Compressive-sensing based damped multi-mode extraction with nonuniform spatial sampling

Abstract

Multi-mode extraction is an important technique providing essential information for waveguide model validation and waveguide condition assessment. In this paper, an extraction method for damped multi-modes is proposed using randomly distributed nonuniform spatial samples. It addresses the problems of the conventional measurement method using uniform sampling, such as high sampling rate and large sample numbers. The proposed method is based on enhanced matrix completion (EMaC) which constructs a Hankel matrix by spatial signal. Using the measured nonuniform spatial samples, EMaC uses nuclear norm compressive sensing (CS) to reconstruct all entries of the Hankel matrix, from which the spatial signal is recovered and modes with their wavenumbers and attenuations are extracted. The bounds in terms of minimum sample numbers, spectrum separation and reconstruction error are analyzed by theory and quantified by simulations. Using the simulated data of a thin Titanium plate waveguide and the experimental data of a water-filled steel pipeline, the proposed method is shown to extract damped multi-modes using just 25% of the whole uniform samples set. The accuracy of wavenumber and attenuation estimates of the proposed method are found to be similar to the conventional method using uniform samples.