Aimed at studying normali zed radial basis function network (NRBFN), this paper introduces the subtractiv e clustering based on a mountain function to construct the initial structure of NR BFN, adopts singular value ...Aimed at studying normali zed radial basis function network (NRBFN), this paper introduces the subtractiv e clustering based on a mountain function to construct the initial structure of NR BFN, adopts singular value decomposition (SVD) to analyze the relationship betwe en neural nodes of the hidden layer and singular values, cumulative contribution ratio, index vector, and optimizes the structure of NRBFN. Finally, simulation and performance comparison show that the algorithm is feasible and effective.展开更多
The problem caused by shortness or excessiveness of snapshots and by coherent sources in underwater acoustic positioning is considered.A matched field localization algorithm based on CS-MUSIC(Compressive Sensing Multi...The problem caused by shortness or excessiveness of snapshots and by coherent sources in underwater acoustic positioning is considered.A matched field localization algorithm based on CS-MUSIC(Compressive Sensing Multiple Signal Classification) is proposed based on the sparse mathematical model of the underwater positioning.The signal matrix is calculated through the SVD(Singular Value Decomposition) of the observation matrix.The observation matrix in the sparse mathematical model is replaced by the signal matrix,and a new concise sparse mathematical model is obtained,which means not only the scale of the localization problem but also the noise level is reduced;then the new sparse mathematical model is solved by the CS-MUSIC algorithm which is a combination of CS(Compressive Sensing) method and MUSIC(Multiple Signal Classification) method.The algorithm proposed in this paper can overcome effectively the difficulties caused by correlated sources and shortness of snapshots,and it can also reduce the time complexity and noise level of the localization problem by using the SVD of the observation matrix when the number of snapshots is large,which will be proved in this paper.展开更多
A complete approximate symmetry classification of a class of perturbed nonlinear wave equations isperformed using the method originated from Fushchich and Shtelen.Moreover,large classes of approximate invariantsolutio...A complete approximate symmetry classification of a class of perturbed nonlinear wave equations isperformed using the method originated from Fushchich and Shtelen.Moreover,large classes of approximate invariantsolutions of the equations based on the Lie group method are constructed.展开更多
The transformation of basic functions is one of the most commonly used techniques for seismic denoising,which employs sparse representation of seismic data in the transform domain. The choice of transform base functio...The transformation of basic functions is one of the most commonly used techniques for seismic denoising,which employs sparse representation of seismic data in the transform domain. The choice of transform base functions has an influence on denoising results. We propose a learning-type overcomplete dictionary based on the K-singular value decomposition( K-SVD) algorithm. To construct the dictionary and use it for random seismic noise attenuation,we replace fixed transform base functions with an overcomplete redundancy function library. Owing to the adaptability to data characteristics,the learning-type dictionary describes essential data characteristics much better than conventional denoising methods. The sparsest representation of signals is obtained by the learning and training of seismic data. By comparing the same seismic data obtained using the learning-type overcomplete dictionary based on K-SVD and the data obtained using other denoising methods,we find that the learning-type overcomplete dictionary based on the K-SVD algorithm represents the seismic data more sparsely,effectively suppressing the random noise and improving the signal-to-noise ratio.展开更多
The functionally generalized variable separation solutions of a general KdV-type equations u_t=u_(xxx) +A(u, u_x)u_(xx) + B(u, u_x) are investigated by developing the conditional Lie-Backlund symmetry method. A comple...The functionally generalized variable separation solutions of a general KdV-type equations u_t=u_(xxx) +A(u, u_x)u_(xx) + B(u, u_x) are investigated by developing the conditional Lie-Backlund symmetry method. A complete classification of the considered equations, which admit multi-dimensional invariant subspaces governed by higher-order conditional Lie-B¨acklund symmetries, is presented. As a result, several concrete examples are provided to construct functionally generalized variable separation solutions of some resulting equations.展开更多
文摘Aimed at studying normali zed radial basis function network (NRBFN), this paper introduces the subtractiv e clustering based on a mountain function to construct the initial structure of NR BFN, adopts singular value decomposition (SVD) to analyze the relationship betwe en neural nodes of the hidden layer and singular values, cumulative contribution ratio, index vector, and optimizes the structure of NRBFN. Finally, simulation and performance comparison show that the algorithm is feasible and effective.
基金supported by the National Natural Science Foundation of China (61202208)
文摘The problem caused by shortness or excessiveness of snapshots and by coherent sources in underwater acoustic positioning is considered.A matched field localization algorithm based on CS-MUSIC(Compressive Sensing Multiple Signal Classification) is proposed based on the sparse mathematical model of the underwater positioning.The signal matrix is calculated through the SVD(Singular Value Decomposition) of the observation matrix.The observation matrix in the sparse mathematical model is replaced by the signal matrix,and a new concise sparse mathematical model is obtained,which means not only the scale of the localization problem but also the noise level is reduced;then the new sparse mathematical model is solved by the CS-MUSIC algorithm which is a combination of CS(Compressive Sensing) method and MUSIC(Multiple Signal Classification) method.The algorithm proposed in this paper can overcome effectively the difficulties caused by correlated sources and shortness of snapshots,and it can also reduce the time complexity and noise level of the localization problem by using the SVD of the observation matrix when the number of snapshots is large,which will be proved in this paper.
文摘A complete approximate symmetry classification of a class of perturbed nonlinear wave equations isperformed using the method originated from Fushchich and Shtelen.Moreover,large classes of approximate invariantsolutions of the equations based on the Lie group method are constructed.
基金Supported by the National"863"Project(No.2014AA06A605)
文摘The transformation of basic functions is one of the most commonly used techniques for seismic denoising,which employs sparse representation of seismic data in the transform domain. The choice of transform base functions has an influence on denoising results. We propose a learning-type overcomplete dictionary based on the K-singular value decomposition( K-SVD) algorithm. To construct the dictionary and use it for random seismic noise attenuation,we replace fixed transform base functions with an overcomplete redundancy function library. Owing to the adaptability to data characteristics,the learning-type dictionary describes essential data characteristics much better than conventional denoising methods. The sparsest representation of signals is obtained by the learning and training of seismic data. By comparing the same seismic data obtained using the learning-type overcomplete dictionary based on K-SVD and the data obtained using other denoising methods,we find that the learning-type overcomplete dictionary based on the K-SVD algorithm represents the seismic data more sparsely,effectively suppressing the random noise and improving the signal-to-noise ratio.
基金Supported by the National Science Foundation of China under Grant Nos.11371293,11501419the Mathematical Discipline Foundation of Shaanxi Province of China under Grant No.14TSXK02+1 种基金the Natural Science Foundation of Weinan Normal University under Grant No.16ZRRC05 and 15YKS005Natural Science Foundation of Hebei Province of China under Grant No.A2018207030
文摘The functionally generalized variable separation solutions of a general KdV-type equations u_t=u_(xxx) +A(u, u_x)u_(xx) + B(u, u_x) are investigated by developing the conditional Lie-Backlund symmetry method. A complete classification of the considered equations, which admit multi-dimensional invariant subspaces governed by higher-order conditional Lie-B¨acklund symmetries, is presented. As a result, several concrete examples are provided to construct functionally generalized variable separation solutions of some resulting equations.
