In the field of impact engineering, one of the most concerned issues is how to exactly know the history of impact force which often difficult or impossible to be measured directly. In reality, information of impact force apply to structure can be identified by means of indirect method from using information of corresponding output responses measured on structure. Namely, by using the output responses (caused by the unknown impact force) such as acceleration, displacement, or strain, etc. in cooperation with the impulse response function, the profile of unknown impact force can be rebuilt. A such indirect method is well known as impact force reconstruction or impact force deconvolution technique. Unfortunately, a simple deconvolution technique for reconstructing impact force has often encountered difficulty due to the ill-posed nature of inversion. Deconvolution technique thus often results in unexpected reconstruction of impact force with the influences of unavoidable errors which is often magnified to a large value in reconstructed result. This large magnification of errors dominates profile of desired impact force. Although there have been some regularization methods in order to improve this ill-posed problem so far, most of these regularizations are considered in the whole-time domain, and this may make the reconstruction inefficient and inaccurate because impact force is normally limited to some portions of impact duration. This work is concerned with the development of deconvolution technique using wavelets transform. Based on the advantages of wavelets (i.e., localized in time and the possibility to be analyzed at different scales and shifts), the mutual reconstruction process is proposed and formulated by considering different scales of wavelets. The experiment is conducted to verify the proposed technique. Results demonstrated the robustness of the present technique when reconstructing impact force with more stability and higher accuracy.
Wavelet deconvolution technique for impact force reconstruction: mutual deconvolution approach