{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T06:12:47Z","timestamp":1768716767579,"version":"3.49.0"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"12","license":[{"start":{"date-parts":[[2020,7,26]],"date-time":"2020-07-26T00:00:00Z","timestamp":1595721600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,7,26]],"date-time":"2020-07-26T00:00:00Z","timestamp":1595721600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Appl Intell"],"published-print":{"date-parts":[[2020,12]]},"DOI":"10.1007\/s10489-020-01804-2","type":"journal-article","created":{"date-parts":[[2020,7,26]],"date-time":"2020-07-26T00:03:32Z","timestamp":1595721812000},"page":"4586-4601","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["DBN based SD-ARX model for nonlinear time series prediction and analysis"],"prefix":"10.1007","volume":"50","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8321-3225","authenticated-orcid":false,"given":"Wenquan","family":"Xu","sequence":"first","affiliation":[]},{"given":"Hui","family":"Peng","sequence":"additional","affiliation":[]},{"given":"Xiaoying","family":"Tian","sequence":"additional","affiliation":[]},{"given":"Xiaoyan","family":"Peng","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,7,26]]},"reference":[{"issue":"2","key":"1804_CR1","doi-asserted-by":"publisher","first-page":"211","DOI":"10.1016\/j.isatra.2007.12.002","volume":"47","author":"B Gu","year":"2008","unstructured":"Gu B, Gupta YP (2008) Control of nonlinear processes by using linear model predictive control algorithms. ISA Transactions 47(2):211\u2013216","journal-title":"ISA Transactions"},{"issue":"10","key":"1804_CR2","doi-asserted-by":"publisher","first-page":"1997","DOI":"10.1016\/j.jprocont.2012.08.007","volume":"22","author":"JK Huusom","year":"2012","unstructured":"Huusom JK, Poulsen NK, Rgensen SB, Rgensen JB (2012) Tuning siso offset-free model predictive control based on ARX models. Journal of Process Control 22(10):1997\u20132007","journal-title":"Journal of Process Control"},{"key":"1804_CR3","unstructured":"Nov\u00e1k, J., Chalupa, P., & Bob\u00e1l, V. (2011). MIMO model predictive control with local linear models. Wseas International Conference on Automatic Control"},{"issue":"5","key":"1804_CR4","doi-asserted-by":"publisher","first-page":"454","DOI":"10.1016\/j.conengprac.2011.01.007","volume":"19","author":"MA Hosen","year":"2011","unstructured":"Hosen MA, Hussain MA, Mjalli FS (2011) Control of polystyrene batch reactors using neural network based model predictive control (NNMPC): an experimental investigation. Control Engineering Practice 19(5):454\u2013467","journal-title":"Control Engineering Practice"},{"issue":"7\u20138","key":"1804_CR5","doi-asserted-by":"publisher","first-page":"643","DOI":"10.1016\/j.jprocont.2007.12.006","volume":"18","author":"M Ekman","year":"2008","unstructured":"Ekman M (2008) Bilinear black-box identification and MPC of the activated sludge process. Journal of Process Control 18(7\u20138):643\u2013653","journal-title":"Journal of Process Control"},{"issue":"4","key":"1804_CR6","doi-asserted-by":"publisher","first-page":"370","DOI":"10.1504\/IJISTA.2007.014032","volume":"2","author":"W Dongli","year":"2007","unstructured":"Dongli W, Yan Z, Xiaoyang H (2007) Radial basis function neural network-based model predictive control for freeway traffic systems. International Journal of Intelligent Systems Technologies and Applications 2(4):370","journal-title":"International Journal of Intelligent Systems Technologies and Applications"},{"issue":"6","key":"1804_CR7","doi-asserted-by":"publisher","first-page":"1225","DOI":"10.1016\/j.compchemeng.2007.05.002","volume":"32","author":"E Aggelogiannaki","year":"2008","unstructured":"Aggelogiannaki E, Sarimveis H (2008) Nonlinear model predictive control for distributed parameter systems using data driven artificial neural network models. Computers and Chemical Engineering 32(6):1225\u20131237","journal-title":"Computers and Chemical Engineering"},{"issue":"2","key":"1804_CR8","doi-asserted-by":"publisher","first-page":"402","DOI":"10.1109\/TNNLS.2015.2465174","volume":"27","author":"HG Han","year":"2015","unstructured":"Han HG, Zhang L, Hou Y, Qiao JF (2015) Nonlinear model predictive control based on a self-organizing recurrent neural network. IEEE Transactions on Neural Networks and Learning Systems 27(2):402","journal-title":"IEEE Transactions on Neural Networks and Learning Systems"},{"issue":"2","key":"1804_CR9","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1016\/j.ins.2009.08.021","volume":"180","author":"B Rezaee","year":"2010","unstructured":"Rezaee B, Zarandi MHF (2010) Data-driven fuzzy modeling for takagi\u2013sugeno\u2013kang fuzzy system. Information Sciences 180(2):241\u2013255","journal-title":"Information Sciences"},{"key":"1804_CR10","doi-asserted-by":"crossref","unstructured":"Box GEP, Jenkins GM (1971) Time series analysis, forecasting and control. Journal of the American Statistical Association 134(3)","DOI":"10.2307\/2344246"},{"issue":"1","key":"1804_CR11","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1109\/TFUZZ.2002.803491","volume":"11","author":"AE Gaweda","year":"2003","unstructured":"Gaweda AE, Zurada JM (2003) Data-driven linguistic modeling using relational fuzzy rules. Fuzzy Systems IEEE Transactions on 11(1):121\u2013134","journal-title":"Fuzzy Systems IEEE Transactions on"},{"issue":"3","key":"1804_CR12","doi-asserted-by":"publisher","first-page":"328","DOI":"10.1109\/91.618271","volume":"5","author":"E Kim","year":"1997","unstructured":"Kim E, Park M, Ji S, Park M (1997) A new approach to fuzzy modeling. IEEE Trans Fuzzy Syst 5(3):328\u2013337","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"4","key":"1804_CR13","doi-asserted-by":"publisher","first-page":"596","DOI":"10.1109\/91.728458","volume":"6","author":"E Kim","year":"1998","unstructured":"Kim E, Park M, Kim S, Park M (1998) A transformed input-domain approach to fuzzy modeling. Fuzzy Systems IEEE Transactions on 6(4):596\u2013604","journal-title":"Fuzzy Systems IEEE Transactions on"},{"issue":"3","key":"1804_CR14","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1016\/0165-0114(91)90110-C","volume":"42","author":"M Sugeno","year":"1991","unstructured":"Sugeno M, Tanaka K (1991) Successive identification of a fuzzy model and its applications to prediction of a complex system. Fuzzy Sets & Systems 42(3):315\u2013334","journal-title":"Fuzzy Sets & Systems"},{"issue":"2","key":"1804_CR15","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1109\/TSMCC.2004.841910","volume":"35","author":"H Wang","year":"2005","unstructured":"Wang H, Kwong S, Jin Y, Wei W, Man KF (2005) Agent-based evolutionary approach for interpretable rule-based knowledge extraction. IEEE Transactions on Systems Man & Cybernetics Part C 35(2):143\u2013155","journal-title":"IEEE Transactions on Systems Man & Cybernetics Part C"},{"key":"1804_CR16","doi-asserted-by":"publisher","unstructured":"Zhao J, Mo H, Deng Y (2020) An efficient network method for time series forecasting based on the DC algorithm and visibility relation. IEEE Access 8(1). https:\/\/doi.org\/10.1109\/ACCESS.2020.2964067","DOI":"10.1109\/ACCESS.2020.2964067"},{"issue":"1","key":"1804_CR17","doi-asserted-by":"publisher","first-page":"102554","DOI":"10.1109\/ACCESS.2019.2926986","volume":"7","author":"F Liu","year":"2019","unstructured":"Liu F, Deng Y (2019) A fast algorithm for network forecasting time series. IEEE Access 7(1):102554\u2013102560","journal-title":"IEEE Access"},{"key":"1804_CR18","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1016\/j.chaos.2018.07.039","volume":"117","author":"P Xu","year":"2018","unstructured":"Xu P, Zhang R, Deng Y (2018) A novel visibility graph transformation of time series into weighted networks. Chaos, Solitons & Fractals 117:201\u2013208","journal-title":"Chaos, Solitons & Fractals"},{"issue":"4","key":"1804_CR19","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1007\/s41066-016-0016-3","volume":"1","author":"L Maciel","year":"2016","unstructured":"Maciel L, Ballini R, Gomide F (2016) Evolving granular analytics for interval time series forecasting. Granular Computing 1(4):213\u2013224","journal-title":"Granular Computing"},{"key":"1804_CR20","doi-asserted-by":"publisher","first-page":"1001","DOI":"10.1007\/s11071-018-4105-5","volume":"92","author":"J Zhang","year":"2018","unstructured":"Zhang J, Chin KS, Lawry\u0144czuk M (2018) Nonlinear model predictive control based on piecewise linear hammerstein models. Nonlinear Dynamics 92:1001\u20131021","journal-title":"Nonlinear Dynamics"},{"key":"1804_CR21","doi-asserted-by":"crossref","unstructured":"Korda M, Mezi\u0107 I (2016) Linear predictors for nonlinear dynamical systems: koopman operator meets model predictive control. Automatica 93","DOI":"10.1016\/j.automatica.2018.03.046"},{"issue":"7","key":"1804_CR22","doi-asserted-by":"publisher","first-page":"655","DOI":"10.1016\/S0959-1524(02)00121-X","volume":"13","author":"LC Ania","year":"2003","unstructured":"Ania LC, Agamennoni OE, Figueroa JL (2003) A nonlinear model predictive control system based on Wiener piecewise linear models. Journal of Process Control 13(7):655\u2013666","journal-title":"Journal of Process Control"},{"issue":"7","key":"1804_CR23","doi-asserted-by":"publisher","first-page":"1129","DOI":"10.1007\/s11432-009-0129-2","volume":"52","author":"M Zhao","year":"2009","unstructured":"Zhao M, Li N, Li SY (2009) Min-Max model predictive control for constrained nonlinear systems via multiple LPV embeddings. Science in China Series F (Information Science) 52(7):1129\u20131135","journal-title":"Science in China Series F (Information Science)"},{"issue":"3","key":"1804_CR24","doi-asserted-by":"publisher","first-page":"60","DOI":"10.1016\/j.jprocont.2013.12.006","volume":"24","author":"B Ding","year":"2014","unstructured":"Ding B, Tao Z (2014) A synthesis approach for output feedback robust model predictive control based-on input\u2013output model. Journal of Process Control 24(3):60\u201372","journal-title":"Journal of Process Control"},{"key":"1804_CR25","doi-asserted-by":"publisher","first-page":"605","DOI":"10.1016\/j.asoc.2019.02.006","volume":"77","author":"W Xu","year":"2019","unstructured":"Xu W, Peng H, Zeng X, Zhou F, Tian X, Peng X (2019) Deep belief network-based AR model for nonlinear time series forecasting. Applied Soft Computing 77:605\u2013621","journal-title":"Applied Soft Computing"},{"issue":"8","key":"1804_CR26","doi-asserted-by":"publisher","first-page":"3002","DOI":"10.1007\/s10489-019-01426-3","volume":"49","author":"W Xu","year":"2019","unstructured":"Xu W, Peng H, Zeng X, Zhou F, Tian X, Peng X (2019) A hybrid modelling method for time series forecasting based on a linear regression model and deep learning. Applied Intelligence 49(8):3002\u20133015","journal-title":"Applied Intelligence"},{"key":"1804_CR27","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1016\/S0096-3003(98)10013-9","volume":"102","author":"W Li","year":"1999","unstructured":"Li W, Szidarovszky F (1999) An elementary result in the stability theory of time-invariant nonlinear discrete dynamical systems. Applied Mathematics and Computation 102:35\u201349","journal-title":"Applied Mathematics and Computation"},{"issue":"5786","key":"1804_CR28","doi-asserted-by":"publisher","first-page":"504","DOI":"10.1126\/science.1127647","volume":"313","author":"GE Hinton","year":"2006","unstructured":"Hinton GE, Salakhutdinov RR (2006) Reducing the dimensionality of data with neural networks. Science. 313(5786):504\u2013507","journal-title":"Science."},{"key":"1804_CR29","doi-asserted-by":"publisher","first-page":"655","DOI":"10.1016\/S0959-1524(02)00121-X","volume":"13","author":"AL Cervantes","year":"2003","unstructured":"Cervantes AL, Agamennoni OE, Figueroa JL (2003) A nonlinear model predictive control system based on Wiener piecewise linear models. Journal of Process Control 13:655\u2013666","journal-title":"Journal of Process Control"},{"key":"1804_CR30","unstructured":"Man, H. (2014). Research on model identification and nonlinear predictive control methods of CSTR process, Ph.D. dissertation, Univ. Dalian University of Technology, Dalian, China"},{"issue":"3","key":"1804_CR31","doi-asserted-by":"publisher","first-page":"462","DOI":"10.1109\/TCYB.2014.2328438","volume":"45","author":"M Gan","year":"2017","unstructured":"Gan M, Li HX, Peng H (2017) A variable projection approach for efficient estimation of RBF-ARX model. IEEE Transactions on Cybernetics 45(3):462\u2013471","journal-title":"IEEE Transactions on Cybernetics"}],"container-title":["Applied Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10489-020-01804-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10489-020-01804-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10489-020-01804-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,11,4]],"date-time":"2022-11-04T14:10:07Z","timestamp":1667571007000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10489-020-01804-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,7,26]]},"references-count":31,"journal-issue":{"issue":"12","published-print":{"date-parts":[[2020,12]]}},"alternative-id":["1804"],"URL":"https:\/\/doi.org\/10.1007\/s10489-020-01804-2","relation":{},"ISSN":["0924-669X","1573-7497"],"issn-type":[{"value":"0924-669X","type":"print"},{"value":"1573-7497","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,7,26]]},"assertion":[{"value":"26 July 2020","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}