Data-driven techniques to estimate parameters in a rate-dependent ferromagnetic hysteresis model

The homogenized energy model (HEM) is a unified framework for modeling hysteresis in ferroelectric, ferromagnetic, and ferroelastic materials. The HEM framework combines energy analysis at the lattice level with stochastic homogenization techniques, based on the assumption that quantities such as interaction and coercive fields are manifestations of underlying densities, to construct macroscopic material models. In this paper, we focus on the homogenized energy model for shape memory alloys (SMA). Specifically, we develop techniques for estimating model parameters based on attributes of measured data. Both the local (mesoscopic) and macroscopic models are described, and the model parameters' relationship to the material's response are discussed. Using these relationships, techniques for estimating model parameters are presented. The techniques are applied to constant-temperature stress-strain and resistance-strain data. These estimates are used in two manners. In one method, the estimates are considered fixed and only the HEM density functions are optimized. For SMA, the HEM incorporates densities for the interaction and relative stress, the width of the hysteresis loop. In the second method, the estimates are included in the optimization algorithm. Both cases are compared to experimental data at various temperatures, and the optimized model parameters are compared to the initial estimates.

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“…Optimizing the density functions (11) and (12) involves finding the coefficients α k,m and β k that minimize the sum of squared errors…”

Section: Densities Onlymentioning

confidence: 99%

“…In the second method, the parameters are incorporated into the optimization process with the density functions. Similar techniques for estimating parameters for ferroelectric and ferromagnetic models are presented in [11,12].…”

Section: Introductionmentioning

confidence: 99%

Data-driven techniques to estimate parameters in the homogenized energy model for shape memory alloys

Crews

Smith

Pender

et al. 2012

Journal of Intelligent Material Systems and Structures

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“…6 Here, we discuss a method introduced by Ernstberger (2008) and Hu et al (2011a) that employs the expansions…”

Section: Hemmentioning

confidence: 99%

Homogenized energy model for characterizing polarization and strains in hysteretic ferroelectric materials: Material properties and uniaxial model development

Smith

2012

Journal of Intelligent Material Systems and Structures

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Ferroelectric materials, such as lead zirconate titanate, lanthanum-doped lead zirconate titanate, and BaTiO3, are being considered, or are already being employed, for a large number of applications including nanopositioning, high-speed valves for fuel injectors, ultrasonic transducers, high-speed camera shutters and autofocusing mechanisms, energy harvesting, and pico air vehicle design. Their advantages include nanometer positioning resolution, broadband frequency responses, moderate power requirements, the capability for miniaturization, and complementary actuator and sensor capabilities. However, they also exhibit creep, rate-dependent hysteresis, and constitutive nonlinearities at essentially all drive levels due to their noncentrosymmetric nature. In this article, we model the hysteretic dependence of strains and polarizations on input fields and stresses using the homogenized energy model framework. At the domain level, the minimization of the Gibbs energy densities yields linear constitutive relations. Nonlinearities and hysteresis due to dipole switching are modeled at the grain level using the Boltzmann theory to specify the evolution of dipole fractions that serve as internal variables. In the final step of the development, stochastic homogenization, based on the assumption that interaction fields and driving forces are manifestations of underlying densities, is used to construct nonlinear constitutive relations for the bulk material. It is demonstrated that these relations are amenable to subsequent development of distributed system models. The article includes significant discussion regarding the mechanisms that produce hysteresis in ferroelectric materials. The capability of the framework for characterizing various hysteretic phenomena, including creep and various rate dependencies, is illustrated by validation with lead zirconate titanate and lanthanum-doped lead zirconate titanate data.

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“…Here p = q. × s is given by (7). Since polarization is typically on the order of 10 −1 and strain on the order of 10 −3 , the weights w P and w ε are chosen to balance the polarization and strain components of (37).…”

Section: Parameter Estimation Problemmentioning

confidence: 99%

The Homogenized Energy Model (HEM) for Characterizing Polarization and Strains in Hysteretic Ferroelectric Materials: Implementation Algorithms and Data-Driven Parameter Estimation Techniques

Hu¹,

Smith²,

Ernstberger³

2012

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Ferroelectric materials, such as PZT, PLZT, PMN and BaTiO 3 , provide unique actuator and sensor capabilities for applications including nanopositioning, high speed valves and fuel injectors, camera focusing and shutter mechanisms, ultrasonic devices for biomedical imaging and treatment, and energy harvesting devices. However, to achieve the full potential of the materials, it is necessary to develop and employ models that quantify the creep, rate-dependent hysteresis, and constitutive nonlinearities that are intrinsic to the materials due to their domain structure. The success of models requires that they be highly efficient to implement since real-time applications can require kHz to MHz rates. The calibration of models for specific materials, devices, and applications, requires efficient and robust parameter estimation algorithms. Finally, control designs can be facilitated by models that admit efficient and robust approximate inversion. The homogenized energy model (HEM) is a multiscale, micromechanical framework that quantifies a range of hysteretic phenomena intrinsic to ferroelectric, ferromagnetic and ferroelastic materials. In this paper, we present highly efficient implementation and parameter estimation algorithms for the ferroelectric model. This includes techniques to construct analytic Jacobians and data-driven algorithms to determine initial parameter estimates to facilitate subsequent optimization. The efficiency of these algorithms facilitates material and device characterization and provides the basis for constructing efficient and robust inverse algorithms for model-based control design. The model implementation, calibration, and validation are illustrated using rate-dependent PZT data and single crystal BaTiO 3 data. i Report Documentation Page Form Approved OMB No. 0704-0188 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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Data-driven techniques to estimate parameters in a rate-dependent ferromagnetic hysteresis model

Cited by 10 publications

References 5 publications

Data-driven techniques to estimate parameters in the homogenized energy model for shape memory alloys

Data-driven techniques to estimate parameters in the homogenized energy model for shape memory alloys

Homogenized energy model for characterizing polarization and strains in hysteretic ferroelectric materials: Material properties and uniaxial model development

The Homogenized Energy Model (HEM) for Characterizing Polarization and Strains in Hysteretic Ferroelectric Materials: Implementation Algorithms and Data-Driven Parameter Estimation Techniques

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