Wideband dispersion reversal of lamb waves

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.

Ellipse of uncertainty based algorithm for quantitative evaluation of defect localization using Lamb waves

Measurement deviation of time of flight (ToF) is inevitable in nondestructive testing based on the sparse array and ultrasonic Lamb waves. It affects the influence zone of temporal-spatial mapping trajectories (TSMTs) of signal parameters in the imaging zone, and further limits the quantitative evaluation of defect localization. In the paper, the ellipse of uncertainty (EOU) of TSMTs was derived from multiple parameters, including the group velocity, ToFs and their measurement deviations, distances between actuators and receivers. Then, an EOU-based algorithm was developed for quantitative evaluation of defect localization. The defects were localized by searching the individual scatterers at the intersection of multiple TSMTs. Based on the eccentricity of the uncertainty ellipse, a fuzzy scaling factor was introduced. It was combined with a fuzzy control parameter to tune the influence zone of TSMTs. Based on the acoustic reciprocity theorem and the fuzzy control parameter, the ToFs of scattering waves were fused to establish the one-to-one relation between individual scatterers and inspection pairs. Experimental results showed that the EOU-based algorithm can reduce the interferences of EOU in the detection; and the quantitative evaluation of defect localization was realized by analyzing the distribution of individuals and their ToF difference to inspection pairs.

Deep Learning Analysis of Ultrasonic Guided Waves for Cortical Bone Characterization

Ultrasonic guided waves (UGWs) propagating in the long cortical bone can be measured via the axial transmission method. The characterization of long cortical bone using UGW is a multiparameter inverse problem. The optimal solution of the inverse problem often includes a complex solving process. Deep neural networks (DNNs) are essentially powerful multiparameter predictors based on universal approximation theorem, which are suitable for solving parameter predictions in the inverse problem by constructing the mapping relationship between UGW and cortical bone material parameters. In this study, we investigate the feasibility of applying the multichannel crossed convolutional neural network (MCC-CNN) to simultaneously estimate cortical thickness and bulk velocities (longitudinal and transverse). Unlike the multiparameter estimation in most previous studies, the technique mentioned in this work avoids solving a multiparameter optimization problem directly. The finite-difference time-domain (FDTD) method is performed to obtain the simulated UGW array signals for training the MCC-CNN. The network that is exclusively trained on simulated data sets can predict cortical parameters from the experimental UGW data. The proposed method is confirmed by using FDTD simulation signals and experimental data obtained from four bone-mimicking plates and from ten ex vivo bovine cortical bones. The estimated root-mean-squared error (RMSE) in the simulated test data for the longitudinal bulk velocity ( V_L ), transverse bulk velocity ( V_T ), and cortical thickness (Th) is 97 m/s, 53 m/s, and 0.089 mm, respectively. The predicted RMSE in the bone-mimicking phantom experiments for V_L|| , V_T|| , and Th is 120 m/s, 80 m/s, and 0.14 mm, respectively. The experimental dispersion trajectories are matched with the theoretical dispersion curves calculated by the predicted parameters in ex vivo bovine cortical bone experiments. Our proposed method demonstrates a feasible approach for the accurate evaluation of long cortical bones based on UGW.

Improved Defect Detection of Guided Wave Testing Using Split-Spectrum Processing

Ultrasonic guided wave (UGW) testing is widely applied in numerous industry areas for the examination of pipelines where structural integrity is of concern. Guided wave testing is capable of inspecting long lengths of pipes from a single tool location using some arrays of transducers positioned around the pipe. Due to dispersive propagation and the multimodal behavior of UGW, the received signal is usually degraded and noisy, that reduce the inspection range and sensitivity to small defects. Therefore, signal interpretation and identifying small defects is a challenging task in such systems, particularly for buried/coated pipes, in that the attenuation rates are considerably higher compared with a bare pipe. In this work, a novel solution is proposed to address this issue by employing an advanced signal processing approach called “split-spectrum processing” (SSP) to minimize the level of background noise and enhance the signal quality. The SSP technique has already shown promising results in a limited trial for a bar pipe and, in this work, the proposed technique has been experimentally compared with the traditional approach for coated pipes. The results illustrate that the proposed technique significantly increases the signal-to-noise ratio and enhances the sensitivity to small defects that are hidden below the background noise.

Suppression of Lamb wave excitation via aperture control of a transducer array for ultrasonic clamp-on flow metering

During ultrasonic clamp-on flow metering, Lamb waves propagating in the pipe wall may limit the measurement accuracy by introducing absolute errors in the flow estimates. Upon reception, these waves can interfere with the up and downstream waves refracting from the liquid, and disturb the measurement of the transit time difference that is used to obtain the flow speed. Thus, suppression of the generation of Lamb waves might directly increase the accuracy of a clamp-on flow meter. Existing techniques apply to flow meters with single element transducers. This paper considers the application of transducer arrays and presents a method to achieve a predefined amount of suppression of these spurious Lamb waves based on appropriate amplitude weightings of the transducer elements. Finite element simulations of an ultrasonic clamp-on flow measurement setting will be presented to show the effect of array aperture control on the suppression of the Lamb waves in a 1-mm-thick stainless steel pipe wall. Furthermore, a proof-of-principle experiment will be shown that demonstrates a good agreement with the simulations.

Nonlinear time-warping made simple: A step-by-step tutorial on underwater acoustic modal separation with a single hydrophone

Classical ocean acoustic experiments involve the use of synchronized arrays of sensors. However, the need to cover large areas and/or the use of small robotic platforms has evoked interest in single-hydrophone processing methods for localizing a source or characterizing the propagation environment. One such processing method is "warping," a non-linear, physics-based signal processing tool dedicated to decomposing multipath features of low-frequency transient signals (frequency f < 500 Hz), after their propagation through shallow water (depth D < 200 m) and their reception on a distant single hydrophone (range r > 1 km). Since its introduction to the underwater acoustics community in 2010, warping has been adopted in the ocean acoustics literature, mostly as a pre-processing method for single receiver geoacoustic inversion. Warping also has potential applications in other specialties, including bioacoustics; however, the technique can be daunting to many potential users unfamiliar with its intricacies. Consequently, this tutorial article covers basic warping theory, presents simulation examples, and provides practical experimental strategies. Accompanying supplementary material provides matlab code and simulated and experimental datasets for easy implementation of warping on both impulsive and frequency-modulated signals from both biotic and man-made sources. This combined material should provide interested readers with user-friendly resources for implementing warping methods into their own research.

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.

Lamb Wave Local Wavenumber Approach for Characterizing Flat Bottom Defects in an Isotropic Thin Plate

This paper aims to use the Lamb wave local wavenumber approach to characterize flat bottom defects (including circular flat bottom holes and a rectangular groove) in an isotropic thin plate. An air-coupled transducer (ACT) with a special incidence angle is used to actuate the fundamental anti-symmetric mode (A0). A laser Doppler vibrometer (LDV) is employed to measure the out-of-plane velocity over a target area. These signals are processed by the wavenumber domain filtering technique in order to remove any modes other than the A0 mode. The filtered signals are transformed back into the time-space domain. The space-frequency-wavenumber spectrum is then obtained by using three-dimensional fast Fourier transform (3D FFT) and a short space transform, which can retain the spatial information and reduce the magnitude of side lobes in the wavenumber domain. The average wavenumber is calculated, as a real signal usually contains a certain bandwidth instead of the singular frequency component. Both simulation results and experimental results demonstrate that the average wavenumber can be used not only to identify shape, location, and size of the damage, but also quantify the depth of the damage. In addition, the direction of an inclined rectangular groove is obtained by calculating the image moments under grayscale. This hybrid and non-contact system based on the local wavenumber approach can be provided with a high resolution.

Fatigue evaluation of long cortical bone using ultrasonic guided waves

Bone fatigue fracture is a progressive disease due to stress concentration. This study aims to evaluate the long bone fatigue damage using the ultrasonic guided waves. Two-dimensional finite-difference time-domain method was employed to simulate the ultrasonic guided wave propagation in the long bone under different elastic modulus. The experiment was conducted on a 3.8 mm-thick bovine bone plate. The phase velocities of two fundamental guided modes, A1 and S1, were measured by using the axial transmission technique. Simulation shows that the phase velocities of guided modes A1 and S1 decrease with the increasing of the fatigue damage. After 20,000 cycles of fatigue loading on the bone plate, the average phase velocities of A1 and S1 modes were 6.6% and 5.3% respectively, lower than those of the intact bone. The study suggests that ultrasonic guided waves can be potentially used to evaluate the fatigue damage in long bones.

Split-spectrum processing technique for SNR enhancement of ultrasonic guided wave

Ultrasonic guided wave (UGW) systems are broadly used in several branches of industry where the structural integrity is of concern. In those systems, signal interpretation can often be challenging due to the multi-modal and dispersive propagation of UGWs. This results in degradation of the signals in terms of signal-to-noise ratio (SNR) and spatial resolution. This paper employs the split-spectrum processing (SSP) technique in order to enhance the SNR and spatial resolution of UGW signals using the optimized filter bank parameters in real time scenario for pipe inspection. SSP technique has already been developed for other applications such as conventional ultrasonic testing for SNR enhancement. In this work, an investigation is provided to clarify the sensitivity of SSP performance to the filter bank parameter values for UGWs such as processing bandwidth, filter bandwidth, filter separation and a number of filters. As a result, the optimum values are estimated to significantly improve the SNR and spatial resolution of UGWs. The proposed method is synthetically and experimentally compared with conventional approaches employing different SSP recombination algorithms. The Polarity Thresholding (PT) and PT with Minimization (PTM) algorithms were found to be the best recombination algorithms. They substantially improved the SNR up to 36.9dB and 38.9dB respectively. The outcome of the work presented in this paper paves the way to enhance the reliability of UGW inspections.

Wave Mode Discrimination of Coded Ultrasonic Guided Waves Using Two-Dimensional Compressed Pulse Analysis

Ultrasonic guided waves testing is a technique successfully used in many industrial scenarios worldwide. For many complex applications, the dispersive nature and multimode behavior of the technique still poses a challenge for correct defect detection capabilities. In order to improve the performance of the guided waves, a 2-D compressed pulse analysis is presented in this paper. This novel technique combines the use of pulse compression and dispersion compensation in order to improve the signal-to-noise ratio (SNR) and temporal-spatial resolution of the signals. The ability of the technique to discriminate different wave modes is also highlighted. In addition, an iterative algorithm is developed to identify the wave modes of interest using adaptive peak detection to enable automatic wave mode discrimination. The employed algorithm is developed in order to pave the way for further in situ applications. The performance of Barker-coded and chirp waveforms is studied in a multimodal scenario where longitudinal and flexural wave packets are superposed. The technique is tested in both synthetic and experimental conditions. The enhancements in SNR and temporal resolution are quantified as well as their ability to accurately calculate the propagation distance for different wave modes.

An Adaptive Array Excitation Scheme for the Unidirectional Enhancement of Guided Waves

Control over the direction of wave propagation allows an engineer to spatially locate defects. When imaging with longitudinal waves, time delays can be applied to each element of a phased array transducer to steer a beam. Because of the highly dispersive nature of guided waves (GWs), this beamsteering approach is suboptimal. More appropriate time delays can be chosen to direct a GW if the dispersion relation of the material is known. Existing techniques, however, need a priori knowledge of material thickness and acoustic velocity, which change as a function of temperature and strain. The scheme presented here does not require prior knowledge of the dispersion relation or properties of the specimen to direct a GW. Initially, a GW is generated using a single element of an array transducer. The acquired waveforms from the remaining elements are then processed and retransmitted, constructively interfering with the wave as it travels across the spatial influence of the transducer. The scheme intrinsically compensates for the dispersion of the waves, and thus can adapt to changes in material thickness and acoustic velocity. The proposed technique is demonstrated in simulation and experimentally. Dispersion curves from either side of the array are acquired to demonstrate the scheme's ability to direct a GW in an aluminum plate. The results show that unidirectional enhancement is possible without a priori knowledge of the specimen using an arbitrary pitch array transducer. The experimental results show a 34-dB enhancement in one direction compared with the other.

Transverse and Oblique Long Bone Fracture Evaluation by Low Order Ultrasonic Guided Waves: A Simulation Study

Ultrasonic guided waves have recently been used in fracture evaluation and fracture healing monitoring. An axial transmission technique has been used to quantify the impact of the gap breakage width and fracture angle on the amplitudes of low order guided wave modes S0 and A0 under a 100 kHz narrowband excitation. In our two dimensional finite-difference time-domain (2D-FDTD) simulation, the long bones are modeled as three layers with a soft tissue overlay and marrow underlay. The simulations of the transversely and obliquely fractured long bones show that the amplitudes of both S0 and A0 decrease as the gap breakage widens. Fixing the crack width, the increase of the fracture angle relative to the cross section perpendicular to the long axis enhances the amplitude of A0, while the amplitude of S0 shows a nonmonotonic trend with the decrease of the fracture angle. The amplitude ratio between the S0 and A0 modes is used to quantitatively evaluate the fracture width and angles. The study suggests that the low order guided wave modes S0 and A0 have potentials for transverse and oblique bone fracture evaluation and fracture healing monitoring.

Multichannel processing for dispersion curves extraction of ultrasonic axial-transmission signals: Comparisons and case studies

Some pioneering studies have shown the clinical feasibility of long bones evaluation using ultrasonic guided waves. Such a strategy is typically designed to determine the dispersion information of the guided modes to infer the elastic and structural characteristics of cortical bone. However, there are still some challenges to extract multimode dispersion curves due to many practical limitations, e.g., high spectral density of modes, limited spectral resolution and poor signal-to-noise ratio. Recently, two representative signal processing methods have been proposed to improve the dispersion curves extraction. The first method is based on singular value decomposition (SVD) with advantages of multi-emitter and multi-receiver configuration for enhanced mode extraction; the second one uses linear Radon transform (LRT) with high-resolution imaging of the dispersion curves. To clarify the pros and cons, a face to face comparison was performed between the two methods. The results suggest that the LRT method is suitable to separate the guided modes at low frequency-thickness-product ( fh) range; for multimode signals in broadband fh range, the SVD-based method shows more robust performances for weak mode enhancement and noise filtering. Different methods are valuable to cover the entire fh range for processing ultrasonic axial transmission signals measured in long cortical bones.

Mechanical strain sensing by broadband time reversal in plates

In a previous work, the ultrasonic measurement of longitudinal strain in a plate using the Time Reversal technique was proved. One drawback of this measurement is the low sensitivity of the signal against changes in strain. This problem can be solved using the inverse filter signal processing. This technique increases sensitivity but also reduces the energy of the signal and, consequently, the signal to noise ratio. Thus, a physical solution is presented in order to improve the sensitivity of the system. Additionally, the one-bit time reversal is introduced in order to simplify the hardware used in this technique. The strain sensing system is composed of a pair of piezocomposite transducers bonded to the surface of the tested plate and used to generate and sense the ultrasonic waves guided through the specimen. The use of time reversal provides phase compensation for dispersion and edge reflections in the propagation of the guided waves in the plate, allowing time recompression of the waves. The measurement principle is based on the detection of changes in the amplitude and time-of-flight of the focused signal when the plate is subjected to longitudinal strains. System sensitivity is improved by using 2-2 piezocomposite transducers designed to operate between 0.2 to 3.0 MHz. In the signal processing, the one-bit time reversal is compared with the conventional time reversal in twelve-bit resolution. A figure of merit is introduced in order to evaluate the influence of the transfer function on strain sensitivity. This figure of merit relates the energy concentrated at the time reversal focus with the total energy of the signal. This value represents the ability of the time reversal process to recompress the signal at the focus. Experiments were conducted by applying strains up to 150 μm/m. Results show a linear response in the change of the focus amplitude. The sensitivity depends on the transducers and it can be related to the proposed figure of merit. The focus quality is kept when one-bit time reversal is used, showing to be also feasible for the measuring technique. All the results agreed with the numerical time-reversal implementation.

Increased range of ultrasonic guided wave testing of overhead transmission line cables using dispersion compensation

Overhead Transmission Line (OVTL) cables can experience structural defects and are, therefore, inspected using Non-Destructive Testing (NDT) techniques. Ultrasonic Guided Waves (UGW) is one NDT technique that has been investigated for inspection of these cables. For practical use, it is desirable to be able to inspect as long a section of cable as possible from a single location. This paper investigates increasing the UGW inspection range on Aluminium Conductor Steel Reinforced (ACSR) cables by compensating for dispersion using dispersion curve data. For ACSR cables, it was considered to be difficult to obtain accurate dispersion curves using modelling due to the complex geometry and unknown coupling between wire strands. Group velocity dispersion curves were, therefore, measured experimentally on an untensioned, 26.5m long cable and a method of calculating theoretical dispersion curves was obtained. Attenuation and dispersion compensation were then performed for a broadband Maximum Length Sequence (MLS) excitation signal. An increase in the Signal to Noise Ratio (SNR) of about 4-8dB compared to that of the dispersed signal was obtained. However, the main benefit was the increased ability to resolve the individual echoes from the end of the cable and an introduced defect in the form of a cut, which was 7 to at least 13dB greater than that of the dispersed signal. Five echoes were able to be clearly detected using MLS excitation signal, indicating the potential for an inspection range of up to 130m in each direction. To the best of the authors knowledge, this is the longest inspection range for ACSR cables reported in the literature, where typically cables, which were only one or two meter long, have been investigated previously. Narrow band tone burst and Hann windowed tone burst excitation signal also showed increased SNR and ability to resolve closely spaced echoes.