Long-memory recursive prediction error method for identification of continuous-time fractional models

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 predi...

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Vydané v:	Nonlinear dynamics Ročník 110; číslo 1; s. 635 - 648
Hlavní autori:	Victor, Stéphane, Duhé, Jean-François, Melchior, Pierre, Abdelmounen, Youssef, Roubertie, François
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Dordrecht Springer Netherlands 01.09.2022 Springer Nature B.V Springer Verlag
Predmet:	Algorithms Approximation Automotive Engineering Classical Mechanics Computer simulation Continuous time systems Control Differentiation Dynamical Systems Engineering Engineering Sciences Errors Identification Lungs Mathematical models Mechanical Engineering Original Paper Parameter estimation Parameters Regularization methods System identification Vibration Prediction error method Fractional-order model Least squares Real-time system identification Recursive identification System identification Long-memory prediction error method Continuous-time models Fractional calculus
ISSN:	0924-090X, 1573-269X
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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.
AbstractList	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.
Author	Abdelmounen, Youssef Victor, Stéphane Duhé, Jean-François Roubertie, François Melchior, Pierre
Author_xml	– sequence: 1 givenname: Stéphane surname: Victor fullname: Victor, Stéphane email: stephane.victor@ims-bordeaux.fr organization: Univ. Bordeaux, CNRS, IMS UMR 5218, Bordeaux INP/enseirb-matmeca – sequence: 2 givenname: Jean-François surname: Duhé fullname: Duhé, Jean-François organization: Univ. Bordeaux, CNRS, IMS UMR 5218, Bordeaux INP/enseirb-matmeca – sequence: 3 givenname: Pierre surname: Melchior fullname: Melchior, Pierre organization: Univ. Bordeaux, CNRS, IMS UMR 5218, Bordeaux INP/enseirb-matmeca – sequence: 4 givenname: Youssef surname: Abdelmounen fullname: Abdelmounen, Youssef organization: IHU Liryc, Electrophysiology and Heart Modeling Institute, Fondation Bordeaux Université, INSERM U1045, Centre de recherche Cardio-Thoracique de Bordeaux, Clinique Saint Augustin – sequence: 5 givenname: François surname: Roubertie fullname: Roubertie, François organization: IHU Liryc, Electrophysiology and Heart Modeling Institute, Fondation Bordeaux Université, INSERM U1045, Centre de recherche Cardio-Thoracique de Bordeaux
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Keywords	Prediction error method Fractional-order model Least squares Real-time system identification Recursive identification System identification Long-memory prediction error method Continuous-time models Fractional calculus
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Snippet	This paper deals with recursive continuous-time system identification using fractional-order models. Long-memory recursive prediction error method is proposed...
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SubjectTerms	Algorithms Approximation Automotive Engineering Classical Mechanics Computer simulation Continuous time systems Control Differentiation Dynamical Systems Engineering Engineering Sciences Errors Identification Lungs Mathematical models Mechanical Engineering Original Paper Parameter estimation Parameters Regularization methods System identification Vibration
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Title	Long-memory recursive prediction error method for identification of continuous-time fractional models
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