{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:49:21Z","timestamp":1753886961044,"version":"3.41.2"},"reference-count":45,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2018,11,8]],"date-time":"2018-11-08T00:00:00Z","timestamp":1541635200000},"content-version":"vor","delay-in-days":311,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["HRD-1547723"],"award-info":[{"award-number":["HRD-1547723"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>In this paper, we present a system identification (SI) procedure that enables building linear time\u2010dependent fractional\u2010order differential equation (FDE) models able to accurately describe time\u2010dependent behavior of complex systems. The parameters in the models are the order of the equation, the coefficients in it, and, when necessary, the initial conditions. The Caputo definition of the fractional derivative, and the Mittag\u2010Leffler function, is used to obtain the corresponding solutions. Since the set of parameters for the model and its initial conditions are nonunique, and there are small but significant differences in the predictions from the possible models thus obtained, the SI operation is carried out via global regression of an error\u2010cost function by a simulated annealing optimization algorithm. The SI approach is assessed by considering previously published experimental data from a shell\u2010and\u2010tube heat exchanger and a recently constructed multiroom building test bed. The results show that the proposed model is reliable within the interpolation domain but cannot be used with confidence for predictions outside this region. However, the proposed system identification methodology is robust and can be used to derive accurate and compact models from experimental data. In addition, given a functional form of a fractional\u2010order differential equation model, as new data become available, the SI technique can be used to expand the region of reliability of the resulting model.<\/jats:p>","DOI":"10.1155\/2018\/8318519","type":"journal-article","created":{"date-parts":[[2018,11,8]],"date-time":"2018-11-08T23:34:28Z","timestamp":1541720068000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Fractional\u2010Derivative Approximation of Relaxation in Complex Systems"],"prefix":"10.1155","volume":"2018","author":[{"given":"Kin M.","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mihir","family":"Sen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0566-6074","authenticated-orcid":false,"given":"Arturo","family":"Pacheco-Vega","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2018,11,8]]},"reference":[{"key":"e_1_2_14_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2012.07.014"},{"volume-title":"Modern Control Systems","year":"2016","author":"Dorf R. 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