Efficient computation of dispersion curves in damped and anisotropic waveguides often requires solving multivariate transcendental equations in a complex-domain parameter space, where the physically admissible solution set occupies only a small fraction of the search volume. This paper presents a multivariate complex-domain root-finding algorithm that combines Shift-Differencing Screening (SDS), occupancy-driven mesh refinement, and localized Modulus-Ratio Convergence Method (MRCM) confirmation. SDS is introduced as a necessary-stage screening paradigm that detects candidate root neighborhoods through shift-based comparisons on precomputed determinant values, thereby reducing dependence on fixed-axis slicing and suppressing pseudo-candidates generated by cellwise scans. The same screening mechanism drives adaptive mesh refinement so that determinant evaluations are concentrated in the small occupied fraction of the domain rather than the full Cartesian grid. MRCM is retained as a sufficient local confirmation stage and applied only to the refined candidates, preserving direct root verification while decoupling it from expensive domain-wide scanning. Relative to conventional UCS--MRCM implementations, the resulting framework reduces determinant evaluations by one to two orders of magnitude while preserving finest-grid-consistent dispersion branches. Numerical results for non-dimensional Lamb waves and a fully triclinic hysteretic plate show improved candidate localization, suppression of valley-type and plateau-type pseudo-roots, and substantial runtime reductions. The formulation is broadly applicable to multivariate complex-domain root-finding problems whenever an analytical or semi-analytical residual is available.

Accurate computation of Hadamard finite-part integrals with oscillatory kernels is challenging due to the existence of second-order singularity and the highly oscillatory kernel in the integrand. In the current scenario, an integrand splitting algorithm is proposed, which divides the Hadamard finite-part integrals into a nonsingular and a singular part integral. Meshless collocation method is implemented to evaluate the non-singular part integral with Fourier type oscillatory function. The singular part integral with oscillatory function is evaluated analytically. The approximate error bounds of the new method are theoretically derived. The proposed method is uniformly convergent for all eta is an element of (-1, 1), which is evidence of the new algorithm. For numerical justification, few test examples with numerical results are included.

Helmholtz equations appear in several model problems in engineering and applied sciences. The oscillatory Helmholtz equation solution contains integrals involving oscillatory Bessel functions of the second and third kinds. The existing quadratures, such as the Gaussian quadrature, make it difficult to compute these integrals for high-frequency regimes. The current work develops new stable algorithms based on Levin quadrature theory to precisely and accurately compute such integrals. We perform a coupling of the Levin approach with the global and compactly supported radial basis functions (CS-RBFs). It is well known that the global RBFs produce dense and ill-conditioned interpolation matrices, especially for large data points. Therefore, this work considers the CS-RBFs to produce sparse and well-conditioned matrices, while coupling the Levin method guarantees the best computation of the oscillatory Bessel integrals. We derived and validated some theoretical facts numerically by solving a few test examples.

The precise detection of concrete mortar slump is a key technical link in intelligent concrete mixing, playing a vital role in ensuring project quality and improving construction efficiency. In this paper, the YOLOv8n algorithm is improved to achieve detection of concrete mortar slump efficiently and precisely. At the algorithm level, the AWGAM (Add Weight Global Attention Mechanism) is integrated with the C2f module, and its innovative design has two versions. One is the Basic version B-AWGAM-C2f (Basic-Add Weight Global Attention Mechanism-C2f). The other is A-AWGAM-C2f (Adaptive-add Weight Global Attention Mechanism-C2f). And the two versions are respectively deployed in the neck network and the backbone network of the model to enhance the multi-scale feature fusion ability of the model. Meanwhile, a depth-separable convolution is introduced into the AWGAM attention mechanism to construct a lightweight module, Light-AWGAM. Then it is placed in the backbone network of the model. The number of parameters of the model has significantly decreased while ensuring detection accuracy. The detection precision and the computational efficiency are balanced effectively. Experiments show that the performance of the improved YOLOv8n model has been significantly enhanced: the precision has increased by 3.3%, the recall has increased by 0.6%, and both mAP50 and mAP50-95 have grown by 0.8%. The model demonstrates significant advantages in detection efficiency and accuracy, enabling concrete mortar slump detection tasks to be completed efficiently.

One of the attractive research problems is the computation of highly oscillatory integrals in the field of applied sciences. For this purpose, many efforts are performed to get an accurate, stable, and efficient analysis of these integrals. The Levin method with Chebyshev polynomials and Chebyshev operators stands out as an attractive procedure in the literature. Despite the attractiveness of the numerical experiments in the literature, there remains a gap that requires further exploration. Therefore, the focus of this work is on connecting Jacobi operators and Jacobi polynomials with the Levin method. The proposed method performs better in accuracy and produces sparse and well-conditioned matrices, in contrast to the Levin method based on Chebyshev polynomials and operators in the literature [Li et al., A universal solution to one-dimensional oscillatory integrals, Sci. China Ser. F: Inf. Sci. 51(10) (2008), pp. 1614-1622; Ma and Liu, A well-conditioned Levin method for calculation of highly oscillatory integrals and its application, J. Comput. Appl. Math. 342 (2018), pp. 451-462]. We perform several numerical experiments to validate the claims of the proposed method.

The Synthetic Aperture Focusing Technique (SAFT), with its strong capability of enhancing resolution and repeatable scanning performance, has been widely applied in immersion environments. However, traditional two-dimensional SAFT only provides planar information and fails to fully characterize the three-dimensional spatial structure and defect distribution. By introducing the y-axis dimension based on the x-z plane, three-dimensional SAFT can achieve volumetric reconstruction of the target. Nevertheless, in multi-medium interfaces such as water and metal, differences in acoustic velocity cause refraction, making the calculation of three-dimensional refraction points complex and time-consuming. To address this issue, this paper proposes a Multi-Layer Perceptron (MLP)-based neural network prediction method for three-dimensional refraction points, which avoids the iterative computation in traditional geometric algorithms and is integrated with three-dimensional immersion SAFT imaging.

In applied sciences, the analysis of Bessel and Airy oscillatory integrals is a demanding problem, particularly for large-scale data points and large frequency parameters. The Levin method, with global radial basis functions, is an accurate tool for approximating these integrals. But as the interpolation points or frequency increase, the interpolation matrix becomes dense and highly ill-conditioned. To ensure a stable and efficient computation of Bessel and Airy integrals, we implement the Levin method with compactly supported radial basis functions. Although the accuracy of the new algorithm has not significantly improved compared to the counterpart methods. Alternatively, the method exhibits faster and well-conditioned behavior, even for large numbers of data points and large frequency parameters. The convergence analysis of the method is performed and numerically verified with several benchmark problems.

Guided wave-based methodologies are a fundamental approach in structural health monitoring and non-destructive testing due to their ability to propagate over extended distances while enabling comprehensive structural coverage with minimal instrumentation and reduced inspection time. This study focuses on the analysis of highly damped viscoelastic multilayered composite structures, which are widely used in aerospace applications and require rigorous investigation to achieve accurate predictive modeling and performance assessment. Conventional viscoelastic models, such as the Hysteretic and Kelvin-Voigt formulations, exhibit limitations in accurately capturing the complex damping behaviors inherent to highly attenuative materials. To address these constraints, the Biot model is introduced as an advanced framework capable of more accurately representing viscoelastic effects within intricate composite laminates. The Moduli Ratio Convergence Method is applied with adaptations, to facilitate an in-depth analysis of wave propagation phenomena in such materials. This enhanced algorithm enables the precise determination of critical parameters, including dissipation amplitude, dispersion characteristics, phase velocity, energy velocity, and mode shape diagrams. These insights are leveraged to investigate unique wave phenomena, such as the veering of dispersion curves and frequency shifts observed in spectrograms projected onto the real plane. A qualitative analysis highlights the distinctive frequency shift phenomenon observed in the Biot model, which does not appear in the Hysteretic and Kelvin-Voigt models, providing deeper insights into the unique wave characteristics introduced by the Biot model. Comparisons with purely elastic media further explore the influence of viscoelasticity on wave propagation behaviors. To validate the analytical framework, comparisons are systematically made between viscoelastic and purely elastic cases. The findings demonstrate the robustness and applicability of the proposed methodologies, offering a reliable foundation for optimizing sensor deployment in SHM applications for anisotropic viscoelastic composite structures.

During shield tunnel construction, grouting is injected between the segment and the surrounding rock to ensure structural safety. However, defects may occur because of insufficient or shrunken grouting. Therefore, nondestructive testing (NDT) of grouting defects behind tunnel shield segments is crucial for ensuring the performance of tunnel structures and preventing disasters. In this paper, a shear horizontal (SH) array ultrasonic wave with double-ray coverage imaging testing technique is proposed. Compared with the traditional single-ray coverage method, it has better performance in focusing imaging and noise resistance. Additionally, the SH wave profile is a simple waveform without apparent conversion wave interference. Numerical simulations considering varying rebar-layer layout configurations and full-scale shield segment model tests were carried out. The proposed method demonstrates superior detection accuracy and resistance to the interference from rebar in the segment; more importantly, compared with ground-penetrating radar (GPR) detection results for the same full-scale model, SH -array ultrasonic testing with double-ray coverage can provide more intuitive imaging of grouting defects without the need for complex manual data processing. Moreover, by applying Gaussian noise interference to the numerical models and a typical grouting defect model on site, it is shown that the double-ray coverage imaging method results in greater noise suppression and better defect focusing effects than does single-ray coverage. Therefore, the SH- array ultrasonic testing technique with double-ray coverage is an effective method for high-precision detection of grouting defects behind tunnel shield segments.

In this paper, a two-dimensional Dirichlet-to-Neumann (DtN) finite element method (FEM) is developed to analyze the scattering of SH guided waves due to an interface delamination in a bi-material plate. During the finite element analysis, it is necessary to determine the far-field DtN conditions at virtual boundaries where both displacements and tractions are unknown. In this study, firstly, the scattered waves at the virtual boundaries are represented by a superposition of guided waves with unknown scattered coefficients. Secondly, utilizing the mode orthogonality, the unknown tractions at virtual boundaries are expressed in terms of the unknown scattered displacements at virtual boundaries via scattered coefficients. Thirdly, this relationship at virtual boundaries can be finally assembled into the global DtN-FEM matrix to solve the problem. This method is simple and elegant, which has advantages on dimension reduction and needs no absorption medium or perfectly matched layer to suppress the reflected waves compared to traditional FEM. Furthermore, the reflection and transmission coefficients of each guided mode can be directly obtained without post-processing. This proposed DtN-FEM will be compared with boundary element method (BEM), and finally validated for several benchmark problems.

Integration of nanobiosensors with acoustic delay lines within planar technologies gives a chance to develop the acousto-nanoelectronic sensors with high sensitivity and selectivity. This type of sensors can be used to register biospecific interactions, to detect various biological objects, to monitor sensitivity of bioobjects towards various antibiotics, etc. In present paper the acoustoelectronic chip sensor implemented on lithium niobate plate with a system of interdigital transducers (IDTs) for exciting proper acoustic wave is developed. The sensor is inserted into the chip holder of the standard socket of knife type. Acoustoelectronic devices is calculated for anti-symmetric (A0) and symmetric (S0) Lamb waves as well as shear-horizontal wave (SH0) of the zero order. The area, 80х80 μm in square, is located in the centre of the chip for formation of a nanostructure. The sensing properties of the nanostructure are modified by its vibration produced by proper acoustic wave, propagating through bio-active area. Fabrication of the integrated sensor is accomplished by standard lithography, various photoresist, and reactive ion etching. The as-developed device is considered as a prototype of a nanoelectronic transducer, where nanostructures or nanogaps for realization of molecular transistors on the basis of proteins-enzymes are created.

This paper presents an efficient Dirichlet-to-Neumann (DtN) finite element method (FEM), for analyzing the scattering phenomenon of guided SH waves travelling through a curved plate with/ without internal defects. By introduction of guided wave mode orthogonality, the displacement and traction fields of the scattered wave on a far-field cross section are expressed as the superposition of a series of propagating guided SH modes with reflection/transmission coefficients to be solved. Consequently, we establish the DtN boundary conditions by introduction of displacement and stress wave structures of each mode. As the application of the method, we calculate the reflected and transmitted wave fields by defects in a curved plate of different locations, and perform parametric analysis. The tendency of reflection coefficients with respect to defects' parameters suggests the potential for quantitative non-destructive evaluation.

In order to reconstruct the possible defects on the plate surface with arrays, a new wave tomography method based on the method of moments is established in this paper. According to the relationship between the probe number and grid amount, two algorithms, that is, the neural network and principal component analysis (PCA), are proposed and used to solve the ill-conditioned inversion equations. The neural network makes imaging feasible even if input data are not enough, and the PCA can greatly improve the computational efficiency via reducing the matrix dimension. Both numerical simulations and experimental measurements are conducted with the algorithm's correctness and high precision validated. After investigating the influence of probe number on imaging quality, it is demonstrated that the algorithm can exactly predict the defect location when the input scattering data is not enough or fewer probes are arranged. More probes are needed for reconstructing the specific shape and thickness, especially when multiple defects are included. The qualitative results and quantitative data are conducive to providing some reference for engineering applications in nondestructive testing and structural health monitoring.

Data-driven quantitative defect reconstruction using ultrasonic guided waves has recently demonstrated great potential in the area of non-destructive testing (NDT) and structural health monitoring (SHM). In this paper, a novel deep learning-based framework, called Deep-guide, has been proposed to convert the inverse guided wave scattering problem into a data-driven manifold learning progress for defect reconstruction. The architecture of Deep-guide network consists of the efficient encoder-projection-decoder blocks to automatically realize the end-to-end mapping of noisy guided wave reflection coefficients in the wavenumber domain to defect profiles in the spatial domain by the manifold distribution principle and intelligent learning. Toward this, results by the modified boundary element method for efficient calculations of scattering fields of guided waves have been generated as acoustic emission signals of the Deep-guide to facilitate the training and extract the features homeomorphically. The correctness, robustness, and efficiency of the proposed framework have been demonstrated throughout several examples and experimental tests of circular defects. It has been noted that Deep-guide has the ability to achieve the high-quality defect reconstructions and provides valuable insights into the development of effective data-driven techniques for structural health monitoring and complex defect reconstructions.

Defect detection of laminated composite plates using ultrasonic guided waves is of great interest nowadays. Nevertheless, it is still a challenging problem to reconstruct the true shape of defects in anisotropic materials. The inverse method proposed in this paper can directly reconstruct the specific shape of defects. Moreover, this method does not need iteration, is simple in form and easy to use. A three-step strategy of this method is performed as follows: Firstly, based on boundary integral equation and Born approximation assumption, flaw shape function and reflection coefficients form a set of Fourier transform pairs; Secondly, we propose an efficient way to quickly obtain Green’s function and bring it to step 1. Finally, the actual shape and location of flaws can be inversely reconstructed by reflection coefficients in the whole frequency domain obtained by modified boundary element method (BEM). This method is implemented to reconstruct cavity-type flaws at the interface in a laminated composite plate. The correctness and effectiveness of the proposed method is finally validated for several benchmark problems, and the effect of frequency range, flaw size and mode selection on accuracy of the inverse reconstruction are discussed in detail.

Flaws have a huge impact on the service life of structures and industrial production safety. As time goes by, more accurate and quantitative flaw evaluation method should be proposed. In this paper, a two-dimensional (2D) Born approximation based linearized quantitative reconstruction method due to interlayer cavity flaws in a laminated orthotropic composite plate is proposed. A two-step strategy of this method is performed as follows: Firstly, a modified boundary element method (BEM) is proposed to obtain the reflection coefficients of each guided mode; Secondly, based on boundary integral equation and Born approximation assumption, flaw shape function and reflection coefficients form a set of Fourier transform pairs. Then the actual shape and location of flaws can be inversely reconstructed by reflection coefficients obtained in the first step. This method is implemented to reconstruct cavity-type flaws at the interface in a laminated composite plate. The correctness and efficiency of the proposed method is finally validated for several benchmark problems, and the effect of frequency range, flaw size and mode selection on accuracy of the inverse reconstruction are discussed in detail.

In this paper, a modified boundary element method (BEM) for time-harmonic scattering computation analysis in two-dimensional (2-D), homogeneous, anisotropic and linear elastic plates is proposed. The aim of modification is to correct the spurious scattering introduced by inevitable model truncation at far-field in the traditional BEM model. The far-field wave displacement fields beyond the truncation points of BEM model are assumed to be the superposition of orthogonal propagating guided wave patterns, and are finally incorporated into BEM equation systems as the modified items to account for the contribution of infinite boundaries traditionally omitted. This method is simple and elegant, which has advantages on dimension reduction and needs no absorption medium or perfectly matched layer to suppress the reflected waves compared to FEM. Also, we can obtain the reflection and transmission coefficients of each mode directly without post-processing. This modified BEM is implemented to solve wave scattering problems due to a cavity-type defect at the interface in an infinite anisotropic multi-layered plate. The formulation is finally validated for several benchmark problems.

The detection and evaluation of corrosion, cracks, flaws, and other imperfections in aged structures are critical for enhancing safety and evaluating residual service life in structural health monitoring (SHM) and nondestructive testing (NDT). A guided wave tomography based on the method of moments (MOM) for exact detection of the surface defects in plates, including their profile, size, and position is proposed in this paper. The mathematical relationship between the plate thickness and the objective function is derived theoretically for the A0 mode. Based on the obtained relationship, a plate thickness imaging technique is proposed. The efficiency of the proposed technique is confirmed by the results of numerical simulation and experimental data. Center and off-center surface defects are considered. 64 probes are evenly distributed in a circle outside the defect to capture omnidirectional wave signals. Both numerical and experimental results demonstrate that the guided wave tomography proposed can effectively reconstruct the spatial plate thickness distribution, enabling the precise identification of the defect's shape, depth, and position. The qualitative analysis and quantitative data provide effective guidance for NDT or SHM technologies in engineering.

Quantitative detection of defects in structures is always a hot research topic in the field of guided wave inverse scattering. Research studies on how to effectively extract the defect-related information encompassed in the multi-frequency and multi-modes scattered wave signals for reconstructions of defects have been paid attention in recent decades. In this paper, a novel deep learning-based quantitative guided wave inverse scattering technique has been proposed to intelligently realize the end-to-end mapping of the multi-frequency, multi-modes scattered signals to defect profiles with high levels of accuracy and efficiency. Based on the manifold distribution principle, the data patterns of scattered SH-wave signals have been investigated, owing to leveraging the capability of the intelligent encoder-projection-decoder neural network. Following that, the manifold-learning-oriented network has been trained using the data generated by the modified boundary element method. Several numerical examples have been examined to demonstrate the correctness and efficiency of the proposed reconstruction approach. It has been concluded that this novel data-driven technique intelligently enables the high-quality solution to inverse scattering problems and provides valuable insight into the development of practical approaches to quantitative detection using multi-frequency and multi-modal acoustic data from scattered ultrasonic guided waves.