Abstract：The flexibility matrix can be obtained approximately by the first few modes of the structure, so it is widely used in structural model updating and damage identification. The generalized flexibility derived from the ordinary flexibility can be obtained more accurately from the low-frequency modal data. Generally, only the first- or second-order modal data are required to obtain the generalized flexibility matrices of high accuracy. Therefore, the generalized flexibility sensitivity method has attracted wide attention in the area of damage identification in recent years. In this paper, the damage identification method based on generalized flexibility sensitivity with different orders is studied in detail. It is found that the accuracy of damage assessment results does not increase with the increase in the order of generalized flexibility matrix. The reason may lie in that the condition number of the coefficient matrix of the generalized flexibility sensitivity equations increases significantly with the increase in the order of generalized flexibility matrix. This means that the higher is the order of generalized flexibility matrix, the more ill-conditioned are the equations, leading to distorted damage identification results. Thus the generalized flexibility sensitivity with the first or second order is recommended for structural model updating or damage identification in engineering practice. Moreover, a feedback singular-value truncation (FSVT) method is proposed in this paper in order to overcome the adverse effects of noisy data and ill-conditioned equations. The essence of the FSVT method is the feedback computation based on the initial result of singular-value truncation. Many undamaged elements are removed in accordance with the feedback evaluation to reduce the number of unknowns in the FSVT. This operation can significantly reduce the computational complexity and obtain more accurate damage evaluation results. The FSVT method is very concise in theory and is simple for implementation. A frame structure and a beam structure with variable cross-sections are used as the numerical examples to demonstrate the proposed method. The numerical results show that the proposed method is superior to the traditional singular-value truncation method in the accuracy of structural damage assessment.
2019, Vol. 40 
