Wavelet‐based dynamic mode decomposition

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.

A Novel Study on a Generalized Model Based on Self-Supervised Learning and Sparse Filtering for Intelligent Bearing Fault Diagnosis

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