Stageless evaluation for a vector Preisach model based on rotational operators

Abstract

Purpose This paper aims to present a novel stageless evaluation scheme for a vector Preisach model that exploits rotational operators for the description of vector hysteresis. It is meant to resolve the discretizational errors that arise during the application of the standard matrix-based implementation of Preisach-based models. Design/methodology/approach The newly developed evaluation uses a nested-list data structure. Together with an adapted form of the Everett function, it allows to represent both the additional rotational operator and the switching operator of the standard scalar Preisach model in a stageless fashion, i.e. without introducing discretization errors. Additionally, presented updating and simplification rules ensure the computational efficiency of the scheme. Findings A comparison between the stageless evaluation scheme and the commonly used matrix approach reveals not only an improvement in accuracy up to machine precision but, furthermore, a reduction of computational resources. Research limitations/implications The presented evaluation scheme is especially designed for a vector Preisach model, which is based on an additional rotational operator. A direct application to other vector Preisach models that do not rely on rotational operators is not intended. Nevertheless, the presented methodology allows an easy adaption to similar vector Preisach schemes that use modified setting rules for the rotational operator and/or the switching operator. Originality/value Prior to this contribution, the vector Preisach model based on rotational operators could only be evaluated using a matrix-based approach that works with discretized forms of rotational and switching operator. The presented evaluation scheme offers reduced computational cost at much higher accuracy. Therefore, it is of great interest for all users of the mentioned or similar vector Preisach models.

Computation of rotational hysteresis losses by vector Preisach models based on rotational operators

“…nÀ1 a;b ; h ! n as well as further details regarding the functionality and the efficient implementation of SVPc and SVPr can be found in studies by Sutor et al(2012Sutor et al( , 2015 and Nierla et al(2017Nierla et al( , 2019 and is not repeated at this point. It shall be remarked, though, that DU will go to zero if the material is driven into saturation, i.e.…”

“…In this context, ΔΦ 0 is a second model-specific parameter for SVPr that has to be retrieved from proper measurements. The actual definition of func(ΔΦ0,trueχ→α,βn−1,trueh→n) as well as further details regarding the functionality and the efficient implementation of SVPc and SVPr can be found in studies by Sutor et al (2012, 2015) and Nierla et al (2017, 2019) and is not repeated at this point. It shall be remarked, though, that ΔΦ will go to zero if the material is driven into saturation, i.e.…”

“…The common concept of both the classical variant (SVPc) and the revised variant (SVPr) is the inclusion of an additional rotational operator to the standard scalar Preisach model. Both variants of this novel vector Preisach model have been shown to offer an accurate and computationally cheap alternative to the Mayergoyz vector model when combined with an efficient Everett-based evaluation scheme (Nierla et al, 2017(Nierla et al, , 2019. So far, however, these models have not been applied to the prediction of rotational hysteresis losses.…”