An Optimal Sensitivity-Enhancing Feedback Control Approach via Eigenstructure Assignment for Structural Damage Identification

The concept of using sensitivity-enhancing feedback control to improve the performance of frequency-shift-based structural damage identification has been recently explored. In previous studies, however, the feedback controller is designed to alter only the closed-loop eigenvalues, and the effect of closed-loop eigenvectors on the sensitivity enhancement performance has not been considered. In this research, it is shown that the sensitivity of the natural frequency shift to the damage in a multi-degree-of-freedom structure can be significantly influenced by the placement of both the eigenvalues and the eigenvectors. A constrained optimization problem is formulated to find the optimal assignment of both the closed-loop eigenvalues and eigenvectors, and then an optimal sensitivity-enhancing control is designed to achieve the desired closed-loop eigenstructure. Another advantage of this scheme is that the dataset of frequency measurement for damage identification can be enlarged by utilizing a series of closed-loop controls, which can be realized by activating different combinations of actuators in the system. Therefore, by using this proposed idea of multiple sensitivity-enhancing feedback controls, we can simultaneously address the two major limitations of frequency-shift-based damage identification: the low sensitivity of frequency shift to damage effects and the deficiency of frequency measurement data. A series of case studies are performed. It is demonstrated that the sensitivity of natural frequency shift to stiffness reduction can be significantly enhanced by using the designed sensitivity-enhancing feedback control, where the optimal placement of closed-loop eigenvectors plays a very important role. It is further verified that such sensitivity enhancement can directly benefit the damage identification accuracy and robustness.