基于加速度反演频域动载荷的一种正则化途径

A Regularization Approach of Dynamic Load Identification in Frequency Domain by Acceleration Responses

基于加速度频响函数矩阵反演频域动载荷是病态逆问题,反求的结果精度差,对数据的小扰动敏感,基于Tikhonov正则化方法,提出一种反演途径,将测点响应与待求激励进行归一化变换,在此基础上引入变换后的频响函数矩阵和正则化泛函进行求解,应用广义交叉验证准则选取最优正则化参数.考虑简支矩形薄板上的4个动载荷的识别问题,分析激励点和响应测点的不同位置以及动载荷大小之间相差程度不同的4个算例,将本文方法与不采用归一化变换的正则化求解结果进行2种相对误差的均方根比较.结果表明,利用归一化变换可提高动载荷反演精度,增强正则化方法的抗噪能力,当测点之间的响应以及各动载荷大小相差较大时,明显改善了识别精度.

Load identification based on acceleration frequency response matrix is an ill-conditioned prob- lem. The identification accuracy can obviously be affected by small perturbations of the response data. Based on Tikhonov regularization method, a new approach is proposed in which both the response data at measured points and the loads to be identified are normalized, the transformed frequency response matrix and regularization function are introduced, and the corresponding problem of functional minimum is solved to obtain the loads. The optimal regularization parameters are determined by generalized cross validation criterion. The identification of four transverse dynamic loads on a rectangular thin plate with simply sup- ported edges is performed. Four numerical examples are designed to have different application locations of loads and measured points as well as different magnitude ratio of dynamic loads in frequency domain. The results show that the new approach of dynamic load identification in frequency domain is effective to im- prove the identification accuracy and the noise resistance. Particularly, the errors of the identification can be significantly reduced in the cases where the large difference between the magnitudes of dynamic loads in frequency domain exists, or when excitation positions are close to structural boundaries.