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On the use of phase laws for the linear sampling method in an elastic waveguide. Application to nondestructive testing

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WAVE MOTION 2025年 133卷

作者： Recoquillay, Arnaud Univ Paris Saclay CEA LIST F-91120 Palaiseau France

This paper presents the use of phased array data as the input of the linear sampling method for elastic waveguides. Indeed, this method enables the high frequency, hence high resolution, inspection of waveguides, which is of interest for example for nondestructive testing applications. However, the use of single emitter data, also known as Full Matrix Capture in the Non Destructive Testing (NDT) context, leads to poor signal to noise ratios as low amplitude signals are emitted and only a fraction of the energy reaches the potential defect. The use of phase laws, that is the simultaneous emission with multiple sensors, enables better signal to noise ratios. However, the drawback may be a loss on the conditioning of the method, which may lead to higher sensitivity to noise in the end. This paper shows how to choose the sensors and the phase laws to obtain a satisfactory imaging results. This is exemplified on experimental data acquired in a steel plate with a circular hole.

关键词： Ultrasonic guided waves Inverse scattering problem linear sampling method Phased arrays

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Shape and parameter identification by the linear sampling method for a restricted Fourier integral operator

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INVERSE PROBLEMS 2024年第9期40卷 095007-095007页

作者： Audibert, Lorenzo Meng, Shixu EDF R&D PRISME 6 Quai Watier F-78400 Chatou France Inst Polytech Paris UMA Inria ENSTA Paris F-91120 Palaiseau France Virginia Tech Dept Math Blacksburg VA 24061 USA

In this paper we provide a new linear sampling method based on the same data but a different definition of the data operator for two inverse problems: the multi-frequency inverse source problem for a fixed observation direction and the Born inverse scattering problems. We show that the associated regularized linear sampling indicator converges to the average of the unknown in a small neighborhood as the regularization parameter approaches to zero. We develop both a shape identification theory and a parameter identification theory which are stimulated, analyzed, and implemented with the help of the prolate spheroidal wave functions and their generalizations. We further propose a prolate-based implementation of the linear sampling method and provide numerical experiments to demonstrate how this linear sampling method is capable of reconstructing both the shape and the parameter.

关键词： linear sampling method shape identification parameter identification inverse source and scattering problems prolate spheroidal wave functions.

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The linear sampling method for Data Generated by Small Random Scatterers\ast

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SIAM JOURNAL ON IMAGING SCIENCES 2024年第4期17卷 2142-2173页

作者： Garnier, Josselin Haddar, Houssem Montanelli, Hadrien Ecole Polytech CMAP IP Paris F-91120 Palaiseau France Inria UMA ENSTA Paris IP Paris F-91120 Palaiseau France

We present an extension of the linear sampling method for solving the sound-soft inverse scattering problem in two dimensions with data generated by randomly distributed small scatterers. The theoretical justification of our novel sampling method is based on a rigorous asymptotic model, a modified Helmholtz-Kirchhoff identity, and our previous work on the linear sampling method for random sources. Our numerical implementation incorporates boundary elements, singular value decomposition, Tikhonov regularization, and Morozov's discrepancy principle. We showcase the robustness and accuracy of our algorithms with a series of numerical experiments.

关键词： active (controlled sources) inverse acoustic scattering problem Helmholtz equation linear sampling method passive imaging singular value decomposition Tikhonov regularization ill-posed problems

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The linear sampling method for Random Sources

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SIAM JOURNAL ON IMAGING SCIENCES 2023年第3期16卷 1572-1593页

作者： Garnier, Josselin Haddar, Houssem Montanelli, Hadrien Inst Polytech Paris Ecole Polytech Ctr Math Appl CNRS F-91120 Palaiseau France Inst Polytech Paris INRIA ENSTA Paris UMA F-91120 Palaiseau France

We present an extension of the linear sampling method for solving the sound-soft inverse acoustic scattering problem with randomly distributed point sources. The theoretical justification of our sampling method is based on the Helmholtz-Kirchhoff identity, the cross-correlation between measurements, and the volume and imaginary near-field operators, which we introduce and analyze. Implementations in MATLAB using boundary elements, the SVD, Tikhonov regularization, and Morozov's discrepancy principle are also discussed. We demonstrate the robustness and accuracy of our algorithms with several numerical experiments in two dimensions.

关键词： words. inverse acoustic scattering problem Helmholtz equation linear sampling method passive imaging singular value decomposition Tikhonov regularization ill-posed problems

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THE linear sampling method FOR RECONSTRUCTING A PENETRABLE CAVITY WITH UNKNOWN EXTERNAL OBSTACLES

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Acta Mathematica Scientia 2023年第2期43卷 751-776页

作者：叶建国严国政 Research Center of Modern Mathematics and Its Application School of Mathematics and StatisticsKashi UniversityKashi 844000China School of Mathematics and Statistics Central China Normal UniversityWuhan 430079China

We consider the interior inverse scattering problem for recovering the shape of a penetrable partially coated cavity with external obstacles from the knowledge of measured scattered waves due to point *** the first part,we obtain the well-posedness of the direct scattering problem by the variational *** the second part,we establish the mathematical basis of the linear sampling method to recover both the shape of the cavity,and the shape of the external obstacle,however the exterior transmission eigenvalue problem also plays a key role in the discussion of this paper.

关键词： inverse scattering mixed boundary value problem exterior transmission eigen-value interior measurements linear sampling method

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Qualitative Defects Detection in Plane linear Piezoelastic Media Using linear sampling method

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MECHANICS OF SOLIDS 2023年第9期58卷 3120-3131页

作者： Manshadi, Hadi Dehghan Mirjalili, Alireza Amiri, Hamidreza Islamic Azad Univ Dept Civil Engn Yazd Branch Yazd Iran

In this paper, the linear sampling method is introduced for cavity detection in a two dimensional (2D) piezoelastic media using measurement of data on the boundary. This method is categorized as a qualitative approach to image the geometrical features of unknown targets. Although this method has been used in the context of inverse problems such as acoustics, electromagnetism and elastostatic, there is no specific attempt to apply this method to identification of cavities in piezoelastic media. This study emphasizes the implementation of the linear sampling method coupled with the finite element method (FEM). A set of numerical simulations on two-dimensional problems is presented to highlight many effective features of the proposed qualitative identification method.

关键词： qualitative inverse problems linear sampling method piezoelastic media cavity detection finite element method

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The linear sampling method for penetrable cylinder with inclusions for obliquely incident polarized electromagnetic waves

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JOURNAL OF INVERSE AND ILL-POSED PROBLEMS 2022年第3期30卷 331-349页

作者： Deng, Xia Guo, Jun Li, Jin Yan, Guozheng Cent China Normal Univ Sch Math & Stat Wuhan 430079 Peoples R China Changsha Normal Univ Sch Math Changsha 410100 Peoples R China South Cent Univ Nationalities Sch Math & Stat Wuhan 430074 Peoples R China Guangdong Univ Petrochem Technol Sch Sci Maoming 525000 Peoples R China

Consider the scattering of electromagnetic waves by a penetrable homogeneous cylinder at oblique incident. The Maxwell equations are then reduced to a system of a pair of the two-dimensional Helmholtz equations for z-components of the electric and magnetic field through coupled oblique boundary conditions. This paper studies an inverse problem of recovering the penetrable obstacle from the far-field pattern of the electric field. The well-known linear sampling method is used to solve this problem. Compared with the usual inverse scattering problem, the coupled system and the oblique derivative boundary condition bring difficulties in theoretical analysis. Some numerical examples are presented to illustrate the validity and feasibility of the proposed method.

关键词： Inverse scattering oblique incidence coupled boundary condition linear sampling method

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Optimal Axial-Probe Design for Foucault-Current Tomography: A Global Optimization Approach Based on linear sampling method

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ENERGIES 2023年第5期16卷 2448-2448页

作者： Benaissa, Brahim Khatir, Samir Jouini, Mohamed Soufiane Riahi, Mohamed Kamel Toyota Technol Inst Dept Mech Syst Engn Design Engn Lab 2 Chome-12-1HisakataTempaku Ward Nagoya 4688511 Japan Univ Ghent Fac Engn & Architecture Soete Lab Technologiepark Zwijnaarde 903 B-9052 Zwijnaarde Belgium Khalifa Univ Sci & Technol Dept Math POB 127788 Abu Dhabi U Arab Emirates Khalifa Univ Sci & Technol Emirates Nucl Technol Ctr ENTC POB 127788 Abu Dhabi U Arab Emirates Khalifa Univ POB 127788Zarkuh BldgSAN Campus Abu Dhabi U Arab Emirates

This paper is concerned with the optimal design of axial probes, commonly used in the Non-Destructive Testing (NDT) of tube boiling in steam generators. The goal is to improve the low-frequency Foucault-current imaging of these deposits by designing a novel probe. The approach uses a combination of an inverse problem solver with global optimization to find the optimal probe characteristics by minimizing a function of merit defined using image processing techniques. The evaluation of the function of merit is computationally intensive and a surrogate optimization approach is used, incorporating a multi-particle search algorithm. The proposed design is validated through numerical experiments and aims to improve the accuracy and efficiency of identifying deposits in steam generator tubes.

关键词： NDT optimal design eddy-current inverse problem linear sampling method finite element method surrogate optimization

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Solving a kind of inverse scattering problem of acoustic waves based on linear sampling method and neural network

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ALEXANDRIA ENGINEERING JOURNAL 2020年第3期59卷 1451-1462页

作者： Meng, Pinchao Su, Lin Yin, Weishi Zhang, Su Changchun Univ Sci & Technol Coll Sci Changchun 130022 Peoples R China Changchun Univ Sci & Technol Expt Ctr Math Changchun 130022 Peoples R China Changchun Univ Sci & Technol Coll Econ & Management Changchun 130022 Peoples R China

This paper explores the inverse scattering problem that reconstructs the obstacle shape with far-field information in the acoustic environment. Taking the planar wave as the incident wave, the authors put forward a shape reconstruction method for an impenetrable obstacle with a sound-soft boundary. Firstly, the linear sampling method (LSM) was performed to acquire the prior information about the obstacle shape. Next, a shape parameter inversion model was constructed based on neural network and gating thought, and it was denoted as the SPIMNNG. The model parameters were updated through self-learning. After that, the shape parameters of obstacle boundary were inversed according to the far-field information and the prior information about obstacle shape. On this basis, the boundary shape of the obstacle was reconstructed. The computing complexity of the SPIMNNG model was also calculated. Finally, several numerical experiments were carried out to verify the proposed method. The results show that our method can effectively inverse the shape parameters of obstacles. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.

关键词： Acoustic inversion linear sampling method Neural network Gating thought Obstacle shape reconstruction

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Accurate and robust inversion of buried objects based on the linear sampling method and differential evolution

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IET RADAR SONAR AND NAVIGATION 2020年第2期14卷 320-327页

作者： Fan, Qimeng Yin, Chengyou Gan, Yongji Natl Univ Def Technol Coll Elect Engn Hefei Peoples R China

The authors propose an accurate and robust method to reconstruct buried objects for half-space scenarios. First, the linear sampling method (LSM) was employed to estimate targets support. A relaxed threshold is defined for LSM to ensure all real targets are included. Despite the low accuracy of the estimation by LSM, the authors were more interested in its insensitivity to noise. Second, differential evolution (DE) optimisation was used to refine the LSM results. Since the magnitudes of LSM indicator functions are related to the probability of support belonging to real targets, different weights for gene elements are allocated according to their indicator values to control mutation and cross probability. A mask-beneficial contrast source inversion (CSI) is employed to evaluate cost function by encoding possible targets support and making it into a support mask. The mask is combined with CSI as a priori information and an accurate mask tends to derive a slight iteration error, whereas those incorrect ones will result in large errors. Thus, by adopting CSI iteration error as a cost function and taking advantage of superior optimisation performance of weighted DE, the authors find an optimum mask and reconstruct contrast with high fidelity. Effectiveness of the proposed method is validated by simulation results.

关键词： image reconstruction probability sampling methods buried object detection iterative methods evolutionary computation robust inversion method linear sampling method half-space scenarios relaxed threshold LSM indicator functions cross probability mask-beneficial contrast source inversion cost function buried objects reconstruction differential evolution optimisation gene elements CSI iteration error control mutation

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