":"Philos. Trans. A Math. Phys. Eng. Sci"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1177\/1475921710365400","article-title":"Damage detection with parallel genetic algorithms and operational modes","volume":"9","author":"Meruane","year":"2010","journal-title":"Struct. Health Monit"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1559","DOI":"10.1016\/j.ymssp.2010.11.020","article-title":"An hybrid real genetic algorithm to detect structural damage using modal properties","volume":"25","author":"Meruane","year":"2011","journal-title":"Mech. Syst. Signal Process"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1491","DOI":"10.1061\/(ASCE)0733-9445(2006)132:9(1491)","article-title":"Structural damage detection via modal data with genetic algorithms","volume":"132","author":"Perera","year":"2006","journal-title":"J. Struct. Eng"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1085","DOI":"10.1002\/nme.1803","article-title":"Co-evolutionary algorithm for structural damage identification using minimal physical testing","volume":"69","author":"Kouchmeshky","year":"2007","journal-title":"Int. J. Numer. Meth. Eng"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2337","DOI":"10.1016\/S0045-7949(03)00313-4","article-title":"Global optimization by coupled local minimizers and its application to FE model updating","volume":"81","author":"Teughels","year":"2003","journal-title":"Comput. Struct"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2481","DOI":"10.1016\/j.sigpro.2003.07.018","article-title":"Novelty detection: a review\u2013part 1: statistical approaches","volume":"83","author":"Markou","year":"2003","journal-title":"Signal Process"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"318","DOI":"10.1088\/0964-1726\/3\/3\/008","article-title":"Damage detection in composite structures using piezoelectric materials (and neural net)","volume":"3","author":"Islam","year":"1994","journal-title":"Smart Mater. Struct"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1088\/0964-1726\/5\/3\/012","article-title":"Delamination prediction in composite beams with built-in piezoelectric devices using modal analysis and neural network","volume":"5","author":"Okafor","year":"1996","journal-title":"Smart Mater. Struct"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1773","DOI":"10.1016\/S0266-3538(00)00063-4","article-title":"A thick composite-beam model for delamination prediction by the use of neural networks","volume":"60","author":"Valoor","year":"2000","journal-title":"Compos. Sci. Tech"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/S1359-8368(01)00019-1","article-title":"Locating and sizing of delamination in composite laminates using computational and experimental methods","volume":"32","author":"Ishak","year":"2001","journal-title":"Compos. B Eng"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.matdes.2004.04.008","article-title":"Artificial neural network based delamination prediction in laminated composites","volume":"26","author":"Chakraborty","year":"2005","journal-title":"Mater. Des"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1541","DOI":"10.1088\/0964-1726\/14\/6\/047","article-title":"Efficiency of genetic algorithms and artificial neural networks for evaluating delamination in composite structures using fibre Bragg grating sensors","volume":"14","author":"Su","year":"2005","journal-title":"Smart Mater. Struct"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1016\/j.compstruct.2013.03.012","article-title":"Vibration-Based Inverse Algorithms for Detection of Delamination in Composites","volume":"102","author":"Zhang","year":"2013","journal-title":"Compos. Struct"},{"key":"ref_25","first-page":"653279:1","article-title":"Real-time structural damage assessment using artificial neural networks and anti-resonant frequencies","volume":"2014","author":"Meruane","year":"2014","journal-title":"Shock Vib"},{"key":"ref_26","unstructured":"Gupta, M.R. (2003). An information theory approach to supervised learning. [PhD thesis, Stanford University]."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"766","DOI":"10.1109\/TPAMI.2006.101","article-title":"Nonparametric supervised learning by linear interpolation with maximum entropy","volume":"28","author":"Gupta","year":"2006","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"620","DOI":"10.1103\/PhysRev.106.620","article-title":"Information theory and statistical mechanics","volume":"106","author":"Jaynes","year":"1957","journal-title":"Phys. Rev"},{"key":"ref_29","unstructured":"Erkan, A.N. (2010). Semi-supervised learning via generalized maximum entropy. [PhD thesis, New York University]."},{"key":"ref_30","unstructured":"Lawson, C.L., and Hanson, R.J. (1974). Solving least squares problems, SIAM."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2167","DOI":"10.1002\/nme.1534","article-title":"Local maximum-entropy approximation schemes: A seamless bridge between finite elements and meshfree methods","volume":"65","author":"Arroyo","year":"2006","journal-title":"Int. J. Numer. Meth. Eng"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1859","DOI":"10.1016\/j.cma.2010.02.013","article-title":"Maximum-entropy meshfree method for compressible and near-incompressible elasticity","volume":"199","author":"Ortiz","year":"2010","journal-title":"Comput. Meth. Appl. Mech. Eng"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"979","DOI":"10.1002\/nme.2606","article-title":"Meshfree co-rotational formulation for two-dimensional continua","volume":"79","author":"Yaw","year":"2009","journal-title":"Int. J. Numer. Meth. Eng"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1605","DOI":"10.1002\/nme.2597","article-title":"Smooth, second order, non-negative meshfree approximants selected by maximum entropy","volume":"79","author":"Cyron","year":"2009","journal-title":"Int. J. Numer. Meth. Eng"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"868","DOI":"10.1002\/nme.2793","article-title":"On the optimum support size in meshfree methods: A variational adaptivity approach with maximum entropy approximants","volume":"82","author":"Rosolen","year":"2010","journal-title":"Int. J. Numer. Meth. Eng"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"741","DOI":"10.1002\/nme.2855","article-title":"A higher order method based on local maximum entropy approximation","volume":"83","author":"Cueto","year":"2010","journal-title":"Int. J. Numer. Meth. Eng"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1541","DOI":"10.1002\/nme.2869","article-title":"Optimal transportation meshfree approximation schemes for fluid and plastic flows","volume":"83","author":"Li","year":"2010","journal-title":"Int. J. Numer. Meth. Eng"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1007\/s00466-009-0405-4","article-title":"Stable meshfree methods in fluid mechanics based on Green\u2019s functions","volume":"46","author":"Cyron","year":"2010","journal-title":"Comput. Mech"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1180","DOI":"10.1002\/fld.2271","article-title":"Information flux maximum-entropy approximation schemes for convection and diffusion problems","volume":"64","author":"Cyron","year":"2010","journal-title":"Int. J. Numer. Meth. Fluid"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"328","DOI":"10.1214\/aos\/1034276632","article-title":"Bayesian methods and maximum entropy for ill-posed inverse problems","volume":"25","author":"Gamboa","year":"1997","journal-title":"Ann. Stat"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1016\/j.jmaa.2008.02.043","article-title":"Maximum entropy solution to ill-posed inverse problems with approximately known operator","volume":"344","author":"Loubes","year":"2008","journal-title":"J. Math. Anal. Appl"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A mathematical theory of communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. Tech. J"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1002\/nme.1885","article-title":"Overview and construction of meshfree basis functions: From moving least squares to entropy approximants","volume":"70","author":"Sukumar","year":"2007","journal-title":"Int. J. Numer. Meth. Eng"},{"key":"ref_44","unstructured":"Kullback, S. (1959). Information Theory and Statistics, Wiley."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1109\/TIT.1980.1056144","article-title":"Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy","volume":"26","author":"Shore","year":"1980","journal-title":"IEEE Trans. Inform. Theor"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/0045-7825(94)00750-H","article-title":"Assessment of computational models for sandwich panels and shells","volume":"124","author":"Burton","year":"1995","journal-title":"Comput. Meth. Appl. Mech. Eng"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1177\/1099636202004001180","article-title":"On the choice of shear correction factor in sandwich structures","volume":"4","author":"Birman","year":"2002","journal-title":"J. Sandw. Struct. and Mater"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1016\/S0045-7825(96)01196-6","article-title":"Assessment of continuum models for sandwich panel honeycomb cores","volume":"145","author":"Burton","year":"1997","journal-title":"Comput. Meth. Appl. Mech. Eng"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1163\/156855401753424433","article-title":"A numerical modeling for eigenvibration analysis of honeycomb sandwich panels","volume":"8","author":"Tanimoto","year":"2001","journal-title":"Compos. Interfac"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"658","DOI":"10.1016\/j.commatsci.2008.08.018","article-title":"Analysis of structural performance of sandwich plates with foam-filled aluminum hexagonal honeycomb core","volume":"45","author":"Burlayenko","year":"2009","journal-title":"Comput. Mater. Sci"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1115\/1.2375141","article-title":"Vibration of delaminated composite laminates: A review","volume":"60","author":"Della","year":"2007","journal-title":"Appl. Mech. Rev"},{"key":"ref_52","first-page":"113","article-title":"Clapping in delaminated sandwich-beams due to forced oscillations","volume":"39","year":"2007","journal-title":"Comput. Mech"},{"key":"ref_53","unstructured":"(2014). Structural dynamics toolbox & FEMLink. Users Guide Version, SDTools."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/16\/5\/2869\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:11:45Z","timestamp":1760217105000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/16\/5\/2869"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,5,23]]},"references-count":53,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2014,5]]}},"alternative-id":["e16052869"],"URL":"https:\/\/doi.org\/10.3390\/e16052869","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,5,23]]}}}