Статті в журналах: "Optimized domain decomposition method"

1

Ouyang, Chun-Juan, Chang-Xin Liu, Ming Leng, and Huan Liu. "An OMP Steganographic Algorithm Optimized by SFLA." International Journal of Pattern Recognition and Artificial Intelligence 31, no. 01 (January 2017): 1754001. http://dx.doi.org/10.1142/s0218001417540015.

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In this paper, we propose a novel steganographic method, which utilizes the sparsity and integrity of the image compressed sensing to reduce the risk of being detected by steganalysis. In the proposed algorithm, the message hiding process is integrated into the image sparse decomposition process without affecting the image perceptibility. First, the cover image is decomposed by the orthogonal matching pursuit algorithm of image sparse decomposition, and the shuffled frog leaping algorithm (SFLA) is used to select the optimal atom in each decomposition iteration. Then, different quantization bits are adopted to quantify the sparse decomposition coefficients. Finally, via LSB[Formula: see text] steganographic strategy, the secret message is embedded in the least significant bits of the quantized coefficients. Experimental results show that the embedded data are invisible perceptually. Simultaneously, experiments show that the new steganography has good expandability in embedding capacity, owing to less sensitivity to the embedding bits. The security of the proposed method is also evaluated comparatively, by using four steganalyzers with rich feature, which indicates superior performance of the proposed method comparing with other steganographies conducted in sparse decomposition domain and the LSB[Formula: see text] methods used in spatial domain and DCT domain.

2

Chen, Jia-Fen, Xian-Ming Gu, Liang Li, and Ping Zhou. "An Optimized Schwarz Method for the Optical Response Model Discretized by HDG Method." Entropy 25, no. 4 (April 19, 2023): 693. http://dx.doi.org/10.3390/e25040693.

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An optimized Schwarz domain decomposition method (DDM) for solving the local optical response model (LORM) is proposed in this paper. We introduce a hybridizable discontinuous Galerkin (HDG) scheme for the discretization of such a model problem based on a triangular mesh of the computational domain. The discretized linear system of the HDG method on each subdomain is solved by a sparse direct solver. The solution of the interface linear system in the domain decomposition framework is accelerated by a Krylov subspace method. We study the spectral radius of the iteration matrix of the Schwarz method for the LORM problems, and thus propose an optimized parameter for the transmission condition, which is different from that for the classical electromagnetic problems. The numerical results show that the proposed method is effective.

3

GOTOH, Hitoshi, Abbas KHAYYER, Hiroyuki IKARI, and Chiemi HORI. "Development of 3D Parallelized CMPS Method with Optimized Domain Decomposition." Journal of Japan Society of Civil Engineers, Ser. B2 (Coastal Engineering) 65, no. 1 (2009): 41–45. http://dx.doi.org/10.2208/kaigan.65.41.

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4

Li, Hui, Bangji Fan, Rong Jia, Fang Zhai, Liang Bai, and Xingqi Luo. "Research on Multi-Domain Fault Diagnosis of Gearbox of Wind Turbine Based on Adaptive Variational Mode Decomposition and Extreme Learning Machine Algorithms." Energies 13, no. 6 (March 16, 2020): 1375. http://dx.doi.org/10.3390/en13061375.

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Since variational mode decomposition (VMD) was proposed, it has been widely used in condition monitoring and fault diagnosis of mechanical equipment. However, the parameters K and α in the VMD algorithm need to be set before decomposition, which causes VMD to be unable to decompose adaptively and obtain the best result for signal decomposition. Therefore, this paper optimizes the VMD algorithm. On this basis, this paper also proposes a method of multi-domain feature extraction of signals and combines an extreme learning machine (ELM) to realize comprehensive and accurate fault diagnosis. First, VMD is optimized according to the improved grey wolf optimizer; second, the feature vectors of the time, frequency, and time-frequency domains are calculated, which are synthesized after dimensionality reduction; ultimately, the synthesized vectors are input into the ELM for training and classification. The experimental results show that the proposed method can decompose the signal adaptively, which produces the best decomposition parameters and results. Moreover, this method can extract the fault features of the signal more completely to realize accurate fault identification.

5

Amattouch, M. R., N. Nagid, and H. Belhadj. "Optimized Domain Decomposition Method for Non Linear Reaction Advection Diffusion Equation." European Scientific Journal, ESJ 12, no. 27 (September 30, 2016): 63. http://dx.doi.org/10.19044/esj.2016.v12n27p63.

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This work is devoted to an optimized domain decomposition method applied to a non linear reaction advection diffusion equation. The proposed method is based on the idea of the optimized of two order (OO2) method developed this last two decades. We first treat a modified fixed point technique to linearize the problem and then we generalize the OO2 method and modify it to obtain a new more optimized rate of convergence of the Schwarz algorithm. To compute the new rate of convergence we have used Fourier analysis. For the numerical computation we minimize this rate of convergence using a global optimization algorithm. Several test-cases of analytical problems illustrate this approach and show the efficiency of the proposed new method.

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Loisel, S., J. Côté, M. J. Gander, L. Laayouni, and A. Qaddouri. "Optimized Domain Decomposition Methods for the Spherical Laplacian." SIAM Journal on Numerical Analysis 48, no. 2 (January 2010): 524–51. http://dx.doi.org/10.1137/080727014.

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Gander, Martin J., and Yingxiang Xu. "Optimized Schwarz methods with nonoverlapping circular domain decomposition." Mathematics of Computation 86, no. 304 (May 17, 2016): 637–60. http://dx.doi.org/10.1090/mcom/3127.

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Ali Hassan, Sarah, Caroline Japhet, Michel Kern, and Martin Vohralík. "A Posteriori Stopping Criteria for Optimized Schwarz Domain Decomposition Algorithms in Mixed Formulations." Computational Methods in Applied Mathematics 18, no. 3 (July 1, 2018): 495–519. http://dx.doi.org/10.1515/cmam-2018-0010.

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AbstractThis paper develops a posteriori estimates for domain decomposition methods with optimized Robin transmission conditions on the interface between subdomains. We choose to demonstrate the methodology for mixed formulations, with a lowest-order Raviart–Thomas–Nédélec discretization, often used for heterogeneous and anisotropic porous media diffusion problems. Our estimators allow to distinguish the spatial discretization and the domain decomposition error components. We propose an adaptive domain decomposition algorithm wherein the iterations are stopped when the domain decomposition error does not affect significantly the overall error. Two main goals are thus achieved. First, a guaranteed bound on the overall error is obtained at each step of the domain decomposition algorithm. Second, important savings in terms of the number of domain decomposition iterations can be realized. Numerical experiments illustrate the efficiency of our estimates and the performance of the adaptive stopping criteria.

9

Dolean, Victorita, St�phane Lanteri, and Fr�d�ric Nataf. "Optimized interface conditions for domain decomposition methods in fluid dynamics." International Journal for Numerical Methods in Fluids 40, no. 12 (2002): 1539–50. http://dx.doi.org/10.1002/fld.410.

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10

Gander, Martin J., and Hui Zhang. "Schwarz methods by domain truncation." Acta Numerica 31 (May 2022): 1–134. http://dx.doi.org/10.1017/s0962492922000034.

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Schwarz methods use a decomposition of the computational domain into subdomains and need to impose boundary conditions on the subdomain boundaries. In domain truncation one restricts the unbounded domain to a bounded computational domain and must also put boundary conditions on the computational domain boundaries. In both fields there are vast bodies of literature and research is very active and ongoing. It turns out to be fruitful to think of the domain decomposition in Schwarz methods as a truncation of the domain onto subdomains. Seminal precursors of this fundamental idea are papers by Hagstrom, Tewarson and Jazcilevich (1988), Després (1990) and Lions (1990). The first truly optimal Schwarz method that converges in a finite number of steps was proposed by Nataf (1993), and used precisely transparent boundary conditions as transmission conditions between subdomains. Approximating these transparent boundary conditions for fast convergence of Schwarz methods led to the development of optimized Schwarz methods – a name that has become common for Schwarz methods based on domain truncation. Compared to classical Schwarz methods, which use simple Dirichlet transmission conditions and have been successfully used in a wide range of applications, optimized Schwarz methods are much less well understood, mainly due to their more sophisticated transmission conditions.A key application of Schwarz methods with such sophisticated transmission conditions turned out to be time-harmonic wave propagation problems, because classical Schwarz methods simply do not work in this case. The past decade has given us many new Schwarz methods based on domain truncation. One review from an algorithmic perspective (Gander and Zhang 2019) showed the equivalence of many of these new methods to optimized Schwarz methods. The analysis of optimized Schwarz methods, however, is lagging behind their algorithmic development. The general abstract Schwarz framework cannot be used for the analysis of these methods, and thus there are many open theoretical questions about their convergence. Just as for practical multigrid methods, Fourier analysis has been instrumental for understanding the convergence of optimized Schwarz methods and for tuning their transmission conditions. Similar to local Fourier mode analysis in multigrid, the unbounded two-subdomain case is used as a model for Fourier analysis of optimized Schwarz methods due to its simplicity. Many aspects of the actual situation, e.g. boundary conditions of the original problem and the number of subdomains, were thus neglected in the unbounded two-subdomain analysis. While this gave important insight, new phenomena beyond the unbounded two-subdomain models were discovered.This present situation is the motivation for our survey: to give a comprehensive review and precise exploration of convergence behaviours of optimized Schwarz methods based on Fourier analysis, taking into account the original boundary conditions, many-subdomain decompositions and layered media. We consider as our model problem the operator $-\Delta + \eta $ in the diffusive case $\eta>0$ (screened Laplace equation) or the oscillatory case $\eta <0$ (Helmholtz equation), in order to show the fundamental difference in behaviour of Schwarz solvers for these problems. The transmission conditions we study include the lowest-order absorbing conditions (Robin), and also more advanced perfectly matched layers (PMLs), both developed first for domain truncation. Our intensive work over the last two years on this review has led to several new results presented here for the first time: in the bounded two-subdomain analysis for the Helmholtz equation, we see strong influence of the original boundary conditions imposed on the global problem on the convergence factor of the Schwarz methods, and the asymptotic convergence factors with small overlap can differ from the unbounded two-subdomain analysis. In the many-subdomain analysis, we find the scaling with the number of subdomains, e.g. when the subdomain size is fixed, robust convergence of the double-sweep Schwarz method for the free-space wave problem, either with fixed overlap and zeroth-order Taylor conditions or with a logarithmically growing PML, and we find that Schwarz methods with PMLs work like smoothers that converge faster for higher Fourier frequencies; in particular, for the free-space wave problem, plane waves (in the error) passing through interfaces at a right angle converge more slowly. In addition to our main focus on analysis in Sections 2 and 3, we start in Section 1 with an expository historical introduction to Schwarz methods, and in Section 4 we give a brief interpretation of the recently proposed optimal Schwarz methods for decompositions with cross-points from the viewpoint of transmission conditions. We conclude in Section 5 with a summary of open research problems. In Appendix A we provide a Matlab program for a block LU form of an optimal Schwarz method with cross-points, and in Appendix B we give the Maple program for the two-subdomain Fourier analysis.

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Dolean, Victorita, Martin J. Gander, and Erwin Veneros. "Asymptotic analysis of optimized Schwarz methods for maxwell’s equations with discontinuous coefficients." ESAIM: Mathematical Modelling and Numerical Analysis 52, no. 6 (November 2018): 2457–77. http://dx.doi.org/10.1051/m2an/2018041.

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Discretized time harmonic Maxwell’s equations are hard to solve by iterative methods, and the best currently available methods are based on domain decomposition and optimized transmission conditions. Optimized Schwarz methods were the first ones to use such transmission conditions, and this approach turned out to be so fundamentally important that it has been rediscovered over the last years under the name sweeping preconditioners, source transfer, single layer potential method and the method of polarized traces. We show here how one can optimize transmission conditions to take benefit from the jumps in the coefficients of the problem, when they are aligned with the subdomain interface, and obtain methods which converge for two subdomains in certain situations independently of the mesh size, which would not be possible without jumps in the coefficients.

12

Xu, Jian, Kean Chen, Lei Wang, and Yazhou Zhang. "Optimization of secondary source configuration in enclosure using plane wave decomposition." Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University 39, no. 4 (August 2021): 794–800. http://dx.doi.org/10.1051/jnwpu/20213940794.

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The optimization of secondary source configuration for an active noise control (ANC) system in its enclosed space generally focuses on noise reduction requirements at discrete points only. This may lead to the poor noise reduction performance in the whole spatial region, and it is necessary to know the information on error sensor positions in advance. To address this problem, a cost function for spatial-region-oriented noise reduction is proposed. The plane wave decomposition of the enclosed sound field is used to obtain the primary field plane waves and the unit secondary field plane wave of each candidate secondary source as the prior knowledge for configuration optimization, so as to formulate a wave-domain ANC cost function. The optimization method adopts the simulated annealing search. Taking a rigid-walled rectangular cavity as an example, the optimization method is firstly compared with two space-domain methods by using analytic values of the wave-domain prior knowledge. The comparison results show that the better reduction of spatial acoustic potential energy can be achieved independent of the error sensor configuration information. Then the estimated values of the wave-domain prior knowledge through measuring randomly distributed microphones are used to optimize the configuration of the ANC system. The optimization results suggest that the noise reduction of spatial acoustic potential energy of the optimized configuration can be better than that of the space-domain method, but the microphone positions have a great influence on the noise reduction performance.

13

Amattouch, M. R., and H. Belhadj. "Combined Optimized Domain Decomposition Method and a Modified Fixed Point Method for Non Linear Diffusion Equation." Applied Mathematics & Information Sciences 11, no. 1 (January 1, 2017): 201–7. http://dx.doi.org/10.18576/amis/110125.

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14

Després, B., A. Nicolopoulos, and B. Thierry. "Corners and stable optimized domain decomposition methods for the Helmholtz problem." Numerische Mathematik 149, no. 4 (November 19, 2021): 779–818. http://dx.doi.org/10.1007/s00211-021-01251-2.

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15

Amattouch, M. R., H. Belhadj, and N. Nagid. "New optimized domain decomposition order 4 method(OO4) applied to reaction advection diffusion equation." Journal of Modern Methods in Numerical Mathematics 9, no. 1-2 (March 28, 2018): 28–41. http://dx.doi.org/10.20454/jmmnm.2018.1296.

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The purpose of this work is the study of a new approach of domain decomposition method, the optimized order 4 method(OO4), to solve a reaction advection diusion equation. This method is a Schwarz waveform relaxation approach extending the known OO2 idea. The OO4 method is a reformulation of the Schwarz algorithm with specific conditions at the interface. This condition are a dierential equation of order 1 in the normal direction and of order 4 in the tangential direction to the interface resulting of artificial boundary conditions. The obtained scheme is solved by a Krylov type algorithm. The main result in this paper is that the proposed OO4 algorithm is more robust and faster than the classical OO2 method. To confirm the performance of our method , we give several numerical test-cases.

16

Ito, Satoshi, Kazuya Goto, and Kenji Ono. "Automatically optimized core mapping to subdomains of domain decomposition method on multicore parallel environments." Computers & Fluids 80 (July 2013): 88–93. http://dx.doi.org/10.1016/j.compfluid.2012.04.024.

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Zhang, Jian Wei, and Yun Lei Yao. "Optimized Research for Mobile Communication Strategy Based on Parallel Computing." Advanced Materials Research 937 (May 2014): 703–6. http://dx.doi.org/10.4028/www.scientific.net/amr.937.703.

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In order to improve the speed of simulation, one of the feasible approaches in mobile communications is parallel computing. In this paper, the operating environment will be achieved with MPICH2. Parallel computing is suitable for large scale computing tasks. An important factor which limits the speed-up ratio improve is that parallel computing cannot be achieved in communication process.Selecting the finite difference method, taking a two-dimensional steady-state heat distribution problem act as an example. By choosing domain decomposition method divide the entire data area into multiple sub-domains. Ultimately, the parallel program is designed in MPI’s Peer-to-Peer Model. By modifying the communication mode and the communication process, the speedup is substantial increased, closing to ideal values.

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Wu, Zedong, and Tariq Alkhalifah. "The optimized expansion based low-rank method for wavefield extrapolation." GEOPHYSICS 79, no. 2 (March 1, 2014): T51—T60. http://dx.doi.org/10.1190/geo2013-0174.1.

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Spectral methods are fast becoming an indispensable tool for wavefield extrapolation, especially in anisotropic media because it tends to be dispersion and artifact free as well as highly accurate when solving the wave equation. However, for inhomogeneous media, we face difficulties in dealing with the mixed space-wavenumber domain extrapolation operator efficiently. To solve this problem, we evaluated an optimized expansion method that can approximate this operator with a low-rank variable separation representation. The rank defines the number of inverse Fourier transforms for each time extrapolation step, and thus, the lower the rank, the faster the extrapolation. The method uses optimization instead of matrix decomposition to find the optimal wavenumbers and velocities needed to approximate the full operator with its explicit low-rank representation. As a result, we obtain lower rank representations compared with the standard low-rank method within reasonable accuracy and thus cheaper extrapolations. Additional bounds set on the range of propagated wavenumbers to adhere to the physical wave limits yield unconditionally stable extrapolations regardless of the time step. An application on the BP model provided superior results compared to those obtained using the decomposition approach. For transversely isotopic media, because we used the pure P-wave dispersion relation, we obtained solutions that were free of the shear wave artifacts, and the algorithm does not require that [Formula: see text]. In addition, the required rank for the optimization approach to obtain high accuracy in anisotropic media was lower than that obtained by the decomposition approach, and thus, it was more efficient. A reverse time migration result for the BP tilted transverse isotropy model using this method as a wave propagator demonstrated the ability of the algorithm.

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Vaupel, T., and V. Hansen. "Integral equation analysis of complex (M)MIC-structures with optimized system matrix decomposition and novel quadrature techniques." Advances in Radio Science 2 (May 27, 2005): 101–5. http://dx.doi.org/10.5194/ars-2-101-2004.

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Abstract. Using integral equation methods for the analysis of complex (M)MIC structures, the computation and storage effort for the solution of the linear systems of equations with their fully populated matrices still forms the main bottleneck. In the last years, remarkable improvements could be achieved by means of diakoptic methods and related preconditiners. In this contribution, we present a method based on the optimized decomposition of the system matrix depending on the circuit topology. The system matrix is splitted in a densely populated matrix and a mainly blockdiagonal matrix with overlapping submatrices. The latter matrix is used for the generation of high performance preconditioners within Krylov subspace methods using sparsified matrix storage methods, adaptive Cholesky decompositions and optimized forward/backward substitutions. Furthermore, we present an integration technique using a complete analytical treatment for the strongly oscillating parts of the spectral domain integrands allowing the analysis of very large structures as compared to the wavelength.

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Kawai, Hiroshi, Masao Ogino, Ryuji Shioya, and Shinobu Yoshimura. "Large Scale Elasto-Plastic Analysis Using Domain Decomposition Method Optimized for Multi-Core CPU Architecture." Key Engineering Materials 462-463 (January 2011): 605–10. http://dx.doi.org/10.4028/www.scientific.net/kem.462-463.605.

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To solve a large scale elasto-plastic dynamics analysis of a complicated structure, such as a seismic analysis of a nuclear power plant and a skyscraper, a new implementation strategy for a parallel finite element code, suitable on a parallel supercomputer with modern multi-core / many core scalar CPUs, has been required. In this work, we propose a new design and programming style to optimize the performance of a parallel finite element code based on the domain-decomposition method (DDM) on multi-core CPUs, considering their cache hierarchy. Instead of a traditional, memory access-intensive approach, DS (Direct solver-based matrix Storage), two new matrix storage-free approaches, DSF (Direct solver-based matrix Storage-Free) and ISF (Iterative solver-based matrix Storage-Free), are proposed. Our new DSF/ISF-based DDM solver is not only more efficient in memory usage but also comparable in computational time against existing DS-based DDM solvers on multi-core CPU architectures.

21

Wei, Xiao-Kun, Wei Shao, Sheng-Bing Shi, You-Feng Cheng, and Bing-Zhong Wang. "An Optimized Higher Order PML in Domain Decomposition WLP-FDTD Method for Time Reversal Analysis." IEEE Transactions on Antennas and Propagation 64, no. 10 (October 2016): 4374–83. http://dx.doi.org/10.1109/tap.2016.2596899.

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Lv, Zhongliang, Baoping Tang, Yi Zhou, and Chuande Zhou. "A Novel Method for Mechanical Fault Diagnosis Based on Variational Mode Decomposition and Multikernel Support Vector Machine." Shock and Vibration 2016 (2016): 1–11. http://dx.doi.org/10.1155/2016/3196465.

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A novel fault diagnosis method based on variational mode decomposition (VMD) and multikernel support vector machine (MKSVM) optimized by Immune Genetic Algorithm (IGA) is proposed to accurately and adaptively diagnose mechanical faults. First, mechanical fault vibration signals are decomposed into multiple Intrinsic Mode Functions (IMFs) by VMD. Then the features in time-frequency domain are extracted from IMFs to construct the feature sets of mixed domain. Next, Semisupervised Locally Linear Embedding (SS-LLE) is adopted for fusion and dimension reduction. The feature sets with reduced dimension are inputted to the IGA optimized MKSVM for failure mode identification. Theoretical analysis demonstrates that MKSVM can approximate any multivariable function. The global optimal parameter vector of MKSVM can be rapidly identified by IGA parameter optimization. The experiments of mechanical faults show that, compared to traditional fault diagnosis models, the proposed method significantly increases the diagnosis accuracy of mechanical faults and enhances the generalization of its application.

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Liu, Yongxiang, and Xuejun Xu. "An optimized Schwarz method with relaxation for the Helmholtz equation: the negative impact of overlap." ESAIM: Mathematical Modelling and Numerical Analysis 53, no. 1 (January 2019): 249–68. http://dx.doi.org/10.1051/m2an/2018061.

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In this paper we study how the overlapping size influences the convergence rate of an optimized Schwarz domain decomposition (DD) method with relaxation in the two subdomain case for the Helmholtz equation. Through choosing suitable parameters, we find that the convergence rate is independent of the wave number k and mesh size h, but sensitively depends on the overlapping size. Furthermore, by careful analysis, we obtain that the convergence behavior deteriorates with the increase of the overlapping size. Numerical results which confirm our theory are given.

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Amattouch, Mohamed Ridouan, and Hassan Belhadj. "A modified fixed point method for biochemical transport." Boletim da Sociedade Paranaense de Matemática 40 (February 2, 2022): 1–5. http://dx.doi.org/10.5269/bspm.46947.

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This work is devoted to a modified fixed point method applied to the bio-chemical transport equation. To have a good accuracy for the solution we treat, we apply an implicit scheme to this equation and use a modified fixed point technique to linearize the problem of transport equation with a generalized nonlinear reaction and diffusion equation. Next, we apply this methods in particular to the the dynamical system of a bio-chemical process. Eventually, we accelerate these algorithms by the optimized domain decomposition methods.Several test-cases of analytical problems illustrate this approach and show the efficiency of the proposednew method.

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Després, B., A. Nicolopoulos, and B. Thierry. "Optimized Transmission Conditions in Domain Decomposition Methods with Cross-Points for Helmholtz Equation." SIAM Journal on Numerical Analysis 60, no. 5 (September 13, 2022): 2482–507. http://dx.doi.org/10.1137/21m1421210.

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Duan, Jing, Gulan Zhang, Chenxi Liang, Yizong Zhan, and Yong Li. "High-efficiency and precision VSP wavefield separation method via DCT." Journal of Geophysics and Engineering 19, no. 2 (April 2022): 192–210. http://dx.doi.org/10.1093/jge/gxac010.

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Abstract The processing efficiency of the widely used time-space (t-x) domain vertical seismic profiling (VSP) wavefield separation methods (such as median and singular value decomposition filtering) via one-dimensional discrete Fourier transform (DFT) depends on the wavefield separation method (or algorithm with processing parameter) and the total number of samples in the input VSP data. Once the wavefield separation method is determined, its processing efficiency is set and cannot be optimized. Although the popular frequency-wavenumber (f-k) domain VSP wavefield separation method via two-dimensional DFT has higher processing efficiency than the t-x domain VSP wavefield separation methods, its processing precision is susceptible to the spatial alias and Gibbs effects. For efficiency and precision improvements, we introduced the discrete cosine transform (DCT) operation into VSP wavefield separation for the first time, and proposed a high-efficiency and precision frequency-space (f-x) domain VSP wavefield separation method via DFT and DCT, in which the wavefield separation efficiency and precision can be optimized using the effective bandwidth cutoff frequency of the input VSP data. Based on the relationship between DFT and DCT, we combined their operations in the proposed method into one step (referred to as DCT–DFT) for further efficiency enhancement, thereby designing a high-efficiency and precision f-x domain VSP wavefield separation method via DCT–DFT. Theory analysis and synthetic and field VSP data examples show that the proposed method is highly efficient and precise, and can be widely used for three-dimensional (3D)-VSP data wavefield separation, especially for large distributed acoustic sensing (DAS)-VSP data.

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Li, Feipeng, Jinghuai Gao, Zhaoqi Gao, Xiudi Jiang, and Wenbo Sun. "A causal imaging condition for reverse time migration using the Discrete Hilbert transform and its efficient implementation on GPU." Journal of Geophysics and Engineering 16, no. 5 (August 29, 2019): 894–912. http://dx.doi.org/10.1093/jge/gxz055.

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Abstract Reverse time migration (RTM) has shown a significant advantage over other imaging algorithms for imaging complex subsurface structures. However, low-wavenumber noise severely contaminates the image, which is one of the main issues in the RTM algorithm. To attenuate the undesired low-wavenumber noise, the causal imaging condition based on wavefield decomposition has been proposed. First, wavefield decompositions are performed to separate the wavefields as up-going and down-going wave components, respectively. Then, to preserve causality, it constructs images by correlating wave components that propagate in different directions. We build a causal imaging condition in this paper. Not only does it consider the up/down wavefield decomposition, but it also applies the decomposition on the horizontal direction to enhance the image quality especially for steeply dipping structures. The wavefield decomposition is conventionally achieved by the frequency-wavenumber (F-K) transform that is very computationally intensive compared with the wave propagation process of the RTM algorithm. To improve the efficiency of the algorithm, we propose a fast implementation to perform wavefield separation using the discrete Hilbert transform via the Graphics Processing Unit. Numerical tests on both the synthetic models and a real data example demonstrate the effectiveness of the proposed method and the efficiency of the optimized implementation scheme. This new imaging condition shows its ability to produce high image quality when applied to both the RTM stack image and also the angle domain common image gathers. The comparison of the total elapsed time for different methods verifies the efficiency of the optimized algorithm.

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Yan, Hao, Huajun Bai, Xianbiao Zhan, Zhenghao Wu, Liang Wen, and Xisheng Jia. "Combination of VMD Mapping MFCC and LSTM: A New Acoustic Fault Diagnosis Method of Diesel Engine." Sensors 22, no. 21 (October 30, 2022): 8325. http://dx.doi.org/10.3390/s22218325.

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Diesel engines have a wide range of functions in the industrial and military fields. An urgent problem to be solved is how to diagnose and identify their faults effectively and timely. In this paper, a diesel engine acoustic fault diagnosis method based on variational modal decomposition mapping Mel frequency cepstral coefficients (MFCC) and long-short-term memory network is proposed. Variational mode decomposition (VMD) is used to remove noise from the original signal and differentiate the signal into multiple modes. The sound pressure signals of different modes are mapped to the Mel filter bank in the frequency domain, and then the Mel frequency cepstral coefficients of the respective mode signals are calculated in the mapping range of frequency domain, and the optimized Mel frequency cepstral coefficients are used as the input of long and short time memory network (LSTM) which is trained and verified, and the fault diagnosis model of the diesel engine is obtained. The experimental part compares the fault diagnosis effects of different feature extraction methods, different modal decomposition methods and different classifiers, finally verifying the feasibility and effectiveness of the method proposed in this paper, and providing solutions to the problem of how to realise fault diagnosis using acoustic signals.

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Qiu, Guangqi, Si Huang, and Yingkui Gu. "Experimental investigation and multi-conditions identification method of centrifugal pump using Fisher discriminant ratio and support vector machine." Advances in Mechanical Engineering 11, no. 9 (September 2019): 168781401987804. http://dx.doi.org/10.1177/1687814019878041.

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For identifying the operation situations of centrifugal pumps by artificial intelligence, we performed an experiment on multi-flow conditions. The multi-flow conditions were simulated by adjusting an automatic flow-regulating valve installed on outlet pipe, and the vertical vibration signals of 20 flow points at the bearing house were collected by the test system. By time-domain analysis, frequency-domain analysis, information entropy, empirical modal decomposition, and wavelet packet decomposition methods, a comprehensive feature space was constructed. In addition, the optimal features were selected by Fisher discriminant ratio, and the dimensionality of the selected optimal features was reduced with principal component analysis. Finally, support vector machine algorithm was employed to identify the real-time flow condition, and the hyper-parameters of support vector machine classifier model were optimized by a grid search technique. Results show that the vibration test can effectively simulate the operation situation of centrifugal pumps under multi-flow conditions, and the proposed multi-flow conditions identification method has achieved a good identification performance.

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Zhang, Qingfeng, Shuang Chen, and Zhan Peng Fan. "Bearing fault diagnosis based on improved particle swarm optimized VMD and SVM models." Advances in Mechanical Engineering 13, no. 6 (June 2021): 168781402110284. http://dx.doi.org/10.1177/16878140211028451.

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To improve the accuracy of fault diagnosis of bearing, the improved particle swarm optimization variational mode decomposition (VMD) and support vector machine (SVM) models are proposed. Aiming at the convergence effect of particle swarm optimization (PSO), dynamic inertia weight, and gradient information are introduced to improve PSO (IPSO). IPSO is used to optimize the optimal number of VMD modal components and the penalty factor, which is applied to the vibration signal decomposition. The fault sample set is constructed by calculating the multi-scale information entropy of each component signal obtained from the bearing vibration signals. At the same time, IPSO is used to optimize the support vector machine (IPSO-SVM), which is used to bearing fault diagnosis. The time-domain feature data set is used as the comparison data set, and the classical PSO, genetic algorithm, and cross-validation method are used as the comparison algorithm to verify the effectiveness of the method in this paper. The research results show that the optimized VMD can effectively decompose the vibration signal and can effectively highlight the fault characteristics. IPSO can increase the accuracy by 2% without adding additional costs. And the accuracy, volatility, and convergence error of IPSO are better than comparison algorithms.

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Leugering, Günter, Vaibhav Mehandiratta, and Mani Mehra. "Non-Overlapping Domain Decomposition for 1D Optimal Control Problems Governed by Time-Fractional Diffusion Equations on Coupled Domains: Optimality System and Virtual Controls." Fractal and Fractional 8, no. 3 (February 22, 2024): 129. http://dx.doi.org/10.3390/fractalfract8030129.

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We consider a non-overlapping domain decomposition method for optimal control problems of the tracking type governed by time-fractional diffusion equations in one space dimension, where the fractional time derivative is considered in the Caputo sense. We concentrate on a transmission problem defined on two adjacent intervals, where at the interface we introduce an iterative non-overlapping domain decomposition in the spirit of P.L. Lions for the corresponding first-order optimality system, such that the optimality system corresponding to the optimal control problem on the entire domain is iteratively decomposed into two systems on the respective sub-domains; this approach can be framed as first optimize, then decompose. We show that the iteration involving the states and adjoint states converges in the appropriate spaces. Moreover, we show that the decomposed systems on the sub-domain can in turn be interpreted as optimality systems of so-called virtual control problems on the sub-domains. Using this property, we are able to solve the original optimal control problem by an iterative solution of optimal control problems on the sub-domains. This approach can be framed as first decompose, then optimize. We provide a mathematical analysis of the problems as well as a numerical finite difference discretization using the L1-method with respect to the Caputo derivative, along with two examples in order to verify the method.

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Chen, Kean, Jian Xu, Lei Wang, and Bing Zhou. "Optimization of Secondary Sources Configuration in Two-Dimensional Space Based on Sound Field Decomposition and Sparsity-Inducing Regularization." Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University 37, no. 4 (August 2019): 697–703. http://dx.doi.org/10.1051/jnwpu/20193740697.

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During the design of transducers configuration for an active noise control system, current optimization methods need to predetermine the error sensors configuration, which significantly increases the workload of later optimization of the secondary sources configuration. In this study, a new method free from specific error sensors configuration information is presented that higher order microphones are used to capture the sound field so as to formulate the cost function in wave domain. In addition, according to sparsity characteristics of the primary sound field, sparsity-inducing regularization is introduced to optimize the secondary sources configuration, including the number and positions, by calculating a sparse approximate solution to underdetermined equations. Effects of the number of candidate secondary sources are discussed, and the comparison with the uniform configuration and the optimized configuration using the genetic algorithm is performed. Results show that the proposed method can optimize the secondary sources configuration effectively independent of the error sensors configuration information. The noise reduction of the proposed method is close to that by the genetic algorithm, while other evaluation metrics for the system are much better, which would benefit the stability of active noise control system.

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Gupta, Akash Kumar, Chinmay Chakraborty, and Bharat Gupta. "Watermarking of EEG Data to Provide Security Based on DWT-SVD and Optimized by Firefly Algorithm." International Journal of Distributed Systems and Technologies 13, no. 8 (July 12, 2022): 1–16. http://dx.doi.org/10.4018/ijdst.307902.

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A watermark embedding into digital media or signal is called digital watermarking for the purpose of enhancing security from copyright encroachment. In this paper, an optimized and advanced watermarking technique has been proposed, which is based on singular value decomposition (SVD) in the discrete wavelet transform (DWT) domain using the firefly algorithm (FA). In this, a watermark logo is embedded into electroencephalogram (EEG) data. To optimize the scaling factor, robustness and imperceptibility have been considered. Further, the performance of the proposed algorithm is also analyzed against various attacks. The results show the adequacy of the proposed algorithm and indicate a higher value of NCC of 0.95 as robustness and PSNR 51.83 as imperceptibility in contrast with the related existing method.

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Yoshida, Takumi, Takeshi Okuzono, and Kimihiro Sakagami. "A Parallel Dissipation-Free and Dispersion-Optimized Explicit Time-Domain FEM for Large-Scale Room Acoustics Simulation." Buildings 12, no. 2 (January 23, 2022): 105. http://dx.doi.org/10.3390/buildings12020105.

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Wave-based acoustics simulation methods such as finite element method (FEM) are reliable computer simulation tools for predicting acoustics in architectural spaces. Nevertheless, their application to practical room acoustics design is difficult because of their high computational costs. Therefore, we propose herein a parallel wave-based acoustics simulation method using dissipation-free and dispersion-optimized explicit time-domain FEM (TD-FEM) for simulating room acoustics at large-scale scenes. It can model sound absorbers with locally reacting frequency-dependent impedance boundary conditions (BCs). The method can use domain decomposition method (DDM)-based parallel computing to compute acoustics in large rooms at kilohertz frequencies. After validation studies of the proposed method via impedance tube and small cubic room problems including frequency-dependent impedance BCs of two porous type sound absorbers and a Helmholtz type sound absorber, the efficiency of the method against two implicit TD-FEMs was assessed. Faster computations and equivalent accuracy were achieved. Finally, acoustics simulation of an auditorium of 2271 m3 presenting a problem size of about 150,000,000 degrees of freedom demonstrated the practicality of the DDM-based parallel solver. Using 512 CPU cores on a parallel computer system, the proposed parallel solver can compute impulse responses with 3 s time length, including frequency components up to 3 kHz within 9000 s.

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Liu, Yingzhi, Yassine Boubendir, Xiaoming He, and Yinnian He. "New Optimized Robin--Robin Domain Decomposition Methods using Krylov Solvers for the Stokes--Darcy System." SIAM Journal on Scientific Computing 44, no. 4 (August 2022): B1068—B1095. http://dx.doi.org/10.1137/21m1417223.

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Flauraud, E., F. Nataf, and F. Willien. "Optimized interface conditions in domain decomposition methods for problems with extreme contrasts in the coefficients." Journal of Computational and Applied Mathematics 189, no. 1-2 (May 2006): 539–54. http://dx.doi.org/10.1016/j.cam.2005.05.019.

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Chen, Xiaojuan, Wenbo Cui, and Tiantong Zhang. "AVOA-LightGBM Power Fiber Optic Cable Event Pattern Recognition Method Based on Wavelet Packet Decomposition." Electronics 12, no. 18 (September 5, 2023): 3743. http://dx.doi.org/10.3390/electronics12183743.

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The type of power fiber optic cable fault event obtained by analyzing the optical time domain reflectometer (OTDR) detection curve is an important basis for ensuring the operation quality of communication lines. To address the issue of low accuracy in recognizing fault event patterns, this research proposes the AVOA-LightGBM method for optical cable fault event pattern recognition based on wavelet packet decomposition. Initially, a three-layer wavelet packet decomposition is performed on different fault events, resulting in eight characteristic signals. These signals are then normalized and used as input for each recognition model. The Light Gradient Boosting Machine (LightGBM) is optimized using the African vulture optimization algorithm (AVOA) for pattern recognition. The experimental results demonstrate that this method achieves a recognition accuracy of 98.24%. It outperforms LightGBM, support vector machine (SVM), and extreme learning machine (ELM) by 3.7%, 19.15%, and 5.67%, respectively, in terms of accuracy. Moreover, it shows a 1.8% improvement compared with the combined model PSO-LightGBM.

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Dong, Shaojiang, Tianhong Luo, Li Zhong, Lili Chen, and Xiangyang Xu. "Fault diagnosis of bearing based on the kernel principal component analysis and optimized k-nearest neighbour model." Journal of Low Frequency Noise, Vibration and Active Control 36, no. 4 (December 2017): 354–65. http://dx.doi.org/10.1177/1461348417744302.

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Aiming to identify the bearing faults level effectively, a new method based on kernel principal component analysis and particle swarm optimization optimized k-nearest neighbour model is proposed. First, the gathered vibration signals are decomposed by time–frequency domain method, i.e., local mean decomposition; as a result, the product functions decomposed from the original signal are derived. Then, the entropy values of the product functions are calculated by Shannon method, which will work as the input features for k-nearest neighbour model. The kernel principal component analysis model is used to reduce the dimension of the features, and then the k-nearest neighbour model which was optimized by the particle swarm optimization method is used to identify the bearing fault levels. Case of test and actually collected signal are analysed. The results validate the effectiveness of the proposed algorithm.

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Aspalli, Pooja, and Prakash Pattan. "Image Registration and Fusion using Moving Frame based Decomposition Framework Algorithm." International Journal of Innovative Technology and Exploring Engineering 10, no. 5 (March 30, 2021): 57–63. http://dx.doi.org/10.35940/ijitee.e8669.0310521.

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Image fusion is an important process in the medical image diagnostics methods. Fusing images by obtaining information from different source and different types of images(modals) called multi-modal image fusion. This paper implements an effective and fast spatial domain based multimodal image fusion using moving frame based decomposition (MFDF)method. Images from two different modalities are taken and decomposed to texture and approximation components. Weight mapping strategy is applied along with the guide filtering to fuse the approximation components using the final map. Weight mapping using the guide filtering is used for the fusing the images from different modalities. MATLAB is used for algorithm implementation. The results obtained are comparatively competitive with the recent publication[11]. Multi modal image fusion thus implemented gives promising results, when compared to moving frame decomposition framework method. The size and the blurring variable of the guiding filter is optimized to obtain a better Structural Similarity Index Measurement (SSIM).

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Ma, Shihe, Tairong Huang, Anyu Wang, Qixian Zhou, and Xiaoyun Wang. "Fast and Accurate: Efficient Full-Domain Functional Bootstrap and Digit Decomposition for Homomorphic Computation." IACR Transactions on Cryptographic Hardware and Embedded Systems 2024, no. 1 (December 4, 2023): 592–616. http://dx.doi.org/10.46586/tches.v2024.i1.592-616.

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The functional bootstrap in FHEW/TFHE allows for fast table lookups on ciphertexts and is a powerful tool for privacy-preserving computations. However, the functional bootstrap suffers from two limitations: the negacyclic constraint of the lookup table (LUT) and the limited ability to evaluate large-precision LUTs. To overcome the first limitation, several full-domain functional bootstraps (FDFB) have been developed, enabling the evaluation of arbitrary LUTs. Meanwhile, algorithms based on homomorphic digit decomposition have been proposed to address the second limitation. Although these algorithms provide effective solutions, they are yet to be optimized. This paper presents four new FDFB algorithms and two new homomorphic decomposition algorithms that improve the state-of-the-art. Our FDFB algorithms reduce the output noise, thus allowing for more efficient and compact parameter selection. Across all parameter settings, our algorithms reduce the runtime by up to 39.2%. Our homomorphic decomposition algorithms also run at 2.0x and 1.5x the speed of prior algorithms. We have implemented and benchmarked all previous FDFB and homomorphic decomposition algorithms and our methods in OpenFHE.

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Wu, Zhenghao, Huajun Bai, Hao Yan, Xianbiao Zhan, Chiming Guo, and Xisheng Jia. "Intelligent Fault Diagnosis Method for Gearboxes Based on Deep Transfer Learning." Processes 11, no. 1 (December 27, 2022): 68. http://dx.doi.org/10.3390/pr11010068.

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The complex operating environment of gearboxes and the easy interference of early fault feature information make fault identification difficult. This paper proposes a fault diagnosis method based on a combination of whale optimization algorithm (WOA), variational mode decomposition (VMD), and deep transfer learning. First, the VMD is optimized by using the WOA, and the minimum sample entropy is used as the fitness function to solve for the K value and penalty parameter α corresponding to the optimal decomposition of the VMD, and the correlation coefficient is used to reconstruct the signal. Second, the reconstructed signal after reducing noise is used to generate a two-dimensional image using the continuous wavelet transform method as the transfer learning target domain data. Finally, the AlexNet model is used as the transfer object, which is pretrained and fine-tuned with model parameters to make it suitable for early crack fault diagnosis in gearboxes. The experimental results show that the method proposed in this paper can effectively reduce the noise of gearbox vibration signals under a complex working environment, and the fault diagnosis method of using transfer learning is effective and achieves high accuracy of fault diagnosis.

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Liu, Min, Xifan Yao, Jianming Zhang, Wocheng Chen, Xuan Jing, and Kesai Wang. "Multi-Sensor Data Fusion for Remaining Useful Life Prediction of Machining Tools by IABC-BPNN in Dry Milling Operations." Sensors 20, no. 17 (August 19, 2020): 4657. http://dx.doi.org/10.3390/s20174657.

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Inefficient remaining useful life (RUL) estimation may cause unpredictable failures and unscheduled maintenance of machining tools. Multi-sensor data fusion will improve the RUL prediction reliability by fusing more sensor information related to the machining process of tools. In this paper, a multi-sensor data fusion system for online RUL prediction of machining tools is proposed. The system integrates multi-sensor signal collection, signal preprocess by a complementary ensemble empirical mode decomposition, feature extraction in time domain, frequency domain and time-frequency domain by such methods as statistical analysis, power spectrum density analysis and Hilbert-Huang transform, feature selection by a Light Gradient Boosting Machine method, feature fusion by a tool wear prediction model based on back propagation neural network optimized by improved artificial bee colony (IABC-BPNN) algorithm, and the online RUL prediction model by a polynomial curve fitting method. An example is used to verify whether if the prediction performance of the proposed system is stable and reliable, and the results show that it is superior to its rivals.

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Zhong, Yongteng, Jiawei Xiang, Xiaoyu Chen, Yongying Jiang, and Jihong Pang. "Multiple Signal Classification-Based Impact Localization in Composite Structures Using Optimized Ensemble Empirical Mode Decomposition." Applied Sciences 8, no. 9 (August 24, 2018): 1447. http://dx.doi.org/10.3390/app8091447.

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Multiple signal classification (MUSIC) algorithm-based structural health monitoring technology is a promising method because of its directional scanning ability and easy arrangement of the sensor array. However, in previous MUSIC-based impact location methods, the narrowband signals at a particular central frequency had to be extracted from the wideband Lamb waves induced by each impact using a wavelet transform. Additionally, the specific center frequency had to be obtained after carefully analyzing the impact signal, which is time consuming. Aiming at solving this problem, this paper presents an improved approach that combines the optimized ensemble empirical mode decomposition (EEMD) and two-dimensional multiple signal classification (2D-MUSIC) algorithm for real-time impact localization on composite structures. Firstly, the impact signal at an unknown position is obtained using a unified linear sensor array. Secondly, the fast Hilbert Huang transform (HHT) with an optimized EEMD algorithm is introduced to extract intrinsic mode functions (IMFs) from impact signals. Then, all IMFs in the whole frequency domain are directly used as the input vector of the 2D-MUSIC model separately to locate the impact source. Experimental data collected from a cross-ply glass fiber reinforced composite plate are used to validate the proposed approach. The results show that the use of optimized EEMD and 2D-MUSIC is suitable for real-time impact localization of composite structures.

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Yao, Gang, Yunce Wang, Mohamed Benbouzid, and Mourad Ait-Ahmed. "A Hybrid Gearbox Fault Diagnosis Method Based on GWO-VMD and DE-KELM." Applied Sciences 11, no. 11 (May 28, 2021): 4996. http://dx.doi.org/10.3390/app11114996.

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In this paper, a vibration signal-based hybrid diagnostic method, including vibration signal adaptive decomposition, vibration signal reconstruction, fault feature extraction, and gearbox fault classification, is proposed to realize fault diagnosis of general gearboxes. The main contribution of the proposed method is the combining of signal processing, machine learning, and optimization techniques to effectively eliminate noise contained in vibration signals and to achieve high diagnostic accuracy. Firstly, in the study of vibration signal preprocessing and fault feature extraction, to reduce the impact of noise and mode mixing problems on the accuracy of fault classification, Variational Mode Decomposition (VMD) was adopted to realize adaptive signal decomposition and Wolf Grey Optimizer (GWO) was applied to optimize parameters of VMD. The correlation coefficient was subsequently used to select highly correlated Intrinsic Mode Functions (IMFs) to reconstruct the vibration signals. With these re-constructed signals, fault features were extracted by calculating their time domain parameters, energies, and permutation entropies. Secondly, in the study of fault classification, Kernel Extreme Learning Machine (KELM) was adopted and Differential Evolutionary (DE) was applied to search its regularization coefficient and kernel parameter to further improve classification accuracy. Finally, gearbox vibration signals in healthy and faulty conditions were obtained and contrast experiences were conducted to validate the effectiveness of the proposed hybrid fault diagnosis method.

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Schaetz, Sebastian, Dirk Voit, Jens Frahm, and Martin Uecker. "Accelerated Computing in Magnetic Resonance Imaging: Real-Time Imaging Using Nonlinear Inverse Reconstruction." Computational and Mathematical Methods in Medicine 2017 (2017): 1–11. http://dx.doi.org/10.1155/2017/3527269.

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Purpose. To develop generic optimization strategies for image reconstruction using graphical processing units (GPUs) in magnetic resonance imaging (MRI) and to exemplarily report on our experience with a highly accelerated implementation of the nonlinear inversion (NLINV) algorithm for dynamic MRI with high frame rates. Methods. The NLINV algorithm is optimized and ported to run on a multi-GPU single-node server. The algorithm is mapped to multiple GPUs by decomposing the data domain along the channel dimension. Furthermore, the algorithm is decomposed along the temporal domain by relaxing a temporal regularization constraint, allowing the algorithm to work on multiple frames in parallel. Finally, an autotuning method is presented that is capable of combining different decomposition variants to achieve optimal algorithm performance in different imaging scenarios. Results. The algorithm is successfully ported to a multi-GPU system and allows online image reconstruction with high frame rates. Real-time reconstruction with low latency and frame rates up to 30 frames per second is demonstrated. Conclusion. Novel parallel decomposition methods are presented which are applicable to many iterative algorithms for dynamic MRI. Using these methods to parallelize the NLINV algorithm on multiple GPUs, it is possible to achieve online image reconstruction with high frame rates.

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Chniti, Chokri. "Optimized interface conditions in domain decomposition methods to solve reaction–diffusion problems with strong heterogeneity in the coefficients in a sectorial domain." Applied Numerical Mathematics 118 (August 2017): 117–30. http://dx.doi.org/10.1016/j.apnum.2017.02.015.

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Yu, Xiao, Bing Xia, Shuxin Yang, Hongshen Yin, Yajie Wang, and Xiaowen Liu. "A Deep Domain-Adversarial Transfer Fault Diagnosis Method for Rolling Bearing Based on Ensemble Empirical Mode Decomposition." Journal of Sensors 2022 (May 18, 2022): 1–18. http://dx.doi.org/10.1155/2022/8959185.

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In recent years, the deep learning-based fault diagnosis methods for rotating mechanical equipment have attracted great concern. However, because the data feature distributions present differences in applications with varying working conditions, the deep learning models cannot provide satisfactory performance of fault prediction in such scenarios. To address this problem, this paper proposes a domain adversarial-based rolling bearing fault transfer diagnosis model EMBRNDNMD. First of all, an EEMD-based time-frequency feature graph (EEMD-TFFG) construction method is proposed, and the time-frequency information of nonlinear nonstationary vibration signal is extracted; secondly, a multi-branch ResNet (MBRN) structure is designed, which is used to extract deep features representing the bearing state from EEMD-TFFG; finally, to solve the model domain adaptation transfer problem under varying working conditions, the adversarial network module and MK-MMD distribution difference evaluation method are introduced to optimize MBRN, so as to reduce the probability distribution difference between the deep features of source domain and target domain, and to improve the accuracy of EMBRNDNMD in state diagnosis of target domain. The results of experiments carried out on two bearing fault test platforms prove that EMBRNDNMD can maintain an average accuracy above 97% in fault transfer diagnosis tasks, and this method also has high stability and strong ability of scene adaptation.

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Gander, Martin, Laurence Halpern, Frédéric Magoulès, and François-Xavier Roux. "Analysis of Patch Substructuring Methods." International Journal of Applied Mathematics and Computer Science 17, no. 3 (October 1, 2007): 395–402. http://dx.doi.org/10.2478/v10006-007-0032-1.

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Analysis of Patch Substructuring MethodsPatch substructuring methods are non-overlapping domain decomposition methods like classical substructuring methods, but they use information from geometric patches reaching into neighboring subdomains, condensated on the interfaces, to enhance the performance of the method, while keeping it non-overlapping. These methods are very convenient to use in practice, but their convergence properties have not been studied yet. We analyze geometric patch substructuring methods for the special case of one patch per interface. We show that this method is equivalent to an overlapping Schwarz method using Neumann transmission conditions. This equivalence is obtained by first studying a new, algebraic patch method, which is equivalent to the classical Schwarz method with Dirichlet transmission conditions and an overlap corresponding to the size of the patches. Our results motivate a new method, the Robin patch method, which is a linear combination of the algebraic and the geometric one, and can be interpreted as an optimized Schwarz method with Robin transmission conditions. This new method has a significantly faster convergence rate than both the algebraic and the geometric one. We complement our results by numerical experiments.

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Tieman, Hans J. "Improving plane‐wave decomposition and migration." GEOPHYSICS 62, no. 1 (January 1997): 195–205. http://dx.doi.org/10.1190/1.1444119.

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Plane‐wave data can be produced by slant stacking common geophone gathers over source locations. Practical difficulties arise with slant stacks over common receiver gathers that do not arise with slant stacks over common‐midpoint gathers. New techniques such as hyperbolic velocity filtering allow the production of high‐quality slant stacks of common‐midpoint data that are relatively free of artifacts. These techniques can not be used on common geophone data because of the less predictive nature of data in this domain. However, unlike plane‐wave data, slant stacks over midpoint gathers cannot be migrated accurately using depth migration. A new transformation that links common‐midpoint slant stacks to common geophone slant stacks allows the use together of optimized methods of slant stacking and accurate depth migration in data processing. Accurate depth migration algorithms are needed to migrate plane‐wave data because of the potentially high angles of propagation exhibited by the data and because of any lateral velocity variations in the subsurface. Splitting the one‐way wave continuation operator into two components (one that is a function of a laterally independent velocity, and a residual term that handles lateral variations in subsurface velocities) results in a good approximation. The first component is applied in the wavenumber domain, the other is applied in the space domain. The approximation is accurate for any angle of propagation in the absence of lateral velocity variations, although with severe lateral velocity variations the accuracy is reduced to 50°. High‐quality plane‐wave data migrated using accurate wave continuation operators results in a high‐quality image of the subsurface. Because of the signal‐to‐noise content of this data the number of sections that need to be migrated can be reduced considerably. This not only saves computer time, more importantly it makes computer‐intensive tasks such as migration velocity analysis based on maximizing stack power more feasible.

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Yan, Jun, and Hong Liu. "Modeling of pure acoustic wave in tilted transversely isotropic media using optimized pseudo-differential operators." GEOPHYSICS 81, no. 3 (May 2016): T91—T106. http://dx.doi.org/10.1190/geo2015-0111.1.

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Conventional modeling and imaging for tilted transversely isotropic (TTI) media may suffer from numerical instabilities and shear artifacts due to the coupling of the P- and SV-wave modes in the coupled equations. On the contrary, the decoupled equations for TTI media provide a more stable solution due to the separated P- and S-wave modes. Because the decoupled equations involve complicated pseudo-differential operators in space, it is more convenient to apply the pseudo-spectral method to these equations. However, the second-order time-stepping scheme of the pseudo-spectral method may suffer from time-stepping errors and instabilities for a large time step. We have developed an optimized pseudo-differential operator (OPO) that incorporates not only the spectral evaluation of the pseudo-differential operator but also a temporal correction term that would effectively compensate the time-stepping errors associated with the time-wavenumber domain extrapolation of the wave equation. The OPO was constructed through multiplying the symbol of the OPO by the normalized pseudo-Laplacian operator, which contains a variable compensation velocity. It was efficiently solved through the low-rank decomposition. We have applied OPOs to solve the TTI decoupled equation to simulate the pure acoustic wave. Our 2D and 3D synthetic results demonstrate that the proposed method has high accuracy in time and space with relaxed stability conditions compared with the conventional pseudo-spectral method. The low rank of symbols of OPOs makes the proposed method more efficient than the dispersion relation-based low-rank wave extrapolation and pseudo-analytical methods.

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