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This paper proposes a damage detection method based on an improved DAS imaging algorithm by introducing time difference due to anisotropy of composite material. First, the finite element characteristic frequency method is used to obtain the dispersion curve of the composite plate, and the validity of the dispersion curve is verified. Next, the average phase velocity of the Lamb wave at mixed modes in the composite plate is obtained by two-dimensional Fourier transform (2-D FFT). The mixed modal group velocity is calculated according to the corresponding phase velocity, the mean change rate of the phase velocity and the dispersion curve obtained by simulation. The time difference due to anisotropy of composite material is investigated, and the damage location is estimated by the delay-and-sum (DAS) imaging algorithm. Experiments on carbon fiber multilayer composite plates verify the effectiveness of the proposed method.

Imaging for damage in plate structure by Lamb waves is one of the most effective methods in the field of structural health monitoring. In order to improve the accuracy of damage localization, a novel method is proposed to modify damage exponent probability imaging algorithm based on delay-and-sum imaging by using time reversal Lamb waves. A new probability distribution function is introduced to improve the damage index probability method and is combined with delay-and-sum method for damage localization. Experimental results on aluminum plate show that the hybrid algorithm achieves better accuracy of damage location and imaging quality than the conventional delay-and-sum method.

Finite element approximation to a decoupled formulation for the quad--curl problem is studied in this paper. The difficulty of constructing elements with certain conformity to the quad--curl problems has been greatly reduced. For convex domains, where the regularity assumption holds for Stokes equation, the approximation to the curl of the true solution has quadratic order of convergence and first order for the energy norm. If the solution shows singularity, an a posterior error estimator is developed and a separate marking adaptive finite element procedure is proposed, together with its convergence proved. Both the a priori and a posteriori error analysis are supported by the numerical examples.

Damage imaging based on scattering signals of ultrasonic Lamb waves in plate structure is considered as one of the most effective ways for structural health monitoring area. To improve location accuracy and reduce the impact of artifacts, a probability weighted four-point arc imaging algorithm for time reversal Lamb wave damage detection is proposed in this paper. By taking the defect as a secondary wave source, the four-point arc positioning method is used to calculate the propagation time of the signal from transducer to defect. And the amplitude of damage signal corresponding to the time of flight is used for imaging. In order to eliminate the artifacts, a damage probability weighting is combined with four-point circular arc imaging algorithm. The effectiveness of the proposed method is experimentally verified in aluminum plate. Experimental results indicate that damage location accuracy and imaging quality has been improved in both single-flaw and double-flaw samples compared with conventional delay-and-sum method.

The application of sparse reconstruction method for damage localization via ultrasonic Lamb waves in structure health monitoring is studied theoretically and experimentally in this paper. In this method, the oblique probes are used to detect damages in thin plate structures by recording all pairwise signals. By using the baseline signals of nondestructive structure and the sparsity of structural damages, a dictionary matrix is constructed through scattering signals from each grid of the detected area. The possible location of damage can be represented by atoms in the dictionary. In order to reduce the effect of noise and unknown sparsity, an adaptive BPDN algorithm is proposed for damage imaging. It combines greedy algorithm and convex optimization algorithm by firstly estimating a sparsity value as the initial iteration step to choose atoms that may contain damages and then renewing the dictionary. The ultrasonic Lamb wave image of the detected plate structure can be obtained by sparsely reconstructing the signals of the new dictionary, and the damages can be located in the image. The results of simulation and experiment manifested the effectiveness of the proposed method.

A refined a priori error analysis of the lowest order (linear) nonconforming Virtual Element Method (VEM) for approximating a model Poisson problem is developed in both 2D and 3D. A set of new geometric assumptions is proposed on shape regularity of polytopal meshes. A new error equation for the lowest order (linear) nonconforming VEM is derived for any choice of stabilization, and a new stabilization using a projection on an extended element patch is introduced for the error analysis on anisotropic elements.

A virtual element method (VEM) with the first-order optimal convergence order is developed for solving two-dimensional Maxwell interface problems on a special class of polygonal meshes that are cut by the interface from a background unfitted mesh. A novel virtual space is introduced on a virtual triangulation of the polygonal mesh satisfying a maximum angle condition, which shares exactly the same degrees of freedom as the usual [Formula: see text]-conforming virtual space. This new virtual space serves as the key to prove that the optimal error bounds of the VEM are independent of high aspect ratio of the possible anisotropic polygonal mesh near the interface.

Food safety continues to threaten public health. Machine learning holds potential in leveraging large, emerging data sets to improve the safety of the food supply and mitigate the impact of food safety incidents. Foodborne pathogen genomes and novel data streams, including text, transactional, and trade data, have seen emerging applications enabled by a machine learning approach, such as prediction of antibiotic resistance, source attribution of pathogens, and foodborne outbreak detection and risk assessment. In this article, we provide a gentle introduction to machine learning in the context of food safety and an overview of recent developments and applications. With many of these applications still in their nascence, general and domain-specific pitfalls and challenges associated with machine learning have begun to be recognized and addressed, which are critical to prospective use and future deployment of large data sets and their associated machine learning models for food safety applications.

This article presents an immersed virtual element method for solving a class of interface problems that combines the advantages of both body-fitted mesh methods and unfitted mesh methods. A background body-fitted mesh is generated initially. On those interface elements, virtual element spaces are constructed as solution spaces to local interface problems, and exact sequences can be established for these new spaces involving discontinuous coefficients. The discontinuous coefficients of interface problems are recast as Hodge star operators that are the key to project immersed virtual functions to classic immersed finite element (IFE) functions for computing numerical solutions. An a priori convergence analysis is established robust with respect to the interface location. The proposed method is capable of handling more complicated interface element configuration and provides better performance than the conventional penalty-type IFE method for the H(curl)-interface problem arising from Maxwell equations. It also brings a connection between various methods such as body-fitted methods, IFE methods, virtual element methods, etc.

An adaptive modified weak Galerkin method (AmWG) for an elliptic problem is studied in this paper, in addition to its convergence and optimality. The modified weak Galerkin bilinear form is simplified without the need of the skeletal variable, and the approximation space is chosen as the discontinuous polynomial space as in the discontinuous Galerkin method. Upon a reliable residual-based a posteriori error estimator, an adaptive algorithm is proposed together with its convergence and quasi-optimality proved for the lowest order case. The primary tool is to bridge the connection between the modified weak Galerkin method and the Crouzeix-Raviart nonconforming finite element. Unlike the traditional convergence analysis for methods with a discontinuous polynomial approximation space, the convergence of AmWG is penalty parameter free. Numerical results are presented to support the theoretical results., Comment: Extended reference to include recent contributions than the published version

In this paper, we introduce a simple local flux recovery for \begin{document}$ \mathcal{Q}_k $\end{document} finite element of a scalar coefficient diffusion equation on quadtree meshes, with no restriction on the irregularities of hanging nodes. The construction requires no specific ad hoc tweaking for hanging nodes on \begin{document}$ l $\end{document}-irregular (\begin{document}$ l\geq 2 $\end{document}) meshes thanks to the adoption of virtual element families. The rectangular elements with hanging nodes are treated as polygons as in the flux recovery context. An efficient a posteriori error estimator is then constructed based on the recovered flux, and its reliability is proved under common assumptions, both of which are further verified in numerics.

This paper introduces a new recovery-based a posteriori error estimator for the lowest order Nedelec finite element approximation to the H ( curl ) interface problem. The error estimator is analyzed by establishing both the reliability and the efficiency bounds and is supported by numerical results. Under certain assumptions, it is proved that the reliability and efficiency constants are independent of the jumps of the coefficients.

Visible light communication (VLC) technique has a wide range of applications in the daily life, the penetration rate of it is further improved in recent years, and it provides a new possibility for information transmission without traditional communication signal coverage like the tunnel or the basement. Based on the analysis of the latest research by domestic and foreign scholars, and the research of the existing device for image transmission through visible light and the particularity of the tunnel environment, this paper studies the optimization of the light source distribution, the measurement of the illuminance at the receiving end, the signal modulation and demodulation, and the encoding and decoding technology. Through the simulation experiment and the selection of existing components and technologies, the optimization of the original device is realized, so that it can be used in the tunnel information transmission and can provide certain reference for future visible light communication technique research.

In this paper, we introduce a novel a posteriori error estimator for the conforming finite element approximation to the H ( curl ) problem with inhomogeneous media and with the right-hand side only in L 2 . The estimator is of the recovery type. Independent with the current approximation to the primary variable (the electric field), an auxiliary variable (the magnetizing field) is recovered in parallel by solving a similar H ( curl ) problem. An alternate way of recovery is presented as well by localizing of the error flux. The estimator is then defined as the sum of the modified element residual and the residual of the constitutive equation defining the auxiliary variable. It is proved that the estimator is approximately equal to the true error in the energy norm without the quasi-monotonicity assumption. Finally, we present numerical results for several H ( curl ) interface problems.