Higher-Order Decompositions for Modal Identification and Model Order Reduction

Abstract

Output only modal analysis is an essential tool for monitoring operations of complex large structures like offshore platforms or studying complex flow dynamics. Here we consider a higher-order singular value and non-Hermitian matrix decompositions and describe how they can be used in linear modal analysis to enhance the currently available output only modal analysis methods such as dynamic mode decomposition or eigenvalue realization algorithm. In addition, we show how these methodologies can be used for empirical nonlinear modal identification to obtain the slow flow dynamics of nonlinear dynamical systems. Finally, we show how this information can be used to obtain high-fidelity robust reduced-order models of nonlinear systems.