On the Use of Variational Autoencoders for Nonlinear Modal Analysis

Linear modal analysis offers a vital and mostly complete framework for the dynamic analysis of simplified engineering systems, with important insights offered from the extraction of natural frequencies and mode shapes. The extracted mode shapes further serve as an invariant basis upon which to build reduced-order models (ROMs) of linear systems. When moving to nonlinear systems, however, the principles upon which modal analysis are based, no longer hold. This issue motivates the development of a framework for nonlinear modal analysis, which can maintain some of the key features of modal analysis. This work is based upon the concept of nonlinear normal modes (NNMs); these consist of invariant manifolds upon which motion for a given NNM is constrained. NNMs can also provide insight into engineering systems as well as offer a basis for construction of nonlinear ROMs.