Development of wavelet deconvolution technique for impact force reconstruction: Application to reconstruction of impact force acting on a load-cell

Deconvolution technique has become a useful solution for indirect measurement of impact force, however, a simple deconvolution technique often encounters difficulty and leads to an unsatisfactory reconstruction due to unavoidable error and the ill-posed nature of the inverse problem. This paper is concerned with a deconvolution technique using wavelet approach for reconstructing impact force. Based on the ability of wavelet transform, impact force reconstruction was formulated and implemented through its expansion coefficients of different scaled and shifted versions of wavelets. The reconstruction of impact force thus becomes the reconstruction of its expansion coefficients which are then used to reproduce the profile of impact force. Considerations of appropriate scales and shifts of wavelets in reconstruction can be regarded as a kind of regularization in order to improve the ill-posed problem. The numerical verification on reconstruction of impact force acting on a load-cell during the impact buckling of thin-walled column showed that the present technique is indeed capable to mitigate the ill-posed nature when the scale level of wavelets is controlled properly. The result also revealed that with an appropriate choice of the shifting parameter at a certain scale level, the noise in reconstructed force has been suppressed further. As a consequence, it has been verified that the present wavelet deconvolution technique can successfully reconstruct the impact force with less noise and higher accuracy in comparison with the conventional methods.