High-resolution Lamb waves dispersion curves estimation and elastic property inversion

Complex sparse Bayesian learning for guided wave dispersion curve estimation in plate-like structures

This paper proposes a new dispersion curve estimation method that employs the complex sparse Bayesian learning (CSBL). It is well accepted that guided wave packets are distorted because of the differences in propagation velocities at different frequencies; thus, the preceding velocity-frequency curve estimation is beneficial for wave packet recovery, feature recognition and defect localization. Conventional dispersion curve estimation methods, such as two-dimensional Fourier transform and multiple signal classification, are suitable for array signal and are restricted by the transducer aperture, leading to a small application scope. According to the frequency-response model of the guided wave, for each frequency, the responses obtained by the transducers can be sparsely represented based on an overcomplete dictionary matrix constructed using multiple discretized wavenumbers and known distances. A CSBL algorithm was developed to infer the posterior probability density function of the weight vector in the sparse representation. The non-zero elements in the sparse weight vector mean that the corresponding dictionary atoms indicated wavenumbers are contained in the frequency response, and the velocity-frequency curve can be finally derived from the wavenumber-frequency curve. The proposed CSBL method has a satisfactory capability to solve this sparse representation of the complex frequency response because a hierarchical form of the Laplace prior is employed to achieve a high degree of sparsity of the weight vector. This method effectively incorporates the real and imaginary parts of the complex frequency response by employing the same hyperparameter to integrate the known information. This method requires only a few randomly placed transducers; thus, it has a wide range of applications. The effectiveness of the proposed approach was validated using multiple guided-wave signals obtained through numerical simulations and an experimental study on a plate structure.

Stiffness tensor estimation of anisotropic crystal using point contact method and unscented Kalman filter

The potential application of Lithium Niobate (LiNbO₃) crystal is immense, specifically in the domain of meta-surfaces and nano-resonators. However, the practical application of LiNbO₃ is impeded due to unreliable experimental techniques and inaccurate inversion algorithms for material characterization. In the current research, material characterization of anisotropic crystal is proposed by exploring the wavefield evolution in the spatial and temporal domains. The presented framework has three major components: a physics-based mathematical model (Christoffel equation), a novel experimental technique, and an inversion algorithm based on Bayesian filtering. An experimental technique based on Coulomb coupling is devised to visualize the propagation of ultrasonic waves in an anisotropic crystal. The crystal is characterized by measuring the directional-dependent acoustic wave velocity from the spatial-temporal information of the wave propagation. The anisotropic constitutive properties of the crystal are estimated by exploring the wave velocity in the Bayesian filtering algorithm. The proposed algorithm is based on the probabilistic framework that integrates the experimental measurement in a physics-based mathematical model for optimal state prediction of stiffness tensor through the Bayesian filtering algorithm. In particular, we utilize the unscented Kalman filter (UKF) in conjunction with the plane-wave Eigen solution to estimate the constitutive parameters. In the presence of measurement uncertainties, the performance of the optimal prediction algorithm is illustrated by comparing the estimated parameter with the corresponding theoretical value. The comparison demonstrates that the proposed inversion algorithm is efficient and robust and performs satisfactorily even with significant measurement uncertainties.

Emotional State Classification from MUSIC-Based Features of Multichannel EEG Signals

Electroencephalogram (EEG)-based emotion recognition is a computationally challenging issue in the field of medical data science that has interesting applications in cognitive state disclosure. Generally, EEG signals are classified from frequency-based features that are often extracted using non-parametric models such as Welch's power spectral density (PSD). These non-parametric methods are not computationally sound due to having complexity and extended run time. The main purpose of this work is to apply the multiple signal classification (MUSIC) model, a parametric-based frequency-spectrum-estimation technique to extract features from multichannel EEG signals for emotional state classification from the SEED dataset. The main challenge of using MUSIC in EEG feature extraction is to tune its parameters for getting the discriminative features from different classes, which is a significant contribution of this work. Another contribution is to show some flaws of this dataset for the first time that contributed to achieving high classification accuracy in previous research works. This work used MUSIC features to classify three emotional states and achieve 97% accuracy on average using an artificial neural network. The proposed MUSIC model optimizes a 95-96% run time compared with the conventional classical non-parametric technique (Welch's PSD) for feature extraction.

Bi-Directional Axial Transmission measurements applied in a clinical environment

Accurate measurement of cortical bone parameters may improve fracture risk assessment and help clinicians on the best treatment strategy. Patients at risk of fracture are currently detected using the current X-Ray gold standard DXA (Dual XRay Absorptiometry). Different alternatives, such as 3D X-Rays, Magnetic Resonance Imaging or Quantitative Ultrasound (QUS) devices, have been proposed, the latter having advantages of being portable and sensitive to mechanical and geometrical properties. The objective of this cross-sectional study was to evaluate the performance of a Bi-Directional Axial Transmission (BDAT) device used by trained operators in a clinical environment with older subjects. The device, positioned at one-third distal radius, provides two velocities: VFAS (first arriving signal) and VA0 (first anti-symmetrical guided mode). Moreover, two parameters are obtained from an inverse approach: Ct.Th (cortical thickness) and Ct.Po (cortical porosity), along with their ratio Ct.Po/Ct.Th. The areal bone mineral density (aBMD) was obtained using DXA at the femur and spine. One hundred and six patients (81 women, 25 men) from Marien Hospital and St. Anna Hospital (Herne, Germany) were included in this study. Age ranged from 41 to 95 years, while body mass index (BMI) ranged from 16 to 47 kg.m-2. Three groups were considered: 79 non-fractured patients (NF, 75±13years), 27 with non-traumatic fractures (F, 80±9years) including 14 patients with non-vertebral fractures (NVF, 84±7years). Weak to moderate significant Spearman correlations (R ranging from 0.23 to 0.53, p < 0.05) were found between ultrasound parameters and age, BMI. Using multivariate Partial Least Square discrimination analyses with Leave-One-Out Cross-Validation (PLS-LOOCV), we found the combination of VFAS and the ratio Ct.Po/Ct.Th to be predictive for all non traumatic fractures (F) with the odds ratio (OR) equals to 2.5 [1.6-3.4] and the area under the ROC curve (AUC) equal to 0.63 [0.62-0.65]. For the group NVF, combination of four parameters VA0. Ct.Th, Ct.Po and Ct.Po/Ct.Po, along with age provides a discrimination model with OR and AUC equals to 7.5 [6.0-9.1] and 0.75 [0.73-0.76]. When restricted to a smaller population (87 patients) common to both BDAT and DXA, BDAT ORs and AUCs are comparable or slightly higher to values obtained with DXA. The fracture risk assessment by BDAT method in older patients, in a clinical setting, suggests the benefit of the affordable and transportable device for the routine use.

Influence of optical transmissivity on signal characteristics of photoacoustic guided waves in long cortical bone

Long cortical bone allows axial transmission of ultrasonic guided waves, which has been utilized for osteoporosis evaluation. Benefiting structural and molecular sensitivity, photoacoustic has been used for tissue composition characterization. However, photoacoustic guided waves (PAGWs) in long cortical bone as well as the influence of optical transmissivity on PAGWs have not been thoroughly investigated. In the study, the influence of optical transmissivity on the signal characteristics of PAGWs was experimentally studied with a 1064 nm pulsed laser ultrasonic system and a tunable laser system (wavelength range: 650-2600 nm). Results show that dispersion curves of PAGWs are not significantly affected by the optical transmissivity; while photoacoustic guided modes and signal spectrum are sensitive to the optical transmissivity in cortical bone. In experiments, the lasers with high transmissivity can emit pure A₀ mode PAGWs at the low frequency, around 22 kHz, in the relatively thick 6.2 mm bone plate; on the contrary, both A₀ and S₀ modes are generated. The slope of power spectrum density (PSD) of PAGWs decreases with the increase of transmissivity, and the decline rate is around -0.229. The study proves the correlation between the signal characteristics of PAGWs and the optical transmissivity, it is helpful for the development of PAGWs in long cortical bone towards the osteoporosis evaluation.

Accuracy Assessment of the 2D-FFT Method Based on Peak Detection of the Spectrum Magnitude at the Particular Frequencies Using the Lamb Wave Signals

The 2D-FFT is described as a traditional method for signal processing and analysis. Due to the possibility to determine the time and frequency (t,f) domains, such a method has a wide application in various industrial fields. Using that method, the obtained results are presented in images only; thus, for the extraction of quantitative values of phase velocities, additional algorithms should be used. In this work, the 2D-FFT method is presented, which is based on peak detection of the spectrum magnitude at particular frequencies for obtaining the quantitative expressions. The radiofrequency signals of ULWs (ultrasonic Lamb waves) were used for the accuracy evaluation of the method. An uncertainty evaluation was conducted to guarantee the metrological traceability of measurement results and ensure that they are accurate and reliable. Mathematical and experimental verifications were conducted by using signals of Lamb waves propagating in the aluminum plate. The obtained mean relative error of 0.12% for the A₀ mode (160 kHz) and 0.05% for the S₀ mode (700 kHz) during the mathematical verification indicated that the proposed method is particularly suitable for evaluating the phase-velocity dispersion in clearly expressed dispersion zones. The uncertainty analysis showed that the plate thickness, the mathematical modeling, and the step of the scanner have a significant impact on the estimated uncertainty of the phase velocity for the A₀ mode. Those components of uncertainty prevail and make about ~92% of the total standard uncertainty in a clearly expressed dispersion range. The S₀ mode analysis in the non-dispersion zone indicates that the repeatability of velocity variations, fluctuations of the frequency of Lamb waves, and the scanning step of the scanner influence significantly the combined uncertainty and represent 98% of the total uncertainty.

On the Identification of Orthotropic Elastic Stiffness Using 3D Guided Wavefield Data

Scanning laser Doppler vibrometry is a widely adopted method to measure the full-field out-of-plane vibrational response of materials in view of detecting defects or estimating stiffness parameters. Recent technological developments have led to performant 3D scanning laser Doppler vibrometers, which give access to both out-of-plane and in-plane vibrational velocity components. In the present study, the effect of using (i) the in-plane component; (ii) the out-of-plane component; and (iii) both the in-plane and out-of-plane components of the recorded vibration velocity on the inverse determination of the stiffness parameters is studied. Input data were gathered from a series of numerical simulations using a finite element model (COMSOL), as well as from broadband experimental measurements by means of a 3D infrared scanning laser Doppler vibrometer. Various materials were studied, including carbon epoxy composite and wood materials. The full-field vibrational velocity response is converted to the frequency-wavenumber domain by means of Fourier transform, from which complex wavenumbers are extracted using the matrix pencil decomposition method. To infer the orthotropic elastic stiffness tensor, an inversion procedure is developed by coupling the semi-analytical finite element (SAFE) as a forward method to the particle swarm optimizer. It is shown that accounting for the in-plane velocity component leads to a more accurate and robust determination of the orthotropic elastic stiffness parameters.

High-resolution modal wavenumber estimation in range-dependent shallow water waveguides using vertical line arrays

Estimation of modal wavenumbers is important for inference of geoacoustic properties and matched field processing in shallow water waveguides. However, it is challenging in a range-dependent environment, because modal content varies locally in response to changes in the environment. Moreover, the scales of the spatial variations in the waveguide may be on the same order as the range aperture required for resolvability of the individual modes. To this end, high-resolution (HR) wavenumber estimation methods have been widely used. In this paper, the matrix pencil and MUSIC algorithms are generalized to geometry involving a synthetic horizontal aperture (SHA) formed by a towed acoustic source and a fixed full-spanning vertical line array (VLA). The performance of the proposed methods is evaluated by simulated data in a noisy shallow water environment. Numerical results show that, when compared with the previous methods, the proposed methods significantly outperform the previous methods in terms of aperture requirement.

Through transmission ultrasonic inspection of fiber waviness for thickness-tapered composites using ultrasound non-reciprocity: Simulation and experiment

This study proposed the use of ultrasound non-reciprocity in periodic structures to inspect fiber waviness in thickness-tapered composites. Ultrasound propagation in plain and thickness-tapered composites with complex microstructure were precisely modelled using TexGen® and OnScale® simulation software. Ultrasound non-reciprocity and attenuation was comparatively calculated to inspect fiber waviness through both simulation and experiment. After comparison, energy of transmitted waves was found to be sensitive to the presence of fiber waviness in plain composites, however, thickness-dependent ultrasound attenuation introduces difficulties in determining the diagnosis baseline for thickness-tapered composites. On the other hand, fiber waviness introduces direction-dependent nonlinearity in the wavy region, which introduces a disparity between the two transmitted signals when the propagation direction is reversed. Ultrasound non-reciprocity, defined by the time-of-flight difference between the two transmitted signals, demonstrated its efficiency for fiber waviness inspection in both plain and thickness-tapered composites regardless of variations in the thickness.

Learning the propagation properties of rectangular metal plates for Lamb wave-based mapping

The inspection of sizeable plate-based metal structures such as storage tanks or marine vessel hulls is a significant stake in the industry, which necessitates reliable and time-efficient solutions. Although Lamb waves have been identified as a promising solution for long-range non-destructive testing, and despite the substantial progress made in autonomous navigation and environment sensing, a Lamb-wave-based robotic system for extensive structure monitoring is still lacking. Following previous work on ultrasonic Simultaneous Localization and Mapping (SLAM), we introduce a method to achieve plate geometry inference without prior knowledge of the material propagation properties, which may be lacking during a practical inspection task in challenging and outdoor environments. Our approach combines focalization to adjust the propagation model parameters and beamforming to infer the plate boundaries location by relying directly on acoustic measurements acquired along the mobile unit trajectory. For each candidate model, the focusing ability of the corresponding beamformer is assessed over high-pass filtered beamforming maps to further improve the robustness of the plate geometry estimates. We then recover the optimal space-domain beamformer through a simulated annealing optimization process. We evaluate our method on three sets of experimental data acquired in different conditions and show that accurate plate geometry inference can be achieved without any prior propagation model. Finally, the results show that the optimal beamformer outperforms the beamformer resulting from the predetermined propagation model in non-nominal acquisition conditions.

Improved Unsupervised Learning Method for Material-Properties Identification Based on Mode Separation of Ultrasonic Guided Waves

Numerical methods, including machine-learning methods, are now actively used in applications related to elastic guided wave propagation phenomena. The method proposed in this study for material-properties characterization is based on an algorithm of the clustering of multivariate data series obtained as a result of the application of the matrix pencil method to the experimental data. In the developed technique, multi-objective optimization is employed to improve the accuracy of the identification of particular parameters. At the first stage, the computationally efficient method based on the calculation of the Fourier transform of Green’s matrix is employed iteratively and the obtained solution is used for filter construction with decreasing bandwidths providing nearly noise-free classified data (with mode separation). The filter provides data separation between all guided waves in a natural way, which is needed at the second stage, where a more laborious method based on the minimization of the slowness residuals is applied to the data. The method might be further employed for material properties identification in plates with thin coatings/interlayers, multi-layered anisotropic laminates, etc.

Experimental Estimation of Lamb Wave Dispersion Curves for Adhesively Bonded Aluminum Plates, Using Two Adjacent Signals

In this study, dispersion curve estimation of a bonded aluminum plate is carried out by proposing a specific signal processing procedure. In this proposed method, the angle beam ultrasonic transducer measurement system in a pitch-catch configuration is used to acquire Lamb wave signals from two adjacent positions. The obtained signals are processed then by using signal processing techniques, including bandpass filters, fast Fourier transform (FFT), and bandpass Gaussian filters. Various transmitted signals with different central frequencies are used to estimate four modes of the utilized bonded specimen for frequencies less than 1 MHz. The dispersion curve results in terms of phase velocity and wavenumbers are compared with theoretical dispersion curves and 2-D FFT. This comparison is carried out by using three different metrics, which shows the maximum mean relative error of 3.46% with low variance.

A Review of Signal Processing Techniques for Ultrasonic Guided Wave Testing

Ultrasonic guided wave testing (UGWT) is a non-destructive testing (NDT) technique commonly used in structural health monitoring to perform wide-range inspection from a single point, thus reducing the time and effort required for NDT. However, the multi-modal and dispersive nature of guided waves makes the extraction of essential information that leads to defect detection an extremely challenging task. The purpose of this article is to give an overview of signal processing techniques used for filtering signals, isolating modes and identifying and localising defects in UGWT. The techniques are summarised and grouped according to the geometry of the studied structures. Although the reviewed techniques have led to satisfactory results, the identification of defects through signal processing remains challenging with space for improvement, particularly by combining signal processing techniques and integrating machine learning algorithms.

Identification of Material Properties of Elastic Plate Using Guided Waves Based on the Matrix Pencil Method and Laser Doppler Vibrometry

Ultrasonic based inspection of thin-walled structures often requires prior knowledge of their mechanical properties. Their accurate estimation could be achieved in a non-destructive manner employing, e.g., elastic guided waves. Such procedures require efficient approaches for experimental data extraction and processing, which is still a challenging task. An advanced automated technique for material properties identification of an elastic waveguide is proposed in this investigation. It relies on the information on dispersion characteristics of guided waves, which are extracted by applying the matrix pencil method to the measurements obtained via laser Doppler vibrometry. Two objective functions have been successfully tested, and the advantages of both approaches are discussed (accuracy vs. computational costs). The numerical analysis employing the synthetic data generated via the mathematical model as well as experimental data shows that both approaches are stable and accurate. The influence of the presence of various modes in the extracted data is investigated. One can conclude that the influence of the corruptions related to the extraction of dispersion curves is not critical if the majority of guided waves propagating in the considered frequency range are presented. Possible extensions of the proposed technique for damaged and multi-layered structures are also discussed.

Reconstruction of Lamb Wave Dispersion Curves in Different Objects Using Signals Measured at Two Different Distances

The possibilities of an effective method of two adjacent signals are investigated for the evaluation of Lamb waves phase velocity dispersion in objects of different types, namely polyvinyl chloride (PVC) film and wind turbine blade (WTB). A new algorithm based on peaks of spectrum magnitude is presented and used for the comparison of the results. To use the presented method, the wavelength-dependent parameter is proposed to determine the optimal distance range, which is necessary in selecting two signals for analysis. It is determined that, in the range of 0.17-0.5 wavelength where δcph is not higher than 5%, it is appropriate to use in the case of an A₀ mode in PVC film sample. The smallest error of 1.2%, in the distance greater than 1.5 wavelengths, is obtained in the case of the S₀ mode. Using the method of two signals analysis for PVC sample, the phase velocity dispersion curve of the A₀ mode is reconstructed using selected distances x₁ = 70 mm and x₂ = 70.5 mm between two spatial positions of a receiving transducer with a mean relative error δcph=2.8%, and for S₀ mode, x₁ = 61 mm and x₂ = 79.7 mm with δcph=0.99%. In the case of the WTB sample, the range of 0.1-0.39 wavelength, where δcph is not higher than 3%, is determined as the optimal distance range between two adjacent signals. The phase velocity dispersion curve of the A₀ mode is reconstructed in two frequency ranges: first, using selected distances x₁ = 225 mm and x₂ = 231 mm with mean relative error δcph=0.3%; and second, x₁ = 225 mm and x₂ = 237 mm with δcph=1.3%.

Imaging of Increasing Damage in Steel Plates Using Lamb Waves and Ultrasound Computed Tomography

This paper concerns the inspection of steel plates, with particular emphasis on the assessment of increasing damage. Non-destructive tests were performed on four plates, one of which was undamaged, while the remaining three had defects in the form of circular holes with diameters of 2, 5 and 10 cm. Guided Lamb waves were used in the research, and the image reconstruction was performed using ultrasound computed tomography. The damage size was estimated by tracking the real course of rays and densifying the pixel grid into which the object was divided. The results showed the great potential of ultrasound tomography in detecting defects in steel elements, together with the possibility of estimating damage size.