Local Wavenumber Research Articles

Local wavenumber imaging in anisotropic structures

Local wavenumber imaging has been proven effective for damage detection in thin-walled structures. Such structures are, however, often inherently anisotropic, posing serious challenges to the known algorithms of local wavenumber mapping. The use of local wavenumber mapping algorithm designed for isotropic, rather than anisotropic, structures results in processing artifacts that may prohibit correct detection and characterization of defects. Therefore, in this work, we propose an improved implementation of the local wavenumber estimation algorithm for anisotropic media (ALWE). The working principle and efficiency of the proposed algorithm are illustrated on datasets coming from numerical simulations and experimental testing on anisotropic carbon fiber reinforced polymer (CFRP) laminates. We demonstrate that the proposed algorithm successfully compensates for the processing artifacts and enhances the overall quality of the wavenumber maps facilitating unequivocal damage detection.

Detection of delamination using laser-generated Lamb waves with improved wavenumber analysis

Abstract Delamination is a typical failure mode in multilayered materials, which may potentially threaten the safety and reliability of the materials if not detected promptly. This paper proposes a novel quantitative detection method for delamination in multilayered materials based on laser-generated Lamb waves with improved wavenumber analysis. First, a three-dimensional(3D) finite element model is established to simulate the interaction between delamination and laser-generated Lamb waves. The propagation characteristics of Lamb waves in multilayered materials without defects and with delamination of three different shapes, i.e., rectangular, circular and triangular are analyzed. And the mechanism that delamination can lead to the appearance of scattered wave and new wavenumber components is investigated, facilitating the quantitative detection of delamination. Then, an improved wavenumber analysis method for quantitative detection of delamination is proposed. The new wavenumber components caused by delamination are extracted by broadband adaptive wavenumber filtering to reduce imaging interference and artifacts caused by irrelevant components, and the spatial wavenumber spectrum is obtained by fast broadband local wavenumber estimation algorithm to enhance the delamination imaging accuracy and spatial resolution. The experimental results indicate that, across various experimental scenarios, the proposed method achieves superior imaging precision compared to traditional wavenumber filtering or local wavenumber estimation methods, and can quantitatively identify delamination defects of various shapes and sizes.

Multi-frequency instantaneous wavenumber damage imaging method based on ultrasonic guided waves induced by laser point-by-point excitation

ABSTRACT A multi-frequency instantaneous wavenumber damage imaging method based on ultrasonic guided waves induced by laser point-by-point excitation is proposed in this paper. The experiment involved using the Nd:YAG pulsed laser is used as the excitation source to excite ultrasonic guided waves point-by-point in the detection area, and the piezoelectric ceramic transducer is used to receive ultrasonic guided wavefield at a fixed position. The wavefield information at different frequencies is extracted by a three-dimensional Fourier transform. The spatial phase distribution of the extracted guided wavefield with different frequencies is obtained by the Hilbert transform and phase unwrapping method. Then, the wavenumber of each detection point and the dispersion relations of the test piece with different thicknesses are calculated. Based on the calculated dispersion relation, the mapping relationship between the wavenumber and the thickness of the test piece is obtained. Furthermore, based on the obtained wavenumber information and wavenumber thickness mapping relationship, the thickness reduction depth of the defect can be calculated. Finally, the quantitative detection of defects is achieved through data fusion. The proposed method is verified through quantitative detection of the rectangular groove defects and the flat bottom defects with variable thickness and complex contour in the aluminium plate. At the same time, the detection results of the proposed method are compared with those of the single-frequency instantaneous wavenumber imaging method, single-frequency local wavenumber imaging method, and multi-frequency local wavenumber imaging method. In the detection results, the method proposed in this paper presents a better defect detection effect.

Damage detection by means of broadband local wavenumber estimation in plate-like structures

This short communication evinces the ability of the CFAT methodology [Q. Leclère, JSV, 2015] to detect and characterize thickness-loss defects on homogeneous flat panels. A contactless measurement of the velocity field of an aluminium plate is performed by scanning laser vibrometry, from which the equivalent rigidity (apparent bending stiffness) is locally estimated within a wide frequency band in the ultrasonic domain. The method allows imaging thickness-reduction defects on the hidden face of an aluminium plate up to several hundreds of kilohertz. The first part details the experimental protocol, followed by a second enhancing the identification of the wavenumbers of symmetric S_0 and antisymmetric A_0 modes. The comparison with theoretical Lamb waves dispersion curves reveals the precision of the method. Finally, the methodology validates the possibility to precisely estimate the local material thickness and as a consequence the location, size and depth of a reference defect in the shape of a flat bottom hole (assuming homogeneous material properties of the plate).

Flexural wave compression behaviors of programmable graded piezoelectric meta-beams

Active electromechanical metamaterials have drawn significant attention due to their remarkable tunability and adaptability in vibration and wave control. Exploiting the electromechanical coupling effect via controlled biased fields enables precise manipulation of the structural vibrations and wave transmissions. In this research, we have developed a programmable graded piezoelectric meta-beam that successfully imitates the wave compression behavior of an acoustic black hole without modifying the structural geometries. The effective parameters of the meta-beam are reshaped into a gradient distribution by tuning the electrical impedances of the digital shunting circuits. With such graded effective parameters, it becomes feasible to tailor the local wavenumber distribution of the meta-beam and hence achieve the desired wave compression. Numerical results validated our proposed paradigm of the programmable black hole in both straight and curved beams. In contrast to the straight beam, curvature of the curved beam reduces the tunable range of the local wavenumber. A comprehensive parametric study was conducted to investigate the influences of the gradient profile, electric damping, and curvature on the wave control function. For a given desired frequency, programmable control of wave compression location and amplified output of electrical signals are achieved.

High-efficiency surface defect detection based on laser ultrasonic state space embedding and compressive sensing

Abstract The laser nonlinear wave modulation spectroscopy(LNWMS) technique has gained considerable attention due to its high sensitivity in detecting small surface defects and its ultra-fast scanning speed. This paper proposes a novel method for synthesizing intact wavefield reference, significantly enhancing the accuracy of surface defect imaging. Moreover, considering the potential for parallel processing of the nonlinearity calculation of ultrasonic signals at scanning points, we incorporate compressive sensing technology to accelerate this process. This innovative approach reduces the computational load to 10% of the original, thereby substantially increasing the imaging speed. The paper validates the method’s superior accuracy and efficiency in defect detection through conducting experiments using a high-speed laser ultrasonic scanning system on aluminum plates and turbine blade, and by comparing with local wavenumber estimation, demonstrating the promising potential of this technology for surface defect analysis.

Two-dimensional stiffness identification by inversion of local wavenumbers based on artificial neural network

Impact and fatigue damages in carbon fiber reinforced polymers (CFRP) are unavoidable in severe operating conditions, which will lead to the stiffness properties degrading and redistributing in space. The local wavenumbers of guided waves at a specific point depend on the stiffness at that spatial location. Therefore, the two-dimensional stiffness properties can be determined by inversion of local wavenumbers. In this paper, the relationship between the local wavenumbers and the stiffness coefficients was established by the artificial neural network (ANN) method. For each spatial point, based on the semi-analytical finite element (SAFE) method, the wavenumbers (inputs of ANN) with different frequencies can be obtained at given stiffness coefficients (outputs of ANN). Furthermore, the accuracy of the ANN method was validated by the finite element model. Results show that the predicted two-dimensional stiffness coefficients of the damaged region are close to the true ones, thus demonstrating the accuracy of the two-dimensional stiffness identification method.

Localised wavenumber estimation and its application to waveguide discontinuities

Wave propagation methods have been widely investigated for the potential application to the detection and localisation of discontinuities in structural waveguides. In the low-mid frequency ranges, previous preliminary works that used the analytic signal theory have considered local wavenumber estimations based on the time domain for the purpose of localisation in mechanical structures. However, these have not fully exploited the potential of this approach. This is accomplished herein for a one-dimensional infinite-like waveguide by means of two methods applied in the spatial domain; namely the Hilbert transform via the wavenumber domain estimator and the Direct Quadrature method. Modifications are proposed to make these methods more suitable to the space-wavenumber application and for the purpose of localisation. A three-dimensional plot is proposed, where local divergences of the wavenumbers indicate the positions of the discontinuities for otherwise uniform waveguides. Numerical simulations and experiments show an accurate estimation of the local wavenumbers and validate the methods with the proposed modifications for the localisation of different types of discontinuities.

Development of a piezo stack – Laser doppler vibrometer sensing approach for characterizing shear wave dispersion and local viscoelastic property distributions

Laser Doppler vibrometry and wavefield analysis have recently shown great potential for nondestructive evaluation, structural health monitoring, and studying wave physics. However, there are limited studies on these approaches for viscoelastic soft materials, especially, very few studies on the laser Doppler vibrometer (LDV)-based acquisition of time–space wavefields of dispersive shear waves in viscoelastic materials and the analysis of these wavefields for characterizing shear wave dispersion and evaluating local viscoelastic property distributions. Therefore, this research focuses on developing a piezo stack-LDV system and shear wave time–space wavefield analysis methods for enabling the functions of characterizing the shear wave dispersion and the distributions of local viscoelastic material properties. Our system leverages a piezo stack to generate shear waves in viscoelastic materials and an LDV to acquire time–space wavefields. We introduced space-frequency-wavenumber analysis and least square regression-based dispersion comparison to analyze shear wave time–space wavefields and offer functions including extracting shear wave dispersion relations from wavefields and characterizing the spatial distributions of local wavenumbers and viscoelastic properties (e.g., shear elasticity and viscosity). Proof-of-concept experiments were performed using a synthetic gelatin phantom. The results show that our system can successfully generate shear waves and acquire time–space wavefields. They also prove that our wavefield analysis methods can reveal the shear wave dispersion relation and show the spatial distributions of local wavenumbers and viscoelastic properties. We expect this research to benefit engineering and biomedical research communities and inspire researchers interested in developing shear wave-based technologies for characterizing viscoelastic materials.

A new automatic geo-electric self-potential imaging technique for diverse sustainable development scenarios

This study introduces a rapid and efficient inversion algorithm designed for the interpretation of self-potential responses originating from mineralized and ore sources and hydrothermal activity, specifically addressing spherical, vertical, and horizontal cylindrical structures. The algorithm leverages local wavenumber and correlation imaging techniques to enhance accuracy in modeling. The correlation factor (Cf value) is crucial in this approach, calculated as the correlation between the local wavenumber of the measured self-potential field and that of the computed field. The algorithm identifies the maximum correlation Cf value (CF-max) as indicative of the optimal true model parameters. To validate the proposed algorithm, it was applied to three theoretical examples—one with contamination from regional background and another with multiple sources with and without different types of noises (random Gaussian and white Gaussian noises). Additionally, the approach was tested on three distinct real field cases related to mining, ore investigation and hydrothermal activity in India, Germany and USA. Through a comprehensive analysis of results from theoretical and real-world scenarios, including comparisons with different available data and literature information, the study concludes that the method is effective, applicable to multiple sources, accurate, and does not necessitate prior knowledge of the source shape. This algorithm presents a promising advancement in the field of self-potential interpretation for mineral exploration and geothermal exploration.

Fluid Focusing Contributes to the BM Vibration Amplification by Boosting the Pressure.

Two hydrodynamic effects are introduced in the standard transmission-line formalism, the focusing of the pressure and fluid velocity fields near the basilar membrane and the viscous damping at the fluid-basilar membrane interface, which significantly affect the cochlear response in the short-wave region. In this region, in which the wavelength is shorter than the cochlear duct height, only a layer of fluid of order of the wavelength is effectively involved in the traveling wave. This has been interpreted [8] as a reduced fluid contribution to the system inertia in the peak region, which is a viewpoint common to the 3-D FEM solutions. In this paper we propose an alternative approach, from a slightly different physical viewpoint. Invoking the fluid flux conservation along the traveling wave propagation direction, we can derive a rigorous propagation equation for the pressure integrated along the vertical axis. Consequently, the relation between the average pressure and the local pressure [4] at the fluid-BM interface can be written. The local pressure is amplified by a factor dependent on the local wavenumber with respect to the average pressure, a phenomenon we refer to as "fluid focusing", which plays a relevant role in the BM total amplification gain. This interpretation of the hydrodynamic boost to the pressure provides a physical justification to the strategy [10] of fitting the BM admittance with a polynomial containing both a conjugated pole and a zero. In the short-wave region, the sharp gradients of the velocity field yield a second important effect, a damping force on the BM motion, proportional to the local wavenumber, which stabilizes active models and shifts the peak of the response towards the base, with respect to the resonant place. This way, the peaked BM response is not that of a proper resonance, corresponding to a sharp maximum of the admittance, but rather a focusing-driven growth toward the resonant place, which is "aborted" before reaching it by the sharply increasing viscous losses. The large values of the wavenumber that ensure strong focusing are ultimately fueled, against viscosity, by the nonlinear OHC mechanism, hence the otherwise puzzling observation of a wide nonlinear gain dynamics with almost level-independent admittance.

Refining protein amide I spectrum simulations with simple yet effective electrostatic models for local wavenumbers and dipole derivative magnitudes.

Analysis of the amide I band of proteins is probably the most wide-spread application of bioanalytical infrared spectroscopy. Although highly desirable for a more detailed structural interpretation, a quantitative description of this absorption band is still difficult. This work optimized several electrostatic models with the aim to reproduce the effect of the protein environment on the intrinsic wavenumber of a local amide I oscillator. We considered the main secondary structures - α-helices, parallel and antiparallel β-sheets - with a maximum of 21 amide groups. The models were based on the electric potential and/or the electric field component along the CO bond at up to four atoms in an amide group. They were bench-marked by comparison to Hessian matrices reconstructed from density functional theory calculations at the BPW91, 6-31G** level. The performance of the electrostatic models depended on the charge set used to calculate the electric field and potential. Gromos and DSSP charge sets, used in common force fields, were not optimal for the better performing models. A good compromise between performance and the stability of model parameters was achieved by a model that considered the electric field at the positions of the oxygen, nitrogen, and hydrogen atoms of the considered amide group. The model describes also some aspects of the local conformation effect and performs similar on its own as in combination with an explicit implementation of the local conformation effect. It is better than a combination of a local hydrogen bonding model with the local conformation effect. Even though the short-range hydrogen bonding model performs worse, it captures important aspects of the local wavenumber sensitivity to the molecular surroundings. We improved also the description of the coupling between local amide I oscillators by developing an electrostatic model for the dependency of the dipole derivative magnitude on the protein environment.

Supergrowth and sub-wavelength object imaging.

We further develop the concept of supergrowth [Quantum Stud.: Math. Found.7, 285 (2020)10.1007/s40509-019-00214-5], a phenomenon complementary to superoscillation, defined as the local amplitude growth rate of a function higher than its largest wavenumber. We identify a canonical oscillatory function's superoscillating and supergrowing regions and find the maximum values of local growth rate and wavenumber. Next, we provide a quantitative comparison of lengths and relevant intensities between the superoscillating and the supergrowing regions of a canonical oscillatory function. Our analysis shows that the supergrowing regions contain intensities that are exponentially larger in terms of the highest local wavenumber compared to the superoscillating regions. Finally, we prescribe methods to reconstruct a sub-wavelength object from the imaging data using both superoscillatory and supergrowing point spread functions. Our investigation provides an experimentally preferable alternative to the superoscillation-based superresolution schemes and is relevant to cutting-edge research in far-field sub-wavelength imaging.

Estimation of ground depth of radioelements sources in Ogun State, Southwestern Nigeria using gradient techniques

Radioelement exploration has gained economic interest recently due to its usefulness in the detection and delineation of mineral deposits. In this study, the airborne radiometric data were analysed for depth estimation of the radioelement deposit in Ogun state, Nigeria. Three enhancement gradient techniques, namely; Analytical Signal Amplitude (ASA), Horizontal Gradient Magnitude (HGM) and Local Wave Number (LWN) were employed to estimate the possible depth of radioelements for mineralization. Geosoft's (Oasis Montaj) software and Potential Field's (PF) software were used to conduct the estimations. The result obtained revealed shallow sources of 0.584 km (LWN) and 0.387 km (ASA), and deep-seated sources of 5.950 km (ASA) and 5.880 km (ASA) for uranium and thorium, respectively. The shallow source and deep source for potassium are 0.259 km (ASA) and 2.540 km (ASA), respectively. In this study, the position and depth of the source were automatically estimated using linear equations based on derivatives without the use of any a priori knowledge. The three gradient methods are therefore found suitable in estimating the depth to radioelement anomalous source.

Improving efficiency of local wavenumber estimation for damage detection in thin-walled structures

Full-field imaging of guided ultrasonic waves is an emerging Nondestructive Testing (NDT) technique for the inspection of thin-walled structures. One of the most effective full-field processing techniques is the Local Wavenumber Estimation (LWE) which can be applied to detect various types of damage in both homogeneous and multilayer specimens. In this paper, we discuss the possibilities for optimizing the efficiency of the LWE algorithm to facilitate its practical applications. We propose several different signal processing approaches to optimize the algorithm's computational efficiency without sacrificing the damage imaging quality. We evaluate the influence of these improvements by measuring the computation time necessary to perform particular processing steps of the LWE process. We also provide the implementation guidelines for the proposed optimization techniques. The proposed improvements allow for a considerable reduction in the processing time of the LWE with respect to the baseline implementation of the algorithm, ranging from a factor of 10 to a factor of 24, depending on the input dataset.

Subsurface Structural Characterization as Deduced from High-Resolution Aeromagnetic Data over The Confluence Zones in Central, Nigeria

This study aimed to delineate the intrusion body that controls the structural setting and formation around the river Niger-Benue confluence zone with particular attention to its solid mineral potentials, this is achieved in mapping subsurface structural features through the analysis of recent high-resolution aeromagnetic (HRAM) data-sets with the purpose of examining their effects on geological structures that characterize the confluence zones from the study area. To obtain the necessary reduction in geomagnetic variation, measurements of regional gradients and time variation were used. After applying the reduction to the magnetic equator (RTE) to the corrected magnetic data that was obtained from the Nigerian Geological Survey Agency, NGSA, it was possible to determine the regional expansions of subsurface structural units for both qualitative and quantitative interpretations. In addition, the edge detection method is used to depict the structures and buried subsurface anomalies. Different handling processes were applied to the (HRAM) data, such as local wavenumber (SPI), power spectrum analysis, and Euler and Werner deconvolution analysis. The RTE magnetic anomaly caused by local structures and anomalous body delineated six sub-basins with low amplitude response, which agrees with the total gradient anomaly (analytic signal) and tilt of angle derivative that clearly outlined and characterize edges of lithostratigraphic of Niger-Benue river confluence zones. The sub-basin delineated are the southern Bida basin and northern Anambra basin. The source parameter imagings as well as the Euler and Werner deconvolution were used to delineate major subsurface structures and determine their source depth. Results showed that the area was affected by different lineament trending NE-SW, E-W, and S-E trends. Directional analysis indicates that the dominant trend agrees with the regional fault orientations. The estimated depth to the top of the lineaments on average varies from 0.3 km to 4.6 km and it is relatively deeper in the basins compared to the surrounding areas giving clues to the amount of sediment infill. A 2D forward model showed a sedimentary thickness ranging from 1 to 7 km, and this estimated depth is consistent with the average of 3.5 km proposed by previous researchers.

Local wavenumber estimation for small damages based on artificial neural network

The local wavenumber feature of ultrasonic guided waves can be used to detect wall-thinning because the thickness at each spatial location determines the wavenumber at that point. However, this paper shows that the accuracy of the local wavenumber estimation results is closely related to the size of the damage. When the size is small to a certain extent, the estimated local wavenumber can be significantly lower than the true value. In order to obtain the local wavenumber accurately, an artificial neural network (ANN) method is introduced in this paper to relate the estimated local wavenumber to the true wavenumber. A two-dimensional finite element guided wave model is developed to generate the rich inputs (estimated local wavenumber), while the outputs (true local wavenumber) are obtained by a semi-analytical finite element (SAFE) method. The ANN method is experimentally validated with a laser-generated ultrasonic system, and the error between the predicted local wavenumber and the true wavenumber is within 5% for a wide range of damage sizes, thus ensuring the accuracy of assessing wall-thinning.

Local wavenumber imaging with low-sampled wavefield for delamination characterization in composite plate

In this paper, a phase unwrapping-based local wavenumber imaging method is proposed for delamination detection in the composite plate. Local wavenumber imaging has shown significant advantages in damage localization and quantification. However, a dense of spatial measurements and a high requirement of sampling intervals are crucial for conventional spatial Fourier transform methods. To address these challenges, a phase unwrapping method adopting low-sampled wavefields for local wavenumber estimation is proposed for damage imaging. Specifically, the wavefield sampling process can divide the detection area into various grids while making each grid consist of four neighbor measurements. Under the far-field assumption, the wave path distances of grid measurements can be approximately obtained by projecting their real distances along the wave vector direction. Meanwhile, by revealing the phase differences of grid measurement pairs with the low-sampled wavefield data, the frequency-related wavenumbers are estimated subsequently. Hence, the local wavenumber can be recovered robustly by averaging the estimated wavenumbers from all measurement pairs in the grid. On this basis, the structural damage can be geometrically imaged and quantitatively evaluated. Both the simulation study and the experimental investigation have shown the efficiency of the phase unwrapping-based method for local wavenumber imaging, which demonstrates the strong capability of damage localization and quantification in composite structures with low-sampled wavefield.

Magnetic inversion modeling of subsurface geologic structures for mineral deposits mapping in southeastern Nigeria

Magnetic inversion techniques have been implemented to infer the extension and geometry of magnetic structures and also evaluate its influence on mineralization within Abakaliki and its environs, southeastern Nigeria. The modeling approach considers the techniques of three-dimensional (3D) magnetic data inversion, Euler deconvolution, analytic signal inversion, Enhanced Local Wavenumber (ELW) Technique and Particle Swarm Optimization (PSO) to estimate source parameters and compare results. Model solutions were interpreted to represent possible geologic units with varying trends, housing mineralization within the study region. Results from inversion computation over some active mine locations show subsurface bodies with magnetic susceptibilities >0.00188 SI. Model results also show structural sources with almost 5.5 km depth extension, stretching 18 km in the EW direction at Ngbo – Ekerigwe location. This could imply significant mineral deposits at the location. Inversion of both magnetic anomaly and analytical signal enabled derivation of the actual subsurface structures in the region, with most of the structures appearing as dykes with depths ranging from 0.2 – 1.8 km at most of the mining sites. Location and depths of some of the modeled intrusions have been corroborated with the active on-site mines. The delineation of mineralization structures by this study would guide systematic exploration in the region.

Quantitative detection of surface defect using laser-generated Rayleigh wave with broadband local wavenumber estimation

Laser ultrasonic technology has been widely used in surface defect detection attribute to its non-contact, non-destructive and high spatial resolution characteristics. This paper proposes a surface defect quantitative detection method using laser-generated Rayleigh wave with broadband local wavenumber estimation. In this method, considering the broadband characteristics of laser-generated Rayleigh wave, the broadband local wavenumber estimation is presented to achieve the defect imaging accurately, and then the defect geometric parameters are estimated based on image segmentation. A surface defect detection experiment using the laser ultrasonic detection system is conducted to verify the effectiveness of the proposed method. The experimental results show that the proposed method has superior imaging effect for vertical and inclined defects than the standing wave energy method or reflected wave energy method. Besides, the geometric parameters such as length, width, and inclination angle of a surface defect can be accurately identified by the proposed method, the errors of vertical defects are 1.6% in length and 4.0% in width respectively, as well as the maximum and minimum error of inclined defects are 5.0% and 1.28% in inclination angle respectively. The research results provide a potential application for the fast and non-destructive surface defect detection of metal structures.