Besselink, Bart

Fey, Rob H.B.

Poort, Luuk

van de Wouw, Nathan

English

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 Abstracted Structure-Preserving Reduction of InterconnectedStructural ModelsCitation for published version (APA):Poort, L., Fey, R. H. B., Besselink, B., & van de Wouw, N. (2022). Abstracted Structure-Preserving Reduction ofInterconnected Structural Models. Abstract from 8th European Congress on Computational Methods in AppliedSciences and Engineering, ECCOMAS 2022, Oslo, Norway.Document status and date:Published: 01/01/2022Document Version:Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers)Please 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: 16. Nov. 2023The 8th European Congress on Computational Methods in Applied Sciences and EngineeringECCOMAS Congress 20225-9 June 2022, Oslo, NorwayABSTRACTED STRUCTURE-PRESERVING REDUCTIONOF INTERCONNECTED STRUCTURAL MODELSLuuk Poort1 ∗, Rob H.B. Fey1, Bart Besselink2, Nathan van de Wouw11 Eindhoven University of Technology, Mechanical EngineeringPO Box 513, 5600 MB Eindhoven, The Netherlandsl.poort@tue.nl, r.h.b.fey@tue.nl and n.v.d.wouw@tue.nl2 University of Groningen, Bernoulli Institute for Math., Computer Science and AIPO Box 407, 9700 AK Groningen, the Netherlandsb.besselink@rug.nlKeywords: Model Order Reduction, Structure-Preserving, Balancing, Coupled ProblemsThe large order of structural, finite element models necessitates the use of model reductiontechniques to allow for dynamic analysis. These models, represented by the system oflinear differential equationsΣ, often consist of an interconnection of substructuresΣj, j =1, . . . , k. In practice, model reduction is often performed on individual substructuresΣj, by, e.g., component mode synthesis methods, because direct reduction of Σ is notcomputationally tractable. However, if the reduction of a substructure Σj to its reducedrepresentation Σ̂j does not take the dynamics of the other substructures into account, theaccuracy of the interconnected, reduced-order model, Σ̂, cannot be guaranteed.In this presentation, we introduce the idea to improve the accuracy of Σ̂ by reducingΣj in interconnection with a low-order approximation of the other substructures. Stateddifferently, instead of considering (and reducing) Σj in isolation, we consider the inter-connection of Σj with an abstraction of its environment. Hereby, a reduction of Σj thattakes this abstraction into account ensures that the reduced Σ̂j is relevant in the scopeof the overall structure.Reduction of the interconnection of Σj and the corresponding abstraction using standardreduction methods, would destroy the interconnection structure and results in one unified,reduced model. Therefore, structure-preserving reduction methods, such as presented in[1], are employed to retain the interconnection structure and thus retain access to thereduced subsystems Σ̂j.Initial results show that this method of abstracted reduction results in an error which iscomparable to a more costly structure-preserving reduction of the complete model Σ [1].This indicates that low-order abstractions are sufficient to capture the relation betweenΣj and Σ, while significantly improving computational tractability of the reduction.REFERENCES[1] H. Sandberg and R. M. Murray, “Model reduction of interconnected linear systems,”Optimal Control Applications and Methods, vol. 30, no. 3, pp. 225–245, May 2009.

Abstracted Structure-Preserving Reduction of Interconnected Structural Models

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Abstracted Structure-Preserving Reduction of Interconnected Structural Models

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