基于正则化与范数归一化的概率损伤识别方法

Probabilistic Damage Identification Method Based on Regularization and Norm Normalization

提出基于正则化与范数归一化的概率损伤识别方法(Regularization and Norm Normalization Based Probabilistic Damage Identification Method,RNbPDI),对不适定性和不确定性条件下的结构损伤识别误差进行量化。以结构损伤前后的模态信息差为目标函数,引入正则化方法,建立结构损伤参数求解的目标函数。考虑到不同模态参数对损伤参数的灵敏度数值范围的差异,将不同模态参数的灵敏度矩阵和残差矩阵分别进行范数归一化处理,以提高损伤识别问题求解的数值稳定性。利用概率方法来量化损伤识别结果的不确定性,给出损伤参数的识别结果的名义值和方差求解公式。通过数值算例分析不同损伤工况、不同传感器测点方案、不同的测试噪声水平对损伤识别结果的影响,通过数值算例和一个四层剪切框架实验表明该方法具有识别精度高、鲁棒性强的特点。

A probabilistic damage identification method based on regularization and norm normalization was proposed to quantify the structural damage identification errors under ill-posed and uncertain conditions.The difference of modal information before and after structural damage was used as the objective function,and the regularization method was introduced to establish the objective function for the solution of structural damage parameters.Considering the difference in the numerical range of sensitivity of different modal parameters to the damage parameters,the sensitivity matrix and residue matrix of different modal parameters were normalized separately to improve the numerical stability of the solution of the damage identification problem.The probabilistic method was used to quantify the uncertainty of the damage identification results,and the nominal value and variance solution formulas for the identification results of the damage parameters were given.The effects of different damage conditions,different sensor measurement point schemes,and different test noise levels on the damage recognition results were analyzed by numerical examples.The numerical examples and a four-layer shear frame experiment show that the proposed method has the characteristics of high recognition accuracy and robustness.