基于高次广义柔度灵敏度的结构损伤识别

柔度矩阵可以由结构的低价模态近似计算获得，因此被广泛用于结构的模型修正和损伤识别中。由普通柔度派生而来的广义柔度，可以由低价模态数据更加精确的获得，且随着广义柔度次数的增高其精度越高，往往只需要第一或二阶模态数据即可获得很准确的高次广义柔度。因此，广义柔度灵敏度方法自提出以来受到广泛关注。本文详细研究了基于高次广义柔度灵敏度的损伤识别计算方法，研究中发现，利用广义柔度灵敏度进行损伤识别计算时，并非越高次的广义柔度其识别结果越准确，随着广义柔度次数的增加，损伤识别结果精度呈现出先提高但随后显著降低的趋势。究其原因在于，虽然随着广义柔度次数的增加，广义柔度本身的精度更高，但与之相应的灵敏度方程组系数矩阵的条件数却也显著增大了，即方程组的病态性反而更加严重了，这导致了基于高次广义柔度计算所得的损伤参数的精度反而不如低次广义柔度的情况。因此，本文的研究表明，工程中利用广义柔度进行模型修正或损伤识别时，一般采用一次广义柔度或二次广义柔度即可，且计算中为了克服方程组的病态性和数据噪声的不利影响，本文提出了一种反馈奇异值截断法，能够明显提高计算精度，获得较准确的识别结果。

Structural Damage Assessment Using the High-order Generalized Flexibility Sensitivity Method

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.