Moving Force Identification based on Wavelet Finite Element Method

The traditional finite element method (TFEM) of analysis requires a large number of elements to have a detailed description of the structure. Other semi-analytical method with additional degree-of-freedoms (DOFs) within an element overcomes this problem, but any revision in the model needs a reformulation of the finite element model for computation. The wavelet finite element method (WFEM) has the advantage of multi-resolution analysis whereby both coarse and detailed descriptions of the structure can be obtained. This paper presents the WFEM based on B-spline wavelet on the interval (BSWI). The shape function is formed by scale function of BSWI and a transformation matrix is constructed between the wavelet and the physical spaces. All the physical parameters in the system are expressed in terms of the transformation matrix and scale function of BSWI. The multi-resolution property of the WFEM is demonstrated with the inverse analysis of moving force identification using several distributed measured dynamic responses. The dynamic programming technique and Tikhonov regularization are used for the identification. Numerical results show that the WFEM has similar accuracy as the TFEM under the same conditions but with fewer finite elements, while the first-order Tikhonov regularization is found capable to remove most of the effect of measurement noise.