{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T03:32:49Z","timestamp":1780371169473,"version":"3.54.1"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"12","license":[{"start":{"date-parts":[[2022,11,25]],"date-time":"2022-11-25T00:00:00Z","timestamp":1669334400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,11,25]],"date-time":"2022-11-25T00:00:00Z","timestamp":1669334400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61863034"],"award-info":[{"award-number":["61863034"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Appl Intell"],"published-print":{"date-parts":[[2023,6]]},"DOI":"10.1007\/s10489-022-04309-2","type":"journal-article","created":{"date-parts":[[2022,11,25]],"date-time":"2022-11-25T20:02:34Z","timestamp":1669406554000},"page":"15711-15726","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Hybrid identification method for fractional-order nonlinear systems based on the multi-innovation principle"],"prefix":"10.1007","volume":"53","author":[{"given":"Zhang","family":"Qian","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wang","family":"Hongwei","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Liu","family":"Chunlei","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2022,11,25]]},"reference":[{"issue":"4","key":"4309_CR1","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1615\/CritRevBiomedEng.2018028368","volume":"47","author":"MA Matlob","year":"2019","unstructured":"Matlob MA, Jamali Y (2019) The concepts and applications of fractional order differential calculus in modeling of viscoelastic systems: a primer. Crit Rev Biomed Eng 47(4):249\u2013276","journal-title":"Crit Rev Biomed Eng"},{"issue":"7","key":"4309_CR2","doi-asserted-by":"publisher","first-page":"1125","DOI":"10.3390\/math10071125","volume":"10","author":"M Yavuz","year":"2022","unstructured":"Yavuz M, Sene N, Y\u0131ld\u0131z M (2022) Analysis of the influences of parameters in the fractional second-grade fluid dynamics. Mathematics 10(7):1125","journal-title":"Mathematics"},{"issue":"2172","key":"4309_CR3","doi-asserted-by":"publisher","first-page":"20200050","DOI":"10.1098\/rsta.2020.0050","volume":"378","author":"G Failla","year":"2020","unstructured":"Failla G, Zingales M (2020) Advanced materials modelling via fractional calculus: challenges and perspectives. Phil Trans R Soc A 378(2172):20200050","journal-title":"Phil Trans R Soc A"},{"issue":"1","key":"4309_CR4","doi-asserted-by":"publisher","DOI":"10.1063\/1.5082907","volume":"29","author":"S Qureshi","year":"2019","unstructured":"Qureshi S, Yusuf A, Shaikh AA, Inc M, Baleanu D (2019) Fractional modeling of blood ethanol concentration system with real data application. Chaos: An Interdisciplinary Journal of Nonlinear Science 29(1):013143","journal-title":"Chaos: An Interdisciplinary Journal of Nonlinear Science"},{"issue":"4","key":"4309_CR5","first-page":"189","volume":"32","author":"L Shulin","year":"2017","unstructured":"Shulin L, Naxin C, Yan L et al (2017) Modeling and state-of-charge estimation of automotive lithium-ion batteries based on fractional-order theory. Chin J Electrotechnical Technol 32(4):189\u2013195","journal-title":"Chin J Electrotechnical Technol"},{"issue":"2","key":"4309_CR6","doi-asserted-by":"publisher","first-page":"1062","DOI":"10.1002\/asjc.2282","volume":"23","author":"A Jajarmi","year":"2021","unstructured":"Jajarmi A, Baleanu D (2021) On the fractional optimal control problems with a general derivative operator. Asian Journal of Control 23(2):1062\u20131071","journal-title":"Asian Journal of Control"},{"key":"4309_CR7","doi-asserted-by":"crossref","unstructured":"Wang S, Takyi-Aninakwa P, Jin S et al (2022) An improved feedforward-long short-term memory modeling method for the whole-life-cycle state of charge prediction of lithium-ion batteries considering current-voltage-temperature variation. Energy 124224","DOI":"10.1016\/j.energy.2022.124224"},{"key":"4309_CR8","doi-asserted-by":"publisher","first-page":"5562","DOI":"10.1016\/j.egyr.2021.08.182","volume":"7","author":"S Wang","year":"2021","unstructured":"Wang S, Jin S, Bai D, Fan Y, Shi H, Fernandez C (2021) A critical review of improved deep learning methods for the remaining useful life prediction of lithium-ion batteries. Energy Rep 7:5562\u20135574","journal-title":"Energy Rep"},{"key":"4309_CR9","doi-asserted-by":"publisher","first-page":"286","DOI":"10.1016\/j.jpowsour.2018.04.033","volume":"390","author":"C Zou","year":"2018","unstructured":"Zou C, Zhang L, Hu X, Wang Z, Wik T, Pecht M (2018) A review of fractional-order techniques applied to lithium-ion batteries, lead-acid batteries, and supercapacitors. J Power Sources 390:286\u2013296","journal-title":"J Power Sources"},{"issue":"4","key":"4309_CR10","doi-asserted-by":"publisher","first-page":"3085","DOI":"10.1007\/s00366-021-01314-w","volume":"38","author":"CJ Z\u00fa\u00f1iga-Aguilar","year":"2022","unstructured":"Z\u00fa\u00f1iga-Aguilar CJ, G\u00f3mez-Aguilar JF, Romero-Ugalde HM, Jahanshahi H, Alsaadi FE (2022) Fractal-fractional neuro-adaptive method for system identification. Eng Comput 38(4):3085\u20133108","journal-title":"Eng Comput"},{"issue":"5","key":"4309_CR11","doi-asserted-by":"publisher","first-page":"4130","DOI":"10.1109\/TVT.2018.2880085","volume":"68","author":"R Xiong","year":"2018","unstructured":"Xiong R, Tian J, Shen W et al (2018) A novel fractional order model for state of charge estimation in lithium ion batteries. IEEE Trans Veh Technol 68(5):4130\u20134139","journal-title":"IEEE Trans Veh Technol"},{"key":"4309_CR12","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1016\/j.camwa.2021.05.005","volume":"116","author":"O Burkovska","year":"2022","unstructured":"Burkovska O, Glusa C, D\u2019elia M (2022) An optimization-based approach to parameter learning for fractional type nonlocal models. Comput Math Appl 116:229\u2013244","journal-title":"Comput Math Appl"},{"issue":"4","key":"4309_CR13","doi-asserted-by":"publisher","first-page":"3215","DOI":"10.1007\/s11071-021-06925-y","volume":"106","author":"Q Zhang","year":"2021","unstructured":"Zhang Q, Wang H, Liu C (2021) Identification of fractional-order Hammerstein nonlinear ARMAX system with colored noise. Nonlinear Dynamics 106(4):3215\u20133230","journal-title":"Nonlinear Dynamics"},{"key":"4309_CR14","doi-asserted-by":"crossref","unstructured":"Zhang Q, Wang H, Liu C (2022) MILM hybrid identification method of fractional order neural-fuzzy Hammerstein model. Nonlinear Dynamics:1\u201315","DOI":"10.1007\/s11071-022-07303-y"},{"issue":"24","key":"4309_CR15","doi-asserted-by":"publisher","first-page":"8097","DOI":"10.1007\/s00500-017-2749-6","volume":"22","author":"MR Rahmani","year":"2018","unstructured":"Rahmani MR, Farrokhi M (2018) Identification of neuro-fractional Hammerstein systems: a hybrid frequency\u2212\/time-domain approach. Soft Comput 22(24):8097\u20138106","journal-title":"Soft Comput"},{"issue":"08","key":"4309_CR16","doi-asserted-by":"publisher","first-page":"1664","DOI":"10.16182\/j.issn1004731x.joss.17-0265","volume":"31","author":"D Ze","year":"2019","unstructured":"Ze D, Ning M (2019) Parameter estimation of fractional-order chaotic systems by differential quantum particle swarm optimization. Journal of System. Simulation 31(08):1664\u20131673. https:\/\/doi.org\/10.16182\/j.issn1004731x.joss.17-0265","journal-title":"Simulation"},{"issue":"57","key":"4309_CR17","doi-asserted-by":"publisher","first-page":"24059","DOI":"10.1016\/j.ijhydene.2022.05.190","volume":"47","author":"H Guo","year":"2022","unstructured":"Guo H, Gu W, Khayatnezhad M, Ghadimi N (2022) Parameter extraction of the SOFC mathematical model based on fractional order version of dragonfly algorithm. Int J Hydrog Energy 47(57):24059\u201324068","journal-title":"Int J Hydrog Energy"},{"key":"4309_CR18","doi-asserted-by":"publisher","first-page":"120203","DOI":"10.1016\/j.jclepro.2020.120203","volume":"255","author":"X Lai","year":"2020","unstructured":"Lai X, He L, Wang S, Zhou L, Zhang Y, Sun T, Zheng Y (2020) Co-estimation of state of charge and state of power for lithium-ion batteries based on fractional variable-order model. J Clean Prod 255:120203","journal-title":"J Clean Prod"},{"key":"4309_CR19","doi-asserted-by":"crossref","unstructured":"Hammar K, Djamah T, Bettayeb M (2015) Fractional hammerstein system identification using particle swarm optimization \/\/2015 7th international conference on modelling, identification and control (ICMIC). IEEE, 1\u20136","DOI":"10.1109\/ICMIC.2015.7409483"},{"key":"4309_CR20","doi-asserted-by":"crossref","unstructured":"Sersour L, Djamah T, Bettayeb M (2015) Identification of wiener fractional model using self-adaptive velocity particle swarm optimization\/\/2015 7th international conference on modelling, identification and control (ICMIC). IEEE, 1\u20136","DOI":"10.1109\/ICMIC.2015.7409484"},{"issue":"1","key":"4309_CR21","doi-asserted-by":"publisher","first-page":"154","DOI":"10.1016\/j.jprocont.2015.09.001","volume":"35","author":"QB Jin","year":"2015","unstructured":"Jin QB, Wang Z, Liu XP (2015) Auxiliary model-based inter-varying multi-innovation least squares identification for multivariable OE-like systems with scarce measurements. J Process Control 35(1):154\u2013168","journal-title":"J Process Control"},{"key":"4309_CR22","doi-asserted-by":"publisher","first-page":"412","DOI":"10.1016\/j.apm.2020.12.035","volume":"93","author":"NI Chaudhary","year":"2021","unstructured":"Chaudhary NI, Raja MAZ, He Y, Khan ZA, Tenreiro Machado JA (2021) Design of multi innovation fractional LMS algorithm for parameter estimation of input nonlinear control autoregressive systems. Appl Math Model 93:412\u2013425","journal-title":"Appl Math Model"},{"key":"4309_CR23","first-page":"1","volume":"71","author":"L Xu","year":"2022","unstructured":"Xu L, Ding F, Zhu Q (2022) Separable synchronous multi-innovation gradient-based iterative signal modeling from on-line measurements. IEEE Trans Instrum Meas 71:1\u201313","journal-title":"IEEE Trans Instrum Meas"},{"key":"4309_CR24","volume-title":"System identification: multi-innovation identification theory and method","author":"F Ding","year":"2016","unstructured":"Ding F (2016) System identification: multi-innovation identification theory and method. Science Press, Beijing"},{"issue":"3","key":"4309_CR25","first-page":"486","volume":"70","author":"JM Mohammad","year":"2018","unstructured":"Mohammad JM, Hamed M, Mohammad T (2018) Recursive identification of multiple-input single-output fractional-order Hammerstein model with time delay. Appl Soft Comput 70(3):486\u2013500","journal-title":"Appl Soft Comput"},{"issue":"5","key":"4309_CR26","doi-asserted-by":"publisher","first-page":"1892","DOI":"10.1002\/asjc.2092","volume":"22","author":"ZD Qi","year":"2020","unstructured":"Qi ZD, Sun Q, Ge WP, He YK (2020) Nonlinear modeling of PEMFC based on fractional order subspace identification. Asian J Control 22(5):1892\u20131900","journal-title":"Asian J Control"},{"issue":"1","key":"4309_CR27","doi-asserted-by":"publisher","first-page":"651","DOI":"10.1016\/j.jfranklin.2019.10.001","volume":"357","author":"JC Wang","year":"2020","unstructured":"Wang JC, Wei YH, Liu TY, Li A, Wang Y (2020) Fully parametric identification for continuous time fractional order Hammerstein systems. J Franklin Inst 357(1):651\u2013666","journal-title":"J Franklin Inst"},{"key":"4309_CR28","doi-asserted-by":"publisher","first-page":"2327","DOI":"10.1007\/s11071-019-05331-9","volume":"98","author":"K Hammar","year":"2019","unstructured":"Hammar K, Djamah T, Bettayeb M (2019, Published online) Nonlinear system identification using fractional Hammerstein-wiener models. Nonlinear Dyn 98:2327\u20132338","journal-title":"Nonlinear Dyn"},{"key":"4309_CR29","unstructured":"Feng D (2014) System identification-performance analysis of identification methods. Science Press.\u00a0(in Chinese)"},{"key":"4309_CR30","first-page":"4","volume":"38","author":"B De Moor","year":"1997","unstructured":"De Moor B, De Gersem P, De Schutter B et al (1997) DAISY: a database for identification of systems. Journal A 38:4\u20135","journal-title":"Journal A"}],"container-title":["Applied Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10489-022-04309-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10489-022-04309-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10489-022-04309-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,1]],"date-time":"2023-06-01T04:02:45Z","timestamp":1685592165000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10489-022-04309-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,25]]},"references-count":30,"journal-issue":{"issue":"12","published-print":{"date-parts":[[2023,6]]}},"alternative-id":["4309"],"URL":"https:\/\/doi.org\/10.1007\/s10489-022-04309-2","relation":{},"ISSN":["0924-669X","1573-7497"],"issn-type":[{"value":"0924-669X","type":"print"},{"value":"1573-7497","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,11,25]]},"assertion":[{"value":"26 October 2022","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 November 2022","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that there is no conflict of interests with respect to the research, authorship, and\/or publication of this article.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interests"}}]}}