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Ultrasonic Guided Waves
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Ultrasonic Guided Waves

A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Acoustics and Vibrations".

Deadline for manuscript submissions: closed (31 March 2019) | Viewed by 93055

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editor

Prof. Dr. Clifford Lissenden

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Guest Editor
Department of Engineering Science and Mechanics, Pennsylvania State University, University Park, PA 16802, USA
Interests: structural health monitoring; ultrasonic guided waves; nondestructive evaluation; mechanical behavior of materials; nonlinear guided waves
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The propagation of ultrasonic guided waves in solids is an important area of scientific inquiry due primarily to their practical applications for nondestructive characterization of materials, such as nondestructive inspection, quality assurance testing, structural health monitoring, and material state awareness. Ultrasonic waves guided by boundaries or interfaces can propagate much further than waves propagating in bulk material due to their higher directivity. Furthermore, they can interrogate otherwise inaccessible material domains. Aspects of wave propagation often leveraged are wave speeds to infer elastic properties, acoustic impedance mismatches that scatter waves to detect defects, time of flight to locate the position of a defect, acoustoelasticity to determine stresses, and harmonic generation associated with material or geometric nonlinearities. The multimodal dispersive nature of guided waves makes mode and frequency selection very important, regardless of the application. A variety of transducers based on piezoelectricity, magnetostriction, the Lorentz force, and laser pulses can be used dependent upon the application needs with respect to environment, coupling, and size. This Special Issue of the journal covers all aspects of ultrasonic guided waves (e.g., phased array transducers, meta-materials to control wave propagation characteristics, scattering, attenuation, and signal processing techniques) from the perspective of modeling, simulation, laboratory experiments, or field testing.

Prof. Clifford J. Lissenden
Guest Editor

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Keywords

  • Wave propagation

  • nondestructive inspection

  • structural health monitoring

  • ultrasonic transducers

  • scattering

  • attenuation

  • signal processing

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Published Papers (21 papers)

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Editorial

Jump to: Research

3 pages, 162 KiB  
Editorial
Applied Sciences Special Issue: Ultrasonic Guided Waves
by Clifford J. Lissenden
Appl. Sci. 2019, 9(18), 3869; https://doi.org/10.3390/app9183869 - 15 Sep 2019
Cited by 3 | Viewed by 2064
Abstract
The propagation of ultrasonic guided waves in solids is an important area of scientific inquiry due primarily to their practical applications for the nondestructive characterization of materials, such as nondestructive inspection, quality assurance testing, structural health monitoring, and for achieving material state awareness [...] Read more.
The propagation of ultrasonic guided waves in solids is an important area of scientific inquiry due primarily to their practical applications for the nondestructive characterization of materials, such as nondestructive inspection, quality assurance testing, structural health monitoring, and for achieving material state awareness [...] Full article
(This article belongs to the Special Issue Ultrasonic Guided Waves)

Research

Jump to: Editorial

13 pages, 1657 KiB  
Article
Analysis of Guided Wave Propagation in a Multi-Layered Structure in View of Structural Health Monitoring
by Yevgeniya Lugovtsova, Jannis Bulling, Christian Boller and Jens Prager
Appl. Sci. 2019, 9(21), 4600; https://doi.org/10.3390/app9214600 - 29 Oct 2019
Cited by 29 | Viewed by 4726
Abstract
Guided waves (GW) are of great interest for non-destructive testing (NDT) and structural health monitoring (SHM) of engineering structures such as for oil and gas pipelines, rails, aircraft components, adhesive bonds and possibly much more. Development of a technique based on GWs requires [...] Read more.
Guided waves (GW) are of great interest for non-destructive testing (NDT) and structural health monitoring (SHM) of engineering structures such as for oil and gas pipelines, rails, aircraft components, adhesive bonds and possibly much more. Development of a technique based on GWs requires careful understanding obtained through modelling and analysis of wave propagation and mode-damage interaction due to the dispersion and multimodal character of GWs. The Scaled Boundary Finite Element Method (SBFEM) is a suitable numerical approach for this purpose allowing calculation of dispersion curves, mode shapes and GW propagation analysis. In this article, the SBFEM is used to analyse wave propagation in a plate consisting of an isotropic aluminium layer bonded as a hybrid to an anisotropic carbon fibre reinforced plastics layer. This hybrid composite corresponds to one of those considered in a Type III composite pressure vessel used for storing gases, e.g., hydrogen in automotive and aerospace applications. The results show that most of the wave energy can be concentrated in a certain layer depending on the mode used, and by that damage present in this layer can be detected. The results obtained help to understand the wave propagation in multi-layered structures and are important for further development of NDT and SHM for engineering structures consisting of multiple layers. Full article
(This article belongs to the Special Issue Ultrasonic Guided Waves)
►▼ Show Figures

Figure 1

Figure 1
<p>Schematic discretisation of: (<b>a</b>) an unbounded (infinite) domain in the scaled boundaty finite element method (SBFEM) (<b>b</b>); a domain in the SBFEM; and (<b>c</b>) in classical FEM.</p> Full article ">Figure 2
<p>Sketch of a simplified structure of a COPV with corresponding sensor placement, adapted from [<a href="#B13-applsci-09-04600" class="html-bibr">13</a>].</p> Full article ">Figure 3
<p>Schematic of the numerical model used in the SBFEM.</p> Full article ">Figure 4
<p>Dispersion curves of: (<b>a</b>) phase and (<b>b</b>) group velocities, calculated for the infinite aluminium-CFRP hybrid plate using SBFEM. The first ten guided wavemodes are numbered in numerical order. The circles mark modes, as chosen for numerical modelling. Recreated from original data from [<a href="#B13-applsci-09-04600" class="html-bibr">13</a>].</p> Full article ">Figure 5
<p>Frequency–wavenumber spectra of wave modes propagating in the aluminium-CFRP plate and reflecting from the 1mm crack in the aluminium: (<b>a</b>) for in-plane and (<b>b</b>) out-of-plane components while exciting Mode 2 at 475 kHz, and (<b>c</b>) for in-plane and (<b>d</b>) out-of-plane components while exciting Mode 5 at 475 kHz.</p> Full article ">Figure 6
<p>Mode shapes of: (<b>a</b>) Mode 2 at 475 kHz; (<b>b</b>) Mode 5 at 475 kHz; (<b>c</b>) Mode 4 at 400 kHz; and (<b>d</b>) Mode 6 at 700 kHz. Red lines mark delamination placed between the second and the third ply (Position (1)), and the third and the fourth ply (Position (2)) (counted from top to bottom).</p> Full article ">Figure 7
<p>Combined phase velocity dispersion curves of: (<b>a</b>) the 2 mm aluminium plate (dashed lines) and the 6 mm aluminium-CFRP plate (solid lines); and (<b>b</b>) the 4 mm CFRP plate with a [90/0/90/90] layup (dash-dotted lines) and the 6mm aluminium-CFRP plate (solid lines). The filled and hollow circles mark modes that did and did not interact with a 1mm crack in aluminium, respectively. Red dashed lines mark two aluminium modes in the aluminium, red dash-dotted lines mark two CFRP modes. Recreated from original data from [<a href="#B13-applsci-09-04600" class="html-bibr">13</a>].</p> Full article ">Figure 8
<p>Frequency–wavenumber spectra of wave modes propagating in the aluminium-CFRP plate and reflecting from the 10mm delamination between the third and the fourth ply [Position (2)]: (<b>a</b>) for in-plane and (<b>b</b>) out-of-plane components while exciting Mode 2 at 475 kHz, and (<b>c</b>) for in-plane and (<b>d</b>) out-of-plane components while exciting Mode 5 at 475 kHz.</p> Full article ">Figure 9
<p>Sketch of an arrangement based on the example considered here for an interdigital SHM system for a composite pressure vessel monitoring.</p> Full article ">
17 pages, 6204 KiB  
Article
A Modified Leakage Localization Method Using Multilayer Perceptron Neural Networks in a Pressurized Gas Pipe
by Qi Wu and Chang-Myung Lee
Appl. Sci. 2019, 9(9), 1954; https://doi.org/10.3390/app9091954 - 13 May 2019
Cited by 22 | Viewed by 4250
Abstract
Leak detection and location in a gas distribution network are significant issues. The acoustic emission (AE) technique can be used to locate a pipeline leak. The time delay between two sensor signals can be determined by the cross-correlation function (CCF), which is a [...] Read more.
Leak detection and location in a gas distribution network are significant issues. The acoustic emission (AE) technique can be used to locate a pipeline leak. The time delay between two sensor signals can be determined by the cross-correlation function (CCF), which is a measure of the similarity of two signals as a function of the time delay between them. Due to the energy attenuation, dispersion effect and reverberation of the leakage-induced signals in the pipelines, the CCF location method performs poorly. To improve the leakage location accuracy, this paper proposes a modified leakage location method based on the AE signal, and combines the modified generalized cross-correlation location method and the attenuation-based location method using multilayer perceptron neural networks (MLPNN). In addition, the wave speed was estimated more accurately by the peak frequency of the leakage-induced AE signal in combination with the group speed dispersive curve of the fundamental flexural mode. To verify the reliability of the proposed location method, many tests were performed over a range of leak-sensor distances. The location results show that compared to using the CCF location method, the MLPNN locator reduces the average of the relative location errors by 14%, therefore, this proposed method is better than the CCF method for locating a gas pipe leak. Full article
(This article belongs to the Special Issue Ultrasonic Guided Waves)
►▼ Show Figures

Figure 1

Figure 1
<p>Schematic of the pressurized piping system.</p> Full article ">Figure 2
<p>Schematic of the implementation of the modified GCC location method.</p> Full article ">Figure 3
<p>Group speed dispersive curves of the flexural modes in the frequency band 0–400 kHz for the given gas pipe.</p> Full article ">Figure 4
<p>The MLPNN with input, hidden, and output layers.</p> Full article ">Figure 5
<p>Experiment system diagram: (i) a gas pipe, (ii) two AE sensors, (iii) an impulse hammer, (iv) a data acquisition card, (v) a PC, and (vi) a hose.</p> Full article ">Figure 6
<p>A simulated leak orifice of the pipe.</p> Full article ">Figure 7
<p>The AE sensor mounted with the magnetic hold down and vacuum grease couplant.</p> Full article ">Figure 8
<p>An impulse hammer.</p> Full article ">Figure 9
<p>The placement of two AE sensors along the pipe.</p> Full article ">Figure 10
<p>Flowchart of the leakage location method for the MLPNN locator.</p> Full article ">Figure 11
<p>Comparison of the power spectral densities of the leakage-induced signal in the different distances (L<sub>1</sub> = 1 m, 2 m) away from the leak source.</p> Full article ">Figure 12
<p>Fitting curves of the signal energy ratios of the AE signals measured by the two sensors.</p> Full article ">Figure 13
<p>Impulse response signals acquired at different distances from sensor 1: (<b>a</b>) 0.4m and (<b>b</b>) 13m.</p> Full article ">Figure 14
<p>Cross-correlation coefficients (CCCs) obtained by two methods: (<b>a</b>) CCF location method, and (<b>b</b>) modified GCC location method.</p> Full article ">Figure 15
<p>Histograms of the relative location errors obtained by two methods: (<b>a</b>) CCF location method and (<b>b</b>) MLPNN locator.</p> Full article ">
14 pages, 4990 KiB  
Article
Signal Strength Enhancement of Magnetostrictive Patch Transducers for Guided Wave Inspection by Magnetic Circuit Optimization
by Jianjun Wu, Zhifeng Tang, Keji Yang and Fuzai Lv
Appl. Sci. 2019, 9(7), 1477; https://doi.org/10.3390/app9071477 - 9 Apr 2019
Cited by 20 | Viewed by 3231
Abstract
Magnetostrictive patch transducers (MPT) with planar coils are ideal candidates for shear mode generation and detection in pipe and plate inspection with the advantages of flexibility, lightness and good directivity. However, the low energy conversion efficiency limits the application of the MPT in [...] Read more.
Magnetostrictive patch transducers (MPT) with planar coils are ideal candidates for shear mode generation and detection in pipe and plate inspection with the advantages of flexibility, lightness and good directivity. However, the low energy conversion efficiency limits the application of the MPT in long distance inspection. In this article, a method for the enhancement of the MPT was proposed by dynamic magnetic field optimization using a soft magnetic patch (SMP). The SMP can reduce the magnetic resistance of the magnetic circuit, which increases the dynamic magnetic field intensity in the magnetostrictive patch during wave generation and restricts the induced dynamic magnetic field within the area around the coils for sensing during wave detection. Numerical simulations carried out at different frequencies verified the improvement of the dynamic magnetic fields by the SMP and influence of different affecting factors. The experimental validations of the signal enhancement in wave generation and detection were performed in an aluminum plate. The amplitude magnification could reach 12.7 dB when the MPTs were covered by the SMPs. Based on the numerical and experimental results, the SMP with a large relative permeability and thickness and close fitting between the SMP and coils were recommended when other application conditions were met. Full article
(This article belongs to the Special Issue Ultrasonic Guided Waves)
►▼ Show Figures

Figure 1

Figure 1
<p>Coils commonly used in the magnetostrictive transducers.</p> Full article ">Figure 2
<p>Magnetic domain movement in the magnetostrictive effect.</p> Full article ">Figure 3
<p>Magnetostrictive patch transducer for shear wave inspection.</p> Full article ">Figure 4
<p>Diagram of dynamic magnetic fields in the MPTs (magnetostrictive patch transducers).</p> Full article ">Figure 5
<p>Numerical model for dynamic magnetic field simulation of magnetostrictive patch transducers.</p> Full article ">Figure 6
<p>Current directions for different types of magnetostrictive patch transducers.</p> Full article ">Figure 7
<p>Magnetic field distribution in magnetostrictive patch transducers at 85 kHz. The magnetic lines are green lines in the case of wave generation and blue lines of wave detection.</p> Full article ">Figure 8
<p>Comparisons of magnetostrictive patch transducers with and without the SMPs at 85 kHz: (<b>a</b>) The magnetic field intensity in Line 1 in wave generation; (<b>b</b>) the magnetic field in Line 2 in wave detection.</p> Full article ">Figure 9
<p>Comparisons of MPTs with and without the SMPs at 55~150 kHz: (<b>a</b>) The magnetic field intensity in Line 1 in wave generation; and (<b>b</b>) the magnetic field in Line 2 in wave detection.</p> Full article ">Figure 10
<p>MPTs with the SMPs of different relative permeabilities: (<b>a</b>) The magnetic field intensity in Line 1 in wave generation; and (<b>b</b>) the magnetic field intensity in Line 2 in wave detection.</p> Full article ">Figure 11
<p>MPTs with the SMPs of different thicknesses: (<b>a</b>) The magnetic field intensity in Line 1 in wave generation; and (<b>b</b>) the magnetic field intensity in Line 2 in wave detection.</p> Full article ">Figure 12
<p>MPTs with the SMPs of different lift-off distances: (<b>a</b>) The magnetic field intensity in Line 1 in wave generation; and (<b>b</b>) the magnetic field intensity in Line 2 in wave detection.</p> Full article ">Figure 13
<p>The diagram of the experiments for transducer improvement with the SMP.</p> Full article ">Figure 14
<p>Original signals of the cases in which T1 and T2 both were with and without the SMPs at 85 kHz. T1 was an actuator and T2 was a sensor.</p> Full article ">Figure 15
<p>Amplitude magnification for the MPTs in wave generation and detection with the SMPs at different frequencies. T1 was an actuator and T2 was a sensor.</p> Full article ">Figure 16
<p>Amplitude magnifications for the MPT with multiple layers of SMPs at different frequencies. T1 was an actuator and sensor.</p> Full article ">Figure 17
<p>Amplitude magnification for the magnetostrictive patch transducer with different lift-off distances of the SMP at several typical frequencies. T1 was an actuator and sensor.</p> Full article ">
24 pages, 4729 KiB  
Article
Defect Detection using Power Spectrum of Torsional Waves in Guided-Wave Inspection of Pipelines
by Houman Nakhli Mahal, Kai Yang and Asoke K. Nandi
Appl. Sci. 2019, 9(7), 1449; https://doi.org/10.3390/app9071449 - 6 Apr 2019
Cited by 11 | Viewed by 4429
Abstract
Ultrasonic Guided-wave (UGW) testing of pipelines allows long-range assessment of pipe integrity from a single point of inspection. This technology uses a number of arrays of transducers separated by a distance from each other to generate a single axisymmetric (torsional) wave mode. The [...] Read more.
Ultrasonic Guided-wave (UGW) testing of pipelines allows long-range assessment of pipe integrity from a single point of inspection. This technology uses a number of arrays of transducers separated by a distance from each other to generate a single axisymmetric (torsional) wave mode. The location of anomalies in the pipe is determined by inspectors using the received signal. Guided-waves are multimodal and dispersive. In practical tests, nonaxisymmetric waves are also received due to the nonideal testing conditions, such as presence of variable transfer function of transducers. These waves are considered as the main source of noise in the guided-wave inspection of pipelines. In this paper, we propose a method to exploit the differences in the power spectrum of the torsional wave and flexural waves, in order to detect the torsional wave, leading to the defect location. The method is based on a sliding moving window, where in each iteration the signals are normalised and their power spectra are calculated. Each power spectrum is compared with the previously known spectrum of excitation sequence. Five binary conditions are defined; all of these need to be met in order for a window to be marked as defect signal. This method is validated using a synthesised test case generated by a Finite Element Model (FEM) as well as real test data gathered from laboratory trials. In laboratory trials, three different pipes with defects sizes of 4%, 3% and 2% cross-sectional area (CSA) material loss were evaluated. In order to find the optimum frequency, the varying excitation frequency of 30 to 50 kHz (in steps of 2 kHz) were used. The results demonstrate the capability of this algorithm in detecting torsional waves with low signal-to-noise ratio (SNR) without requiring any change in the excitation sequence. This can help inspectors by validating the frequency response of the received sequence and give more confidence in the detection of defects in guided-wave testing of pipelines. Full article
(This article belongs to the Special Issue Ultrasonic Guided Waves)
►▼ Show Figures

Figure 1

Figure 1
<p>(<b>a</b>) Example dispersion curve of T(0,1) wave mode in an 8″ schedule 40 steel pipe. (<b>b</b>) The effect of dispersion on a simulated flexural wave for two propagation distances [<a href="#B20-applsci-09-01449" class="html-bibr">20</a>].</p> Full article ">Figure 2
<p>Flowchart of the initialisation.</p> Full article ">Figure 3
<p>Flowchart of conditions.</p> Full article ">Figure 4
<p>Flowchart of the main loop.</p> Full article ">Figure 5
<p>Synthesised data generated from finite element model (FEM) test case.</p> Full article ">Figure 6
<p>Example of an outlier case detected using Condition Zero (C0), where (<b>a</b>) shows the time domain of the iteration window and (<b>b</b>) is its respective power spectrum. The red lines (dotted, +) show the references achieved from excitation sequence and the black lines (x, solid) show the results from each iteration.</p> Full article ">Figure 7
<p>Example of an outlier case detected using Condition One (C1), where (<b>a</b>) shows the time domain of the iteration window and (<b>b</b>) is its respective power spectrum. The red lines show (dotted, +) the references achieved from excitation sequence and the black lines (solid, x) show the results from each iteration.</p> Full article ">Figure 8
<p>Example of an outlier case detected using Condition Two (C2), where (<b>a</b>) shows the time domain of the iteration window and (<b>b</b>) is its respective power spectrum. The red lines (dotted, +) show the references achieved from excitation sequence and the black lines (solid, x) show the results from each iteration.</p> Full article ">Figure 9
<p>Example of an outlier case detected using Condition Three (C3), where (<b>a</b>) shows the time domain of the iteration window and (<b>b</b>) is its respective power spectrum. The red lines (dotted, +) show the references achieved from excitation sequence and the black lines (solid, x) show the results from each iteration.</p> Full article ">Figure 10
<p>Example of an outlier case detected using Condition Four (C4), where (<b>a</b>) shows the time domain of the iteration window and (<b>b</b>) is its respective power spectrum. The red lines (dotted, +) show the references achieved from excitation sequence and the black lines (solid, x) show the results from each iteration.</p> Full article ">Figure 11
<p>The final result (red line) overlaid on the time-domain signal (black line) from the FEM Case. The defect size is 3% cross-sectional area (CSA) and the excitation frequency is 30 kHz.</p> Full article ">Figure 12
<p>The generated results from the FEM test case.</p> Full article ">Figure 13
<p>The generated results from the experimental pipe with a defect of 3% CSA and testing frequency of 38 kHz.</p> Full article ">Figure 14
<p>The final result (red line) overlaid on the time-domain signal (black line) from experimental test case with the excitation frequency of 38 kHz and defect size of 3% CSA.</p> Full article ">Figure 15
<p>Torsional mode reception route for laboratory trials.</p> Full article ">Figure 16
<p>Schematic of the saw-cut defects introduced in the wall of the pipe (not to scale).</p> Full article ">Figure 17
<p>Signal-to-noise ratio (SNR) of the defect signal in each experimental test case.</p> Full article ">Figure 18
<p>Results achieved using the algorithm where (<b>a</b>) shows the detection amplitude of defect signal and (<b>b</b>) shows the detection amplitude of the outlier. Each line represents a defect with different CSA size. The red dotted line represents the amplitude threshold for filtering the outliers.</p> Full article ">Figure 19
<p>(<b>a</b>) The signal received from pipe end using 50 kHz and (<b>b</b>) its corresponding power spectrum. The red lines (dotted, +) show the references achieved from excitation sequence and the black lines (solid, x) show the results from each iteration.</p> Full article ">Figure 20
<p>The ratio of detection amplitude of defect to outliers. In cases where the defect is not detected, the ratio is set as zero.</p> Full article ">
16 pages, 2430 KiB  
Article
Research on a Rail Defect Location Method Based on a Single Mode Extraction Algorithm
by Bo Xing, Zujun Yu, Xining Xu, Liqiang Zhu and Hongmei Shi
Appl. Sci. 2019, 9(6), 1107; https://doi.org/10.3390/app9061107 - 15 Mar 2019
Cited by 14 | Viewed by 3130
Abstract
This paper proposes a rail defect location method based on a single mode extraction algorithm (SMEA) of ultrasonic guided waves. Simulation analysis and verification were conducted. The dispersion curves of a CHN60 rail were obtained using the semi-analytical finite element method, and the [...] Read more.
This paper proposes a rail defect location method based on a single mode extraction algorithm (SMEA) of ultrasonic guided waves. Simulation analysis and verification were conducted. The dispersion curves of a CHN60 rail were obtained using the semi-analytical finite element method, and the modal data of the guided waves were determined. According to the inverse transformation of the excitation response algorithm, modal identification under low-frequency and high-frequency excitation was realized, and the vibration displacements at other positions of a rail were successfully predicted. Furthermore, an SMEA for guided waves is proposed, through which the single extraction results of four modes were successfully obtained when the rail was excited along different excitation directions at a frequency of 200 Hz. In addition, the SMEA was applied to defect location detection, and the single reflection mode waveform of the defect was extracted. Based on the group velocity of the mode and its propagation time, the distance between the defect and the excitation point was measured, and the defect location was predicted as a result. Moreover, the SMEA was applied to locate the railhead defect. The detection mode, the frequency, and the excitation method Were selected through the dispersion curves and modal identification results, and a series of signals of the sampling nodes were obtained using the three-dimensional finite element software ANSYS. The distance between the defect and the excitation point was calculated using the SMEA result. When compared with the structure of the simulated model, the errors obtained were all less than 0.5 m, proving the efficacy of this method in precisely locating rail defects, thus providing an innovated solution for rail defect location. Full article
(This article belongs to the Special Issue Ultrasonic Guided Waves)
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Figure 1

Figure 1
<p>CHN60 rail coordinate system.</p> Full article ">Figure 2
<p>Discretization of the cross-section of the CHN60 rail.</p> Full article ">Figure 3
<p>(<b>a</b>) Phase velocity; and (<b>b</b>) group velocity dispersion curves.</p> Full article ">Figure 4
<p>Schematic diagram of defect location.</p> Full article ">Figure 5
<p>Rail model with head defect.</p> Full article ">Figure 6
<p>Comparison between the simulation results and prediction results: (<b>a</b>) 200 Hz; and (<b>b</b>) 60 kHz.</p> Full article ">Figure 7
<p>Modal identification results under three excitation conditions (200 Hz).</p> Full article ">Figure 8
<p>SMEA results: (<b>a</b>) longitudinal excitation; (<b>b</b>) horizontal excitation; and (<b>c</b>) vertical excitation.</p> Full article ">Figure 9
<p>Defect location algorithm flow chart.</p> Full article ">Figure 10
<p>Rail mode shapes (60 kHz).</p> Full article ">Figure 11
<p>Group velocity dispersion curves of modes No. 7 and No. 14.</p> Full article ">Figure 12
<p>Modal identification results under three excitation conditions (60 kHz).</p> Full article ">Figure 13
<p>Schematic diagram of rail defect location.</p> Full article ">Figure 14
<p>Acquisition waveforms for all modes with distances of: (<b>a</b>) 1.5 m; (<b>b</b>) 4.5 m; and (<b>c</b>) 6 m between excitation points and sampling points.</p> Full article ">Figure 15
<p>The reflection waveforms of mode No. 7 at a distance from the excitation point of: (<b>a</b>) 1.5 m; (<b>b</b>) 4.5 m; and (<b>c</b>) 6 m.</p> Full article ">
18 pages, 5645 KiB  
Article
Numerical and Experimental Investigation of Guided Wave Propagation in a Multi-Wire Cable
by Pengfei Zhang, Zhifeng Tang, Fuzai Lv and Keji Yang
Appl. Sci. 2019, 9(5), 1028; https://doi.org/10.3390/app9051028 - 12 Mar 2019
Cited by 17 | Viewed by 6163
Abstract
Ultrasonic guided waves (UGWs) have attracted attention in the nondestructive testing and structural health monitoring (SHM) of multi-wire cables. They offer such advantages as a single measurement, wide coverage of the acoustic field, and long-range propagation ability. However, the mechanical coupling of multi-wire [...] Read more.
Ultrasonic guided waves (UGWs) have attracted attention in the nondestructive testing and structural health monitoring (SHM) of multi-wire cables. They offer such advantages as a single measurement, wide coverage of the acoustic field, and long-range propagation ability. However, the mechanical coupling of multi-wire structures complicates the propagation behaviors of guided waves and signal interpretation. In this paper, UGW propagation in these waveguides is investigated theoretically, numerically, and experimentally from the perspective of dispersion and wave structure, contact acoustic nonlinearity (CAN), and wave energy transfer. Although the performance of all possible propagating wave modes in a multi-wire cable at different frequencies could be obtained by dispersion analysis, it is ineffective to analyze the frequency behaviors of the wave signals of a certain mode, which could be analyzed using the CAN effect. The CAN phenomenon of two mechanically coupled wires in contact was observed, which was demonstrated by numerical guided wave simulation and experiments. Additionally, the measured guided wave energy of wires located in different layers of an aluminum conductor steel-reinforced cable accords with the theoretical prediction. The model of wave energy distribution in different layers of a cable also could be used to optimize the excitation power of transducers and determine the effective monitoring range of SHM. Full article
(This article belongs to the Special Issue Ultrasonic Guided Waves)
►▼ Show Figures

Figure 1

Figure 1
<p>Phase and group velocity dispersion curves for (<b>a</b>) a single 7-mm-diameter steel wire and (<b>b</b>) a single steel and aluminum wire with a diameter of 2.5 mm and 3.2 mm, respectively.</p> Full article ">Figure 2
<p>The vibration displacement distribution of (<b>a</b>) longitudinal, (<b>b</b>) torsional, and (<b>c</b>) flexural waves in a 7-mm-diameter steel wire. Wave structure of the (<b>d</b>) L(0,1) and (<b>e</b>) F(1,1) modes at different frequencies.</p> Full article ">Figure 3
<p>A schematic drawing of contact acoustic nonlinearity (CAN) at the rough contact interface of a pair of coupled cylindrical waveguides.</p> Full article ">Figure 4
<p>A model of the wave energy transfer between two adjacent wires. The results of the active wire are plotted by a red line, and the results of the passive wire are plotted by a blue line. The transient finite element (FE) simulation data of the two wires obtained in <a href="#sec3dot2-applsci-09-01028" class="html-sec">Section 3.2</a>. are marked by asterisks.</p> Full article ">Figure 5
<p>The excitation signal and fast Fourier transform (FFT) spectrum: the triangular pulse with a broadband of 500 kHz in the (<b>a</b>) time domain and (<b>b</b>) frequency domain; the Hann-windowed, five-cycle, 60 kHz sinusoidal tone burst in the (<b>c</b>) time domain signal and (<b>d</b>) frequency domain.</p> Full article ">Figure 6
<p>Guided waves in a single wire were excited using three loading methods: (<b>a</b>) an oblique triangular pulse with three equal components along the <span class="html-italic">x</span>, <span class="html-italic">y</span>, and <span class="html-italic">z</span> directions, (<b>b</b>) a perpendicular triangular pulse along the <span class="html-italic">z</span>-direction, and (<b>c</b>) a perpendicular sinusoidal tone burst along the <span class="html-italic">z</span>-direction.</p> Full article ">Figure 7
<p>The phase velocity dispersion spectra obtained from nodal accelerations with different excitation methods: (<b>a</b>) an oblique triangular pulse signal with three equal components, and (<b>b</b>) a perpendicular triangular pulse signal with a <span class="html-italic">z</span>-axial component. The theoretical phase velocity dispersion curves obtained in <a href="#applsci-09-01028-f001" class="html-fig">Figure 1</a>a are represented by the black dotted lines.</p> Full article ">Figure 8
<p>The phase velocity dispersion spectrum from nodal accelerations with a Hann-windowed, five-cycle, 60 kHz sinusoidal tone burst along the <span class="html-italic">z</span>-direction. The theoretical phase velocity dispersion curve of the L(0,1) mode obtained in <a href="#applsci-09-01028-f001" class="html-fig">Figure 1</a>a is represented by a black dotted line.</p> Full article ">Figure 9
<p>The phase velocity dispersion spectra of two wires from nodal accelerations with an equal components triangular pulse force along the <span class="html-italic">x</span>, <span class="html-italic">y</span>, and <span class="html-italic">z</span> directions: (<b>a</b>) the active wire and (<b>b</b>) the passive wire. The theoretical phase velocity dispersion curves obtained in <a href="#applsci-09-01028-f001" class="html-fig">Figure 1</a>a are represented by the black dotted lines.</p> Full article ">Figure 10
<p>The phase velocity dispersion spectra of wires from nodal accelerations with a Hann-windowed, five-cycle, 60 kHz sinusoidal tone burst along the <span class="html-italic">z</span>-axial direction: (<b>a</b>) the active wire and (<b>b</b>) the passive wire. The theoretical dispersion curve of L(0,1) obtained in <a href="#applsci-09-01028-f001" class="html-fig">Figure 1</a>a is represented by white dotted lines. (<b>c</b>) The FFT spectra of a representative received signal of the active wire and (<b>d</b>) part of the representative acceleration time-domain-received signals in the active wire.</p> Full article ">Figure 11
<p>The experimental setup for guided wave excitation and reception in three types of samples. (<b>a</b>) The schematic of the experiment. Photos of (<b>b</b>) the piezoelectric (PZT) transducer, (<b>c</b>) the single wire experiment case, and (<b>d</b>) the two contact wires.</p> Full article ">Figure 12
<p>The time-frequency analysis spectrum using a continuous wavelet transform (CWT) for a single 7-mm-diameter steel wire at a 60-kHz frequency: (<b>a</b>) horizontal excitation and horizontal reception, (<b>b</b>) horizontal excitation but lateral reception, (<b>c</b>) lateral excitation but horizontal reception, and (<b>d</b>) lateral excitation and lateral reception. The theoretical group velocity dispersion curves obtained in <a href="#applsci-09-01028-f001" class="html-fig">Figure 1</a>a are represented by the dotted line.</p> Full article ">Figure 13
<p>The wave signals and FFT spectrum for the two contact wires with an exciting center frequency of 60 kHz: (<b>a</b>) the time domain signal of the active wire, (<b>b</b>) the FFT spectrum of the active wire, (<b>c</b>) the time domain signal of the passive wire, and (<b>d</b>) the FFT spectrum of the passive wire.</p> Full article ">Figure 14
<p>Guided wave propagation experiments on the aluminum conductor steel-reinforced (ACSR) cable: (<b>a</b>) a photo of the exciting and receiving transducers installation, (<b>b</b>) the received time domain signals of each layer, and (<b>c</b>) the simulated and measured time average wave energy distribution in each layer.</p> Full article ">
23 pages, 9538 KiB  
Article
Improved Defect Detection Using Adaptive Leaky NLMS Filter in Guided-Wave Testing of Pipelines
by Houman Nakhli Mahal, Kai Yang and Asoke K. Nandi
Appl. Sci. 2019, 9(2), 294; https://doi.org/10.3390/app9020294 - 15 Jan 2019
Cited by 8 | Viewed by 3545
Abstract
Ultrasonic guided wave (UGW) testing of pipelines allows long range assessments of pipe integrity from a single point of inspection. This technology uses a number of arrays of transducers, linearly placed apart from each other to generate a single axisymmetric wave mode. The [...] Read more.
Ultrasonic guided wave (UGW) testing of pipelines allows long range assessments of pipe integrity from a single point of inspection. This technology uses a number of arrays of transducers, linearly placed apart from each other to generate a single axisymmetric wave mode. The general propagation routine of the device results in a single time domain signal, which is then used by the inspectors to detect the axisymmetric wave for any defect location. Nonetheless, due to inherited characteristics of the UGW and non-ideal testing conditions, non-axisymmetric (flexural) waves will be transmitted and received in the tests. This adds to the complexity of results’ interpretation. In this paper, we implement an adaptive leaky normalized least mean square (NLMS) filter for reducing the effect of non-axisymmetric waves and enhancement of axisymmetric waves. In this approach, no modification in the device hardware is required. This method is validated using the synthesized signal generated by a finite element model (FEM) and real test data gathered from laboratory trials. In laboratory trials, six different sizes of defects with cross-sectional area (CSA) material loss of 8% to 3% (steps of 1%) were tested. To find the optimum frequency, several excitation frequencies in the region of 30–50 kHz (steps of 2 kHz) were used. Furthermore, two sets of parameters were used for the adaptive filter wherein the first set of tests the optimum parameters were set to the FEM test case and, in the second set of tests, the data from the pipe with 4% CSA defect was used. The results demonstrated the capability of this algorithm for enhancing a defect’s signal-to-noise ratio (SNR). Full article
(This article belongs to the Special Issue Ultrasonic Guided Waves)
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<p>Example of received FEM signals from the array from different sections of a pipe [<a href="#B31-applsci-09-00294" class="html-bibr">31</a>].</p> Full article ">Figure 2
<p>(<b>a</b>) Example dispersion curve of T(0,1) wave mode in an 8-inch schedule 40 steel pipe. (<b>b</b>) The effect of dispersion on a simulated flexural wave, two propagation distances [<a href="#B31-applsci-09-00294" class="html-bibr">31</a>].</p> Full article ">Figure 3
<p>Categories of the signals in the guided-wave inspection [<a href="#B31-applsci-09-00294" class="html-bibr">31</a>].</p> Full article ">Figure 4
<p>Flowchart of general propagation routine currently used in guided-wave devices.</p> Full article ">Figure 5
<p>Adaptive linear prediction algorithm for noise cancellation where the red marked parameters are fixed by the user.</p> Full article ">Figure 6
<p>Schematic of the FEM with test tool and defect located at 1 m and 4 m, respectively, from the back end [<a href="#B30-applsci-09-00294" class="html-bibr">30</a>].</p> Full article ">Figure 7
<p>Example of designed transfer functions wherein (<b>a</b>) three different source points are compared and (<b>b</b>) the maximum, average, and minimum amplitudes across all of the applied transfer functions used in an individual test are shown.</p> Full article ">Figure 8
<p>The used reception points of each ring in the FEM.</p> Full article ">Figure 9
<p>Torsional mode reception route in the FEM test cases.</p> Full article ">Figure 10
<p>Torsional mode reception route for laboratory trials.</p> Full article ">Figure 11
<p>FEM signals (30 kHz) where two defect regions and the flexural noises are marked where blue and red lines show the first and second sets of the signals respectively.</p> Full article ">Figure 12
<p>Two sets of results after swapping the inputs to adaptive filter where (<b>a</b>) shows the signals received from the backward direction, (<b>b</b>) shows the flexural noise, and (<b>c</b>) shows the defect signal.</p> Full article ">Figure 13
<p>Comparison of the result achieved from NLMS (black) vs leaky LMS (orange) where (<b>a</b>) shows the time-domain results and (<b>b</b>–<b>f</b>) show the normalized magnitudes of filter order 1 to 5, respectively.</p> Full article ">Figure 14
<p>Results achieved using fixed model parameters for all frequencies where (<b>a</b>) shows the achieved SNR and (<b>b</b>) shows the amount of improvement in comparison to the general propagation routine.</p> Full article ">Figure 15
<p>Results achieved using experimental parameters, which are variable for each frequency, where (<b>a</b>) shows the achieved SNR and (<b>b</b>) shows the amount of improvement compared to the general propagation routine.</p> Full article ">Figure 16
<p>Amount of improvement achieved by experimental parameters as opposed to model parameters.</p> Full article ">Figure 17
<p>Example of filtered signals using 30 kHz excitation and model parameters where defect size is varying.</p> Full article ">Figure 18
<p>The result of (<b>a</b>) general propagation routine vs (<b>b</b>) filtered signal with their corresponding inputs (blue and red lines) of noise (left side) and defect (right side) with the excitation frequency of 34 kHz gathered from an experimental pipe with defect size of 3% CSA.</p> Full article ">Figure 19
<p>The result of (<b>a</b>) general propagation routine vs (<b>b</b>) filtered signal with their corresponding inputs (blue and red lines) of noise (left side) and defect (right side) with the excitation frequency of 38 kHz gathered from an experimental pipe with defect size of 3% CSA.</p> Full article ">Figure A1
<p>SNR of tests using general propagation routine.</p> Full article ">
9 pages, 3259 KiB  
Article
Clamping Resonators for Low-Frequency S0 Lamb Wave Reflection
by Christopher Hakoda, Cliff J. Lissenden and Parisa Shokouhi
Appl. Sci. 2019, 9(2), 257; https://doi.org/10.3390/app9020257 - 12 Jan 2019
Cited by 8 | Viewed by 3500
Abstract
A recent elastic metamaterial study found that resonators that “clamp” a plate waveguide can be used to create a frequency stop-band gap. The result was that the resonator array can prohibit the propagation of an A0 Lamb wave mode. This study investigates whether [...] Read more.
A recent elastic metamaterial study found that resonators that “clamp” a plate waveguide can be used to create a frequency stop-band gap. The result was that the resonator array can prohibit the propagation of an A0 Lamb wave mode. This study investigates whether the concept can be extended to S0 Lamb wave modes by designing resonators that can prohibit the propagation of S0 Lamb wave modes in a 1-mm aluminum plate waveguide at 50 kHz. The frequency-matched resonators did not reduce the transmitted signal, leading to the conclusion that the design concept of frequency-matched resonators is not always effective. On the other hand, the resonators designed to clamp the upper surface of the plate were very effective and reduced the transmitted signal by approximately 75%. Full article
(This article belongs to the Special Issue Ultrasonic Guided Waves)
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<p>Schematic (not to scale) of experimental setup: (<b>a</b>) top-view of the transducer positions with respect to the resonator array, and (<b>b</b>) a zoomed in view of the resonator array that shows how the resonators are positioned with respect the wave-propagation direction. The squares are the contact areas between the resonators and the plate waveguide.</p> Full article ">Figure 2
<p>The 2DFFT of the transmission measurements for (<b>a</b>) the Baseline, (<b>b</b>) the Frequency-matched Resonator and (<b>c</b>) the Clamping Resonator. The diagonal lines are the dispersion curves for the forward and backward propagating S0 Lamb wave modes. The vertical and horizontal lines show where the frequency- and wavenumber-spectrum slices shown in Figure 6 are obtained. The peak values are noted in each figure.</p> Full article ">Figure 3
<p>(<b>a</b>) Isometric view of a clamping resonator, and (<b>b</b>) the 30 clamping resonators in an array according to the spacing shown in <a href="#applsci-09-00257-f001" class="html-fig">Figure 1</a>b.</p> Full article ">Figure 4
<p>(<b>a</b>) The frequency spectra of the transmitted signal, which were extracted from the 2DFFTs shown in <a href="#applsci-09-00257-f002" class="html-fig">Figure 2</a> at a wavenumber of −58.1 rad/m; (<b>b</b>) The wavenumber spectra of the transmitted signal, which were extracted from the 2DFFTs shown <a href="#applsci-09-00257-f002" class="html-fig">Figure 2</a> at a frequency of 53.9 kHz.</p> Full article ">Figure 5
<p>A-scans measured 69 cm from the transmitting transducer. The A-scan (black) from the plate with clamping resonators has a reduced amplitude around 200 µs when compared to the baseline (grey). These A-scan examples were some of the noisier signals that were measured.</p> Full article ">Figure 6
<p>(<b>a</b>) Schematic of transducer positioning with respect to the resonator array for measuring reflected waves; (<b>b</b>) The 2DFFT of the incident/reflection measurements. The diagonal blue lines are the dispersion curves for the forward and backward propagating S0 Lamb wave. The vertical black line is where the wavenumber-spectrum slice data at a frequency of 53.9 kHz are obtained for (<b>c</b>) the wavenumber spectrum.</p> Full article ">Figure 7
<p>Finite-element predictions of the <span class="html-italic">x</span>-component displacement of an S0 Lamb wave at 50 kHz plotted along the <span class="html-italic">x</span>-axis showing that the clamping resonators block wave propagation, while the frequency-matched resonators do not.</p> Full article ">Figure 8
<p>Finite-element-predicted wavenumber spectrum of the guided waves that were allowed to transmit past the resonator array. This spectrum is expected to only contain forward (+<span class="html-italic">x</span>) traveling waves.</p> Full article ">
23 pages, 7694 KiB  
Article
Detection of Defects Using Spatial Variances of Guided-Wave Modes in Testing of Pipes
by Houman Nakhli Mahal, Kai Yang and Asoke K. Nandi
Appl. Sci. 2018, 8(12), 2378; https://doi.org/10.3390/app8122378 - 24 Nov 2018
Cited by 6 | Viewed by 3458
Abstract
In the past decade, guided-wave testing has attracted the attention of the non-destructive testing industry for pipeline inspections. This technology enables the long-range assessment of pipelines’ integrity, which significantly reduces the expenditure of testing in terms of cost and time. Guided-wave testing collars [...] Read more.
In the past decade, guided-wave testing has attracted the attention of the non-destructive testing industry for pipeline inspections. This technology enables the long-range assessment of pipelines’ integrity, which significantly reduces the expenditure of testing in terms of cost and time. Guided-wave testing collars consist of several linearly placed arrays of transducers around the circumference of the pipe, which are called rings, and can generate unidirectional axisymmetric elastic waves. The current propagation routine of the device generates a single time-domain signal by doing a phase-delayed summation of each array element. The segments where the energy of the signal is above the local noise region are reported as anomalies by the inspectors. Nonetheless, the main goal of guided-wave inspection is the detection of axisymmetric waves generated by the features within the pipes. In this paper, instead of processing a single signal obtained from the general propagation routine, we propose to process signals that are directly obtained from all of the array elements. We designed an axisymmetric wave detection algorithm, which is validated by laboratory trials on real-pipe data with two defects on different locations with varying cross-sectional area (CSA) sizes of 2% and 3% for the first defect, and 4% and 5% for the second defect. The results enabled the detection of defects with low signal-to-noise ratios (SNR), which were almost buried in the noise level. These results are reported with regard to the three different developed methods with varying excitation frequencies of 30 kHz, 34 kHz, and 37 kHz. The tests demonstrated the advantage of using the information received from all of the elements rather than a single signal. Full article
(This article belongs to the Special Issue Ultrasonic Guided Waves)
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<p>Spatial signal reception from two rings of 32 source points from various features where the red, blue, and black dotted lines are showing the first ring, second ring, and the reference offset.</p> Full article ">Figure 2
<p>Temporal domain of cases (d)–(i) from <a href="#applsci-08-02378-f001" class="html-fig">Figure 1</a></p> Full article ">Figure 3
<p>System flowchart.</p> Full article ">Figure 4
<p>Signal reception routes.</p> Full article ">Figure 5
<p>Baseline signals of pipe with no defect with frequencies of (<b>a</b>) 30 kHz; (<b>b</b>) 34 kHz; and (<b>c</b>) 37 kHz. The first marked region (3–3.5 m) is the location of the first defect, and the second marked region (4.1–4.5) is the location of the second defect.</p> Full article ">Figure 6
<p>Example signal achieved using general routine, tested by 34 kHz where the first two red dotted lines shows the defect region, and the third and fourth ones show the pipe end.</p> Full article ">Figure 7
<p>Comparison of the first and second thresholding versions on the Test 5 signal where the two zoomed regions are showing the backward leakage, defect, noise, and pipe end, respectively. The black and red signals are showing the first and second versions, respectively.</p> Full article ">Figure 8
<p>Calculated percentage of sensors with same phase, where the offset (mean values) are removed (orange); the black signal is showing the filtered version for better illustration.</p> Full article ">Figure 9
<p>Calculated threshold using method three on Test 5 (red) against the second version comparisonValue (black). In the case of method one, the threshold would be a constant line instead of changing based on the iteration.</p> Full article ">Figure 10
<p>Method three result (green signal) using the average value against the temporal signal (black) for testing a 2% CSA defect.</p> Full article ">Figure 11
<p>Minimum, average, and maximum values of method one of the first set of tests.</p> Full article ">Figure 12
<p>Limits achieved using method two on the first set of tests.</p> Full article ">Figure 13
<p>Limits achieved using method three in the first set of tests.</p> Full article ">Figure 14
<p>The increments achieved using the second version of thresholding in the first set of tests.</p> Full article ">Figure 15
<p>Bar graphs of the Safe zone margins of all methods in the first set of tests.</p> Full article ">Figure 16
<p>Bar graphs of the detection length of the defect using the average value of all of the methods in the first set of tests.</p> Full article ">Figure 17
<p>Minimum, average, and maximum values of method one of the second test cases.</p> Full article ">Figure 18
<p>Limits achieved using method two on the second set of tests.</p> Full article ">Figure 19
<p>Limits achieved using method three on the second set of tests.</p> Full article ">Figure 20
<p>The increments achieved using the second version of thresholding in the second set of tests.</p> Full article ">Figure 21
<p>Bar graphs of the Safe zone margins of all methods in the second set of tests.</p> Full article ">Figure 22
<p>Bar graphs of detection length of the defect using the average value of all of the methods in the second set of tests.</p> Full article ">
17 pages, 4536 KiB  
Article
Enhancement of Ultrasonic Guided Wave Signals Using a Split-Spectrum Processing Method
by Seyed Kamran Pedram, Peter Mudge and Tat-Hean Gan
Appl. Sci. 2018, 8(10), 1815; https://doi.org/10.3390/app8101815 - 3 Oct 2018
Cited by 14 | Viewed by 5542
Abstract
Ultrasonic guided wave (UGW) systems are broadly utilised in several industry sectors where the structural integrity is of concern, in particular, for pipeline inspection. In most cases, the received signal is very noisy due to the presence of unwanted wave modes, which are [...] Read more.
Ultrasonic guided wave (UGW) systems are broadly utilised in several industry sectors where the structural integrity is of concern, in particular, for pipeline inspection. In most cases, the received signal is very noisy due to the presence of unwanted wave modes, which are mainly dispersive. Hence, signal interpretation in this environment is often a challenging task, as it degrades the spatial resolution and gives a poor signal-to-noise ratio (SNR). The multi-modal and dispersive nature of such signals hampers the ability to detect defects in a given structure. Therefore, identifying a small defect within the noise level is a challenging task. In this work, an advanced signal processing technique called split-spectrum processing (SSP) is used firstly to address this issue by reducing/removing the effect of dispersive wave modes, and secondly to find the limitation of this technique. The method compared analytically and experimentally with the conventional approaches, and showed that the proposed method substantially improves SNR by an average of 30 dB. The limitations of SSP in terms of sensitivity to small defects and distances are also investigated, and a threshold has been defined which was comparable for both synthesised and experimental data. The conclusions reached in this work paves the way to enhance the reliability of UGW inspection. Full article
(This article belongs to the Special Issue Ultrasonic Guided Waves)
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<p>guided wave testing (GWT) signals: an excitation (<b>a</b>) time domain and (<b>b</b>) frequency domain signal, received (<b>c</b>) time domain and (<b>d</b>) frequency domain signal.</p> Full article ">Figure 2
<p>Split-spectrum processing (SSP) block diagram.</p> Full article ">Figure 3
<p>Filter bank parameters of SSP.</p> Full article ">Figure 4
<p>Synthesised setup for an eight inch pipe with a wall thickness of 8.179 mm and an outside diameter of 219.08 mm.</p> Full article ">Figure 5
<p>Results for the synthesised signal before and after applying SSP ((polarity thresholding &amp; Polarity thresholding with minimisation)PT &amp; PTM). The defect and the pipe end are located at X = 3 m and X = 4.5 m from the excitation signal. The defect sizes are (<b>a</b>) 6% cross-section area (CSA); (<b>b</b>) 4% CSA; (<b>c</b>) 2% CSA; and (<b>d</b>) 1% CSA.</p> Full article ">Figure 6
<p>Results for the synthesised signal before and after applying SSP (PT &amp; PTM). The defect (X = 3.5 m) is moved towards the pipe end (X = 4.5 m) in steps of 0.1 m. The defect distances are X= (<b>a</b>) 3.5 m; (<b>b</b>) 3.6 m; (<b>c</b>) 3.7 m; (<b>d</b>) 3.8 m; (<b>e</b>) 3.9 m; (<b>f</b>) 4 m; (<b>g</b>) 4.1 m; (<b>h</b>) 4.2 m.</p> Full article ">Figure 6 Cont.
<p>Results for the synthesised signal before and after applying SSP (PT &amp; PTM). The defect (X = 3.5 m) is moved towards the pipe end (X = 4.5 m) in steps of 0.1 m. The defect distances are X= (<b>a</b>) 3.5 m; (<b>b</b>) 3.6 m; (<b>c</b>) 3.7 m; (<b>d</b>) 3.8 m; (<b>e</b>) 3.9 m; (<b>f</b>) 4 m; (<b>g</b>) 4.1 m; (<b>h</b>) 4.2 m.</p> Full article ">Figure 7
<p>Experimental setup up for an eight inch steel pipe with a wall thickness of 8.179 mm and an OD of 219.08 mm (<b>a</b>,<b>b</b>), and (<b>c</b>) its flaw size plan.</p> Full article ">Figure 8
<p>Zoom in around the defect area from 0.5% CSA up to 8% CSA.</p> Full article ">Figure 9
<p>SNR calculation–peak amplitude of the defect (S) to the root mean square (RMS) value of the noise region (N) for 44 kHz.</p> Full article ">Figure 10
<p>Experimental setup for the same eight inch pipe (<a href="#applsci-08-01815-f007" class="html-fig">Figure 7</a>) with two saw cut defects.</p> Full article ">Figure 11
<p>Zoom in result with two defects. (<b>a</b>) Unprocessed signal; (<b>b</b>) SSP signal.</p> Full article ">
27 pages, 9335 KiB  
Article
Lamb Wave Local Wavenumber Approach for Characterizing Flat Bottom Defects in an Isotropic Thin Plate
by Guopeng Fan, Haiyan Zhang, Hui Zhang, Wenfa Zhu and Xiaodong Chai
Appl. Sci. 2018, 8(9), 1600; https://doi.org/10.3390/app8091600 - 10 Sep 2018
Cited by 14 | Viewed by 4998
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Ultrasonic Guided Waves)
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<p>Dispersion curves of an aluminum plate. (<b>a</b>) Phase velocity; (<b>b</b>) incidence angle; (<b>c</b>) wavenumber.</p> Full article ">Figure 2
<p>Schematic diagram of Lamb wave transmission and reception.</p> Full article ">Figure 3
<p>Flow chart of the local wavenumber approach.</p> Full article ">Figure 4
<p>Finite element model.</p> Full article ">Figure 5
<p>The excitation signal in the (<b>a</b>) time-domain; (<b>b</b>) frequency-domain.</p> Full article ">Figure 6
<p>Snapshots of Lamb waves. (<b>a</b>) 74.18 us; (<b>b</b>) 91.31 us; (<b>c</b>) 105.89 us; (<b>d</b>) 111.60 us; (<b>e</b>) 114.14 us; (<b>f</b>) 120.48 us. The white circle denotes the incident point of the air-coupled transducer (ACT). The black circle represents the actual location of a defect.</p> Full article ">Figure 7
<p>Mode separation based on the spatial-wavenumber filtering technique. (<b>a</b>) Wavenumber spectrum for the pristine plate; (<b>b</b>) wavenumber spectrum for the damaged plate; (<b>c</b>) high-pass filter in the wavenumber domain; (<b>d</b>) filtered wavenumber spectrum. White circles are theoretical wavenumber curves for the S0 and A0 modes.</p> Full article ">Figure 8
<p>The acquisition of average wavenumber for Case 1. (<b>a</b>) Wavenumber distribution obtained at f = 155 kHz; (<b>b</b>) wavenumber distribution obtained at f = 170 kHz; (<b>c</b>) wavenumber distribution obtained at f = 185 kHz; (<b>d</b>) wavenumber distribution obtained at f = 200 kHz; (<b>e</b>) wavenumber distribution obtained at f = 215 kHz; (<b>f</b>) wavenumber distribution obtained at f = 230 kHz; (<b>g</b>) wavenumber distribution obtained at f = 245 kHz; (<b>h</b>) average wavenumber distribution.</p> Full article ">Figure 9
<p>The test results obtained under various window radii. (<b>a</b>) 8 mm; (<b>b</b>) 9 mm; (<b>c</b>) 10 mm; (d) 11 mm; (<b>e</b>) 12 mm; (<b>f</b>) 13 mm. The white circle represents the actual location of the damage. The central frequency of the excitation signal is 200 kHz.</p> Full article ">Figure 10
<p>The maximum wavenumber obtained under various window radii. The central frequency of the excitation signal is 200 kHz.</p> Full article ">Figure 11
<p>Simulation results of Case 1 to Case 3. (<b>a</b>) Wavenumber distribution of Case 1; (<b>b</b>) depth distribution of Case 1; (<b>c</b>) wavenumber distribution of Case 2; (<b>d</b>) depth distribution of Case 2; (<b>e</b>) wavenumber distribution of Case 3; (<b>f</b>) depth distribution of Case 3. The white circle represents the actual location of the damage. The actual defect depth of Case 1 and Case 3 is 1 mm, while the actual defect depth of Case 2 is 0.5 mm.</p> Full article ">Figure 12
<p>Simulation results of Case 4 to Case 7. (<b>a</b>) Wavenumber distribution of Case 4; (<b>b</b>) depth distribution of Case 4; (<b>c</b>) wavenumber distribution of Case 5; (<b>d</b>) depth distribution of Case 5; (<b>e</b>) wavenumber distribution of Case 6; (<b>f</b>) depth distribution of Case 6; (<b>g</b>) wavenumber distribution of Case 7; (<b>h</b>) depth distribution of Case 7. The white circle represents the actual location of the damage. The actual depth of the defect is 1 mm.</p> Full article ">Figure 13
<p>Simulation results of Case 8 and Case 9. (<b>a</b>) Wavenumber distribution of Case 8; (<b>b</b>) depth distribution of Case 8; (<b>c</b>) wavenumber distribution of Case 9; (<b>d</b>) depth distribution of Case 9. The white circle represents the actual location of the damage. The actual depth of the defect is 1 mm.</p> Full article ">Figure 14
<p>Simulation results of Case 10 and Case 11. (<b>a</b>) Wavenumber distribution of Case 10; (<b>b</b>) depth distribution of Case 10; (<b>c</b>) wavenumber distribution of Case 11; (<b>d</b>) depth distribution of Case 11. The white rectangle represents the actual location of the damage. The actual depth of the defect is 1 mm.</p> Full article ">Figure 15
<p>The direction identification of an inclined rectangular groove based on the numerical result. (<b>a</b>) 90°; (<b>b</b>) 135°. The red plus (+) indicates the centroid location. The blue dashed line is the spindle. The green dash line is the boundary of the inclined rectangular groove. The background image is a grayscale image which is processed by a threshold at the level of −3 dB.</p> Full article ">Figure 16
<p>Schematic of the experimental setup.</p> Full article ">Figure 17
<p>Band-pass filtering of an experimental signal. (<b>a</b>) Original signal; (<b>b</b>) spectrum of the original signal; (<b>c</b>) filtered signal; (<b>d</b>) spectrum of the filtered signal.</p> Full article ">Figure 18
<p>Experimental results of Case 1 to Case 3. (<b>a</b>) Wavenumber distribution of Case 1; (<b>b</b>) depth distribution of Case 1; (<b>c</b>) wavenumber distribution of Case 2; (<b>b</b>) depth distribution of Case 2; (<b>d</b>) wavenumber distribution of Case 3; (<b>e</b>) depth distribution of Case 3. The white circle represents the actual location of the damage. The actual defect depth of Case 1 and Case 3 is 1 mm, while the actual defect depth of Case 2 is 0.5 mm.</p> Full article ">Figure 19
<p>Experimental results of Case 5 and Case 7. (<b>a</b>) Wavenumber distribution of Case 5; (<b>b</b>) depth distribution of Case 5; (<b>c</b>) wavenumber distribution of Case 7; (<b>d</b>) depth distribution of Case 7. The white circle represents the actual location of the damage. The actual depth of the defect is 1 mm.</p> Full article ">Figure 20
<p>Experimental results of Case 8 and Case 9. (<b>a</b>) Wavenumber distribution of Case 8; (<b>b</b>) depth distribution of Case 8; (<b>c</b>) wavenumber distribution of Case 9; (<b>d</b>) depth distribution of Case 9. The white circle represents the actual location of the damage. The actual depth of the defect is 1 mm.</p> Full article ">Figure 21
<p>Experimental results of Case 10 and Case 11. (<b>a</b>) Wavenumber distribution of Case 10; (<b>b</b>) depth distribution of Case 10; (<b>c</b>) wavenumber distribution of Case 11; (<b>d</b>) depth distribution of Case 11. The white rectangle represents the actual location of the damage. The actual depth of the defect is 1 mm.</p> Full article ">Figure 22
<p>The direction identification of an inclined rectangular groove based on the experimental result. (<b>a</b>) 90°; (<b>b</b>) 135°. The red plus (+) indicates the centroid location. The blue dashed line is the spindle. The green dash line is boundary of the inclined rectangular groove. The background image is a grayscale image which is processed by a threshold at the level of −3 dB.</p> Full article ">Figure 23
<p>The wavenumber distributions of the spatial window when different conditions are taken into consideration. (<b>a</b>) Condition 1; (<b>b</b>) condition 2; (<b>c</b>) condition 3; (<b>d</b>) condition 4; (<b>e</b>) condition 5; (<b>f</b>) condition 6. The conditions are listed in <a href="#applsci-08-01600-t009" class="html-table">Table 9</a>.</p> Full article ">Figure 24
<p>The test results obtained under various window radii. (<b>a</b>) 5 mm; (<b>b</b>) 6 mm; (<b>c</b>) 7 mm; (<b>d</b>) 8 mm; (<b>e</b>) 9 mm; (<b>f</b>) 10 mm; (<b>g</b>) 11 mm; (<b>h</b>) 12 mm. The white circle represents the actual location of the damage. The central frequency of the excitation signal is 400 kHz. A circular flat bottom hole is located in (185, 185).</p> Full article ">Figure 25
<p>The maximum wavenumber obtained under various window radii. The central frequency of the excitation signal is 400 kHz.</p> Full article ">
18 pages, 4478 KiB  
Article
Ultrasonic Guided Wave-Based Circumferential Scanning of Plates Using a Synthetic Aperture Focusing Technique
by Jianjun Wu, Zhifeng Tang, Keji Yang, Shiwei Wu and Fuzai Lv
Appl. Sci. 2018, 8(8), 1315; https://doi.org/10.3390/app8081315 - 7 Aug 2018
Cited by 7 | Viewed by 4211
Abstract
Tanks are essential facilities for oil and chemical storage and transportation. As indispensable parts, the tank floors have stringent nondestructive testing requirements owing to their severe operating conditions. In this article, a synthetic aperture focusing technology method is proposed for the circumferential scanning [...] Read more.
Tanks are essential facilities for oil and chemical storage and transportation. As indispensable parts, the tank floors have stringent nondestructive testing requirements owing to their severe operating conditions. In this article, a synthetic aperture focusing technology method is proposed for the circumferential scanning of the tank floor from the edge outside the tank using ultrasonic guided waves. The zeroth shear horizontal (SH0) mode is selected as an ideal candidate for plate inspection, and the magnetostrictive sandwich transducer (MST) is designed and manufactured for the generation and receiving of the SH0 mode. Based on the exploding reflector model (ERM), the relationships between guided wave fields at different radii of polar coordinates are derived in the frequency domain. The defect spot is focused when the sound field is calculated at the radius of the defect. Numerical and experimental validations are performed for the defect inspection in an iron plate. The angular bandwidth of the defect spot is used as an index for the angular resolution. The results of the proposed method show significant improvement compared to those obtained by the B-scan method, and it is found to be superior to the conventional method—named delay and sum (DAS)—in both angular resolution and calculation efficiency. Full article
(This article belongs to the Special Issue Ultrasonic Guided Waves)
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<p>The diagram of the circumferential scanning using guided waves.</p> Full article ">Figure 2
<p>Dispersion curves of iron plates: (<b>a</b>) phase velocity curves; (<b>b</b>) group velocity curves.</p> Full article ">Figure 3
<p>Wave structures of shear horizontal (SH) modes in the main vibration direction <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mn>2</mn> </msub> </mrow> </semantics></math>: (<b>a</b>) SH0; (<b>b</b>) SH1; (<b>c</b>) SH2; (<b>d</b>) SH3.</p> Full article ">Figure 3 Cont.
<p>Wave structures of shear horizontal (SH) modes in the main vibration direction <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mn>2</mn> </msub> </mrow> </semantics></math>: (<b>a</b>) SH0; (<b>b</b>) SH1; (<b>c</b>) SH2; (<b>d</b>) SH3.</p> Full article ">Figure 4
<p>The structure of the magnetostrictive sandwich transducer (MST).</p> Full article ">Figure 5
<p>The sound fields and divergence angles of the MSTs with different lengths: (<b>a</b>) 2L = 30 mm; (<b>b</b>) 2L = 50 mm; (<b>c</b>) 2L = 70 mm; (<b>d</b>) 2L = 90 mm.</p> Full article ">Figure 5 Cont.
<p>The sound fields and divergence angles of the MSTs with different lengths: (<b>a</b>) 2L = 30 mm; (<b>b</b>) 2L = 50 mm; (<b>c</b>) 2L = 70 mm; (<b>d</b>) 2L = 90 mm.</p> Full article ">Figure 6
<p>The relationship between the divergence angles of the main lobes and the lengths of the MSTs.</p> Full article ">Figure 7
<p>The diagram of the numerical model.</p> Full article ">Figure 8
<p>The excitation signals with different cycles and their amplitude spectrums: (<b>a</b>) three cycles; (<b>b</b>) five cycles; (<b>c</b>) seven cycles; (<b>d</b>) nine cycles. The half-decline frequency bandwidth of the signals is marked.</p> Full article ">Figure 8 Cont.
<p>The excitation signals with different cycles and their amplitude spectrums: (<b>a</b>) three cycles; (<b>b</b>) five cycles; (<b>c</b>) seven cycles; (<b>d</b>) nine cycles. The half-decline frequency bandwidth of the signals is marked.</p> Full article ">Figure 9
<p>The results for the angular step <math display="inline"><semantics> <mrow> <mn>0.5</mn> <mo>°</mo> <mtext> </mtext> </mrow> </semantics></math>by different methods: (<b>a</b>) B-scan, (<b>b</b>) delay and sum (DAS), (<b>c</b>) circumferential synthetic aperture focusing technique (CSAFT). The excitation signal is a tone-burst signal with three cycles.</p> Full article ">Figure 10
<p>Comparisons of three methods with different factors: (<b>a</b>) the angular bandwidth <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mi>w</mi> </msub> </mrow> </semantics></math> by the transducer with different lengths; (<b>b</b>) Calculation times with different numbers of signals. The excitation signal is a tone-burst signal with three cycles.</p> Full article ">Figure 11
<p>Comparisons of the results by the B-scan (<b>Left</b>), DAS (<b>Middle</b>), and CSAFT (<b>Right</b>) methods for different angular steps: (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>1</mn> <mo>°</mo> </mrow> </semantics></math>; (<b>b</b>)<math display="inline"><semantics> <mrow> <mtext> </mtext> <msub> <mi>θ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>1.5</mn> <mo>°</mo> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>2.0</mn> <mo>°</mo> </mrow> </semantics></math>. The excitation signal is a tone-burst signal with three cycles.</p> Full article ">Figure 12
<p>Comparisons of the results by the CSAFT method for excitation signals with different cycles: (<b>a</b>) five cycles; (<b>b</b>) seven cycles; (<b>c</b>) nine cycles. <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mi>w</mi> </msub> </mrow> </semantics></math> is the angular bandwidth of the defect spot.</p> Full article ">Figure 13
<p>The magnetostrictive guided wave inspection system for circumferential scanning in the plate.</p> Full article ">Figure 14
<p>Circumferential scanning in the iron plate using guided waves.</p> Full article ">Figure 15
<p>Experimental images by the three methods: (<b>a</b>) B-scan; (<b>b</b>) DAS; (<b>c</b>) CSAFT.</p> Full article ">
15 pages, 7008 KiB  
Article
Calculation of Guided Wave Dispersion Characteristics Using a Three-Transducer Measurement System
by Borja Hernandez Crespo, Charles R. P. Courtney and Bhavin Engineer
Appl. Sci. 2018, 8(8), 1253; https://doi.org/10.3390/app8081253 - 29 Jul 2018
Cited by 35 | Viewed by 5971
Abstract
Guided ultrasonic waves are of significant interest in the health monitoring of thin structures, and dispersion curves are important tools in the deployment of any guided wave application. Most methods of determining dispersion curves require accurate knowledge of the material properties and thickness [...] Read more.
Guided ultrasonic waves are of significant interest in the health monitoring of thin structures, and dispersion curves are important tools in the deployment of any guided wave application. Most methods of determining dispersion curves require accurate knowledge of the material properties and thickness of the structure to be inspected, or extensive experimental tests. This paper presents an experimental technique that allows rapid generation of dispersion curves for guided wave applications when knowledge of the material properties and thickness of the structure to be inspected are unknown. The technique uses a single source and measurements at two points, making it experimentally simple. A formulation is presented that allows calculation of phase and group velocities if the wavepacket propagation time and relative phase shift can be measured. The methodology for determining the wavepacket propagation time and relative phase shift from the acquired signals is described. The technique is validated using synthesized signals, finite element model-generated signals and experimental signals from a 3 mm-thick aluminium plate. Accuracies to within 1% are achieved in the experimental measurements. Full article
(This article belongs to the Special Issue Ultrasonic Guided Waves)
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<p>Wavepacket arriving at <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>0</mn> </msub> </mrow> </semantics></math> at time <math display="inline"><semantics> <mrow> <msub> <mi>t</mi> <mn>0</mn> </msub> </mrow> </semantics></math> with phase <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mn>0</mn> </msub> </mrow> </semantics></math> propagating at group velocity <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>g</mi> </msub> </mrow> </semantics></math>. <math display="inline"><semantics> <mrow> <mi>G</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> is represented as the envelope of the wavepacket.</p> Full article ">Figure 2
<p>S<sub>0</sub>-mode wavepacket of 5 cycles at 150 kHz after propagating 1.2 m, with dispersion and without dispersion.</p> Full article ">Figure 3
<p>Methodology’s block diagram to extract the optimum phase shift and time delay.</p> Full article ">Figure 4
<p>Schematic of the test setup.</p> Full article ">Figure 5
<p>Wavepacket detection and boundary determination established by the algorithm for two signals acquired at: (<b>a</b>) 30 cm and (<b>b</b>) 35 cm from the transmitter using a d<sub>33</sub>-type transducer.</p> Full article ">Figure 6
<p>Shortening of the signals to reduce computational time. The same limits are used to truncate each signal in order to maintain the time difference between wavepackets. Signals acquired at: (<b>a</b>) 30 cm and (<b>b</b>) 35 cm from the transmitter.</p> Full article ">Figure 7
<p>Comparison of the phase velocity and group velocity of <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">S</mi> <mn>0</mn> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">A</mi> <mn>0</mn> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>SH</mi> </mrow> <mn>0</mn> </msub> </mrow> </semantics></math> between the results from the synthesized signals (black circles) and theoretical values (grey lines).</p> Full article ">Figure 7 Cont.
<p>Comparison of the phase velocity and group velocity of <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">S</mi> <mn>0</mn> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">A</mi> <mn>0</mn> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>SH</mi> </mrow> <mn>0</mn> </msub> </mrow> </semantics></math> between the results from the synthesized signals (black circles) and theoretical values (grey lines).</p> Full article ">Figure 8
<p>Comparison of the phase shift of S<sub>0</sub>, A<sub>0</sub> and SH<sub>0</sub> between the results from the synthesized signals (black circles) and theoretical values (grey lines).</p> Full article ">Figure 9
<p>Images of the finite elementsimulation of the wave propagation in polar-coordinate instantaneous displacement is shown 76 µs after excitation. (<b>a</b>) Radial displacement, (<b>b</b>) tangential displacement and (<b>c</b>) out-of-plane displacement. Scale bars in meters.</p> Full article ">Figure 10
<p>Signal acquired at 33 cm from excitation point at 60 kHz.</p> Full article ">Figure 11
<p>Comparison of the phase velocity and group velocity of S<sub>0</sub>, A<sub>0</sub> and SH<sub>0</sub> between the results from the synthesized signals (black circles) and theoretical values (grey lines).</p> Full article ">Figure 12
<p>Experiment setup: <b>Left</b>–diagram of the experiment, <b>Right</b>–photo of the real experiment environment.</p> Full article ">Figure 13
<p>Schematics of the shear transducer. (<b>a</b>) Undeformed, (<b>b</b>) deformed.</p> Full article ">Figure 14
<p>Phase velocity and group velocity created from experimental signals for 5 cm propagation distance (black circles) and theoretical values (grey lines).</p> Full article ">Figure 15
<p>Phase velocity and group velocity created from experimental signals for 10 cm propagation distance (black circles) and theoretical values (grey lines).</p> Full article ">
22 pages, 3402 KiB  
Article
Using the Partial Wave Method for Wave Structure Calculation and the Conceptual Interpretation of Elastodynamic Guided Waves
by Christopher Hakoda and Cliff J. Lissenden
Appl. Sci. 2018, 8(6), 966; https://doi.org/10.3390/app8060966 - 12 Jun 2018
Cited by 19 | Viewed by 5283
Abstract
The partial-wave method takes advantage of the Christoffel equation’s generality to represent waves within a waveguide. More specifically, the partial-wave method is well known for its usefulness when calculating dispersion curves for multilayered and/or anisotropic plates. That is, it is a vital component [...] Read more.
The partial-wave method takes advantage of the Christoffel equation’s generality to represent waves within a waveguide. More specifically, the partial-wave method is well known for its usefulness when calculating dispersion curves for multilayered and/or anisotropic plates. That is, it is a vital component of the transfer-matrix method and the global-matrix method, which are used for dispersion curve calculation. The literature suggests that the method is also exceptionally useful for conceptual interpretation, but gives very few examples or instruction on how this can be done. In this paper, we expand on this topic of conceptual interpretation by addressing Rayleigh waves, Stoneley waves, shear horizontal waves, and Lamb waves. We demonstrate that all of these guided waves can be described using the partial-wave method, which establishes a common foundation on which many elastodynamic guided waves can be compared, translated, and interpreted. For Lamb waves specifically, we identify the characteristics of guided wave modes that have not been formally discussed in the literature. Additionally, we use what is demonstrated in the body of the paper to investigate the leaky characteristics of Lamb waves, which eventually leads to finding a correlation between oblique bulk wave propagation in the waveguide and the transmission amplitude ratios found in the literature. Full article
(This article belongs to the Special Issue Ultrasonic Guided Waves)
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Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>Depiction of the characteristics of (<b>a</b>) region 1, (<b>b</b>) region 2, and (<b>c</b>) region 3 with respect to the slowness curves of an isotropic solid. Slowness curves with solid lines denote real-valued <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>z</mi> </msub> </mrow> </semantics></math> solutions, and dotted lines denote imaginary-valued <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>z</mi> </msub> </mrow> </semantics></math> solutions. This figure is a compilation of elements from the figures in Auld [<a href="#B2-applsci-08-00966" class="html-bibr">2</a>] and Crandall [<a href="#B6-applsci-08-00966" class="html-bibr">6</a>].</p> Full article ">Figure 2
<p>Lamb wave dispersion curves for an aluminum plate divided according to the three regions shown in <a href="#applsci-08-00966-f001" class="html-fig">Figure 1</a>.</p> Full article ">Figure 3
<p>Conceptual depiction of the partial waves, which are necessary for the Rayleigh-wave problem, overlaid on a traction-free boundary of an aluminum half-space.</p> Full article ">Figure 4
<p>Conceptual depiction of the partial waves from tungsten and aluminum, which are necessary for the Stoneley wave problem, overlaid on the two half-spaces.</p> Full article ">Figure 5
<p>Wave structure of a Stoneley wave calculated using the partial-wave method at an aluminum/tungsten interface. Blue lines are the coordinate axis. −<math display="inline"><semantics> <mi>z</mi> </semantics></math> is in the tungsten half-space, and +<math display="inline"><semantics> <mi>z</mi> </semantics></math> is in the aluminum half-space.</p> Full article ">Figure 6
<p>Conceptual depiction of the partial waves, which are necessary for the A0 Lamb wave problem, overlaid on a plate in vacuum.</p> Full article ">Figure 7
<p>Conceptual depiction of the partial waves, which are necessary for the S0 Lamb wave problem, overlaid on a plate in vacuum. The angle for the propagation direction of the shear vertical partial waves was calculated using <math display="inline"><semantics> <mrow> <msup> <mrow> <mi>tan</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>(</mo> <mrow> <msub> <mi>k</mi> <mi>x</mi> </msub> <mo>/</mo> <msub> <mi>k</mi> <mi>z</mi> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math>.</p> Full article ">Figure 8
<p>Amplitude of the (<b>a</b>) longitudinal (i.e., <math display="inline"><semantics> <mrow> <msubsup> <mi>B</mi> <mrow> <mi>a</mi> <mi>v</mi> <mi>g</mi> </mrow> <mrow> <mrow> <mo>(</mo> <mi>L</mi> <mo>)</mo> </mrow> </mrow> </msubsup> </mrow> </semantics></math>) and (<b>b</b>) shear vertical (i.e., <math display="inline"><semantics> <mrow> <msubsup> <mi>B</mi> <mrow> <mi>a</mi> <mi>v</mi> <mi>g</mi> </mrow> <mrow> <mrow> <mo>(</mo> <mrow> <mi>S</mi> <mi>V</mi> </mrow> <mo>)</mo> </mrow> </mrow> </msubsup> </mrow> </semantics></math>) partial waves after normalizing and averaging the magnitude for various points on the Lamb wave dispersion curves for a 1-mm thick aluminum plate.</p> Full article ">Figure 9
<p><math display="inline"><semantics> <mi>q</mi> </semantics></math> value which is indicative of the phase difference between the top and bottom partial waves for various points on the Lamb wave dispersion curves for a 1-mm thick aluminum plate. The color axis is constrained to <math display="inline"><semantics> <mrow> <mo>+</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </semantics></math>.</p> Full article ">Figure 10
<p>Depiction of the aluminum slowness curves compared with the slowness curve for air. Slowness curves with solid lines denote real-valued <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>z</mi> </msub> </mrow> </semantics></math> solutions, and dotted lines denote imaginary-valued <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>z</mi> </msub> </mrow> </semantics></math> solutions (figure not to scale).</p> Full article ">Figure 11
<p>Amplitude of the longitudinal partial waves in the air half-space after normalizing and averaging the magnitude for various points on the Lamb wave dispersion curves for a 1-mm thick aluminum plate. The Lamb wave dispersion curves were calculated assuming traction-free boundary conditions (BC).</p> Full article ">Figure 12
<p>Depiction of the oblique plane wave problem being considered.</p> Full article ">Figure 13
<p>(<b>a</b>) The absolute value, (<b>b</b>) real part, and (<b>c</b>) imaginary part of the amplitude ratios for an incident shear vertical bulk wave at an aluminum–air interface.</p> Full article ">
14 pages, 2421 KiB  
Article
A Hybrid Ultrasonic Guided Wave-Fiber Optic System for Flaw Detection in Pipe
by Joseph L. Rose, Jason Philtron, Guigen Liu, Yupeng Zhu and Ming Han
Appl. Sci. 2018, 8(5), 727; https://doi.org/10.3390/app8050727 - 5 May 2018
Cited by 18 | Viewed by 5755
Abstract
The work presented in this paper shows that Fiber Bragg Grating (FBG) optical fiber sensors can potentially be used as receivers in a long-range guided wave torsional-mode pipe inspection system. Benefits over the conventional pulse-echo method arise due to reduced total travel distance [...] Read more.
The work presented in this paper shows that Fiber Bragg Grating (FBG) optical fiber sensors can potentially be used as receivers in a long-range guided wave torsional-mode pipe inspection system. Benefits over the conventional pulse-echo method arise due to reduced total travel distance of the ultrasonic guided wave reflections, since reflections from defects and structural features do not need to propagate a full round trip back to the transmitting collar. This is especially important in pipe configurations with high attenuation, such as coated and buried pipelines. The use of FBGs as receivers instead of conventional piezoelectric or magnetostrictive elements also significantly reduces cabling, since multiple FBG receivers can be placed along a single optical fiber which has a diameter on the order of only around 100 ?m. The basic approach and sample results are presented in the paper. Additionally, a brief overview of some topics in ultrasonic guided waves is presented as a background to understand the inspection problem presented here. Full article
(This article belongs to the Special Issue Ultrasonic Guided Waves)
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<p>Global hybrid ultrasonic guided wave and fiber optic inspection system concept. The range of a conventional collar at position 0 can be increased beyond position X using a fiber optic sensor attached near position X. This allows the hybrid system to detect a flaw at a further distance, position Y.</p> Full article ">Figure 2
<p>Schematic of the 21-foot pipe specimen. The SMS collar and the initial FBG sensor locations were 3 feet from the pipe end. Flaws were introduced at 13 feet and 10 feet from the pipe end. The side with flaw 2 will be referred to as the right side. Number and locations of the optical fiber sensors vary in the different experiments.</p> Full article ">Figure 3
<p>Schematic of the integrated ultrasonic-optical system setup. A servo controller was used to keep the laser wavelength locked to the slope of the FBG spectrum for each channel. The optical signal was converted to a voltage signal and recorded using conventional ultrasonic hardware.</p> Full article ">Figure 4
<p>F-Scan generated using an FBG sensor directly bonded to the bottom side of the pipe at 3 feet from the pipe end, collocated with SMS sending collar. Flaw indications are shown at 7 feet and 10 feet from the sensor. Pipe end reflections are shown at −3 feet and 18 feet. Indications at 3 feet and 13 feet are due to waves traveling from the SMS collar in the reverse direction and bouncing off the near end of the pipe at −3 feet, a result of imperfect directional control. The optical fiber sensor can clearly be used for flaw detection.</p> Full article ">Figure 5
<p>F-Scan generated using the SMS collar in pulse-echo mode at 3 feet from the pipe end. Flaw indications are shown at 7 feet and 10 feet from the sensor. Pipe end reflections are shown at −3 feet and 18 feet. There is a higher signal-to-noise ratio for this setup. Note also that the dual coils allow for directional control of the received wave, suppressing the reverse waves shown in <a href="#applsci-08-00727-f004" class="html-fig">Figure 4</a>.</p> Full article ">Figure 6
<p>Waveform data (amplitude envelope) for SHM states with flaw growth of 0 to 2% CSA for the flaw located 7 feet from the optical fiber sensor. Waveforms are shown for an excitation frequency of 76 kHz using the SMS collar and a single direct-bonded FBG optical fiber sensor used as a receiver. As the flaw grows, the reflected ultrasonic wave energy from the flaw increases. The optical fiber sensor can clearly be used for flaw sizing.</p> Full article ">Figure 7
<p>F-Scans collected using a direct-bonded FBG receiver collocated with the sending collar at several circumferential locations: (<b>a</b>) top; (<b>b</b>) right side; (<b>c</b>) bottom; and (<b>d</b>) left side of the pipe. Since the receiver is relatively far from the flaws, both flaws (red ovals) are clearly detectable at all circumferential locations. Flaw indications are marked by the red ovals. Arrows indicate the axial location of the fiber optic receiver. Distance is indicated from source/receiver position. When the receiver is relatively far from the flaw, i.e., multiple pipe circumferences, flaw detection is reliable at any circumferential location. Note that the indication in (<b>c</b>) at 13 feet (rectangle) is due to a reverse wave reflection.</p> Full article ">Figure 8
<p>F-Scans collected using a direct-bonded FBG receiver 6 feet in front of the sending collar at several circumferential locations: (<b>a</b>) top; (<b>b</b>) right side; (<b>c</b>) bottom; and (<b>d</b>) left side of the pipe. Since the receiver is relatively close to the flaws, the best flaw detection occurs directly in line with the flaw location, while the detection at other circumferential locations is unreliable. Clear flaw indications are marked by the red ovals and less clear or undetectable flaw indications are marked by dashed red ovals. Arrows indicate the axial location of the fiber optic receiver. Distance is indicated from the sending collar. When the receiver is near the flaw, but not at the same circumferential location, flaw detection is not reliable, due to the use of a point-like sensor.</p> Full article ">Figure 9
<p>Schematic showing sensor locations for array groups 1 (<b>above</b>) and 2 (<b>below</b>). Fiber optic sensors are indicated by green rectangles and the optical fiber is indicated by the blue line. Dashed lines indicate the optical fiber and sensor on the far side of the pipe. The pipe is being viewed from the right side (flaw 2 side).</p> Full article ">Figure 10
<p>F-Scans of the processed group waveforms for both (<b>a</b>) group 1 and (<b>b</b>) group 2 fiber optic sensor arrays. Flaws (red ovals) are clearly detected at 7 feet and 10 feet from the sending collar across a wide range of frequencies. The far pipe end reflection is detected at 18 feet. Note that groups 1 and 2 both detect the flaws even though group 2 has multiple sensors near flaws in non-ideal locations for efficient flaw detection.</p> Full article ">
13 pages, 878 KiB  
Article
Rapid High-Resolution Wavenumber Extraction from Ultrasonic Guided Waves Using Adaptive Array Signal Processing
by Shigeaki Okumura, Vu-Hieu Nguyen, Hirofumi Taki, Guillaume Haïat, Salah Naili and Toru Sato
Appl. Sci. 2018, 8(4), 652; https://doi.org/10.3390/app8040652 - 23 Apr 2018
Cited by 21 | Viewed by 4409
Abstract
Quantitative ultrasound techniques for assessment of bone quality have been attracting significant research attention. The axial transmission technique, which involves analysis of ultrasonic guided waves propagating along cortical bone, has been proposed for assessment of cortical bone quality. Because the frequency-dependent wavenumbers reflect [...] Read more.
Quantitative ultrasound techniques for assessment of bone quality have been attracting significant research attention. The axial transmission technique, which involves analysis of ultrasonic guided waves propagating along cortical bone, has been proposed for assessment of cortical bone quality. Because the frequency-dependent wavenumbers reflect the elastic parameters of the medium, high-resolution estimation of the wavenumbers is required at each frequency with low computational cost. We use an adaptive array signal processing method and propose a technique that can be used to estimate the numbers of propagation modes that exist at each frequency without the need for time-consuming calculations. An experimental study of 4-mm-thick copper and bone-mimicking plates showed that the proposed method estimated the wavenumbers accurately with estimation errors of less than 4% and a calculation time of less than 0.5 s when using a laptop computer. Full article
(This article belongs to the Special Issue Ultrasonic Guided Waves)
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<p>System model used in this study. In this study, we used a 4-mm-thick copper (homogeneous isotropic) plate and a 4-mm-thick bone mimicking (transversely isotropic) plate.</p> Full article ">Figure 2
<p>Proposed diagonal loading (DL) technique.</p> Full article ">Figure 3
<p>Dependence of the proposed method on sub-array size. The black solid line and the dotted line show the results for arrays composed of different numbers of receivers. The vertical black dotted lines show the horizontal values with <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <msub> <mi>N</mi> <mi mathvariant="normal">R</mi> </msub> <mo>/</mo> <mn>2</mn> </mrow> </semantics></math>, i.e., <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mi>sub</mi> </msub> <mo>−</mo> <mn>1</mn> <mo>=</mo> <msub> <mi>N</mi> <mi mathvariant="normal">R</mi> </msub> <mo>/</mo> <mn>2</mn> </mrow> </semantics></math>.</p> Full article ">Figure 4
<p>Wavenumbers of the 4-mm-thick copper plate estimated using the conventional singular value decomposition (SVD) method. The color intensity map shows the results obtained using the conventional SVD method. Solid white lines show the theoretical curves.</p> Full article ">Figure 5
<p>Wavenumbers of the 4-mm-thick copper plate estimated using the proposed method and the conventional SVD method. Red dots show the estimates obtained using the proposed method. The color intensity map shows the results obtained using the conventional SVD method. Solid white lines show the theoretical curves.</p> Full article ">Figure 6
<p>Wavenumbers of the 4-mm-thick bone-mimicking plate estimated using the conventional SVD method. The color intensity map shows the results obtained using the conventional SVD method. Solid white lines show the theoretical curves.</p> Full article ">Figure 7
<p>Wavenumbers of the 4-mm-thick bone-mimicking plate estimated using the proposed method and the conventional SVD method. Red dots show the estimates obtained using the proposed method. The color intensity map shows the results obtained using the conventional SVD method. Solid white lines show the theoretical curves.</p> Full article ">Figure 8
<p>Depiction of the wavenumbers obtained using the proposed method and the spectrum obtained using the conventional method at 1.0 MHz. This is the cross-sectional view at the white dotted line shown in <a href="#applsci-08-00652-f007" class="html-fig">Figure 7</a>. The vertical blue dotted lines indicate the theoretical values.</p> Full article ">Figure 9
<p>Wavenumbers of the 4-mm-thick bone-mimicking plate estimated using the conventional estimation of signal parameters via rotational invariance technique (ESPRIT) algorithm at a fixed threshold of <math display="inline"><semantics> <mrow> <mo>−</mo> <mn>40</mn> </mrow> </semantics></math> dB and the proposed method. Red dots show the estimates obtained using the proposed method and blue cross marks show the estimates obtained using the conventional method. Solid gray lines show the theoretical curves.</p> Full article ">Figure 10
<p>Wavenumbers of the 4-mm-thick bone-mimicking plate estimated using the conventional ESPRIT algorithm at a fixed threshold of <math display="inline"><semantics> <mrow> <mo>−</mo> <mn>30</mn> </mrow> </semantics></math> dB and the proposed method. Red dots show the estimates obtained using the proposed method and blue cross marks show the estimates obtained using the conventional method. Solid gray lines show the theoretical curves.</p> Full article ">Figure 11
<p>Wavenumbers estimated for differently sized sub-arrays. Red cross marks and blue circles show the results obtained for <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mi>sub</mi> </msub> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math> and 26, respectively. Black lines show the theoretical curves.</p> Full article ">
19 pages, 1823 KiB  
Article
Damage Imaging in Lamb Wave-Based Inspection of Adhesive Joints
by Magdalena Rucka, Erwin Wojtczak and Jacek Lachowicz
Appl. Sci. 2018, 8(4), 522; https://doi.org/10.3390/app8040522 - 29 Mar 2018
Cited by 36 | Viewed by 4829
Abstract
Adhesive bonding has become increasingly important in many industries. Non-destructive inspection of adhesive joints is essential for the condition assessment and maintenance of a structure containing such joints. The aim of this paper was the experimental investigation of the damage identification of a [...] Read more.
Adhesive bonding has become increasingly important in many industries. Non-destructive inspection of adhesive joints is essential for the condition assessment and maintenance of a structure containing such joints. The aim of this paper was the experimental investigation of the damage identification of a single lap adhesive joint of metal plate-like structures. Nine joints with different defects in the form of partial debonding were considered. The inspection was based on ultrasonic guided wave propagation. The Lamb waves were excited at one point of the analyzed specimen by means of a piezoelectric actuator, while the guided wave field was measured with the use of a laser vibrometer. For damage imaging, the recorded out-of-plane vibrations were processed by means of the weighted root mean square (WRMS). The influence of different WRMS parameters (i.e., the time window and weighting factor), as well as excitation frequencies, were analyzed using statistical analysis. The results showed that two-dimensional representations of WRMS values allowed for the identification of the presence of actual defects in the adhesive film and determined their geometry. Full article
(This article belongs to the Special Issue Ultrasonic Guided Waves)
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Figure 1
<p>Geometry of the analyzed single lap joint: (<b>a</b>) plan view; and, (<b>b</b>) side view.</p> Full article ">Figure 2
<p>Investigated specimens: intact (#1) and with defects (#2–#9).</p> Full article ">Figure 3
<p>Photographs of the investigated specimens after separation (regions outlined with yellow line denote kissing defects).</p> Full article ">Figure 4
<p>Experimental setup: (<b>a</b>) instrumentation for generation and acquisition of Lamb waves; and, (<b>b</b>) detail showing the piezo actuator attached to the specimen.</p> Full article ">Figure 5
<p>Investigated specimen with indicated scanning points.</p> Full article ">Figure 6
<p>Experimental and theoretical dispersion curves obtained for different excitation frequencies of 50 kHz, 100 kHz, and 200 kHz: (<b>a</b>) steel 3 mm plate (<span class="html-italic">E</span> = 195.2 GPa, <span class="html-italic">v</span> = 0.3, <span class="html-italic">ρ</span> = 7741.7 kg/m<sup>3</sup>); and (<b>b</b>) two adhesively jointed steel 3 mm plates (<span class="html-italic">E</span> = 195.2 GPa, <span class="html-italic">v</span> = 0.3, <span class="html-italic">ρ</span> = 7741.7 kg/m<sup>3</sup>) adhesively bonded with the adhesive layer of a thickness of 0.2 mm (<span class="html-italic">E</span> = 5 GPa, <span class="html-italic">v</span> = 0.35, <span class="html-italic">ρ</span> = 1130 kg/m<sup>3</sup>).</p> Full article ">Figure 7
<p>Scanning laser Doppler vibrometry (SLDV) maps of considered joints at the time instance 27.7 μs (dimensions of the joint are given in meters; the adhesive was 0.06–0.12 m).</p> Full article ">Figure 8
<p>Weighted root mean square (WRMS) maps (values in (m/s)) for specimen #5 for different weighting factors <span class="html-italic">w<sub>r</sub></span> = 1 (first column), <span class="html-italic">w<sub>r</sub></span> = <span class="html-italic">r</span> (second column), <span class="html-italic">w<sub>r</sub></span> = <span class="html-italic">r</span><sup>2</sup> (third column) and varying time window: (<b>a</b>) <span class="html-italic">T</span> = 0.03 ms; (<b>b</b>) <span class="html-italic">T</span> = 0.05 ms; (<b>c</b>) <span class="html-italic">T</span> = 0.50 ms; (<b>d</b>) <span class="html-italic">T</span> = 1.00 ms; (<b>e</b>) <span class="html-italic">T</span> = 2.00 ms; and, (<b>f</b>) <span class="html-italic">T</span> = 3.00 ms.</p> Full article ">Figure 9
<p>WRMS maps (values in (m/s)) for joints with internal defects for constant time window (<span class="html-italic">T</span> = 3.00 ms) and different weighting factors <span class="html-italic">w<sub>r</sub></span> = 1 (first column), <span class="html-italic">w<sub>r</sub></span> = <span class="html-italic">r</span> (second column), <span class="html-italic">w<sub>r</sub></span> = <span class="html-italic">r</span><sup>2</sup> (third column): (<b>a</b>) specimen #8; and, (<b>b</b>) specimen #9.</p> Full article ">Figure 10
<p>WRMS maps (values in (m/s)) for specimens #1–#9 (<span class="html-italic">T</span> = 3.00 ms, <span class="html-italic">w<sub>r</sub></span> = <span class="html-italic">r</span>).</p> Full article ">Figure 11
<p>WRMS maps (values in (m/s)) for specimens #1–#9 (<span class="html-italic">T</span> = 3.00 ms, <span class="html-italic">w<sub>r</sub></span> = <span class="html-italic">r</span><sup>2</sup>).</p> Full article ">Figure 12
<p>WRMS maps (values in (m/s)) with linear weighting factor (<span class="html-italic">w<sub>r</sub></span> = <span class="html-italic">r</span>), time window <span class="html-italic">T</span> = 3.00 ms and with different excitation frequencies <span class="html-italic">f</span> = 200 kHz (first column), <span class="html-italic">f</span> = 100 kHz (second column), <span class="html-italic">f</span> = 50 kHz (third column): (<b>a</b>) specimen #6; and (<b>b</b>) specimen #7.</p> Full article ">Figure 13
<p>WRMS maps (values in (m/s)) with square weighting factor (<span class="html-italic">w<sub>r</sub></span> = <span class="html-italic">r</span><sup>2</sup>), time window <span class="html-italic">T</span> = 3.00 ms and with different excitation frequencies <span class="html-italic">f</span> = 200 kHz (first column), <span class="html-italic">f</span> = 100 kHz (second column), <span class="html-italic">f</span> = 50 kHz (third column): (<b>a</b>) specimen #6; and, (<b>b</b>) specimen #7.</p> Full article ">Figure 14
<p>Histograms of WRMS values (<span class="html-italic">w<sub>r</sub></span> = <span class="html-italic">r</span>) for specimen #5 with different time windows: (<b>a</b>) <span class="html-italic">T</span> = 0.03 ms; (<b>b</b>) <span class="html-italic">T</span> = 0.05 ms; (<b>c</b>) <span class="html-italic">T</span> = 0.50 ms; (<b>d</b>) <span class="html-italic">T</span> = 1.00 ms; (<b>e</b>) <span class="html-italic">T</span> = 2.00 ms; and, (<b>f</b>) <span class="html-italic">T</span> = 3.00 ms.</p> Full article ">Figure 15
<p>Histograms of WRMS values (<span class="html-italic">w<sub>r</sub></span> = <span class="html-italic">r</span><sup>2</sup>) for specimen #5 with different time windows: (<b>a</b>) <span class="html-italic">T</span>= 0.03 ms; (<b>b</b>) <span class="html-italic">T</span> = 0.05 ms; (<b>c</b>) <span class="html-italic">T</span> = 0.50 ms; (<b>d</b>) <span class="html-italic">T</span> = 1.00 ms; (<b>e</b>) <span class="html-italic">T</span> = 2.00 ms; and, (<b>f</b>) <span class="html-italic">T</span> = 3.00 ms.</p> Full article ">Figure 16
<p>Histogram of WRMS values for specimens #1–#9 (<span class="html-italic">T</span> = 3.00 ms, <span class="html-italic">w<sub>r</sub></span> = <span class="html-italic">r</span>).</p> Full article ">Figure 17
<p>Histogram of WRMS values for specimens #1–#9 (<span class="html-italic">T</span> = 3.00 ms, <span class="html-italic">w<sub>r</sub></span> = <span class="html-italic">r</span><sup>2</sup>).</p> Full article ">Figure 18
<p>Relationships between the relative peak distance of WRMS histograms and weighting factor (represented by power <span class="html-italic">m</span>) for specimens #2–#6.</p> Full article ">Figure 19
<p>Relationships between the relative defect surface and weighting factor (represented by power <span class="html-italic">m</span>) for specimens #2–#6.</p> Full article ">Figure 20
<p>Histograms of WRMS values for specimen #6 with different excitation frequencies (<span class="html-italic">T</span> = 3.00 ms, <span class="html-italic">w<sub>r</sub></span> = <span class="html-italic">r</span>).</p> Full article ">
17 pages, 1953 KiB  
Article
Forward and Inverse Studies on Scattering of Rayleigh Wave at Surface Flaws
by Bin Wang, Yihui Da and Zhenghua Qian
Appl. Sci. 2018, 8(3), 427; https://doi.org/10.3390/app8030427 - 12 Mar 2018
Cited by 5 | Viewed by 3376
Abstract
The Rayleigh wave has been frequently applied in geological seismic inspection and ultrasonic non-destructive testing, due to its low attenuation and dispersion. A thorough and effective utilization of Rayleigh wave requires better understanding of its scattering phenomenon. The paper analyzes the scattering of [...] Read more.
The Rayleigh wave has been frequently applied in geological seismic inspection and ultrasonic non-destructive testing, due to its low attenuation and dispersion. A thorough and effective utilization of Rayleigh wave requires better understanding of its scattering phenomenon. The paper analyzes the scattering of Rayleigh wave at the canyon-shaped flaws on the surface, both in forward and inverse aspects. Firstly, we suggest a modified boundary element method (BEM) incorporating the far-field displacement patterns into the traditional BEM equation set. Results show that the modified BEM is an efficient and accurate approach for calculating far-field reflection coefficients. Secondly, we propose an inverse reconstruction procedure for the flaw shape using reflection coefficients of Rayleigh wave. By theoretical deduction, it can be proved that the objective function of flaw depth d(x1) is approximately expressed as an inverse Fourier transform of reflection coefficients in wavenumber domain. Numerical examples are given by substituting the reflection coefficients obtained from the forward analysis into the inversion algorithm, and good agreements are shown between the reconstructed flaw images and the geometric characteristics of the actual flaws. Full article
(This article belongs to the Special Issue Ultrasonic Guided Waves)
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Figure 1

Figure 1
<p>Problem configuration.</p> Full article ">Figure 2
<p>Two steps of calculating scattering wave field, (<b>a</b>) Step 1; (<b>b</b>) Step 2.</p> Full article ">Figure 3
<p>Boundary element method (BEM) discretization by constant elements.</p> Full article ">Figure 4
<p>Numerical examples: (<b>a</b>) a half-space with an arc-shaped canyon flaw; (<b>b</b>) a half-space with double canyons.</p> Full article ">Figure 5
<p>Time-domain signal of the incident wave.</p> Full article ">Figure 6
<p>Comparisons of the surface displacements obtained by the modified BEM and those in Kawase [<a href="#B10-applsci-08-00427" class="html-bibr">10</a>].</p> Full article ">Figure 7
<p>Displacement at different surface points in time-domain (<b>a</b>) <span class="html-italic">x</span><sub>1</sub> component; (<b>b</b>) <span class="html-italic">x</span><sub>2</sub> component.</p> Full article ">Figure 8
<p>Reflection amplitudes obtained by BEM and half-space scattering equation respectively.</p> Full article ">Figure 9
<p>Inverse reconstruction results of surface canyon-shaped flaws with different depth–radius ratios (<b>a</b>) <math display="inline"> <semantics> <mrow> <msub> <mi>d</mi> <mrow> <mi>max</mi> </mrow> </msub> <mo>/</mo> <mi>r</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics> </math>; (<b>b</b>) <math display="inline"> <semantics> <mrow> <msub> <mi>d</mi> <mrow> <mi>max</mi> </mrow> </msub> <mo>/</mo> <mi>r</mi> <mo>=</mo> <mn>0.2</mn> </mrow> </semantics> </math>; (<b>c</b>) <math display="inline"> <semantics> <mrow> <msub> <mi>d</mi> <mrow> <mi>max</mi> </mrow> </msub> <mo>/</mo> <mi>r</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics> </math>.</p> Full article ">Figure 10
<p>Inverse reconstruction results of surface canyon-shaped flaws with different frequency ranges (<b>a</b>) <math display="inline"> <semantics> <mrow> <msub> <mi>d</mi> <mrow> <mi>max</mi> </mrow> </msub> <mo>/</mo> <mi>r</mi> <mo>=</mo> <mn>0.2</mn> </mrow> </semantics> </math>; (<b>b</b>) <math display="inline"> <semantics> <mrow> <msub> <mi>d</mi> <mrow> <mi>max</mi> </mrow> </msub> <mo>/</mo> <mi>r</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics> </math>.</p> Full article ">Figure 11
<p>Inverse reconstruction results of double-canyon flaws (<b>a</b>) <math display="inline"> <semantics> <mrow> <mi>l</mi> <mo>/</mo> <mi>r</mi> <mo>=</mo> <mn>2.0</mn> </mrow> </semantics> </math>; (<b>b</b>) <math display="inline"> <semantics> <mrow> <mi>l</mi> <mo>/</mo> <mi>r</mi> <mo>=</mo> <mn>0.2</mn> </mrow> </semantics> </math>.</p> Full article ">
24 pages, 11813 KiB  
Article
The Study of Non-Detection Zones in Conventional Long-Distance Ultrasonic Guided Wave Inspection on Square Steel Bars
by Lei Zhang, Yuan Yang, Xiaoyuan Wei and Wenqing Yao
Appl. Sci. 2018, 8(1), 129; https://doi.org/10.3390/app8010129 - 17 Jan 2018
Cited by 9 | Viewed by 4385
Abstract
In a low-frequency ultrasonic guided wave dual-probe flaw inspection of a square steel bar with a finite length boundary, the flaw reflected pulse wave cannot be identified using conventional time monitoring when the flaw is located near the reflection terminal; therefore, the conventional [...] Read more.
In a low-frequency ultrasonic guided wave dual-probe flaw inspection of a square steel bar with a finite length boundary, the flaw reflected pulse wave cannot be identified using conventional time monitoring when the flaw is located near the reflection terminal; therefore, the conventional ultrasonic echo method is not applicable and results in a non-detection zone. Using analysis and simulations of ultrasonic guided waves for the inspection of a square steel bar, the reasons for the appearance of the non-detection zone and its characteristics were analyzed and the range of the non-detection zone was estimated. Subsequently, by extending the range of the conventional detection time domain, the envelope of the specific reflected pulse signal was extracted by a combination of simulations and related envelope calculations to solve the problem of the non-detection zone in conventional inspection methods. A comparison between the simulation and the experimental results demonstrate that the solution is feasible. This study has certain practical significance for ultrasonic guided wave structural monitoring. Full article
(This article belongs to the Special Issue Ultrasonic Guided Waves)
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Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>The equivalent model in low-frequency (<b>a</b>) The equivalent model of low-frequency ultrasonic guided wave in a square steel bar; (<b>b</b>) Low-frequency phase velocities of <span class="html-italic">S</span>0 and <span class="html-italic">A</span>0 modes provided by the beam, plate and elastic layer models.</p> Full article ">Figure 2
<p>The simulation settings.</p> Full article ">Figure 3
<p>Waveforms of the reflected pulses in the simulation, (<b>a</b>) <span class="html-italic">D</span>0 = 0 mm; (<b>b</b>) <span class="html-italic">D</span>0 = 5 mm, <span class="html-italic">L</span> = 3500 mm; (<b>c</b>) <span class="html-italic">D</span>0 = 5 mm, <span class="html-italic">L</span> = 4000 mm; (<b>d</b>) <span class="html-italic">D</span>0 = 5 mm, <span class="html-italic">L</span> = 4500 mm; (<b>e</b>) <span class="html-italic">D</span>0 = 5 mm, <span class="html-italic">L</span> = 5000 mm; (<b>f</b>) <span class="html-italic">D</span>0 = 5 mm, <span class="html-italic">L</span> = 5500 mm.</p> Full article ">Figure 3 Cont.
<p>Waveforms of the reflected pulses in the simulation, (<b>a</b>) <span class="html-italic">D</span>0 = 0 mm; (<b>b</b>) <span class="html-italic">D</span>0 = 5 mm, <span class="html-italic">L</span> = 3500 mm; (<b>c</b>) <span class="html-italic">D</span>0 = 5 mm, <span class="html-italic">L</span> = 4000 mm; (<b>d</b>) <span class="html-italic">D</span>0 = 5 mm, <span class="html-italic">L</span> = 4500 mm; (<b>e</b>) <span class="html-italic">D</span>0 = 5 mm, <span class="html-italic">L</span> = 5000 mm; (<b>f</b>) <span class="html-italic">D</span>0 = 5 mm, <span class="html-italic">L</span> = 5500 mm.</p> Full article ">Figure 4
<p>Establishment of the experimental platform (<b>a</b>) square steel bar with a length of 6000 mm; (<b>b</b>) picture of experimental instruments; (<b>c</b>) the diagram of the establishment of experimental platform.</p> Full article ">Figure 5
<p>The reflected pulse waves with different values of <span class="html-italic">D</span>0 at 5500 mm.</p> Full article ">Figure 6
<p>Schematic of the distance covered by the <span class="html-italic">S</span>0 mode pulse wave in (<b>a</b>) the first terminal-reflected pulse wave and (<b>b</b>) the flaw-reflected pulse wave in Interval I.</p> Full article ">Figure 7
<p>Curves of the non-detection zone ranges for different materials.</p> Full article ">Figure 8
<p>Simulated waveforms of the square steel bar with a length of 6000 mm at <span class="html-italic">L</span> ∈ [5300 mm, 5900 mm].</p> Full article ">Figure 9
<p>Envelope calculation results of the pulse wave at different locations of flaw: (<b>a</b>) <span class="html-italic">L</span> = 5400 mm <span class="html-italic">D</span>0 = 10 mm (<b>b</b>) <span class="html-italic">L</span> = 5500 mm <span class="html-italic">D</span>0 = 10 mm (<b>c</b>) <span class="html-italic">L</span> = 5600 mm <span class="html-italic">D</span>0 = 10 mm (<b>d</b>) <span class="html-italic">L</span> = 5700 mm <span class="html-italic">D</span>0 = 10 mm (<b>e</b>) <span class="html-italic">L</span> = 5800 mm <span class="html-italic">D</span>0 = 10 mm (<b>f</b>) <span class="html-italic">L</span> = 5900 mm <span class="html-italic">D</span>0 = 10 mm.</p> Full article ">Figure 9 Cont.
<p>Envelope calculation results of the pulse wave at different locations of flaw: (<b>a</b>) <span class="html-italic">L</span> = 5400 mm <span class="html-italic">D</span>0 = 10 mm (<b>b</b>) <span class="html-italic">L</span> = 5500 mm <span class="html-italic">D</span>0 = 10 mm (<b>c</b>) <span class="html-italic">L</span> = 5600 mm <span class="html-italic">D</span>0 = 10 mm (<b>d</b>) <span class="html-italic">L</span> = 5700 mm <span class="html-italic">D</span>0 = 10 mm (<b>e</b>) <span class="html-italic">L</span> = 5800 mm <span class="html-italic">D</span>0 = 10 mm (<b>f</b>) <span class="html-italic">L</span> = 5900 mm <span class="html-italic">D</span>0 = 10 mm.</p> Full article ">Figure 10
<p>The schematic diagram of the envelope approximation method.</p> Full article ">Figure 11
<p>Location of the flaw through the envelope approximation method: (<b>a</b>) The envelope of experimental data processing (<b>b</b>) The comparison of multiple envelopes in the effective comparison interval.</p> Full article ">Figure 12
<p>Location of a triangle flaw. (<b>a</b>) The triangle type of the flaw on the steel square bar; (<b>b</b>) The comparison of multiple envelopes in the effective comparison interval for the triangle flaw.</p> Full article ">Figure 12 Cont.
<p>Location of a triangle flaw. (<b>a</b>) The triangle type of the flaw on the steel square bar; (<b>b</b>) The comparison of multiple envelopes in the effective comparison interval for the triangle flaw.</p> Full article ">
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Article
Compensation for Group Velocity of Polychromatic Wave Measurement in Dispersive Medium
by Seung Jin Chang and Seung-Il Moon
Appl. Sci. 2017, 7(12), 1306; https://doi.org/10.3390/app7121306 - 18 Dec 2017
Cited by 2 | Viewed by 3879
Abstract
The estimation of instantaneous frequency (IF) method is introduced to compensate for the group velocity of electromagnetic wave in dispersive medium. The location of the reflected signal can be obtained by using the time-frequency cross correlation (TFCC), following which it is used to [...] Read more.
The estimation of instantaneous frequency (IF) method is introduced to compensate for the group velocity of electromagnetic wave in dispersive medium. The location of the reflected signal can be obtained by using the time-frequency cross correlation (TFCC), following which it is used to extract the transmitted signal from the total signal acquired. The signal propagated in the dispersive medium is attenuated and distorted by the attenuation characteristics, which depend on the frequency of the medium. By using the IF curve calculated for the transmitted signal, the changed center frequency and time terms can be obtained. The obtained terms are used to compensate for the group velocity error induced by signal distortion and attenuation. Through experiments and simulation, the accuracy of the proposed method is 2% higher than that of the conventional method when the signal propagates over a long distance. Full article
(This article belongs to the Special Issue Ultrasonic Guided Waves)
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Figure 1

Figure 1
<p>Illustration of compensation method based on IF curves.</p> Full article ">Figure 2
<p>Experimental setup.</p> Full article ">Figure 3
<p>The results of acquired signals: 40 m lossy cable, 80 m lossy cable, lossless cable (<b>a</b>) total signal; (<b>b</b>) reflected signal.</p> Full article ">Figure 4
<p>The results of (<b>a</b>) acquired signals, (<b>b</b>) TFCC graph.</p> Full article ">Figure 5
<p>(<b>a</b>) Estimation of instantaneous phase, (<b>b</b>) frequency band of transmitted signal.</p> Full article ">
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