Wavelet‐based dynamic mode decomposition. (10th March 2021)

• Record Type: Journal Article
• Authors: Krishnan, Manu; Gugercin, Serkan; Tarazaga, Pablo
• Other Names: Gräßle C. guestEditor.; Mlinarić P. guestEditor.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 20(2020)Supplement 1
• Page Start: n/a
• Page End: n/a
• Publication Date: 2021-03-10
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.202000355
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: Dynamic mode decomposition (DMD) has emerged as a leading data‐driven technique to identify the spatio‐temporal coherent structure in dynamical systems, owing to its strong relation with the Koopman operator. For dynamical systems with external forcing, the identified model should not only be suitable for a specific forcing function but should generally approximate the input‐output behavior of the data source. In this work, we propose a novel methodology, called the wavelet‐based DMD (WDMD), that integrates wavelet decompositions with ioDMD to approximate dynamical systems from partial measurement data. The method is validated using a numerical and experimental case study involving modal analysis on a simple finite element model and free‐free beam respectively.