基于不完备频响函数的结构损伤统计识别研究

基于不完备频响函数数据,结合概率统计方法,提出了一种能同时考虑模型参数不确定性和测试噪声影响的结构损伤统计识别方法。首先,基于频响函数某一行向量在不同频率下的幅值数据,利用矩阵拉直运算建立了关于损伤系数的确定性识别方程。其次,假设模型参数误差和测试噪声为零均值的高斯随机变量,根据摄动理论,推导了损伤后结构刚度参数的前二阶矩。随后,利用结构损伤前后的概率分布得到了结构损伤存在概率。最后,通过一个平面桁架结构模型验证了本文方法的有效性。数值算例的研究结果表明,损伤单元的损伤存在概率远大于非损伤单元;测试噪声对识别结果的影响比模型参数不确定性的影响更为显著。

Statistical damage identification of structures using incomplete FRF data

The motivation of this paper is to develop a statistical structural damage identification method in which only a few of frequency response function(FRF) data are utilized. This method can simultaneously consider the uncertainty of model parameters and the influence of test noise. Firstly, based on the amplitude data of a certain row vector of the FRF at different frequencies,a deterministic damage detection equation for the damage coefficient is presented by using the matrix straightening operation. Secondly, assuming that the error of model parameter and test noise are zero mean Gaussian random variables, the first two moments of the damaged structural stiffness parameters are derived based on the perturbation theory. Then, the structural probability of damage existence is obtained by using the probability distribution before and after damage. Finally, the effectiveness of the proposed method is verified by a planar truss structure model. The results of numerical examples show that the damage probability of damaged elements is much larger than intact elements and test noise has greater influence on recognition results than the uncertainty of model parameters.