10. Optimal Estimation Example the Dynamic Parameters from Ambient Vibration for Modal Identification

A novel approach of system characteristic matrix’s correction in modal identification from ambient vibration is presented. As a result of this approach, actual system characteristic matrices are determined more accurately with minimum error. It is reflected on to updating system parameters more reliable. In first approximation, actual system characteristic matrices determined by singular value decomposition of block Hankel matrix, which build from the response correlation matrix. In second approximation, to make the system characteristic matrices optimal definite, for black-box modeling the input–output relation of the system used Kalman theory. Covariance of the nonmeasurable process noise and measurement noise matrixes are contained in Riccati equation are determined by expressing Hankel matrix’s multiplicities from eigensolution of the system state matrix obtained in previous iteration. Another word process and measurement noises covariance matrixes indirectly is constructed only from measured output data. These iterations are repeated until satisfying estimated error. As a result of these iterations, actual system characteristic matrices are determined more accurately with minimum error. Then, from determined system characteristic, matrices are extracted system modal parameters. These system modal parameters are used for the system modal updating for which direct and iterative methods are applied. Supporting to this algorithm realized code maybe interfaced with finite element codes.