The change of modal characteristics directly provides an indication of structural damage. Based on changes in frequencies and mode shapes of vibration, a damage identification technique is proposed in this paper for predicting damage location and severity. The method is applied at an element level with a conventional finite-element model. The element damage equations have been established through the eigenvalue equations that characterize the dynamic behavior. Several solution techniques are discussed and compared. The influence of simulated noise in the modal data is also presented. The method has been verified by a number of damage scenarios for simulated beams and has found the exact location and severity of damage. It is demonstrated that multiplying the damaged eigenvalue equations with the undamaged or damaged mode shapes provides more equations and guarantees the damage localization. The resulting equations, however, become more sensitive to the deviation of modal data and the direct solution often yields poor results. Numerical results show that the non-negative least-squares method can lead to satisfactory results in most cases. A regularization algorithm with error-based truncation is necessary to ensure the right solutions.
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