The perturbational reanalysis technique of matrix singular value decomposition is applicable to many theoretical and practical problems in mathematics, mechanics, control theory, engineering, etc.. An indirect perturb...The perturbational reanalysis technique of matrix singular value decomposition is applicable to many theoretical and practical problems in mathematics, mechanics, control theory, engineering, etc.. An indirect perturbation method has previously been proposed by the author in this journal, and now the direct perturbation method has also been presented in this paper. The second-order perturbation results of non-repeated singular values and the corresponding left and right singular vectors are obtained. The results can meet the general needs of most problems of various practical applications. A numerical example is presented to demonstrate the effectiveness of the direct perturbation method.展开更多
The perturbation method for the reanalysis of the singular value decomposition (SVD) of general real matrices is presented in this paper. This is a simple but efficient reanalysis technique for the SVD, which is of gr...The perturbation method for the reanalysis of the singular value decomposition (SVD) of general real matrices is presented in this paper. This is a simple but efficient reanalysis technique for the SVD, which is of great worth to enhance computational efficiency of the iterative analysis problems that require matrix singular value decomposition repeatedly. The asymptotic estimate formulas for the singular values and the corresponding left and right singular vectors up to second-order perturbation components are derived. At the end of the paper the way to extend the perturbation method to the case of general complex matrices is advanced.展开更多
In this paper, we investigate the linear solver in least square support vector machine（LSSVM） for large-scale data regression. The traditional methods using the direct solvers are costly. We know that the linear equ...In this paper, we investigate the linear solver in least square support vector machine（LSSVM） for large-scale data regression. The traditional methods using the direct solvers are costly. We know that the linear equations should be solved repeatedly for choosing appropriate parameters in LSSVM, so the key for speeding up LSSVM is to improve the method of solving the linear equations. We approximate large-scale kernel matrices and get the approximate solution of linear equations by using randomized singular value decomposition（randomized SVD）. Some data sets coming from University of California Irvine machine learning repository are used to perform the experiments. We find LSSVM based on randomized SVD is more accurate and less time-consuming in the case of large number of variables than the method based on Nystrom method or Lanczos process.展开更多
Condition monitoring and fault diagnosis of gearboxes play an important role in the maintenance of mechanical systems.The vibration signal of gearboxes is characterized by complex spectral structure and strong time va...Condition monitoring and fault diagnosis of gearboxes play an important role in the maintenance of mechanical systems.The vibration signal of gearboxes is characterized by complex spectral structure and strong time variability,which brings challenges to fault feature extraction.To address this issue,a new demodulation technique,based on the Fourier decomposition method and resonance demodulation,is proposed to extract fault-related information.First,the Fourier decomposition method decomposes the vibration signal into Fourier intrinsic band functions(FIBFs)adaptively in the frequency domain.Then,the original signal is segmented into short-time vectors to construct double-row matrices and the maximum singular value ratio method is employed to estimate the resonance frequency.Then,the resonance frequency is used as a criterion to guide the selection of the most relevant FIBF for demodulation analysis.Finally,for the optimal FIBF,envelope demodulation is conducted to identify the fault characteristic frequency.The main contributions are that the proposed method describes how to obtain the resonance frequency effectively and how to select the optimal FIBF after decomposition in order to extract the fault characteristic frequency.Both numerical and experimental studies are conducted to investigate the performance of the proposed method.It is demonstrated that the proposed method can effectively demodulate the fault information from the original signal.展开更多
The truncated singular value decomposition has been widely used in many areas of science including engineering,and statistics,etc.In this paper,the original truncated complex singular value decomposition problem is fo...The truncated singular value decomposition has been widely used in many areas of science including engineering,and statistics,etc.In this paper,the original truncated complex singular value decomposition problem is formulated as a Riemannian optimiza-tion problem on a product of two complex Stiefel manifolds,a practical algorithm based on the generic Riemannian trust-region method of Absil et al.is presented to solve the underlying problem,which enjoys the global convergence and local superlinear conver-gence rate.Numerical experiments are provided to illustrate the efficiency of the proposed method.Comparisons with some classical Riemannian gradient-type methods,the existing Riemannian version of limited-memory BFGS algorithms in the MATLAB toolbox Manopt and the Riemannian manifold optimization library ROPTLIB,and some latest infeasible methods for solving manifold optimization problems,are also provided to show the merits of the proposed approach.展开更多
The current manuscript makes use of the prominent iterative procedure, called the Adomian Decomposition Method (ADM), to tackle some important special differential equations. The equations of curiosity in this study a...The current manuscript makes use of the prominent iterative procedure, called the Adomian Decomposition Method (ADM), to tackle some important special differential equations. The equations of curiosity in this study are the singular equations that arise in many physical science applications. Thus, through the application of the ADM, a generalized recursive scheme was successfully derived and further utilized to obtain closed-form solutions for the models under consideration. The method is, indeed, fascinating as respective exact analytical solutions are accurately acquired with only a small number of iterations.展开更多
The normal mode interference characteristic in shallow water waveguide is a valu- able topic in the fields of underwater acoustic. A method for extracting the interference components of normal modes from broadband aco...The normal mode interference characteristic in shallow water waveguide is a valu- able topic in the fields of underwater acoustic. A method for extracting the interference components of normal modes from broadband acoustic propagation data recorded by a single hy- drophone without any prior information is present in this paper. First, a Hermitian matrix is formed by the power spectral density. Second, a singular value decomposition （SVD） is performed on the Hermitian matrix to obtain the orthonormal eigenvectors, which are proportional to the interference components of normal modes. The fundamental equations of the new extracting method are derived based on normal mode and waveguide invariant theory. And the validity of the present method is verified by the numerical simulation and experimental results. In addition, the extracted results of normal-mode interference components are intended to be used for passive ranging of broadband sources.展开更多
本文基于多窗谱分析—奇异值分解(MTM-SVD)方法对长江中下游降水和热带太平洋海表面温度(SST)进行不同时间尺度信号的分离和时空重构,研究了年际时间尺度上与厄尔尼诺—南方涛动(ENSO)相关的热带太平洋SST强迫对长江中下游降水的影响及...本文基于多窗谱分析—奇异值分解(MTM-SVD)方法对长江中下游降水和热带太平洋海表面温度(SST)进行不同时间尺度信号的分离和时空重构,研究了年际时间尺度上与厄尔尼诺—南方涛动(ENSO)相关的热带太平洋SST强迫对长江中下游降水的影响及可能机制。结果表明,长江中下游地区降水和热带太平洋SST存在着准两年(2.4年)和准四年(3.7年)的协同变化周期,且这两个年际主导模态分别与El Niño的中太平洋(CP)型和东太平洋(EP)型有关。与两类El Niño事件相关的SST强迫会引发不同的东亚大气环流异常响应,均有利于长江中下游地区降水偏多。在准两年周期上,CP El Niño成熟期会引发东亚—太平洋型大气遥相关;在准四年周期上,EP El Niño成熟期会产生经向偶极型分布的东亚大气活动中心。此外,两类El Niño事件成熟期均会激发西北太平洋异常反气旋环流。上述大气环流系统变化共同增强了从南海向长江中下游地区的水汽输送,造成该地区在两类El Niño成熟期间降水偏多。对2002年中国降水事件的个例分析表明,准两年和准四年周期变率对同期长江中下游地区降水变化的相对贡献存在差异。准四年周期变率有利于2002年春季长江中下游降水的偏多,而准两年周期变率起到减少的作用;2002年秋季的情况与之相反。本研究结果有助于深化对热带太平洋多时间尺度SST强迫影响长江中下游降水年际变化机制的认识,并提高长江中下游地区降水预测的准确性。展开更多
The present work describes the application of the method of fundamental solutions （MFS） along with the analog equation method （AEM） and radial basis function （RBF） approximation for solving the 2D isotropic and ...The present work describes the application of the method of fundamental solutions （MFS） along with the analog equation method （AEM） and radial basis function （RBF） approximation for solving the 2D isotropic and anisotropic Helmholtz problems with different wave numbers. The AEM is used to convert the original governing equation into the classical Poisson＇s equation, and the MFS and RBF approximations are used to derive the homogeneous and particular solutions, respectively. Finally, the satisfaction of the solution consisting of the homogeneous and particular parts to the related governing equation and boundary conditions can produce a system of linear equations, which can be solved with the singular value decomposition （SVD） technique. In the computation, such crucial factors related to the MFS-RBF as the location of the virtual boundary, the differential and integrating strategies, and the variation of shape parameters in multi-quadric （MQ） are fully analyzed to provide useful reference.展开更多
The aim of this study was to design and construct an improved response surface method(RSM) based on weighted regression for the anti-slide reliability analysis of concrete gravity dam.The limitation and lacuna of the ...The aim of this study was to design and construct an improved response surface method(RSM) based on weighted regression for the anti-slide reliability analysis of concrete gravity dam.The limitation and lacuna of the traditional RSM were briefly analyzed.Firstly,based on small experimental points,research was devoted to an improved RSM with singular value decomposition techniques.Then,the method was used on the basis of weighted regression and deviation coefficient correction to reduce iteration times and experimental points and improve the calculation method of checking point.Finally,a test example was given to verify this method.Compared with other conventional algorithms,this method has some strong advantages:this algorithm not only saves the arithmetic operations but also greatly enhances the calculation efficiency and the storage efficiency.展开更多
A novel numerical method for eliminating the singular integral and boundary effect is processed. In the proposed method, the virtual boundaries corresponding to the numbers of the true boundary arguments are chosen to...A novel numerical method for eliminating the singular integral and boundary effect is processed. In the proposed method, the virtual boundaries corresponding to the numbers of the true boundary arguments are chosen to be as simple as possible. An indirect radial basis function network （IRBFN） constructed by functions resulting from the indeterminate integral is used to construct the approaching virtual source functions distributed along the virtual boundaries. By using the linear superposition method, the governing equations presented in the boundaries integral equations （BIE） can be established while the fundamental solutions to the problems are introduced. The singular value decomposition （SVD） method is used to solve the governing equations since an optimal solution in the least squares sense to the system equations is available. In addition, no elements are required, and the boundary conditions can be imposed easily because of the Kronecker delta function properties of the approaching functions. Three classical 2D elasticity problems have been examined to verify the performance of the method proposed. The results show that this method has faster convergence and higher accuracy than the conventional boundary type numerical methods.展开更多
An important problem that arises in different areas of science and engineering is that of computing the limits of sequences of vectors , where , N being very large. Such sequences arise, for example, in the solution o...An important problem that arises in different areas of science and engineering is that of computing the limits of sequences of vectors , where , N being very large. Such sequences arise, for example, in the solution of systems of linear or nonlinear equations by fixed-point iterative methods, and are simply the required solutions. In most cases of interest, however, these sequences converge to their limits extremely slowly. One practical way to make the sequences converge more quickly is to apply to them vector extrapolation methods. Two types of methods exist in the literature: polynomial type methods and epsilon algorithms. In most applications, the polynomial type methods have proved to be superior convergence accelerators. Three polynomial type methods are known, and these are the minimal polynomial extrapolation (MPE), the reduced rank extrapolation (RRE), and the modified minimal polynomial extrapolation (MMPE). In this work, we develop yet another polynomial type method, which is based on the singular value decomposition, as well as the ideas that lead to MPE. We denote this new method by SVD-MPE. We also design a numerically stable algorithm for its implementation, whose computational cost and storage requirements are minimal. Finally, we illustrate the use of SVD-MPE with numerical examples.展开更多
针对工业机械设备实时监测中不可控因素导致的振动信号数据缺失问题,提出一种基于自适应二次临近项交替方向乘子算法(adaptive quadratic proximity-alternating direction method of multipliers, AQ-ADMM)的压缩感知缺失信号重构方法...针对工业机械设备实时监测中不可控因素导致的振动信号数据缺失问题,提出一种基于自适应二次临近项交替方向乘子算法(adaptive quadratic proximity-alternating direction method of multipliers, AQ-ADMM)的压缩感知缺失信号重构方法。AQ-ADMM算法在经典交替方向乘子算法算法迭代过程中添加二次临近项,且能够自适应选取惩罚参数。首先在数据中心建立信号参考数据库用于构造初始字典,然后将K-奇异值分解(K-singular value decomposition, K-SVD)字典学习算法和AQ-ADMM算法结合重构缺失信号。对仿真信号和两种真实轴承信号数据集添加高斯白噪声后作为样本,试验结果表明当信号压缩率在50%~70%时,所提方法性能指标明显优于其它传统方法,在重构信号的同时实现了对含缺失数据机械振动信号的快速精确修复。展开更多
Nowadays,the modeling of systems may be quite large,even up to tens of thousands orders.In spite of the increasing computational powers,direct simulation of these large-scale systems may be impractical.Thus,to industr...Nowadays,the modeling of systems may be quite large,even up to tens of thousands orders.In spite of the increasing computational powers,direct simulation of these large-scale systems may be impractical.Thus,to industry requirements,analytically tractable and computationally cheap models must be designed.This is the essence task of Model Order Reduction(MOR).This article describes the basics of MOR optimization,various way of designing MOR,and gives the conclusion about existing methods.In addition,it proposed some heuristic footpath.展开更多
文摘The perturbational reanalysis technique of matrix singular value decomposition is applicable to many theoretical and practical problems in mathematics, mechanics, control theory, engineering, etc.. An indirect perturbation method has previously been proposed by the author in this journal, and now the direct perturbation method has also been presented in this paper. The second-order perturbation results of non-repeated singular values and the corresponding left and right singular vectors are obtained. The results can meet the general needs of most problems of various practical applications. A numerical example is presented to demonstrate the effectiveness of the direct perturbation method.
文摘The perturbation method for the reanalysis of the singular value decomposition (SVD) of general real matrices is presented in this paper. This is a simple but efficient reanalysis technique for the SVD, which is of great worth to enhance computational efficiency of the iterative analysis problems that require matrix singular value decomposition repeatedly. The asymptotic estimate formulas for the singular values and the corresponding left and right singular vectors up to second-order perturbation components are derived. At the end of the paper the way to extend the perturbation method to the case of general complex matrices is advanced.
基金Supported by the National Natural Science Foundation of China(10901125,11471253)
文摘In this paper, we investigate the linear solver in least square support vector machine（LSSVM） for large-scale data regression. The traditional methods using the direct solvers are costly. We know that the linear equations should be solved repeatedly for choosing appropriate parameters in LSSVM, so the key for speeding up LSSVM is to improve the method of solving the linear equations. We approximate large-scale kernel matrices and get the approximate solution of linear equations by using randomized singular value decomposition（randomized SVD）. Some data sets coming from University of California Irvine machine learning repository are used to perform the experiments. We find LSSVM based on randomized SVD is more accurate and less time-consuming in the case of large number of variables than the method based on Nystrom method or Lanczos process.
基金supported by the National Key R&D Program of China(No.2019YFB2004604)the National Natural Science Foundation of China(No.52075477)the Key R&D Program of Zhejiang Province(No.2021C01139),China。
文摘Condition monitoring and fault diagnosis of gearboxes play an important role in the maintenance of mechanical systems.The vibration signal of gearboxes is characterized by complex spectral structure and strong time variability,which brings challenges to fault feature extraction.To address this issue,a new demodulation technique,based on the Fourier decomposition method and resonance demodulation,is proposed to extract fault-related information.First,the Fourier decomposition method decomposes the vibration signal into Fourier intrinsic band functions(FIBFs)adaptively in the frequency domain.Then,the original signal is segmented into short-time vectors to construct double-row matrices and the maximum singular value ratio method is employed to estimate the resonance frequency.Then,the resonance frequency is used as a criterion to guide the selection of the most relevant FIBF for demodulation analysis.Finally,for the optimal FIBF,envelope demodulation is conducted to identify the fault characteristic frequency.The main contributions are that the proposed method describes how to obtain the resonance frequency effectively and how to select the optimal FIBF after decomposition in order to extract the fault characteristic frequency.Both numerical and experimental studies are conducted to investigate the performance of the proposed method.It is demonstrated that the proposed method can effectively demodulate the fault information from the original signal.
基金supported by the National Natural Science Foundation of China(Grant Nos.12261026,11961012,12201149)by the Natural Science Foundation of Guangxi Province(Grant Nos.2016GXNSFAA380074,2023GXNSFAA026067)+4 种基金by the Innovation Project of GUET Graduate Education(Grant No.2022YXW01)by the GUET Graduate Innovation Project(Grant No.2022YCXS142)by the Guangxi Key Laboratory of Automatic Detecting Technology and Instruments(Grant Nos.YQ23103,YQ21103,YQ22106)by the Special Fund for Science and Technological Bases and Talents of Guangxi(Grant No.2021AC06001)by the Guizhou Science and Technology Program of Projects(Grant No.ZK2021G339)。
文摘The truncated singular value decomposition has been widely used in many areas of science including engineering,and statistics,etc.In this paper,the original truncated complex singular value decomposition problem is formulated as a Riemannian optimiza-tion problem on a product of two complex Stiefel manifolds,a practical algorithm based on the generic Riemannian trust-region method of Absil et al.is presented to solve the underlying problem,which enjoys the global convergence and local superlinear conver-gence rate.Numerical experiments are provided to illustrate the efficiency of the proposed method.Comparisons with some classical Riemannian gradient-type methods,the existing Riemannian version of limited-memory BFGS algorithms in the MATLAB toolbox Manopt and the Riemannian manifold optimization library ROPTLIB,and some latest infeasible methods for solving manifold optimization problems,are also provided to show the merits of the proposed approach.
文摘The current manuscript makes use of the prominent iterative procedure, called the Adomian Decomposition Method (ADM), to tackle some important special differential equations. The equations of curiosity in this study are the singular equations that arise in many physical science applications. Thus, through the application of the ADM, a generalized recursive scheme was successfully derived and further utilized to obtain closed-form solutions for the models under consideration. The method is, indeed, fascinating as respective exact analytical solutions are accurately acquired with only a small number of iterations.
文摘The normal mode interference characteristic in shallow water waveguide is a valu- able topic in the fields of underwater acoustic. A method for extracting the interference components of normal modes from broadband acoustic propagation data recorded by a single hy- drophone without any prior information is present in this paper. First, a Hermitian matrix is formed by the power spectral density. Second, a singular value decomposition （SVD） is performed on the Hermitian matrix to obtain the orthonormal eigenvectors, which are proportional to the interference components of normal modes. The fundamental equations of the new extracting method are derived based on normal mode and waveguide invariant theory. And the validity of the present method is verified by the numerical simulation and experimental results. In addition, the extracted results of normal-mode interference components are intended to be used for passive ranging of broadband sources.
文摘本文基于多窗谱分析—奇异值分解(MTM-SVD)方法对长江中下游降水和热带太平洋海表面温度(SST)进行不同时间尺度信号的分离和时空重构,研究了年际时间尺度上与厄尔尼诺—南方涛动(ENSO)相关的热带太平洋SST强迫对长江中下游降水的影响及可能机制。结果表明,长江中下游地区降水和热带太平洋SST存在着准两年(2.4年)和准四年(3.7年)的协同变化周期,且这两个年际主导模态分别与El Niño的中太平洋(CP)型和东太平洋(EP)型有关。与两类El Niño事件相关的SST强迫会引发不同的东亚大气环流异常响应,均有利于长江中下游地区降水偏多。在准两年周期上,CP El Niño成熟期会引发东亚—太平洋型大气遥相关;在准四年周期上,EP El Niño成熟期会产生经向偶极型分布的东亚大气活动中心。此外,两类El Niño事件成熟期均会激发西北太平洋异常反气旋环流。上述大气环流系统变化共同增强了从南海向长江中下游地区的水汽输送,造成该地区在两类El Niño成熟期间降水偏多。对2002年中国降水事件的个例分析表明,准两年和准四年周期变率对同期长江中下游地区降水变化的相对贡献存在差异。准四年周期变率有利于2002年春季长江中下游降水的偏多,而准两年周期变率起到减少的作用;2002年秋季的情况与之相反。本研究结果有助于深化对热带太平洋多时间尺度SST强迫影响长江中下游降水年际变化机制的认识,并提高长江中下游地区降水预测的准确性。
文摘The present work describes the application of the method of fundamental solutions （MFS） along with the analog equation method （AEM） and radial basis function （RBF） approximation for solving the 2D isotropic and anisotropic Helmholtz problems with different wave numbers. The AEM is used to convert the original governing equation into the classical Poisson＇s equation, and the MFS and RBF approximations are used to derive the homogeneous and particular solutions, respectively. Finally, the satisfaction of the solution consisting of the homogeneous and particular parts to the related governing equation and boundary conditions can produce a system of linear equations, which can be solved with the singular value decomposition （SVD） technique. In the computation, such crucial factors related to the MFS-RBF as the location of the virtual boundary, the differential and integrating strategies, and the variation of shape parameters in multi-quadric （MQ） are fully analyzed to provide useful reference.
基金supported by the National Basic Research Program of China (Nos. 2007CB714107 and 90510018)the Trans-Century Training Programme Foundation for the Talents by the State Education Com-mission (No. NCET-06-0270),China
文摘The aim of this study was to design and construct an improved response surface method(RSM) based on weighted regression for the anti-slide reliability analysis of concrete gravity dam.The limitation and lacuna of the traditional RSM were briefly analyzed.Firstly,based on small experimental points,research was devoted to an improved RSM with singular value decomposition techniques.Then,the method was used on the basis of weighted regression and deviation coefficient correction to reduce iteration times and experimental points and improve the calculation method of checking point.Finally,a test example was given to verify this method.Compared with other conventional algorithms,this method has some strong advantages:this algorithm not only saves the arithmetic operations but also greatly enhances the calculation efficiency and the storage efficiency.
文摘A novel numerical method for eliminating the singular integral and boundary effect is processed. In the proposed method, the virtual boundaries corresponding to the numbers of the true boundary arguments are chosen to be as simple as possible. An indirect radial basis function network （IRBFN） constructed by functions resulting from the indeterminate integral is used to construct the approaching virtual source functions distributed along the virtual boundaries. By using the linear superposition method, the governing equations presented in the boundaries integral equations （BIE） can be established while the fundamental solutions to the problems are introduced. The singular value decomposition （SVD） method is used to solve the governing equations since an optimal solution in the least squares sense to the system equations is available. In addition, no elements are required, and the boundary conditions can be imposed easily because of the Kronecker delta function properties of the approaching functions. Three classical 2D elasticity problems have been examined to verify the performance of the method proposed. The results show that this method has faster convergence and higher accuracy than the conventional boundary type numerical methods.
文摘An important problem that arises in different areas of science and engineering is that of computing the limits of sequences of vectors , where , N being very large. Such sequences arise, for example, in the solution of systems of linear or nonlinear equations by fixed-point iterative methods, and are simply the required solutions. In most cases of interest, however, these sequences converge to their limits extremely slowly. One practical way to make the sequences converge more quickly is to apply to them vector extrapolation methods. Two types of methods exist in the literature: polynomial type methods and epsilon algorithms. In most applications, the polynomial type methods have proved to be superior convergence accelerators. Three polynomial type methods are known, and these are the minimal polynomial extrapolation (MPE), the reduced rank extrapolation (RRE), and the modified minimal polynomial extrapolation (MMPE). In this work, we develop yet another polynomial type method, which is based on the singular value decomposition, as well as the ideas that lead to MPE. We denote this new method by SVD-MPE. We also design a numerically stable algorithm for its implementation, whose computational cost and storage requirements are minimal. Finally, we illustrate the use of SVD-MPE with numerical examples.
文摘针对工业机械设备实时监测中不可控因素导致的振动信号数据缺失问题,提出一种基于自适应二次临近项交替方向乘子算法(adaptive quadratic proximity-alternating direction method of multipliers, AQ-ADMM)的压缩感知缺失信号重构方法。AQ-ADMM算法在经典交替方向乘子算法算法迭代过程中添加二次临近项,且能够自适应选取惩罚参数。首先在数据中心建立信号参考数据库用于构造初始字典,然后将K-奇异值分解(K-singular value decomposition, K-SVD)字典学习算法和AQ-ADMM算法结合重构缺失信号。对仿真信号和两种真实轴承信号数据集添加高斯白噪声后作为样本,试验结果表明当信号压缩率在50%~70%时,所提方法性能指标明显优于其它传统方法,在重构信号的同时实现了对含缺失数据机械振动信号的快速精确修复。
文摘Nowadays,the modeling of systems may be quite large,even up to tens of thousands orders.In spite of the increasing computational powers,direct simulation of these large-scale systems may be impractical.Thus,to industry requirements,analytically tractable and computationally cheap models must be designed.This is the essence task of Model Order Reduction(MOR).This article describes the basics of MOR optimization,various way of designing MOR,and gives the conclusion about existing methods.In addition,it proposed some heuristic footpath.
