High-Dimensional Data Analytics for Sparse Recovery of Guided-Waves Dispersion Curves Using B-Splines

Abstract

This research presents a technique to recover the dispersion curves of guidedwaves by utilizing the inherent sparsity of these signals in the frequency-wavenumber domain. The proposed methodology is a data-driven approach that combines physicsbased knowledge with high-dimensional analysis to obtain the dispersion curves of the medium from experimental signals. Initially, a sparse two-dimensional dispersion matrix is constructed using sparse wavenumber analysis. Then, B-splines are fitted to non-zero elements of this matrix to establish an initial estimate of the dispersion curve parameters. These parameters are further optimized using the quasi-Newton algorithm to improve the accuracy of signal prediction. The results demonstrate that this method can significantly reduce the dimensions of Lamb waves signals to approximately 0.05%, which avoids overfitting. The retrieved signals in the frequency-distance domain exhibit a correlation of approximately 50% with the original signals. In comparison with sparse wavenumber analysis, this technique requires two orders of magnitude fewer parameters to represent the medium's dispersion curves.