Experimental Dispersion Curves Research Articles

Subsurface anomaly assessment in asphalt layers using Rayleigh waves dispersion characteristics: a test-pit study

ABSTRACT Any subsurface anomaly present in asphalt pavement layers may lead to their localised progressive structural failure. The detrimental effects of such anomalies are not visible on the top surface in the early stages. It may cause a major cost escalation if gone unnoticed during construction or maintenance works. Hence, there is a need for their quick and reliable detection and assessment. Present study explores the non-destructive assessment of subsurface anomalies (such as void/buried utility, etc.) in asphalt layers. This work developed a simple experimental approach using the two-receiver Spectral Analysis of Surface Waves (SASW) method to generate the experimental dispersion curves (EDC) whose shape characteristics are utilised for the detection, location, and identification of subsurface anomalies. An in-situ asphalt pavement test-pit facility was developed consisting of a number of different sub-sections with various anomaly conditions. A test system utilising high-frequency accelerometers was custom-integrated for such assessments. Based on the EDC shape characteristics, a direct information extraction technique was developed which does not require backcalculation procedures. The study found the proposed technique to be reasonably applicable for a quick, non-destructive detection and assessment of the subsurface anomalies. Further extensive testing with different profiles, anomalies, and test conditions will help in further acceptance of this simple approach.

Cortical bone plate properties assessment using inversion of axially transmitted low frequency ultrasonic guided waves.

Over the past few decades, early osteoporosis detection using ultrasonic bone quality evaluation has gained prominence. Specifically, various studies focused on axial transmission using ultrasonic guided waves and have highlighted this technique's sensitivity to intrinsic properties of long cortical bones. This work aims to demonstrate the potential of low-frequency ultrasonic guided waves to infer the properties of the bone inside which they are propagating. A proprietary ultrasonic transducer, tailored to transmit ultrasonic guided waves under 500 kHz, was used for the data collection. The gathered data underwent two-dimensional fast Fourier transform processing to extract experimental dispersion curves. The proposed inversion scheme compares experimental dispersion curves with simulated dispersion curves calculated through the semi-analytical iso-geometric analysis (SAIGA) method. The numerical model integrates a bone phantom plate coupled with a soft tissue layer on its top surface, mimicking the experimental bone phantom plates. Subsequently, the mechanical properties of the bone phantom plates were estimated by reducing the misfit between the experimental and simulated dispersion curves. This inversion leaned heavily on the dispersive trajectories and amplitudes of ultrasonic guided wave modes. Results indicate a marginal discrepancy under 5% between the mechanical properties ascertained using the SAIGA-based inversion and those measured using bulk wave pulse-echo measurements.

Stochastic inversion of soil dynamic parameters based on non-intrusive data

The prediction and evaluation of environmental vibrations generated by traffic loads have been playing more and more important role during the planning and designing of high-quality traffic system. From the traffic source to sensitive building, the subsoil is the one of key propagation media, so the determination of soil dynamic parameters is very crucial in studying the transmitting and attenuation of environmental vibration. Due to the spatial variability of natural soil layers, the soil dynamic parameters are actually not certain but probabilistic with stochastic characteristics. However, most current inversion methods of soil parameters cannot consider the uncertainty. In this paper, an efficient inversion method is proposed to obtain the random distribution of soil dynamic parameters based on the combination of field experiment, forward soil modelling, and Bayesian theory. Take the shear modulus and damping ratio of subsoil as the typical parameters, the experimental dispersion curve and spatial attenuation curve can be obtained by field experiment, while the corresponding theoretical ones can be calculated by the thin-layered soil model with perfectly matched layer. The combining of experimental and theoretical curves generates the likelihood function. A prior probability distribution model is firstly established, and subsequently the posterior probability distribution model is deduced by genetic algorithm, Monte Carlo-Markov chain algorithm, and Bayesian theory. In order to verify the proposed inversion method, an on-site experiment based on Multichannel Analysis of Surface Waves(MASW) was conducted in an open field in Beijing. The results show the mean values of inversed soil parameters were close to the determined parameters provided by geological exploration. Compared to the traditional determined inversion, the proposed stochastic inversion method can consider the variety of soil parameters within small depth by providing probability distribution, mean and root-mean-square error, which has greater applicability in the further probabilistic prediction of environmental vibration.

Assessment of cortical bone phantom properties using ultrasonic guided waves transduced with a multi-element transducer

The past decade has seen extensive exploration of alternative methods for the early diagnosis of osteoporosis through the assessment of the the bone quality. Previous research on axial transmission of ultrasonic guided waves demonstrated their sensitivity to the intrinsic properties of elongated cortical bones. This study highlights the capacity of low-frequency guided waves to ascertain bone properties through the inversion of dispersion curves. The proposed inversion scheme relies on dispersion curves simulated using the semi-analytical iso-geometric analysis (SAIGA) method. The model incorporates the excitability of ultrasonic guided wave modes to ensure that the inversion uses both the dispersive trajectories and amplitudes of the modes. Two models were examined: (1) a cortical bone phantom plate covered with a soft tissue mimicking material and (2) a quasi-cylinder cortical bone phantom surrounded by a soft tissue mimicking material. A proprietary axial transmission multielement ultrasonic transducer, designed for exciting guided waves under 500 kHz, was employed to capture experimental dispersion curves on phantoms through the 2D-FFT. The mechanical properties of the bone phantoms were inferred by minimizing disparities between experimental and simulated dispersion curves. Inverse properties exhibited an error of less than 4% compared to reference values. The axial transmission probe demonstrated its proficiency in accurately measuring modes propagating inside the cortical layer.

Simultaneous Determination of Young's Modulus and Density of Ultrathin Low‐k Films Using Surface Acoustic Waves

The nondestructive testing (NDT) of mechanical properties in ultrathin low dielectric constant (low‐k) films is a major challenge in integrated circuit manufacturing. Young's modulus and density are closely related parameters for low‐k films. This study presents a method for NDT of Young's modulus and density of porous low‐k black diamond (SiOC:H, BD) films. A linear frequency modulation (LFM) surface acoustic wave (SAW) interdigital transducer (IDT) with a frequency range of 20–250 MHz is designed to generate SAW signals on the samples. The series of SAW waveforms obtained on the samples are processed to obtain experimental SAW dispersion curves across a broad frequency range. By comparing these experimental curves with theoretical dispersion curves, as well as their first‐order derivatives, Young's modulus and density of porous low‐k BD films with thicknesses of 100, 300, 500, and 1000 nm are characterized. To verify Young's modulus measurements from the SAW method, a control experiment using nanoindentation is conducted. The results demonstrate that the SAW method can reduce the impact of the substrate and is independent of the film thickness. This study presents a highly accurate measuring method for simultaneous multiparameter evaluation of ultra‐thin low‐k films.

Biological dispersion in the time domain using finite element method software

Biological tissue exhibits a strong dielectric dispersion from DC to GHz. Implementing biological dispersion in the time domain with commercial finite element method software could help improve engineering analysis of electrical transient phenomena. This article describes the steps required to implement time-domain biological dispersion with commercial finite element method software. The study begins with the presentation of a genetic algorithm to fit the experimental dispersion curve of Solanum tuberosum (potato tuber) to multipoles of first-order Debye dispersion. The results show that it is possible to represent the biological dispersion of S. tuberosum from 40 Hz to 10 MHz in a 4-pole Debye dispersion. Then, a set of auxiliary differential equations is used to transform the multipole Debye dispersion from the frequency domain to the time domain. The equations are implemented in the commercial software COMSOL Multiphysics. A comparison between the frequency and time domain simulations was used to validate the method. An analysis of the electric current with square-wave pulsed voltage was performed. We found that the computer implementation proposed in this work can describe the biological dispersion and predict the electric current.

Shear-wave velocity determination by combining data from passive and active source field investigations in Kumamoto city, Japan

We present the 1D subsoil structure and local site effects at KUMA strong ground motion station in Kumamoto City, Japan. We analyze data from a field campaign conducted in the framework of the Blind Prediction BP1 test of the 6th IASPEI/IAEE International Symposium: Effects of Surface Geology on Seismic Motion. In parallel with other participants of the BP1 test, we process data from passive and active source measurements aiming to determine the shear-wave velocity, Vs, structure and the site response at KUMA station. Passive measurements are associated to five microtremor arrays. In each array, seven seismometers have been deployed in a common-center triangle shape, recording microtremors simultaneously for 1 to 2 h. The vertical component of microtremors was analyzed using the spatial autocorrelation (SPAC) method. Cross-correlation coefficients were computed for all station pairs available for each array. By fitting the average SPAC’s coefficients to the first-kind zero-order Bessel function, J0, and assuming that microtremors primarily comprise fundamental mode Rayleigh waves, phase velocity dispersion curves were determined. Phase velocity values for frequencies > 15 Hz were obtained from data of a close-by active source geophone profile. We integrated the data with those of the passive measurements and obtained an experimental phase velocity dispersion curve. The resulting curve shows low velocity variation, from 150 to 200 m/s, in the surface layers, whereas significant dispersion appears in frequencies below 2.5 Hz. By inverting this curve, we achieved to determine the 1D shear-wave velocity structure at KUMA station. Site response characteristics were determined by applying the Horizontal-to-Vertical-Spectral-Ratios method. Significantly amplified peaks in the frequency range between 0.3 to 1.5 Hz dominate HVSR spectral ratios. These peaks correspond to resonant frequencies of soils and originate from different impedance contrasts within the substratum of the site.Graphical

Cortical bone properties assessment using axially transmitted low frequency (<500 kHz) guided waves

The early diagnosis of osteoporosis through bone quality assessment has been extensively studied in the past decade. Research in axial transmission using ultrasonic guided waves has shown the method to be sensitive to intrinsic properties of long cortical bone. The aim of this work is, therefore, to show the capability of low frequency guided waves to enable the inversion of dispersion curves into bone properties. The proposed inversion scheme relies on dispersion curves simulated using the semi-analytical iso-geometric analysis (SAIGA) method. The model used in simulation comprised a bone phantom plate with a layer of soft tissue attached to the top surface in accordance with experimental bone phantom plates. A proprietary axial transmission multielement ultrasonic transducer specifically designed to excite ultrasonic guided waves under 500 kHz was used for measurements. Acquired data were processed using the 2-D Fast Fourier Transform to extract dispersion curves. The mechanical properties of the bone phantom plates were obtained by minimizing the difference between the experimental and simulated dispersion curves. The inversion was based on the dispersive properties of ultrasonic guided waves as well as their amplitudes. Results show a difference around 5% between the mechanical properties found with the SAIGA based inversion and those provided by the manufacturer of the plates.

Wavenumber identification of 1D complex structures using Algebraic Wavenumber Identification (AWI) technique under complex conditions

The dynamic characterization of complex structures raises the need for a robust experiment-based wavenumber identification method, especially when they are tested under complex conditions. To this end, this paper presents an optimized Algebraic Wavenumber Identification (AWI) method and describes the dynamic behavior of three complex structures under a series of complex conditions through AWI. The first novelty of this paper is to optimize AWI in terms of computation efficiency and accuracy by two solutions: (a) the multiple integral of AWI, which acts as a filter, is explicitly solved by the least squares fitting method, significantly reducing the computation cost, especially when multiple samples are used as input parameters; (b) a sampling strategy is provided to further improve the robustness of the AWI to measurement errors. On this basis, an AWI implementation procedure is proposed for experimental tests under complex conditions. The second novelty of this paper is on the applications of AWI in wave propagation parameters identification of complex structures, including the damping loss factor estimation of a viscoelastic beam and a honeycomb sandwich beam, the band gap identification of a meta-structure, and experimental dispersion curves extraction of these three complex structures. The third novelty of this paper is the experimental validation of AWI under a series of complex conditions, including signal noise, non-periodic sampling, and uncertainty of measuring points’ geometric coordinates. The experimental and numerical results have been compared to two popular inverse methods, namely, Inhomogeneous Wave Correlation (IWC) and INverse COnvolution MEthod (INCOME), demonstrating the validity of the AWI implementation procedure proposed in this paper.

Laser-Generated Guided Waves for Damage Detection in Metal-Lined Composite-Overwrapped Pressure Vessels.

This paper characterizes laser-generated guided waves in a metal-lined composite-overwrapped pressure vessel (COPV) to assess typical damage, including interfacial debonding and low-velocity impact damage. First, an eigenfrequency approach that avoids additional coding is utilized to theoretically analyze the dispersion characteristics of a COPV. The theoretical results show that interfacial debonding significantly alters dispersion curves, and the wavenumber of the L(0, 1) mode is sensitive to impact damage. Experimental verifications were conducted based on the full wavefield acquired using a scanning laser-ultrasonic system with a repetition rate of 1 kHz. By comparing the experimental dispersion curves with the theoretical ones, it was found that the metal-composite interface was not bonded. In addition, a local wavenumber estimation method was established to detect the impact damage by obtaining the spatial distribution of the wavenumber of the L(0, 1) mode.

Simulation-Based Inversion for the Characterization of Adhesively Bonded Joints Using Ultrasonic Guided Waves.

Adhesively bonded structures are widely used to facilitate the manufacturing process and enhance the performance of critical components in the aerospace, automotive, and energy industries. The assessment of the bond layer using the propagation of ultrasonic guided waves has been extensively investigated in the literature using several different approaches. In this study, a finite element (FE) model was used to simulate the dispersion curves of the modes propagating in an aluminum/adhesive/aluminum bonded structure. The simulated dispersion curves were systematically compared with the experimental measurements to retrieve the shear modulus of the adhesive layer during its curing process. The optimization procedure was able to perform inversion with minimum prior knowledge of the adhesive layer properties. In general, the proposed FE-based forward model was able to match the experimental dispersion curves during curing. Notwithstanding some discrepancies observed in the early to intermediate state of curing, the predicted model parameters were in agreement within 6% of the values obtained by the reference methods. The optimal shear modulus was estimated at 1.55 GPa at the end of the curing, against a reference value of 1.47 GPa.

Meta-Learning Analysis of Ultrasonic Guided Waves for Coated Cortical Bone Characterization.

Due to its sensitivity to geometrical and mechanical properties of waveguides, ultrasonic guided waves (UGWs) propagating in cortical bones play an important role in the early diagnosis of osteoporosis. However, as impacts of overlaid soft tissues are complex, it remains challenging to retrieve bone properties accurately. Meta-learning, i.e., learning to learn, is capable of extracting transferable features from a few data and, thus, suitable to capture potential characteristics, leading to accurate bone assessment. In this study, we investigate the feasibility to apply the multichannel identification neural network (MCINN) to estimate the thickness and bulk velocities of coated cortical bone. It minimizes the effects of soft tissue by extracting specific features of UGW, which shares the same cortical properties, while the overlaid soft tissue varies. Distinguished from most reported methods, this work moves from the hand-design inversion scheme to data-driven assessment by automatically mapping features of UGW to the space of bone properties. The MCINN was trained and validated using simulated datasets produced by the finite-difference time-domain (FDTD) method and then applied to experimental data obtained from cortical bovine bone plates overlaid with soft tissue mimics. A good match was found between experimental trajectories and theoretical dispersion curves. The results demonstrated that the proposed method was feasible to assess the thickness of coated cortical bone plates.

Single-ply elastic properties determination in CFRP laminates using a combined ultrasonic method

Estimation of the elastic properties in composite laminates is very important. Researchers usually consider the laminate as a whole and identify its equivalent stiffness properties. However, determining the elastic properties of each layer within a laminate can provide more comprehensive information to the users. In this paper, an ultrasonic method is proposed to reconstruct the single-ply elastic properties by combing bulk and guided waves. Herein, a novel double-side-transmitted bulk wave method is developed to identify the stacking sequences, providing the necessary information for further evaluation of the single-ply elastic properties. The double-side-transmitted bulk wave method is demonstrated under various layup scenarios, allowing the detection of more layers than conventional techniques. The laser-generated guided wave velocities are then inverted by genetic algorithms (GAs) to reconstruct the single-ply elastic properties. An effective indicator, the coefficient of variation, is designed to represent the accuracy of the identified single-ply material properties. And the experimental dispersion curves are in good agreement with the theoretical dispersion curves under the identified material properties.

Time-weighted average shear wave velocity profiles from surface wave tests through a wavelength-depth transformation

We investigate the possibility of obtaining time-weighted average shear wave velocity profiles through a wavelength-depth transformation of experimental dispersion curves from surface wave tests, without a formal solution of the inverse problem. We evaluate this approach on a wide flat-file database (Polito Surface Wave Database, PSWD) of experimental dispersion curves and related shear wave velocity profiles, both from dispersion curve inversion and invasive tests. The results show that the proposed wavelength-depth transformation can be valuable for seismic site evaluations offering an estimation of time-weighted average shear wave velocity profiles very similar to a state-of-the-art inversion of the experimental dispersion curves and with similar uncertainty with respect to invasive tests. This transformation has the advantage of avoiding time-consuming inversion processes, with related uncertainty sources, and any assumption on layer parameterization and a-priori information. Moreover, in conjunction with an experimental evaluation of the fundamental frequency of the site, from independent surveys, the wavelength-depth transformation can be used to get a direct and fast estimate of the position of the engineering bedrock.

Experimental elastic wave control in a piezoelectric phononic crystal with spatio-temporal modulation of electrical conditions

This work concerns the propagation of elastic waves in a piezoelectric phononic crystal made of several identical piezoelectric elements separated by electrodes. In such a structure, electrical conditions prescribed to the electrodes can be modulated in space and in time and therefore can strongly modify the dispersion curves of the phononic crystal. For example, a periodic grounding of the electrodes introduces a Bragg band gap which does not exist when the electrodes have a floating potential condition [Degraeve et al., J. Appl. Phys. 115, (2014)]. When the electrical conditions of the electrodes are modulated in space and in time, dispersion curves are tilted with respect to the configuration in the reference medium and nonreciprocal wave propagation may occur at some modulation speeds in specific frequency bands [Croënne et al., Appl. Phys. Lett.110, (2017)]. The experimental set-up is based on a stack of 113 piezoelectric rings and 114 electrodes. The spatio-temporal modulation of the electrical conditions is performed using a digital signal processor (DSP) in order to reach high modulation speeds. This modulation is performed by shifting the position of the periodic ground conditions of the electrodes versus time. The experimental dispersion curves are obtained using measurements of the normal displacement of the piezoelectric rings with a scanning laser vibrometer. The evolution of dispersion curves as a function of modulation speed is analyzed and compared to finite element simulation results.

Embroidered Spoof Surface Plasmon Polariton Transmission Line for Wireless Body Sensor Network

A wearable Spoof Surface Plasmon Polariton Transmission Line (SSPP TL) operating at 2.45 GHz designed for embroidery production and on-body communication is proposed. The SSPP TL supports both even and odd modes launched by near field coupling with a dipole antenna perpendicular and parallel to the TL, respectively. First, the experimental dispersion curves and transmission for the even and odd modes are favourably compared to simulations. Then, experimental transmission for each mode is compared with the Line-Of-Sight (LOS) transmission between two parallel-oriented antennas. At 2.45 GHz, a transmission enhancement of 16 dB is measured for the even mode and it reaches up to 37 dB for the odd mode. A transmission enhancement of 30 dB is also measured at 2.45 GHz between two antennas with orthogonal orientations. Performances of the SSPP TL for Wireless Body Sensor Network are evaluated. Transmission is sustained for the SSPP TL under curvature and right angle bending. Transmission measured when both an arm and a copper plate obstacle between antennas were surrounded by the curved SSPP TL is compared with the obstructed LOS transmission. Measurements show a transmission enhancement up to 22 and 25 dB for the even and odd modes, respectively.

Evaluation of thermal material properties based on SAW dispersion in the laser-induced dynamic subsurface temperature gradient

Dispersion of surface acoustic waves (SAWs) caused by a dynamic surface heating–cooling cycle has been applied for evaluation of thermal properties. A laser-generated broad-band SAW pulse is propagated through the material whose elastic properties and density were modified by the dynamic inhomogeneous temperature field produced by laser heating and subsequent cooling. A sample with depth-dependent material properties introduces a phase velocity dispersion in SAW propagation. Dispersion was measured by a differential technique, which helped to isolate the thermally induced dispersion and eliminate the contributions of other possible sources of dispersion. The dispersion curves were measured at several time instants, which allowed evaluation of the following parameters: thermal diffusivity, temperature dependence of the shear modulus, and the temperature magnitude. The inverse problem was solved by fitting the experimental dispersion curves into the theoretical ones by means of differential evolution techniques.

Quantitative and nondestructive determination of residual stress for SiO2 thin film by laser-generated surface acoustic wave technique

The laser-generated surface acoustic wave (SAW) technique is a promising method to measure the mechanical properties of thin films quickly and nondestructively. Residual stress is inevitable during the processing and manufacturing of integrated circuits, which will have a major impact on the physical and mechanical properties of the thin film materials and cause deterioration to the structural strength. In this study, the SAW technique based method is proposed for quantitative and nondestructive measuring the residual stress in the nanostructured films. The method is verified by the experiment measuring the SiO2 films in the thickness range of 100–2000 nm. The experimental procedures, including signal excitation, reception and processing, are described in detail. By matching the SAW experimental dispersion curve with the calculated theoretical dispersion curve containing the residual stress, the residual stress of the SiO2 films along [110] and [100] crystallographic orientation of the Si wafer is successfully quantified. The determination results are ranged from −65.5 to 421.1 MPa and the stress value increases as the film thickness decreases, revealing the residual stress of the SiO2 film is compressive. Meanwhile, the conventional substrate curvature method as a comparison is used to verify the correctness and superiority of the proposed SAW method for the residual stress determination.

Synchrosqueezed wavelet transform-based method for characterizing the dispersive nature of laser-excited surface acoustic waves propagating through the coated or damaged medium

Dispersion of surface acoustic waves (SAWs) can be used for determination of the mechanical parameters of the film or the damaged layer. The correct evaluation of the experimental dispersion curves is important for backcalculation. In this paper, we present a method to identify experimental dispersion curves from two-station time-varying signals based on time–frequency analysis. Synchrosqueezed wavelet transform (SWT) provides the quantitative description of the propagation of different frequency components of SAWs. Discrete phase velocity estimation is accomplished based on the cross-correlation function. Rényi entropy-based SWT spectrum noise reduction and cosine interpolation are applied for improving the quality of dispersion curves. An example is presented to illustrate the application of the proposed method. Finally, laser ultrasonic experiments are performed on the surface of three typical test samples. The comparison of the resulting dispersion curves shows the effectiveness of the proposed method and the necessity of noise reduction and interpolation.

Dispersion of guided-waves in heterogeneous and anisotropic elastic plates: A probabilistic approach

In this paper, we present a new approach to study Lamb-type waves of anisotropic elastic plates in a probabilistic framework. The study and analysis are carried out on an elastic plate whose randomly varied elastic properties in the through-thickness direction. By introducing a stochastic model for quantitative description of heterogeneous elastic properties in the plate, the effect of material heterogeneity on Lamb modes may be investigated from a stochastic point of view. To the our best knowledge, this study is the first to investigate Lamb-type waves in a probabilistic framework. Different plate thicknesses are considered and associated dispersion curves are computed. A sensitivity study is performed, highlighting effect of the uncertainty of elasticity properties on the fluctuation of Lamb modes via phase velocities, energy velocities and modes shapes. Next, we discuss the relevance of introducing random media to identify branches associated with experimental dispersion curves.