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

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.

Reconstruction of Composite Stiffness Matrix with Array-Guided Wave-Based Genetic Algorithm

Accurate measurement of the material parameters of composite in a nondestructive manner is of great significance for evaluating mechanical performance. This study proposes to use a genetic algorithm (GA) to reconstruct the stiffness matrix of carbon fiber reinforced polymer (CFRP) with array-guided wave (GW)-based GA. By comparing the numerically calculated GW dispersion curves with the experimental wave number-frequency contour calculated with a two-dimensional Fourier transform (2D-FFT), the matching coefficient is directly obtained as the objective function of the GA, avoiding the overhead of sorting out the respective GW modes. Then the measured stiffness matrix with tensile testing and the longitudinal wave in the unidirectional CFRP is compared with the reconstructed parameters from unidirectional, cross-ply, and quasi-isotropic CFRPs with the GA. For the four independent parameters, excluding C12, an average value of 11.62% for the maximum deviation is achieved among the CFRPs with three stacking sequences, and an average deviation of 11.03% in unidirectional CFRPs is achieved for the parameters measured with different methods. A further correction of fiber orientation results in a relative deviation of only 2.72% for the elastic modulus along the tensile direction, and an expansion of the GW frequency range for the GA narrows down the relative deviation of C12 to 3.9%. The proposed GW-based GA opens up a way of in situ and nondestructive measurement for the composite stiffness matrix.

Ultrasonic Guided Waves in Bone: A Decade of Advancement in Review

The use of guided wave ultrasonography as a means to assess cortical bone quality has been a significant practice in bone quantitative ultrasound for more than 20 years. In this article, the key developments within the technology of ultrasonic guided waves (UGW) in long bones during the past decade are documented. The covered topics include data acquisition configurations available for measuring bone guided waveforms, signal processing techniques applied to bone UGW, numerical modeling of ultrasonic wave propagation in cortical long bones, formulation of inverse approaches to extract bone properties from observed ultrasonic signals, and clinical studies to establish the technology's application and efficacy. The review concludes by highlighting specific challenging problems and future research directions. In general, the primary purpose of this work is to provide a comprehensive overview of bone guided-wave ultrasound, especially for newcomers to this scientific field.

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.

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.

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

Ultrasonic Lamb waves have been widely used for non-destructive evaluation and testing. However, the inversion from the measured guided signals to the material properties is still a challenging task in terms of multimodal dispersive signal processing and parameter estimation. This paper presents a robust strategy including the high-resolution extraction of the multimodal dispersion curves and model-based elastic property estimation. First, the estimation of signal parameters via rotation invariant technique (ESPRIT) is employed to extract the dispersion curves of the Lamb waves in the plates. Then, the particle swarm optimization (PSO) algorithm is used to retrieve the optimal model parameters by maximizing the objective function built from the dispersion equations. The elastic properties (i.e., two independent constants for the isotropic plate and four constants for the transversely isotropic plate) can thus be determined. Results of the steel, aluminum and composite plates demonstrate that the estimates are in agreement with the references. The root mean squared errors (RMSEs) between the estimated and theoretical dispersion curves calculated by the inversed model parameters for simulation, steel, aluminum and composite experiments are 0.027 rad/mm, 0.032 rad/mm, 0.033 rad/mm and 0.102 rad/mm respectively. The estimated error of thickness is less than 1%. The proposed model-based inversion strategy offers several advantages: (1) the high-resolution estimation of dispersion curves allows the objective function built for the parameter inversion without a peak-finding process. (2) The ESPRIT based dispersion curves extraction strategy offers a sharp objective function in the parameter space. (3) The inverse problem for ultrasonic waveguide characterization is solved using the PSO optimizer which can be implemented with ease and few parameters need to be tuned.

Automatic mode extraction of ultrasonic guided waves using synchrosqueezed wavelet transform

Multimodal and dispersive characteristics of ultrasonic guided waves (GWs) cause the wave-packet overlapping in time domain and frequency domain, which challenges the signal interpretation. In this study, we propose an automatic method for individual mode extraction. The inversible synchrosqueezed wavelet transform (SWT) is employed to obtain the high-resolution time-frequency representation (TFR) of the GW signal. Then, two image processing steps, i.e., watershed transform and region growing, are used to process the TFR distributions and extract the TFR trajectory of each individual component. After the TFR segmentation, the individual modes are reconstructed by using the inverse SWT. The algorithm performance is investigated by synthesized multimodal signals. The results show that the reconstructed individual modes are consistent with the original ones. The experimental results measured in a bovine tibia plate and a steel plate are further employed to testify the proposed algorithm. Results suggest that the presented study provides a robust tool for processing multimodal ultrasonic GW signals.

Ultrasound-Based Estimates of Cortical Bone Thickness and Porosity Are Associated With Nontraumatic Fractures in Postmenopausal Women: A Pilot Study

Recent ultrasound (US) axial transmission techniques exploit the multimode waveguide response of long bones to yield estimates of cortical bone structure characteristics. This pilot cross-sectional study aimed to evaluate the performance at the one-third distal radius of a bidirectional axial transmission technique (BDAT) to discriminate between fractured and nonfractured postmenopausal women. Cortical thickness (Ct.Th) and porosity (Ct.Po) estimates were obtained for 201 postmenopausal women: 109 were nonfractured (62.6 ± 7.8 years), 92 with one or more nontraumatic fractures (68.8 ± 9.2 years), 17 with hip fractures (66.1 ± 10.3 years), 32 with vertebral fractures (72.4 ± 7.9 years), and 17 with wrist fractures (67.8 ± 9.6 years). The areal bone mineral density (aBMD) was obtained using DXA at the femur and spine. Femoral aBMD correlated weakly, but significantly with Ct.Th (R = 0.23, p < 0.001) and Ct.Po (R = -0.15, p < 0.05). Femoral aBMD and both US parameters were significantly different between the subgroup of all nontraumatic fractures combined and the control group (p < 0.05). The main findings were that (1) Ct.Po was discriminant for all nontraumatic fractures combined (OR = 1.39; area under the receiver operating characteristic curve [AUC] equal to 0.71), for vertebral (OR = 1.96; AUC = 0.84) and wrist fractures (OR = 1.80; AUC = 0.71), whereas Ct.Th was discriminant for hip fractures only (OR = 2.01; AUC = 0.72); there was a significant association (2) between increased Ct.Po and vertebral and wrist fractures when these fractures were not associated with any measured aBMD variables; (3) between increased Ct.Po and all nontraumatic fractures combined independently of aBMD neck; and (4) between decreased Ct.Th and hip fractures independently of aBMD femur. BDAT variables showed comparable performance to that of aBMD neck with all types of fractures (OR = 1.48; AUC = 0.72) and that of aBMD femur with hip fractures (OR = 2.21; AUC = 0.70). If these results are confirmed in prospective studies, cortical BDAT measurements may be considered useful for assessing fracture risk in postmenopausal women. © 2019 American Society for Bone and Mineral Research.