A Regularization Approach of Dynamic Load Identification in Frequency Domain by Acceleration Responses
Load identification based on acceleration frequency response matrix is an ill-conditioned problem. 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 supported 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 improve 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.
Keywords: dynamic loads, frequency response function, inverse problem, regularization, normalization
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