Premium
Wavelet‐based dynamic mode decomposition
Author(s) -
Krishnan Manu,
Gugercin Serkan,
Tarazaga Pablo
Publication year - 2021
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.202000355
Subject(s) - dynamic mode decomposition , wavelet , dynamical systems theory , operator (biology) , forcing (mathematics) , dynamical system (definition) , computer science , algorithm , finite element method , modal , modal analysis , mode (computer interface) , function (biology) , mathematics , decomposition , relation (database) , simple (philosophy) , mathematical analysis , physics , artificial intelligence , data mining , philosophy , repressor , ecology , chemistry , biology , operating system , biochemistry , epistemology , quantum mechanics , machine learning , evolutionary biology , transcription factor , thermodynamics , polymer chemistry , gene
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.