IMPACT FORCE RECONSTRUCTION USING WAVELET DECONVOLUTION TECHNIQUE

Abstract

Reconstruction or deconvolution of impact force history from corresponding impact responses such as strain, acceleration, and displacement has been considered as a useful indirect method for measuring the impact force. However, due to the ill-posed nature of deconvolution problem, impact force is often inaccurately and unstably reconstructed. This paper introduces and applies the deconvolution technique using wavelets as a robust method for reconstructing impact force with the advantageous properties of wavelets. First, an analytical process of impact force reconstruction by using the wavelet technique in terms of scaling and translating the Haar wavelet is formulated. The unknown impact force is represented by the expanded coefficients at different scales and shifts of Haar wavelet which is compactly supported in the time domain (finite in time). Then, based on the governing equation of impact force deconvolution, the reconstruction process of these expanded coefficients is formulated. Second, a structural model is built by finite element method to obtain impulse response function numerically. After that, the wavelet technique is applied to reconstruct the impact forces acting on the structure to verify its effectiveness. The comparisons between reconstructed forces and finite element analysis results demonstrate the success of the present technique in accurately reconstructing the numerical impact forces acting on the thin-walled column. These achievements show remarkable ability of the wavelet technique for reconstructing accurately any input forces.