基于偏最小二乘线性求解的结构损伤识别

Structural damage identification based on partial least squares linear solving

基于模态参数化线性求解结构损伤的识别方法在工程中具有较为广泛的应用。然而,在噪声的干扰下,当结构可测量的模态阶数较少时,利用该方法求解的结果会出现大量的虚假损伤,严重扰乱真实的损伤信息。针对此问题,引入了一种基于偏最小二乘多线性回归建模的方法来对损伤识别结果进行降噪处理。通过对损伤结构的频率和振型信息添加一定水平的噪声干扰,分析确定结构单元的损伤参数,并利用偏最小二乘法重构线性方程组。同时,选择识别结果较为稀疏的解作为标准样本点,利用奇异值分解法回代求解结构的损伤参数。以桁架模型为例的数值模拟结果表明,在噪声干扰下,该方法与传统最小二乘法和奇异值分解法相比,不仅损伤识别结果准确,而且能够最大程度抑制虚假损伤的产生。

The identification method of structural damage based on modal parametric linear solution is widely used in engineering.However,when the measurable modal order of the structure is small,a large number of false damage will appear in the results of this method under the interference of noise.It severely confuses the true information of damage.For this problem,this paper introduces a method based on partial least squares(PLS)multiple linear regression modeling and it can reduce the noise of structural damage identification results.To determine the damage parameters of structural elements,a certain level of noise interference has been added to the frequency and vibration mode information of the damaged structure.The linear equations have been reconstructed by PLS.Meanwhile,the solution with sparse identification results is selected as the standard sample point.The singular value decomposition method is used to solve the damage parameters of the structure.The numerical simulation results of the truss model show that the proposed method has better performance than the traditional least square method and singular value decomposition method.It can not only identify the results accurately,but also can restrain the generation of false damage to the maximum extent.