State-space Modeling of Large Domain Wave Propagation Systems by Partitioned C-matrices

Reduced-order models represent an enabling technology in the representation of large-scale dynamic systems. This technology often involves identification of linear state-space models with system matrix A, input matrix B, and output matrix C. Our focus is partitioned C-matrices that facilitate creation of reduced-order discrete-time state-space models appropriate for simulation of large-output wave propagation systems. The Cy-partition method, used to generate the partitioned C-matrices, is suitable when the output dimension is orders of magnitude higher than the number of discrete time samples specifying the time duration of interest. The resulting state-space model is characterized by a relatively small C-matrix component relating a small number of “anchored” or basis outputs to the inputs, and a large C-matrix component relating all remaining outputs to the anchored outputs. The partitioned C-matrix and the associated A, B matrices can be identified from input-output data directly using time-domain signals, without the necessity of identifying or computing transfer functions. The resulting models can be used for accurate and rapid prediction of wave-field responses. The theory is general for modeling short-duration dynamics and the applications include modeling of vibrations propagating through a large flexible structure (for damage assessment for example).