Long-memory recursive prediction error method for identification of continuous-time fractional models |
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Authors: | Victor Stéphane Duhé Jean-François Melchior Pierre Abdelmounen Youssef Roubertie François |
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Affiliation: | 1.Univ. Bordeaux, CNRS, IMS UMR 5218, Bordeaux INP/enseirb-matmeca, 351 cours de la Libération, 33405, Talence Cedex, France ;2.IHU Liryc, Electrophysiology and Heart Modeling Institute, Fondation Bordeaux Université, 33000, Bordeaux Cedex, France ;3.INSERM U1045, Centre de recherche Cardio-Thoracique de Bordeaux, 33000, Bordeaux Cedex, France ;4.Clinique Saint Augustin, Bordeaux Cedex, France ; |
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Abstract: | This paper deals with recursive continuous-time system identification using fractional-order models. Long-memory recursive prediction error method is proposed for recursive estimation of all parameters of fractional-order models. When differentiation orders are assumed known, least squares and prediction error methods, being direct extensions to fractional-order models of the classic methods used for integer-order models, are compared to our new method, the long-memory recursive prediction error method. Given the long-memory property of fractional models, Monte Carlo simulations prove the efficiency of our proposed algorithm. Then, when the differentiation orders are unknown, two-stage algorithms are necessary for both parameter and differentiation-order estimation. The performances of the new proposed recursive algorithm are studied through Monte Carlo simulations. Finally, the proposed algorithm is validated on a biological example where heat transfers in lungs are modeled by using thermal two-port network formalism with fractional models. |
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