Deconvolution filter for parameter estimation of composite stress wave propagating in the wooden cylindrical structure

Abstract

Through-transmission using the embedded waveguide technique in the cross-section plane of cylindrical structure produces radial and Rayleigh modes. These two modes propagate in the heart and shell regions of the plane, allowing a comprehensive characterization of the material. The significant spatial difference generates a distinct temporal separation between the two modes for large cylindrical structures, allowing direct mode characterization. For cylindrical structures with smaller diameters, the pronounced multi-path interference produces an erroneous energy response that hinders the accurate mode characterization. In this so-called multiple-input-single-output (MISO) system, the arrival time and amplitude estimations are an underdetermined problem. This work presents a novel decomposition filter design consisting of three steps. (1) Gabor’s wavelet transforms the stress wave signal in the time-frequency domain; (2) The approximation of the inverse point-spread-function (PSF) response via a series of frequency polynomials generates a set of optimal coefficients; (3) Derive the inverse deconvolution kernel via the dual derivative operator from the obtained optimal coefficients in step 2. This presentation will demonstrate the algorithmic formulation with numerical and empirical validations. Its broader impact will enhance the parametric estimation of the diagnostic stress wave for material characterization.