Randomness and fluctuations in wind power output may cause changes in important parameters(e.g.,grid frequency and voltage),which in turn affect the stable operation of a power system.However,owing to external factors...Randomness and fluctuations in wind power output may cause changes in important parameters(e.g.,grid frequency and voltage),which in turn affect the stable operation of a power system.However,owing to external factors(such as weather),there are often various anomalies in wind power data,such as missing numerical values and unreasonable data.This significantly affects the accuracy of wind power generation predictions and operational decisions.Therefore,developing and applying reliable wind power interpolation methods is important for promoting the sustainable development of the wind power industry.In this study,the causes of abnormal data in wind power generation were first analyzed from a practical perspective.Second,an improved complete ensemble empirical mode decomposition with adaptive noise(ICEEMDAN)method with a generative adversarial interpolation network(GAIN)network was proposed to preprocess wind power generation and interpolate missing wind power generation sub-components.Finally,a complete wind power generation time series was reconstructed.Compared to traditional methods,the proposed ICEEMDAN-GAIN combination interpolation model has a higher interpolation accuracy and can effectively reduce the error impact caused by wind power generation sequence fluctuations.展开更多
Let f∈C[-1,1]and R. (r≥1 ) be the reneralized Pal iner polation polynomials satisf ying the conditions Rn, where{xk} are the roots of n-th Jacobi polynomial Pn and are the roots of In this paper,we prove that Rn hol...Let f∈C[-1,1]and R. (r≥1 ) be the reneralized Pal iner polation polynomials satisf ying the conditions Rn, where{xk} are the roots of n-th Jacobi polynomial Pn and are the roots of In this paper,we prove that Rn holds uniformly on [0,1].展开更多
In this paper, a three dimensional matrix valued rational interpolant (TGMRI) is first constructed by making use of the generalized inverse of matrices. The interpolants are of the Thiele type branched continued fract...In this paper, a three dimensional matrix valued rational interpolant (TGMRI) is first constructed by making use of the generalized inverse of matrices. The interpolants are of the Thiele type branched continued fraction form, with matrix numerator and scalar denominator. Some properties of TGMRI are given. An efficient recursive algorithm is proposed. The results in the paper can be extend to n variable.展开更多
Practical techniques for smooth geodesic patterning of membrane structures were investigated.For the geodesic search,adjustment of the subplane of the extracted elements series was proposed,and various spline approxim...Practical techniques for smooth geodesic patterning of membrane structures were investigated.For the geodesic search,adjustment of the subplane of the extracted elements series was proposed,and various spline approximation methods were used to flatten the strip for the generation of a smooth pattern.This search approach is very simple,and the geodesic line could be easily attained by the proposed method without the need for a difficult computation method.Smooth cutting patterning can also be generated by spline approximation without the noise in discrete nodal information.Additionally,the geodesic cutting pattern saved about 21%of the required area for the catenary model due to the reduction of the curvature of the planar pattern seam line.展开更多
In this paper, a general family of derivative-free n + 1-point iterative methods using n + 1 evaluations of the function and a general family of n-point iterative methods using n evaluations of the function and only o...In this paper, a general family of derivative-free n + 1-point iterative methods using n + 1 evaluations of the function and a general family of n-point iterative methods using n evaluations of the function and only one evaluation of its derivative are constructed by the inverse interpolation with the memory on the previous step for solving the simple root of a nonlinear equation. The order and order of convergence of them are proved respectively. Finally, the proposed methods and the basins of attraction are demonstrated by the numerical examples.展开更多
Boyd^interpolation theorem for quasilinear operators is generalized in this paper,which gives a generalization for both the Marcinkiewicz interpolation theorem and Boyd^interpolation theorem.By using this new interpol...Boyd^interpolation theorem for quasilinear operators is generalized in this paper,which gives a generalization for both the Marcinkiewicz interpolation theorem and Boyd^interpolation theorem.By using this new interpolation theorem,we study the spherical fractional maximal functions and the fractional maximal commutators on rearrangement-invariant quasi-Banach function spaces.In particular,we obtain the mapping properties of the spherical fractional maximal functions and the fractional maximal commutators on generalized Lorentz spaces.展开更多
General interpolation formulae for barycentric interpolation and barycentric rational Hermite interpolation are established by introducing multiple parameters,which include many kinds of barycentric interpolation and ...General interpolation formulae for barycentric interpolation and barycentric rational Hermite interpolation are established by introducing multiple parameters,which include many kinds of barycentric interpolation and barycentric rational Hermite interpolation. We discussed the interpolation theorem, dual interpolation and special cases. Numerical example is given to show the effectiveness of the method.展开更多
The aim of this survey paper is to propose a new concept "generator".In fact,generator is a single function that can generate the basis as well as the whole function space.It is a more fundamental concept th...The aim of this survey paper is to propose a new concept "generator".In fact,generator is a single function that can generate the basis as well as the whole function space.It is a more fundamental concept than basis.Various properties of generator are also discussed.Moreover,a special generator named multiquadric function is introduced.Based on the multiquadric generator,the multiquadric quasi-interpolation scheme is constructed,and furthermore,the properties of this kind of quasi-interpolation are discussed to show its better capacity and stability in approximating the high order derivatives.展开更多
Generalized Least Squares (least squares with prior information) requires the correct assignment of two prior covariance matrices: one associated with the uncertainty of measurements;the other with the uncertainty of ...Generalized Least Squares (least squares with prior information) requires the correct assignment of two prior covariance matrices: one associated with the uncertainty of measurements;the other with the uncertainty of prior information. These assignments often are very subjective, especially when correlations among data or among prior information are believed to occur. However, in cases in which the general form of these matrices can be anticipated up to a set of poorly-known parameters, the data and prior information may be used to better-determine (or “tune”) the parameters in a manner that is faithful to the underlying Bayesian foundation of GLS. We identify an objective function, the minimization of which leads to the best-estimate of the parameters and provide explicit and computationally-efficient formula for calculating the derivatives needed to implement the minimization with a gradient descent method. Furthermore, the problem is organized so that the minimization need be performed only over the space of covariance parameters, and not over the combined space of model and covariance parameters. We show that the use of trade-off curves to select the relative weight given to observations and prior information is not a form of tuning, because it does not, in general maximize the posterior probability of the model parameters, and can lead to a different weighting than the procedure described here. We also provide several examples that demonstrate the viability, and discuss both the advantages and limitations of the method.展开更多
The aim of this paper is to obtain the numerical solutions of generalized space-fractional Burgers' equations with initial-boundary conditions by the Jacobi spectral collocation method using the shifted Jacobi-Gau...The aim of this paper is to obtain the numerical solutions of generalized space-fractional Burgers' equations with initial-boundary conditions by the Jacobi spectral collocation method using the shifted Jacobi-Gauss-Lobatto collocation points. By means of the simplifed Jacobi operational matrix, we produce the diferentiation matrix and transfer the space-fractional Burgers' equation into a system of ordinary diferential equations that can be solved by the fourth-order Runge-Kutta method. The numerical simulations indicate that the Jacobi spectral collocation method is highly accurate and fast convergent for the generalized space-fractional Burgers' equation.展开更多
We construct a quadrature formula of the singular integral with the Chebyshev weight of the second kind by using Lagrange interpolation based on the rational system {1/(x-a 1),1/(x-a 2),...} , and both the remainder a...We construct a quadrature formula of the singular integral with the Chebyshev weight of the second kind by using Lagrange interpolation based on the rational system {1/(x-a 1),1/(x-a 2),...} , and both the remainder and convergence of the quadrature formula established here are discussed. Our results extend some classical ones.展开更多
In [3], a kind of matrix-valued rational interpolants (MRIs) in the form of Rn(x) = M(x)/D(x) with the divisibility condition D(x) | ‖M(x)‖2, was defined, and the characterization theorem and uniqueness theorem for ...In [3], a kind of matrix-valued rational interpolants (MRIs) in the form of Rn(x) = M(x)/D(x) with the divisibility condition D(x) | ‖M(x)‖2, was defined, and the characterization theorem and uniqueness theorem for MRIs were proved. However this divisibility condition is found not necessary in some cases. In this paper, we remove this restricted condition, define the generalized matrix-valued rational interpolants (GMRIs) and establish the characterization theorem and uniqueness theorem for GMRIs. One can see that the characterization theorem and uniqueness theorem for MRIs are the special cases of those for GMRIs. Moreover, by defining a kind of inner product,we succeed in unifying the Samelson inverses for a vector and a matrix.展开更多
在数字示波器中,当最高采样率都不能满足系统要求的时候,我们需要对其进行相应倍数的插值。文章介绍了使用XILINX System Generator for DSP工具在MATLAB/Simulink的环境下完成算法的建模,然后生成相应的工程代码,来开发基于FPGA的插值...在数字示波器中,当最高采样率都不能满足系统要求的时候,我们需要对其进行相应倍数的插值。文章介绍了使用XILINX System Generator for DSP工具在MATLAB/Simulink的环境下完成算法的建模,然后生成相应的工程代码,来开发基于FPGA的插值数字滤波器,借助Modelsim工具验证实现结果。大大消除了原先系统工程师和软硬件工程师之间的隔阂,同时也简化了传统的FPGA开发流程。展开更多
基金This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11171125, 11271118, 91130003）, the National Natural Science Foundation of China （Tianyuan Fund for Mathematics, Grant No. 11226170）, the Natural Science Foundation of Hunan Province （Grant No. 13JJ4095）, the Postdoctoral Foundation of China （Grant No. 20100471182）, the Construct Program of the Key Discipline in Hunan Province, and the Key Foundation of Hunan Provincial Education Department （Grant No. 11A043）.
基金We gratefully acknowledge the support of National Natural Science Foundation of China(NSFC)(Grant No.51977133&Grant No.U2066209).
文摘Randomness and fluctuations in wind power output may cause changes in important parameters(e.g.,grid frequency and voltage),which in turn affect the stable operation of a power system.However,owing to external factors(such as weather),there are often various anomalies in wind power data,such as missing numerical values and unreasonable data.This significantly affects the accuracy of wind power generation predictions and operational decisions.Therefore,developing and applying reliable wind power interpolation methods is important for promoting the sustainable development of the wind power industry.In this study,the causes of abnormal data in wind power generation were first analyzed from a practical perspective.Second,an improved complete ensemble empirical mode decomposition with adaptive noise(ICEEMDAN)method with a generative adversarial interpolation network(GAIN)network was proposed to preprocess wind power generation and interpolate missing wind power generation sub-components.Finally,a complete wind power generation time series was reconstructed.Compared to traditional methods,the proposed ICEEMDAN-GAIN combination interpolation model has a higher interpolation accuracy and can effectively reduce the error impact caused by wind power generation sequence fluctuations.
基金Supported by the Science Foundation of CSBTB the Natural Science Foundatioin of Zhejiang.
文摘Let f∈C[-1,1]and R. (r≥1 ) be the reneralized Pal iner polation polynomials satisf ying the conditions Rn, where{xk} are the roots of n-th Jacobi polynomial Pn and are the roots of In this paper,we prove that Rn holds uniformly on [0,1].
文摘In this paper, a three dimensional matrix valued rational interpolant (TGMRI) is first constructed by making use of the generalized inverse of matrices. The interpolants are of the Thiele type branched continued fraction form, with matrix numerator and scalar denominator. Some properties of TGMRI are given. An efficient recursive algorithm is proposed. The results in the paper can be extend to n variable.
基金Project(12 High-tech Urban C22)supported by High-tech Urban Development Program,Ministry of Land,Transport and Moritime Affairs of Korea
文摘Practical techniques for smooth geodesic patterning of membrane structures were investigated.For the geodesic search,adjustment of the subplane of the extracted elements series was proposed,and various spline approximation methods were used to flatten the strip for the generation of a smooth pattern.This search approach is very simple,and the geodesic line could be easily attained by the proposed method without the need for a difficult computation method.Smooth cutting patterning can also be generated by spline approximation without the noise in discrete nodal information.Additionally,the geodesic cutting pattern saved about 21%of the required area for the catenary model due to the reduction of the curvature of the planar pattern seam line.
文摘In this paper, a general family of derivative-free n + 1-point iterative methods using n + 1 evaluations of the function and a general family of n-point iterative methods using n evaluations of the function and only one evaluation of its derivative are constructed by the inverse interpolation with the memory on the previous step for solving the simple root of a nonlinear equation. The order and order of convergence of them are proved respectively. Finally, the proposed methods and the basins of attraction are demonstrated by the numerical examples.
文摘Boyd^interpolation theorem for quasilinear operators is generalized in this paper,which gives a generalization for both the Marcinkiewicz interpolation theorem and Boyd^interpolation theorem.By using this new interpolation theorem,we study the spherical fractional maximal functions and the fractional maximal commutators on rearrangement-invariant quasi-Banach function spaces.In particular,we obtain the mapping properties of the spherical fractional maximal functions and the fractional maximal commutators on generalized Lorentz spaces.
基金supported by the grant of Key Scientific Research Foundation of Education Department of Anhui Province, No. KJ2014A210
文摘General interpolation formulae for barycentric interpolation and barycentric rational Hermite interpolation are established by introducing multiple parameters,which include many kinds of barycentric interpolation and barycentric rational Hermite interpolation. We discussed the interpolation theorem, dual interpolation and special cases. Numerical example is given to show the effectiveness of the method.
基金Supported by the 973program-2006CB303102SGST 09DZ 2272900NSFC No.11026089
文摘The aim of this survey paper is to propose a new concept "generator".In fact,generator is a single function that can generate the basis as well as the whole function space.It is a more fundamental concept than basis.Various properties of generator are also discussed.Moreover,a special generator named multiquadric function is introduced.Based on the multiquadric generator,the multiquadric quasi-interpolation scheme is constructed,and furthermore,the properties of this kind of quasi-interpolation are discussed to show its better capacity and stability in approximating the high order derivatives.
文摘Generalized Least Squares (least squares with prior information) requires the correct assignment of two prior covariance matrices: one associated with the uncertainty of measurements;the other with the uncertainty of prior information. These assignments often are very subjective, especially when correlations among data or among prior information are believed to occur. However, in cases in which the general form of these matrices can be anticipated up to a set of poorly-known parameters, the data and prior information may be used to better-determine (or “tune”) the parameters in a manner that is faithful to the underlying Bayesian foundation of GLS. We identify an objective function, the minimization of which leads to the best-estimate of the parameters and provide explicit and computationally-efficient formula for calculating the derivatives needed to implement the minimization with a gradient descent method. Furthermore, the problem is organized so that the minimization need be performed only over the space of covariance parameters, and not over the combined space of model and covariance parameters. We show that the use of trade-off curves to select the relative weight given to observations and prior information is not a form of tuning, because it does not, in general maximize the posterior probability of the model parameters, and can lead to a different weighting than the procedure described here. We also provide several examples that demonstrate the viability, and discuss both the advantages and limitations of the method.
基金This work is supported by the National Natural Science Foundation of China(Grant Nos.11701358,11774218)。
文摘The aim of this paper is to obtain the numerical solutions of generalized space-fractional Burgers' equations with initial-boundary conditions by the Jacobi spectral collocation method using the shifted Jacobi-Gauss-Lobatto collocation points. By means of the simplifed Jacobi operational matrix, we produce the diferentiation matrix and transfer the space-fractional Burgers' equation into a system of ordinary diferential equations that can be solved by the fourth-order Runge-Kutta method. The numerical simulations indicate that the Jacobi spectral collocation method is highly accurate and fast convergent for the generalized space-fractional Burgers' equation.
文摘We construct a quadrature formula of the singular integral with the Chebyshev weight of the second kind by using Lagrange interpolation based on the rational system {1/(x-a 1),1/(x-a 2),...} , and both the remainder and convergence of the quadrature formula established here are discussed. Our results extend some classical ones.
基金Supported by the National Natural Science Foundation of China(10171026 and 60473114)
文摘In [3], a kind of matrix-valued rational interpolants (MRIs) in the form of Rn(x) = M(x)/D(x) with the divisibility condition D(x) | ‖M(x)‖2, was defined, and the characterization theorem and uniqueness theorem for MRIs were proved. However this divisibility condition is found not necessary in some cases. In this paper, we remove this restricted condition, define the generalized matrix-valued rational interpolants (GMRIs) and establish the characterization theorem and uniqueness theorem for GMRIs. One can see that the characterization theorem and uniqueness theorem for MRIs are the special cases of those for GMRIs. Moreover, by defining a kind of inner product,we succeed in unifying the Samelson inverses for a vector and a matrix.
文摘在数字示波器中,当最高采样率都不能满足系统要求的时候,我们需要对其进行相应倍数的插值。文章介绍了使用XILINX System Generator for DSP工具在MATLAB/Simulink的环境下完成算法的建模,然后生成相应的工程代码,来开发基于FPGA的插值数字滤波器,借助Modelsim工具验证实现结果。大大消除了原先系统工程师和软硬件工程师之间的隔阂,同时也简化了传统的FPGA开发流程。
