基于多项式拟合均匀荷载面曲率曲线的结构损伤识别方法

Structural damage identification method based on polynomial fitting of uniform load surface curvature curve

为仅利用结构损伤状态的柔度矩阵对结构进行损伤程度识别,先对损伤状态的均匀荷载面曲率曲线进行最小二乘法拟合。根据曲率曲线差判断结构的损伤位置,对损伤位置的点进行剔除后,再利用未损伤位置上的点进行局部最小二乘法拟合,代替损伤前的均匀荷载面曲率曲线,用于结构的损伤定位与定量。通过一简支梁数值算例,先以理论的二次多项式进行拟合,考虑单损伤和多损伤的情况,进行损伤识别分析,再分析多项式次数、测点数目以及不同噪声水平对损伤定量精度的影响。结果表明:在一定范围内,次数越高拟合误差越小,但差别不明显,采用理论的二次多项式拟合即可满足结构损伤识别要求,无噪声的情况下,测点数目减半不影响损伤识别的精度,该方法具有一定的抗噪声能力。

In order to identify the damage degree of structure by just using the structural flexibility state, starting from this point, the least square method was used to fit the curvature curve of the face （ULS） in damage matrix of damage uniform load sur- state~ According to the difference of curvature curve to judge the structural damage location, after removing the point of the damaged damage damage position, the local least square method was used to fit the position to replace the curvature of the ULS before damage ~ The fitting curve was used localization and quantification. Through a numerical example of a retical quadratic polynomial was used to fit the ULS curvature curve, the sidering single damage point of the un- for the structural simply supported beam, firstly, the theo- damage identification was analyzed, con- and multi-damage. Then the influence of the degree of polynomial, the number of measuring points, different noise levels on the quantitative precision of damage degree were analyzed. It can be seen that： within a certain range, the higher the degree of polynomial, the smaller the fitting error is, but the difference is not obvious, and the theoretical quadratic polynomial fitting can meet the requirement of structural damage identification. In the case without noise, the number of measuring points halved does not affect the accuracy of damage identification, and the method has a certain anti-noise ability.