基于Chebyshev多项式的神经网络中长期负荷预测研究

高精度负荷预测在提高电力系统的安全性和经济性方面有着极其重要的意义,而现有的负荷预测方法因参数有限,难以完全反映其内在规律,因而导致预测结果不够准确.为此提出了一种基于Chebyshev多项式神经网络模型的预测方法.该方法使用递推最小二乘法训练神经网络权值系数,以获得高精度的参数估计,从而实现Chebyshev多项式神经网络模型对负荷量的最优拟合,再利用训练好的Chebyshev多项式神经网络模型实现中长期负荷预测.研究结果表明,该方法能较好模拟负荷变化规律,有效提高了负荷预测精度,在电力系统负荷预测中有较大的应用价值.     

等维Cartan-Hartogs域双全纯映射的特征

本文考虑了等维Cartan-Hartogs域之间的全纯映射.如果Cartan-Hartogs域Ω^Bm(μ)不是球,则它上面存在一函数X使得它在Ω^Bm(μ)的任一全纯自同构作用下不变.通过直接计算得到:如果等维Cartan-Hartogs域间的全纯映射F保持函数X不变,则F必是双全纯映射.由此可得如果Cartan-Hartogs域Ω^Bm(μ)不是球,Ω^Bm(μ)的全纯自映射是自同构的充要条件是F保持函数X不变.     

实对称五对角矩阵Procrustes问题

本文研究了实对称五对角矩阵Procrustes.利用矩阵的奇异值分解简化问题,得到了实对称五对角矩阵X极小化,最后给出数值算例说明方法的有效性.     

A new framework for implicit restarting of the Krylov–Schur algorithm

This paper introduces a new framework for implicit restarting of the Krylov–Schur algorithm. It is shown that restarting with arbitrary polynomial filter is possible by reassigning some of the eigenvalues of the Rayleigh quotient through a rank‐one correction, implemented using only the elementary transformations (translation and similarity) of the Krylov decomposition. This framework includes the implicitly restarted Arnoldi (IRA) algorithm and the Krylov–Schur algorithm with implicit harmonic restart as special cases. Further, it reveals that the IRA algorithm can be turned into an eigenvalue assignment method. Copyright © 2014 John Wiley & Sons, Ltd.     

Numerical discretization-based kernel type estimation methods for ordinary differential equation models

We consider the problem of parameter estimation in both linear and nonlinear ordinary differential equation(ODE) models. Nonlinear ODE models are widely used in applications. But their analytic solutions are usually not available. Thus regular methods usually depend on repetitive use of numerical solutions which bring huge computational cost. We proposed a new two-stage approach which includes a smoothing method(kernel smoothing or local polynomial fitting) in the first stage, and a numerical discretization method(Eulers discretization method, the trapezoidal discretization method,or the Runge–Kutta discretization method) in the second stage. Through numerical simulations, we find the proposed method gains a proper balance between estimation accuracy and computational cost.Asymptotic properties are also presented, which show the consistency and asymptotic normality of estimators under some mild conditions. The proposed method is compared to existing methods in term of accuracy and computational cost. The simulation results show that the estimators with local linear smoothing in the first stage and trapezoidal discretization in the second stage have the lowest average relative errors. We apply the proposed method to HIV dynamics data to illustrate the practicability of the estimator.     

New q‐Hermite polynomials: characterization,operators algebra and associated coherent states

This paper addresses a construction of new q‐Hermite polynomials with a full characterization of their main properties and corresponding raising and lowering operator algebra. The three‐term recursive relation as well as the second‐order differential equation obeyed by these new polynomials are explicitly derived. Relevant operator actions, including the eigenvalue problem of the deformed oscillator and the self‐adjointness of the related position and momentum operators, are investigated and analyzed. The associated coherent states are constructed and discussed with an explicit resolution of the induced moment problem. The phase collapse in a q‐deformed boson system is studied.     

AN ENTROPY VARIABLE FORMULATION AND APPLICATIONS FOR THE TWO-DIMENSIONAL SHALLOW WATER EQUATIONS

A new symmetric formulation of the two-dimensional shallow water equations and a streamline upwind Petrov–Galerkin (SUPG) scheme are developed and tested. The symmetric formulation is constructed by means of a transformation of dependent variables derived from the relation for the total energy of the water column. This symmetric form is well suited to the SUPG approach as seen in analogous treatments of gas dynamics problems based on entropy variables. Particulars related to the construction of the upwind test functions and an appropriate discontinuity-capturing operator are included. A formal extension to the viscous, dissipative problem and a stability analysis are also presented. Numerical results for shallow water flow in a channel with (a) a step transition, (b) a curved wall transition and (c) a straight wall transition are compared with experimental and other computational results from the literature.     

矩阵多项式可逆的充要条件——兼与吴华安先生商榷

给出了矩阵多项式可逆的另一个充要条件,并指出文[1]中的错误.     

Hecke特征值相邻极大值的均值估计

取f为权为偶数k的全模群Γ = SL(2,Z)的Hecke特征型.定义Asymmf(n)为与f关联的m阶对称幂次L-函数的Dirichlet展开式的第n个正规化系数.本文中,我们给出了Σn0为一个正数.     

基于对称响应的无基准Lamb波损伤监测

兰姆(Lamb)波结构损伤监测是结构健康监测领域的研究热点.针对现有研究和应用中,基于基准响应的损伤监测方法受环境工况等条件的差异性影响问题,在分析Lamb波传播基本过程和损伤作用机理基础上,研究了基于对称响应分析的无基准Lamb波损伤监测方法.该方法通过对称布置压电阵列,实现对称响应信号的获取,进一步借助于皮尔逊相关...