Linear system identification using proper orthogonal decomposition

A least-square-based method to identify the system matrices of linear dynamical systems is proposed. The primary focus is on the identification of a reduced-order model of the system operating in the mid-frequency range of vibration. Proper orthogonal decomposition (POD) is used for the model reduction. Such reduced-order model circumvents the limitations of traditional modal analysis which, although well-adapted in the low-frequency range, is prone to computational and conceptual difficulties in the mid-frequency range. The inverse problem involving the identification of the mass, damping and stiffness matrices is posed in the framework of a linear least-square estimation problem. To achieve this objective, Kronecker algebra is aptly exploited for a concise mathematical formulation to identify these matrix-valued variables. Tikhonov regularisation is used to satisfy the symmetry property of the system matrices. The application of the proposed methodology is demonstrated using an example of multiple degree-of-freedom discrete linear dynamical system. The robustness of the new methodology is investigated using a noise sensitivity study.