Abstract
Preisach density is drawing increasing attention for interpreting material properties for memory and storage electronics. Preisach density can be linked to the observed hysteresis loops via the Preisach model that is based on the superposition of relay operators. Reconstructing Preisach density from hysteresis is an ill-posed problem with nonunique solutions. To alleviate ambiguities, we address Preisach density reconstruction as a constrained subset selection task utilizing structured sparsity regularizations. We validate our approach under various simulation settings and apply it on experimental band-excitation piezoresponse spectroscopy (BEPS) datasets to gain insights in microstructure-dependent properties of the tip-surface contact.
Highlights
The hysteric response to an external stimulus is a pervasive phenomenon in vast dynamical and physical processes
Preisach model is commonly used to study hysterical behaviors, which is defined via the superposition of Preisach operators distributed over the Preisach plane
For robust recovery of Preisach density shapes, we formulate the estimation of PD from hysteresis measurements as a constrained subset selection problem, utilizing the elastic net regularization to suppress spurious patterns in PD and to solidify the shape of PD
Summary
The hysteric response to an external stimulus is a pervasive phenomenon in vast dynamical and physical processes. Model consisting of larger number of relay operators has less hysteresis reconstruction error but at higher computational cost [6], [20]. Li et al [21], [22] utilized discrete empirical interpolation method (DEIM) [23] to reduce the number of relay operators without losing accuracy of reconstructing hysteresis, leading to successful applications on actuator control tasks. We care about both the number and the positions of relay operators in the model This is physically pertinent as recent work [11] demonstrated broadening of PD directly relates to the materials’ morphology. To deal with high collinearity, we formulate Preisach density reconstruction as a constrained subset selection problem with structured sparsity regularizations.
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