Curti, Mitrofan

Daniels, Bram

Lomonova, Elena A.

Overboom, Timo

Zeinali, Reza

English

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 Constrained Spline-Based Everett Map for Static HysteresisModelingCitation for published version (APA):Daniels, B., Zeinali, R., Overboom, T., Curti, M., & Lomonova, E. A. (2023). Constrained Spline-Based EverettMap for Static Hysteresis Modeling. Poster session presented at 24th International Conference on theComputation of Electromagnetic Fields, COMPUMAG 2023, Kyoto, Japan.Document status and date:Published: 25/05/2023Document Version:Accepted manuscript including changes made at the peer-review stagePlease check the document version of this publication:• A submitted manuscript is the version of the article upon submission and before peer-review. There can beimportant differences between the submitted version and the official published version of record. Peopleinterested in the research are advised to contact the author for the final version of the publication, or visit theDOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and pagenumbers.Link to publicationGeneral rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.            • Users may download and print one copy of any publication from the public portal for the purpose of private study or research.            • You may not further distribute the material or use it for any profit-making activity or commercial gain            • You may freely distribute the URL identifying the publication in the public portal.If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, pleasefollow below link for the End User Agreement:www.tue.nl/taverneTake down policyIf you believe that this document breaches copyright please contact us at:openaccess@tue.nlproviding details and we will investigate your claim.Download date: 05. Oct. 2023The Everett map in this work is constructed from, easy tomeasure, concentric hysteresis loops, laid out on a plane.These data points are captured by a B-spline surface tobe applied in the Preisach model of hysteresis, in order toreconstruct hysteresis behavior with high precision, byHere, 𝜇 is the Preisach weight function, given by thesecond derivative of the Everett map, 𝜉, as followsAny inaccuracies in the data points are easily reflected inthe surface fit and the reconstructed hysteresis behavior,observed as the crossing of hysteresis branches.Therefore, constrains must be applied during fitting.AimThis work investigates the quality of hysteresis loops, reconstructed by the Preisach model and governed by a B-splinebased Everett map, that was fitted with constraints on measured concentric hysteresis loop data, to eliminate artifacts.SummaryMany electromechanical devices contain soft-magnetic materials with complex hysteresis behavior. This behavior is oftendescribed by the Preisach model and an Everett map. This map, fitted on measured hysteresis data points, must beconstructed properly, to enable interpolation of the data and ensure accurate and artifact-free modeled hysteresis loops.Problem statementResultsA benchmark input with nested minor loops, very differentfrom the concentric source data, is reconstructed by thetwo fitted maps, and compared with measurement data.The unconstrained loops contain noticeable artifacts,while the constrained loops manage to describe thecomplicated benchmark input properly, albeit at the costof deviating slightly from the measured reference data.Fitted B-spline surface and its optimal control grid.The second derivative of the surface, i.e. weight function; with constraints applied (left), and unconstrained fit with problematic negative values (right).The reconstructed benchmark hysteresis loops and reference measurement.Constrained Spline-Based Everett Map for Static Hysteresis ModelingBram Daniels1,*, Reza Zeinali1, Timo T. Overboom2, Mitrofan Curti1, Elena A. Lomonova11Eindhoven University of Technology, Eindhoven, The Netherlands; 2Royal SMIT Transformers (SGB-SMIT Group), Nijmegen, The NetherlandsPC-M2: 11Measured concentric hysteresis loops and the data points on the Everett map.𝑓 𝑡 = ඵ𝛼≥𝛽𝜇 𝛼, 𝛽 ො𝛾𝛼,𝛽𝑢 𝑡 𝑑𝛼𝑑𝛽 .𝜇 𝛼, 𝛽 = −𝜕2𝜉 𝛼, 𝛽𝜕𝛼𝜕𝛽.Applied constraintsThe constraints applied during fitting, to the B-splinebased Everett map as well as its second derivate, are• A strictly increasing/decreasing slope, e.g. Τ𝜕𝜉 𝜕𝛼 ≥ 0,• No negative values in the weight function, 𝜇 ≥ 0.Constrained B-spline surfaceThe fitting procedure yields an optimal control grid, thatapproximates the source data points with a closed-formB-spline surface, while adhering to the constraints.Conclusions• The unconstrained Everett map introduces noticeable artifacts in the modeled hysteresis branches,• Constraining the fit procedure is a necessary step to reliably eliminate any problematic negative values,• The constrained Everett map properly reproduces a benchmark input notably different from its source data.*b.daniels@tue.nl

Constrained Spline-Based Everett Map for Static Hysteresis Modeling

https://pure.tue.nl/ws/files/300729830/Compumag_poster.pdf

Constrained Spline-Based Everett Map for Static Hysteresis Modeling

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