Characteristic value decomposition: A unifying paradigm for data-driven modal analysis

Abstract

Data-driven modal analysis is an indispensable means to understand the dynamic behavior of engineered structures and natural systems. It effectively captures active dynamic behavior and embeds them in a set of identified linear modal subspaces, unveiling complex dynamic behavior via the superposition of simpler hierarchical spatiotemporal dynamics. Despite the existence of many methods, there is no unified perspective connecting these modal analysis techniques. This paper proposes a new modal decomposition method, the characteristic value decomposition (CVD), that provides a unifying paradigm for data-driven modal analysis. CVD identifies identical spatial modes and temporal coordinates from two measurement data matrices. The modal parameters are identified through an eigendecomposition to a quotient of auto-covariance and cross-covariance matrices of the two data matrices. This paper shows that several data-driven modal analysis methods, namely, the state-variable decomposition, the dynamic mode decomposition, the Ibrahim time domain method, and the eigensystem realization algorithm, are special cases of CVD when the two data matrices are appropriately selected. Moreover, the CVD identifies the modal parameters with higher accuracy and is robust to added noise compared to established methods, as demonstrated using numerical experiments. It is also shown that the CVD flexibly utilizes data from multiple experiments and undersampled data sets to unveil system dynamics.