Electrical modeling of a CaCu&lt;inf&gt;3&lt;/inf&gt;Ti&lt;inf&gt;4&lt;/inf&gt;O&lt;inf&gt;12&lt;/inf&gt; ceramic for capacitor applications

Montseny²

2009

We present a new identification method for nonlinear Volterra models of the form HX = F (u, X) + v with H a causal convolution operator. It is based first on a suitable parameterization of H deduced from the so-called diffusive representation, devoted to state representations of integral operators, and second on a suitable operatorial transformation of the problem with the property that the nonlinear term F (u, X) is cancelled, allowing to identify the operator H(∂ t ) alone. Then, the nonlinear term can be identified from standard regression methods. For illustration, we implement this method on a concrete numerical example.

Section: Diffusive Formulation Of Causal Convolution Operatorsmentioning

confidence: 99%

“…• thermic phenomena (we will consider in section 4 the combustion model elaborated in Joulin (1985)), • electrical engineering (Rumeau (2006) …”

Section: Introductionmentioning

confidence: 99%

Diffusive Identification of Volterra Models by Cancellation of the Nonlinear Term

Montseny²

2009

“…Various applications and questions relating to this approach will be found for example in (Audounet et al [1998], Carmona and Coutin [1998], Degerli et al [Ap. 1999], Garcia and Bernussou [1998], Lenczner and Montseny [2005], Levadoux and Montseny [2003], Montseny [2007], Mouyon and Imbert [2002], Rumeau et al [2006]). …”

Section: Diffusive Formulation Of Causal Convolution Operatorsmentioning

confidence: 99%

“…In particular, the so-identified symbol H(iω) is in general ill adapted to the construction of efficient time-realizations. This is partly due to excessive numerical cost of quadrature approximations resulting from the intrinsic convolution nature of the associated operator, sometimes with long memory (Rumeau et al [2006]) or even delay-like behaviors (Montseny [2007]). Another shortcoming is that frequency methods are incompatible with real-time identification (and so with pursuit when the symbol has the ability to evolve slowly).…”

Section: Introductionmentioning

confidence: 99%

Identification of Time-non local Models under Diffusive Representation

2010

Abstract:In this paper, we show how the so-called diffusive representation can be used in order to identify nonlinear Volterra models of the form H(∂ t )X = f (u, X) + v. Several methods are described, all being based on a suitable parameterization of H(∂ t ) by means of its γ-symbol. Following this idea, the complex dynamic nature of H(∂ t ) can be summarized by a few parameters on which the identification of the dynamic part of the model will focus. For illustration, we implement the methods on a concrete numerical example.

“…A complete theoretical statement will be found in Montseny [2005] and various applications to non trivial problems will be found in , Carmona and Coutin [1998a,b], Carmona et al [2003], Casenave andMontseny [2009, 2008], Degerli et al [Ap. 1999], Garcia and Bernussou [1998], Lenczner and Montseny [2005], Lenczner et al [2010], Levadoux and Montseny [2003], Montseny [2007], Mouyon and Imbert [2002], Rumeau et al [2006], Bidan et al [2001], , , Devy-Vareta and , Helie and Matignon [2006], Laudebat et al [2004], Lavernhe et al [2001], Lavernhe and Solhusvik [1998], Leger and Pontier [1999], Lubich and Schädler [2002], Matignon [July 2001], Matignon and Prieur [2005], Mbodge et al [1994], Mbodge and Montseny [1995], Montseny [2002bMontseny [ ,a, 1998], Montseny et al [2000], Nihtila and Tervo [2002], Rouzaud [1998].…”

Section: H(t S)u(s)dsmentioning

confidence: 99%

Introduction to Diffusive Representation

Montseny

2010

Diffusive representation is an operator theory elaborated during the last years. It is devoted to time-nonlocal problems, allowing significant simplifications for analysis and numerical realization of integral time operators encountered in many physical situations. Namely, most of the shortcomings induced by time-nonlocal formulations are by-passed by use of suitable time-local state realizations deduced from diffusive representation and whose numerical approximations are straightforward, thanks to good properties of diffusion equations. In this paper, we introduce the notion of diffusive representation and its dual one: the diffusive symbol, and we briefly describe the associated mathematical framework and numerical techniques. The interest of this approach is highlighted by numerical examples.