Continuous-Time Covariance Approaches for Modal Analysis

Proper orthogonal decomposition (POD) can be used to obtain complete information about the linear normal modes of structural systems only when special conditions are met, principally related to the knowledge of mass distribution and to the absence of damping. The main advantage of POD is the possibility to directly use covariance matrices estimated from time responses for the modal identification of the structure under investigation. This paper proposes a method to extend this covariance-based identification to general cases where significant damping is present and when no data is available on mass distribution. A least-square based decomposition is used to infer information about modal characteristics of the system. This decomposition is applied to three different cases: the first one uses records related to the free response of the system, while the remaining two use records of the system under persistent white noise excitations. In those latter cases the information on the excitation input time history can either be used, or treated as unknown. Basic, yet complete examples are presented to illustrate the properties of the proposed technique.