Decomposing stress wave interference in a cylindrical wooden medium using an inverse deconvolution filter

Excitation of an embedded waveguide in the cross section plane of a cylindrical structure produces Rayleigh modes propagating primarily in circumferential regions of the propagating medium. In many applications, this region is critical to the overall strength of the structure. Using the through-transmission technique, the Rayleigh mode in cylindrical symmetry produces clockwise and counterclockwise trajectories that interfere with each other at the receiver, producing a composite energy response in the temporal domain that hinders the accurate mode characterization. This work presents a decomposition algorithm consisting of three processing steps: (1) analytical continuous wavelet transforms of the raw waveform; (2) frequency polynomial approximation of the inverse point spread function using L2 norm optimization; and (3) derivation of the inverse deconvolution filter via the dual derivative operator. This work demonstrates the mathematical formulation and algorithm implementation with numerical and empirical validations. The proposed decomposition filter can achieve the overall time and energy estimation accuracy with a relative root mean square error of 0.07. Its broader impact will enhance the parametric estimation of the diagnostic stress wave for material characterization.