Optimal Determination of Structural Dynamical Parameters Using Ambient Vibration

Abstract

By using ambient vibration, a new approach based on improvement and correction of system characteristic matrix in modal vibration is provided. The result is that actual system characteristic matrices are accurately made such that the error is minimized at great extent. This clearly shows how the system parameters can be updated in a more reliable way. Firstly, by approximation, the actual system characteristic matrices are determined using the singular value decomposition of block Hankel matrix that is built from response correlation matrix. Secondly, by black-box modeling approximation, the input-output relation of the system through Kalman theory is made in order to make the system characteristic matrices optimal definite. Furthermore, by expressing Hankel matrix’s multiplicities from Eigen solution of the system state matrix obtained in previous iteration, it is possible to determine both the covariance of non-measurable process noise and measurement noise matrixes which are present in the Riccati equation. This means that both measurement and process covariance noises’ matrixes are indirectly built only from measured out-put data. The repetition of iterations is done until the error is sufficiently minimized. And then system modal parameters are extracted from these obtained system characteristic matrices. This system is used for modal update of the system in which modal parameters are applied directly and iterative methods. The code supporting this algorithm can be interfaced with the codes of the finite elements.