On the identification of Preisach measures

Shirley, Matthew Edward; Venkataraman, R.

doi:10.1117/12.499462

Cited by 32 publications

(27 citation statements)

References 11 publications

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“…As a prelude, we state the following theorem which is Theorem 5.24.8 from [13]. (15) and (16). The integral operator given by (17) is then a compact operator.…”

Section: Y(e) = Kq(e)mentioning

confidence: 99%

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Parameter Estimation Techniques for a Class of Nonlinear Hysteresis Models

Smith¹,

Hatch²

2005

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This paper addresses the development of parameter estimation techniques for a class of models used to characterize hysteresis and constitutive nonlinearities inherent to ferroelectric, ferromagnetic and ferroelastic materials employed in a wide range of actuators and sensors. These models are formulated as integral equations with known kernels and unknown densities to be identified through least squares techniques. Due to the compactness of the integral operators, the resulting discretized models inherit ill-posedness which must be accommodated through regularization. The accuracy of regularized finite-dimensional models is illustrated through comparison with experimental data.i Report Documentation PageForm Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.

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“…As a prelude, we state the following theorem which is Theorem 5.24.8 from [13]. (15) and (16). The integral operator given by (17) is then a compact operator.…”

Section: Y(e) = Kq(e)mentioning

confidence: 99%

“…These three approaches are homogenized energy models [8, 10, 18-20, 24, 25], Preisach formulations [2,3,5,7,16,26], and domain wall models [6,8,14,21,22].…”

Section: Introductionmentioning

confidence: 99%

Parameter Estimation Techniques for a Class of Nonlinear Hysteresis Models

Smith¹,

Hatch²

2005

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“…For general characterization, the weight or measure ν can be estimated from measured data through techniques analogous to those described in [27,28]. The advantage of the Preisach methodology lies in its generality.…”

Section: Preisach Frameworkmentioning

confidence: 99%

“…For conditions in which thermal after-effects [2] are negligible, the local average magnetization M at the lattice level is determined by minimizing the Gibbs relations (26) or (27) whereas the Gibbs energy must be balanced with the thermal energy through Boltzmann principles if thermal effects are significant. We consider these two regimes in Sections 3.1.1 and 3.1.2 and then illustrate in Section 3.1.3 that the model which incorporates thermal energy limits to the case of no thermal activation when reference volumes V are taken to be arbitrarily large.…”

Section: Local Magnetizationmentioning

confidence: 99%

A homogenized energy framework for ferromagnetic hysteresis

Smith

Dapino

2006

IEEE Trans. Magn.

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In this paper we develop a macroscopic framework quantifying the hysteresis and constitutive nonlinearities inherent to ferromagnetic materials. In the first step of the development, we construct Helmholtz and Gibbs energy relations at the mesoscopic or lattice level based on the assumption that magnetic moments or spins are restricted to two orientations. Direct minimization of the Gibbs energy yields local average magnetization relations appropriate for operating regimes in which relaxation mechanisms are negligible whereas the balance of the Gibbs and relative thermal energies through Boltzmann principles provides local models which incorporate mechanisms such as thermal after-effects. To construct macroscopic relations that incorporate material nonhomogeneities, polycrystallinity, and variable effective fields, we employ stochastic homogenization techniques based on the assumption that parameters such as local coercive and interaction fields are manifestations of underlying distributions. The resulting framework quantifies in a natural manner the anhysteretic magnetization provided by decaying AC fields and guarantees the closure of biased minor loops once transient accommodation and after-effects are complete. Furthermore, noncongruency is achieved with certain choices for the energy functionals. Hence the framework provides an energy basis for certain extended Preisach models and the relation of the framework to several macroscopic hysteresis models is detailed. The behavior of both the nonlinear anhysteretic relations and full hysteresis model are validated through comparison with experimental steel and nickel data.i Report Documentation PageForm Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.

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“…A number of modeling strategies for these compounds have been proposed but three stand out in the sense that they provide unified frameworks for characterizing hysteresis in ferroelectric, ferromagnetic and ferroelastic materials, which are collectively referred to as ferroic compounds. These three approaches are the following: (i) homogenized free energy models [9,13,18], (ii) Preisach formulations [1,2,12,19], and (iii) domain wall models [6,8,11,14,15]. The first two are formulated as integral equations whereas the domain wall models are typically posed as differential equations.…”

Section: Introductionmentioning

confidence: 99%

Parameter Estimation Techniques for a Polarization Hysteresis Model

Smith¹,

Hatch²

2004

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This paper focuses on the development of parameter estimation techniques for models quantifying hysteresis and constitutive nonlinearities in ferroelectric materials. These models are formulated as integral equations with known kernels and unknown densities to be identified through least squares fit to data. Due to the compactness of the integral operators, the resulting discretized models inherit ill-posedness which often must be accommodated through regularization. The accuracy of regularized finite-dimensional models is illustrated through comparison with experimental data.

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On the identification of Preisach measures

Cited by 32 publications

References 11 publications

Parameter Estimation Techniques for a Class of Nonlinear Hysteresis Models

Parameter Estimation Techniques for a Class of Nonlinear Hysteresis Models

A homogenized energy framework for ferromagnetic hysteresis

Parameter Estimation Techniques for a Polarization Hysteresis Model

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