Sparse SVD Method for High-Resolution Extraction of the Dispersion Curves of Ultrasonic Guided Waves

Abstract

The 2-D Fourier transform analysis of multichannel signals is a straightforward method to extract the dispersion curves of guided modes. Basically, the time signals recorded at several positions along the waveguide are converted to the wavenumber-frequency space, so that the dispersion curves (i.e., the frequency-dependent wavenumbers) of the guided modes can be extracted by detecting peaks of energy trajectories. In order to improve the dispersion curve extraction of low-amplitude modes propagating in a cortical bone, a multiemitter and multireceiver transducer array has been developed together with an effective singular vector decomposition (SVD)-based signal processing method. However, in practice, the limited number of positions where these signals are recorded results in a much lower resolution in the wavenumber axis than in the frequency axis. This prevents a clear identification of overlapping dispersion curves. In this paper, a sparse SVD (S-SVD) method, which combines the signal-to-noise ratio improvement of the SVD-based approach with the high wavenumber resolution advantage of the sparse optimization, is presented to overcome the above-mentioned limitation. Different penalty constraints, i.e., l -norm, Frobenius norm, and revised Cauchy norm, are compared with the sparse characteristics. The regularization parameters are investigated with respect to the convergence property and wavenumber resolution. The proposed S-SVD method is investigated using synthetic wideband signals and experimental data obtained from a bone-mimicking phantom and from an ex-vivo human radius. The analysis of the results suggests that the S-SVD method has the potential to significantly enhance the wavenumber resolution and to improve the extraction of the dispersion curves.

Rapid High-Resolution Wavenumber Extraction from Ultrasonic Guided Waves Using Adaptive Array Signal Processing

“…We used two test specimens: (1) a 4-mm-thick copper plate (with a shear wave velocity of 2260 m/s and a longitudinal wave velocity of 4650 m/s) and (2) a 4-mm-thick transversely isotropic bone-mimicking plate (Sawbones, Vashon, WA, USA). The elastic parameters of the bone-mimicking plate have been determined in previous studies [20,21]. The density, shear wave velocity, longitudinal wave velocity along fibers, and longitudinal wave velocity orthogonal to the fibers are 1.64 g·cm −3 , 1620 m/s, 3570 m/s, and 2910 m/s, respectively [20,21].…”

“…The elastic parameters of the bone-mimicking plate have been determined in previous studies [20,21]. The density, shear wave velocity, longitudinal wave velocity along fibers, and longitudinal wave velocity orthogonal to the fibers are 1.64 g·cm −3 , 1620 m/s, 3570 m/s, and 2910 m/s, respectively [20,21]. We put the probe parallel to the fibers.…”

“…However, the measurement resolution is determined by the aperture size, and it is necessary to estimate the number of propagation modes in the received signal. Xu et al proposed the sparse SVD (S-SVD) method, which combines the Radon transform method proposed by Tran et al with the SVD method [21]. The resulting method acquires super-resolution estimates using a combination of SVD and an iterative process.…”

A Sparse Signal Reconstruction Method Based on Improved Double Chains Quantum Genetic Algorithm

“…Get the inner products of the residuals signal and the atoms, namely obtain the fitness value of each chromosome according to Equation (4). Record the current optimal solution and the corresponding optimal chromosome ∼ p .…”

Accurate Sparse Recovery of Rayleigh Wave Characteristics Using Fast Analysis of Wave Speed (FAWS) Algorithm for Soft Soil Layers

“…Thus, in order to reduce the redundant geophones used in conventional measurements, this paper contributes to this objective by exploring a novel in-site technique based on compressive sensing (CS) to reduce the number of required geophone and measurements for the estimation of surface wave velocity of the subsoil. CS has been applied to recover the multimodal and dispersive properties of Lamb wave from observed data in the laboratory for analysis, reconstruction, and prediction of guided waves [14][15][16][17][18][19][20]. Jiang et al applied CS to ultrasonic computerized tomography to reduce observation times for estimation of a steel tube slab structure [21,22].…”