Damage identification using the information of natural frequency shift (before and after damage occurrence) has been studied extensively. For a closed-loop system, the sensitivity of natural frequency shift to structural parameter variation is related to both the closed-loop eigenvalues and eigenvectors. With multiple control inputs/actuators, one may have the freedom of assigning closed-loop eigenvalues as well as eigenvectors by using singular value decomposition (SVD) based eigenstructure assignment technique. In this research, we formulate an algorithm to optimally assign the eigenvalues and eigenvectors that yield enhanced closed-loop natural frequency sensitivity, which leads to improved damage detection performance. Meanwhile, by activating different combinations of the multiple actuators in such system, we may develop a series of closed-loop controls for the same monitored structure for sensitivity enhancement. These multiple closed-loop controls utilizing the same set of hardware will result in a much enlarged dataset of frequency-shift information for damage identification. This proposed methodology can simultaneously solve the two main issues in frequency shift based damage identification: low sensitivity and deficiency of measurement data. Numerical studies on a benchmark beam structure demonstrate that the sensitivity of natural frequency changes to small stiffness reduction due to damage can be significantly enhanced, whereas the optimal assignment of eigenvectors plays a very important role. The effect of measurement noise on the performance of the proposed damage detection method is evaluated. Our analyses show that, by using this proposed approach, the location and severity of the structural damage can be successfully identified with much improved performance even in the presence of significant measurement noise.
The objective of this paper is to advance the state-of-art of frequency-shift-based damage identification method using tunable piezoelectric transducer circuitry. More specifically, we aim at improving the current methodology  by developing a more accurate and efficient approach. The basic principle of this new approach is to include the high order terms in the eigensolution perturbation formulation, and use an iterative procedure in conjunction with a constrained optimization scheme. In addition, guidelines on how to tune the inductance in the circuit to best capture the damage features are proposed based on a detailed analysis of eigenvalue loci veering and variation of eigenvalue changes with respect to the changing inductance. Results show that more information of the structural damage features can be included in the vector of eigenvalue changes and sensitivity matrices if we tune the inductance inside the eigenvalue veering ranges. Numerical results on identifying single and multiple damages in a cantilever beam example are provided to demonstrate the accuracy of the improved method for structural damage identification.