{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,17]],"date-time":"2026-07-17T14:59:16Z","timestamp":1784300356336,"version":"3.55.0"},"reference-count":84,"publisher":"Elsevier BV","issue":"12","license":[{"start":{"date-parts":[[1995,12,1]],"date-time":"1995-12-01T00:00:00Z","timestamp":817776000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Automatica"],"published-print":{"date-parts":[[1995,12]]},"DOI":"10.1016\/0005-1098(95)00120-8","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T01:31:06Z","timestamp":1027647066000},"page":"1691-1724","source":"Crossref","is-referenced-by-count":1549,"title":["Nonlinear black-box modeling in system identification: a unified overview"],"prefix":"10.1016","volume":"31","author":[{"given":"Jonas","family":"Sj\u00f6berg","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qinghua","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lennart","family":"Ljung","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Albert","family":"Benveniste","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bernard","family":"Delyon","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pierre-Yves","family":"Glorennec","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"H\u00e5kan","family":"Hjalmarsson","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Anatoli","family":"Juditsky","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/0005-1098(95)00120-8_BIB1","doi-asserted-by":"crossref","first-page":"930","DOI":"10.1109\/18.256500","article-title":"Universal approximation bounds for superpositions of a sigmoidal function","volume":"IT-39","author":"Barron","year":"1993","journal-title":"IEEE Trans. Inf. Theory"},{"key":"10.1016\/0005-1098(95)00120-8_BIB2","series-title":"Neural Information Processing Systems","first-page":"52","article-title":"Supervised learning of probability distributions by neural networks","author":"Baum","year":"1988"},{"key":"10.1016\/0005-1098(95)00120-8_BIB3","doi-asserted-by":"crossref","first-page":"999","DOI":"10.1109\/18.256506","article-title":"Hinging hyperplanes for regression, classification and function approximation","volume":"IT-39","author":"Breiman","year":"1993","journal-title":"IEEE Trans. Inf. Theory"},{"key":"10.1016\/0005-1098(95)00120-8_BIB4","author":"Brown","year":"1994"},{"key":"10.1016\/0005-1098(95)00120-8_BIB5","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1080\/00207179208934317","article-title":"Neural networks for nonlinear dynamic system modelling and identification","volume":"56","author":"Chen","year":"1992","journal-title":"Int. J. Control"},{"key":"10.1016\/0005-1098(95)00120-8_BIB6","doi-asserted-by":"crossref","first-page":"1191","DOI":"10.1080\/00207179008934126","article-title":"Non-linear system identification using neural networks","volume":"51","author":"Chen","year":"1990","journal-title":"Int. J. Control"},{"key":"10.1016\/0005-1098(95)00120-8_BIB7","doi-asserted-by":"crossref","first-page":"1873","DOI":"10.1080\/00207178908953472","article-title":"Orthogonal least squares methods and their application to non-linear system identification","volume":"50","author":"Chen","year":"1989","journal-title":"Int. J. Control"},{"key":"10.1016\/0005-1098(95)00120-8_BIB8","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1109\/72.80341","article-title":"Orthogonal least squares learning algorithm for radial basis function networks","volume":"NN-2","author":"Chen","year":"1991","journal-title":"IEEE Trans. Neural Networks"},{"key":"10.1016\/0005-1098(95)00120-8_BIB9","author":"Chui","year":"1992"},{"key":"10.1016\/0005-1098(95)00120-8_BIB10","author":"Cover","year":"1991"},{"key":"10.1016\/0005-1098(95)00120-8_BIB11","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1007\/BF02551274","article-title":"Approximation by superposition of a sigmoidal function","volume":"2","author":"Cybenko","year":"1989","journal-title":"Math. Control, Signals and Syst."},{"key":"10.1016\/0005-1098(95)00120-8_BIB12","doi-asserted-by":"crossref","first-page":"961","DOI":"10.1109\/18.57199","article-title":"The wavelet transform, timefrequency","volume":"IT-36","author":"Daubechies","year":"1990","journal-title":"IEEE Trans. Inf. Theory"},{"key":"10.1016\/0005-1098(95)00120-8_BIB13","article-title":"CBMSNSF Regional Series in Applied Mathematics","author":"Daubechies","year":"1992"},{"key":"10.1016\/0005-1098(95)00120-8_BIB14","author":"De Boor","year":"1978"},{"key":"10.1016\/0005-1098(95)00120-8_BIB15","doi-asserted-by":"crossref","first-page":"332","DOI":"10.1109\/72.363469","article-title":"Accuracy analysis for wavelet networks","volume":"NN-6","author":"Delyon","year":"1995","journal-title":"IEEE Trans. Neural Networks"},{"key":"10.1016\/0005-1098(95)00120-8_BIB16","author":"Dennis","year":"1983"},{"key":"10.1016\/0005-1098(95)00120-8_BIB17","author":"Devroye","year":"1985"},{"key":"10.1016\/0005-1098(95)00120-8_BIB18","author":"Draper","year":"1981"},{"key":"10.1016\/0005-1098(95)00120-8_BIB19","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/0165-0114(91)90050-Z","article-title":"Fuzzy sets in approximate reasoning, part 1","volume":"40","author":"Dubois","year":"1992","journal-title":"Fuzzy Sets and Systems"},{"key":"10.1016\/0005-1098(95)00120-8_BIB20","doi-asserted-by":"crossref","first-page":"817","DOI":"10.1080\/01621459.1981.10477729","article-title":"Projection pursuit regression","volume":"76","author":"Friedman","year":"1981","journal-title":"J. Am. Statist. Assoc."},{"key":"10.1016\/0005-1098(95)00120-8_BIB21","doi-asserted-by":"crossref","first-page":"817","DOI":"10.1080\/01621459.1981.10477729","article-title":"Projection pursuit regression","volume":"76","author":"Friedman","year":"1981","journal-title":"J. Am. Statist. Assoc."},{"key":"10.1016\/0005-1098(95)00120-8_BIB22","first-page":"1039","article-title":"A general class of fuzzy inference systems","volume":"Vol. III","author":"Glorennec","year":"1993"},{"key":"10.1016\/0005-1098(95)00120-8_BIB23","article-title":"Modelling of a flexible mechanical system containing hydralic actuators","author":"Gunnarsson","year":"1990"},{"key":"10.1016\/0005-1098(95)00120-8_BIB24","author":"Haykin","year":"1994"},{"key":"10.1016\/0005-1098(95)00120-8_BIB25","first-page":"97","article-title":"Partial least squares regression and statistical models","volume":"17","author":"Helland","year":"1990","journal-title":"Scand. J. Statist."},{"key":"10.1016\/0005-1098(95)00120-8_BIB26","first-page":"3.207","article-title":"Identification with generalized orthonormal basis functions \u2014statistical analysis and error bounds","volume":"Vol. 3","author":"van den Hof","year":"1994"},{"key":"10.1016\/0005-1098(95)00120-8_BIB27","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1214\/aos\/1176349519","article-title":"Projection pursuit (with discussion)","volume":"13","author":"Huber","year":"1985","journal-title":"Ann. Statist."},{"key":"10.1016\/0005-1098(95)00120-8_BIB28","article-title":"Wavelets in identification","author":"Juditsky","year":"1994"},{"key":"10.1016\/0005-1098(95)00120-8_BIB29","doi-asserted-by":"crossref","first-page":"1725","DOI":"10.1016\/0005-1098(95)00119-1","article-title":"Nonlinear black-box models in system identification: mathematical foundations","volume":"31","author":"Hjalmarsson","year":"1995","journal-title":"Automatica"},{"key":"10.1016\/0005-1098(95)00120-8_BIB30","article-title":"Multi-dimensional wavelet frames","author":"Kugarajah","year":"1995"},{"key":"10.1016\/0005-1098(95)00120-8_BIB31","author":"Kung","year":"1993"},{"key":"10.1016\/0005-1098(95)00120-8_BIB32","article-title":"Fuzzy logic in control systems, parts i and ii","volume":"SMC-20","author":"Lee","year":"1990","journal-title":"IEEE Trans. Syst., Man, Cyber"},{"key":"10.1016\/0005-1098(95)00120-8_BIB33","author":"Ljung","year":"1987"},{"key":"10.1016\/0005-1098(95)00120-8_BIB34","author":"Ljung","year":"1994"},{"key":"10.1016\/0005-1098(95)00120-8_BIB35","author":"Ljung","year":"1983"},{"key":"10.1016\/0005-1098(95)00120-8_BIB36","unstructured":"McAvoy, T. (1992). Personal communication."},{"key":"10.1016\/0005-1098(95)00120-8_BIB37","article-title":"Bayesian methods for adaptive models","author":"MacKay","year":"1991"},{"key":"10.1016\/0005-1098(95)00120-8_BIB38","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1162\/neco.1992.4.3.415","article-title":"Baysian interpolation","volume":"4","author":"MacKay","year":"1992","journal-title":"Neural Comput."},{"key":"10.1016\/0005-1098(95)00120-8_BIB39","first-page":"69","article-title":"Multiresolution approximation and wavelets orthonormal bases of l2(r)","volume":"315","author":"Mallat","year":"1989","journal-title":"Trans. Am. Math. Soc."},{"key":"10.1016\/0005-1098(95)00120-8_BIB40","article-title":"Matching pursuit with time-frequency dictionaries","volume":"619","author":"Mallat","year":"1993"},{"key":"10.1016\/0005-1098(95)00120-8_BIB41","article-title":"Surveillance de turbine \u00e0 gaz","author":"Mathis","year":"1994"},{"key":"10.1016\/0005-1098(95)00120-8_BIB42","article-title":"On the uniform approximation of nonlinear discrete-time fading-memory systems using neural network models","author":"Matthews","year":"1992"},{"key":"10.1016\/0005-1098(95)00120-8_BIB43","author":"Meyer","year":"1990"},{"key":"10.1016\/0005-1098(95)00120-8_BIB44","article-title":"The effective number of parameters: an analysis of generalization and regularization in nonlinear learning systems","volume":"4","author":"Moody","year":"1992"},{"key":"10.1016\/0005-1098(95)00120-8_BIB45","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1137\/1109020","article-title":"On estimating regression","volume":"9","author":"Nadaraya","year":"1964","journal-title":"Theory of Prob. and Applic."},{"key":"10.1016\/0005-1098(95)00120-8_BIB46","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1109\/72.80202","article-title":"Identification and control of dynamical systems using neural networks","volume":"NN-1","author":"Narendra","year":"1990","journal-title":"IEEE Trans. Neural Networks"},{"key":"10.1016\/0005-1098(95)00120-8_BIB47","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1162\/neco.1993.5.2.165","article-title":"Neural networks and nonlinear adaptive filtering: unifying concepts and new algorithms","volume":"5","author":"Nerrand","year":"1993","journal-title":"Neural Comput."},{"key":"10.1016\/0005-1098(95)00120-8_BIB48","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1109\/72.279183","article-title":"Training recurrent neural networks: why and how? An illustration in dynamical process modeling","volume":"NN-5","author":"Nerrand","year":"1994","journal-title":"IEEE Trans. Neural Networks"},{"key":"10.1016\/0005-1098(95)00120-8_BIB49","first-page":"1481","article-title":"Networks for approximation and learning","volume":"78","author":"Poggio","year":"1990"},{"key":"10.1016\/0005-1098(95)00120-8_BIB50","doi-asserted-by":"crossref","first-page":"978","DOI":"10.1126\/science.247.4945.978","article-title":"Regularization algorithms for learning that are equivalent to multilayer networks","volume":"247","author":"Poggio","year":"1990","journal-title":"Science"},{"key":"10.1016\/0005-1098(95)00120-8_BIB51","article-title":"On the hinge finding algorithm for hinging hyperplanes","author":"Pucar","year":"1995"},{"key":"10.1016\/0005-1098(95)00120-8_BIB52","article-title":"On the parameterization of hinging hyperplane models","author":"Pucar","year":"1995"},{"key":"10.1016\/0005-1098(95)00120-8_BIB53","doi-asserted-by":"crossref","DOI":"10.1016\/0165-1684(94)90174-0","article-title":"Signal representation using adaptive normalized Gaussian functions","volume":"36","author":"Qian","year":"1994","journal-title":"Signal Process"},{"key":"10.1016\/0005-1098(95)00120-8_BIB54","first-page":"740","article-title":"Pruning algorithms\u2014a survey","volume":"NN-4","author":"Reed","year":"1993"},{"key":"10.1016\/0005-1098(95)00120-8_BIB55","article-title":"Mod\u00e9lisation et commande de processus par r\u00e9seaux de neurones; application au pilotage d'un v\u00e9hicule autonome","author":"Rivals","year":"1995"},{"key":"10.1016\/0005-1098(95)00120-8_BIB56","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1038\/323533a0","article-title":"Learning representations by back-propagating errors","volume":"323","author":"Rumelhart","year":"1986","journal-title":"Nature"},{"key":"10.1016\/0005-1098(95)00120-8_BIB57","series-title":"Wavelets and Their Applications","author":"Ruskai","year":"1992"},{"key":"10.1016\/0005-1098(95)00120-8_BIB58","doi-asserted-by":"crossref","first-page":"693","DOI":"10.1137\/0914044","article-title":"Ill-conditioning in neural network training problems","volume":"14","author":"Saarinen","year":"1993","journal-title":"SIAM J. Sci. Comput."},{"key":"10.1016\/0005-1098(95)00120-8_BIB59","author":"Schumaker","year":"1981"},{"key":"10.1016\/0005-1098(95)00120-8_BIB60","author":"Silverman","year":"1986"},{"key":"10.1016\/0005-1098(95)00120-8_BIB61","series-title":"Preprints 4th IFAC Symp. on Adaptive Systems in Control and Signal Processing","first-page":"669","article-title":"Overtraining, regularization and searching for minimum in neural networks","author":"Sj\u00f6berg","year":"1992"},{"key":"10.1016\/0005-1098(95)00120-8_BIB62","first-page":"49","article-title":"Neural networks in system identification","volume":"Vol. 2","author":"Sj\u00f6berg","year":"1994"},{"key":"10.1016\/0005-1098(95)00120-8_BIB63","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0893-6080(94)90052-3","article-title":"Minimisation methods for training feedforward neural networks","volume":"7","author":"van der Smagt","year":"1994","journal-title":"Neural Networks"},{"key":"10.1016\/0005-1098(95)00120-8_BIB64","doi-asserted-by":"crossref","first-page":"346","DOI":"10.1109\/TAC.1981.1102596","article-title":"Nonlinear regulation: the piecewise linear approach","volume":"AC-26","author":"Sontag","year":"1981","journal-title":"IEEE Trans. Autom. Control"},{"key":"10.1016\/0005-1098(95)00120-8_BIB65","series-title":"Essays on Control: Perspectives in the Theory and its Applications","first-page":"339","article-title":"Neural networks for control","author":"Sontag","year":"1993"},{"key":"10.1016\/0005-1098(95)00120-8_BIB66","doi-asserted-by":"crossref","first-page":"1040","DOI":"10.1214\/aos\/1176345969","article-title":"Optimal global rates of convergence for nonparametric regression","volume":"10","author":"Stone","year":"1982","journal-title":"Ann. Statist."},{"key":"10.1016\/0005-1098(95)00120-8_BIB67","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1109\/TFUZZ.1993.390281","article-title":"fuzzy logic based approach to qualitative modelling","volume":"FS-1","author":"Sugeno","year":"1993","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"10.1016\/0005-1098(95)00120-8_BIB68","doi-asserted-by":"crossref","first-page":"819","DOI":"10.1016\/0893-6080(94)90103-1","article-title":"Static and dynamic stabilizing neural controllers, applicable to transition between equilibrium points","volume":"7","author":"Suykens","year":"1994","journal-title":"Neural Networks"},{"key":"10.1016\/0005-1098(95)00120-8_BIB69","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1109\/TSMC.1985.6313399","article-title":"Fuzzy identification of systems and its application to modelling and control","volume":"SMC-15","author":"Takagi","year":"1985","journal-title":"IEEE Trans. Syst. Man Cyber"},{"key":"10.1016\/0005-1098(95)00120-8_BIB70","series-title":"Wavbox. Public domain MATLAB toolbox","author":"Taswell","year":"1993"},{"key":"10.1016\/0005-1098(95)00120-8_BIB71","series-title":"Inverse and Ill-posed Problems","article-title":"Three topics in ill-posed problems","author":"Wahba","year":"1987"},{"key":"10.1016\/0005-1098(95)00120-8_BIB72","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1109\/9.76361","article-title":"System identification using Laguerre models","volume":"AC-36","author":"Wahlberg","year":"1991","journal-title":"IEEE Trans. Autom. Control"},{"key":"10.1016\/0005-1098(95)00120-8_BIB73","doi-asserted-by":"crossref","first-page":"1276","DOI":"10.1109\/9.293196","article-title":"System identification using kautz models","volume":"AC-39","author":"Wahlberg","year":"1994","journal-title":"IEEE Trans. Autom. Control"},{"key":"10.1016\/0005-1098(95)00120-8_BIB74","series-title":"Proc. 1st IEEE Conf.","first-page":"1163","article-title":"Fuzzy systems are universal approximators","author":"Wang","year":"1992"},{"key":"10.1016\/0005-1098(95)00120-8_BIB75","author":"Wang","year":"1994"},{"key":"10.1016\/0005-1098(95)00120-8_BIB76","first-page":"359","article-title":"Smooth regression analysis","volume":"26","author":"Watson","year":"1969","journal-title":"Sankhya, Ser. A"},{"key":"10.1016\/0005-1098(95)00120-8_BIB77","article-title":"Beyond regression: new tools for prediction and analysis in the behavioral sciences","author":"Werbos","year":"1974"},{"key":"10.1016\/0005-1098(95)00120-8_BIB78","first-page":"743","article-title":"The collinearity problem in linear regression: the partial least squares approach to generalized inverses","volume":"5","author":"Wold","year":"1984","journal-title":"S1AM J. Sci. Statist. Comput."},{"key":"10.1016\/0005-1098(95)00120-8_BIB79","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1145\/175247.175255","article-title":"Fuzzy logic, neural networks and soft computing","volume":"37","author":"Zadeh","year":"1994","journal-title":"Commun. ACM"},{"key":"10.1016\/0005-1098(95)00120-8_BIB80","article-title":"Contribution \u00e0 la surveillance de proc\u00e9d\u00e9s industriels","author":"Zhang","year":"1991"},{"key":"10.1016\/0005-1098(95)00120-8_BIB81","series-title":"Wavenet. Public domain MATLAB toolbox","author":"Zhang","year":"1993"},{"key":"10.1016\/0005-1098(95)00120-8_BIB82","article-title":"Using wavelet network in nonparametric estimation","volume":"833","author":"Zhang","year":"1994"},{"key":"10.1016\/0005-1098(95)00120-8_BIB83","doi-asserted-by":"crossref","first-page":"889","DOI":"10.1109\/72.165591","article-title":"Wavelet networks","volume":"NN-3","author":"Zhang","year":"1992","journal-title":"IEEE Trans. Neural Networks"},{"key":"10.1016\/0005-1098(95)00120-8_BIB84","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/0005-1098(94)90231-3","article-title":"Early warning of slight changes in systems and plants with application to condition based maintenance","volume":"30","author":"Zhang","year":"1994","journal-title":"Automatica"}],"container-title":["Automatica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:0005109895001208?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:0005109895001208?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,4,15]],"date-time":"2019-04-15T17:52:42Z","timestamp":1555350762000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/0005109895001208"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,12]]},"references-count":84,"journal-issue":{"issue":"12","published-print":{"date-parts":[[1995,12]]}},"alternative-id":["0005109895001208"],"URL":"https:\/\/doi.org\/10.1016\/0005-1098(95)00120-8","relation":{},"ISSN":["0005-1098"],"issn-type":[{"value":"0005-1098","type":"print"}],"subject":[],"published":{"date-parts":[[1995,12]]}}}