递推阻尼最小二乘法的收敛性与稳定性

递推最小二乘法是参数辨识中最常用的方法,但容易产生参数爆发现象,因此对一种更稳定的辨识方法－－递推阻尼最小二乘法进行了收敛特性的分析,在使用算法之前先旭一化测量向量,结果表明,参数化距离收敛于一个零均值随机变量并且在持续激励条件下,适应增益矩阵的条件数有界。参数化距离的方差有 。     

等效系统参数辨识法在飞行品质评价中的应用

分析了等效系统参数辨识方法,采用最小二乘法与频域极大似然法求解先进飞机的低阶等效系统.通过计算,对两种辨识方法的优缺点进行了对比研究,并通过动态仿真验证了方法的有效性.最后依据参数辨识结果,对某型飞机的飞行品质进行了评估.     

非参数频响函数辨识的约束局部多项式法

对于线性系统中频响函数的估计问题,文章提出一种新的非参数辨识法-局部多项式法.与其它基于加窗策略的非参数辨识法相比较可知,在不使用周期输入激励信号下,局部多项式法在应用离散傅里叶变换时可有效地降低泄露误差的影响.将频响函数和泄露项围绕某中心频率处的窄窗展开成两个局部多项式模型,局部参数的估计可通过多个局部最小二乘问题来求解.当考虑相邻频率处多项式系数间的约束时,对局部多项式法做改进得到约束局部多项式法.改进后的约束局部多项式法通过多目标最小二乘准则来求解,并可降低频响函数估计的均方误差.最后用仿真算例验证文章辨识方法的有效性.     

残差自回归半参数模型的参数估计

研究了残差自回归半参数模型的参数估计,运用广义最小二乘法估计了参数部分．用随机模拟说明了运用广义最小二乘（GLSE）估计出的参数部分优于运用普通最小二乘法（OKSE）得到的估计．     

最小二乘法在地基土工参数获取中的应用

本文利用最小二乘的L-M方法建立了关于地基土工参数的优化计算模型,并基于MATLAB得出计算结果．从而证明利用最小二乘法可有效地获取土工参数．     

Hénon混沌系统的模糊广义预测控制与同步

针对Hénon混沌系统,本文给出了一种基于T-S模糊模型的混沌系统广义预测控制算法。该方法将模糊辨识和广义预测控制结合起来应用到Hénon混沌系统中。首先,应用T-S模糊模型对Hénon混沌系统进行辨识,模糊聚类法辨识模型的前件参数,递推最小二乘法辨识结论参数。基于辨识模型,采用广义预测控制算法对其进行控制,实现了系统的跟踪与同步。仿真结果表明,与其它算法相比,该算法能够保证系统输出快速、有效地跟踪设定值。     

基于自适应模糊聚类的T-S模糊辨识方法

针对模糊建模在进行结构辨识时需事先设定聚类数的问题,本文在改进模糊分割聚类算法的基础上,对算法中聚类数c给出优选方法,提出了参数自适应模糊聚类算法,并结合递推最小二乘法构建T-S模糊辨识算法。为了验证本文提出的模糊辨识方法的有效性,采用该算法对熟知的Box-Jenkins煤气炉数据和实际的电液位置伺服系统数据进行建模,结果显示该辨识方法具有较高的逼近精度和较好的泛化能力。     

助推偏最小二乘法（BPLS）及其应用

在生物统计以及数据挖掘中,分类预测是最基本的任务之一。本文将探讨一种新的方法-助推偏最小二乘法（BPLS）。它结合了一系列收缩的偏最小二乘模型,每个模型只有一个主成分。这种新方法和传统的偏最小二乘方法不同,它不需要选择一系列的偏最小二乘成分。只需要确定两个参数即可。通过对真实数据的训练,得以证明这种新方法比传统的偏最小二乘法在防止过度拟合方面有更好的表现,同时能够保证精确度。     

基于最小二乘法的空间坐标转换的非迭代算法

利用最小二乘法讨论三维空间的坐标转换问题,先对已知数据进行中心化处理使得坐标转换化为向量形式的最小二乘线性拟合问题,进而化为矩阵形式的最小二乘问题,最后得到法方程以及最小二乘解.如果已知数据量大且维数高,可通过奇异值分解确定相应的转换参数.和现有方法比较,方法的拟合过程不需迭代,简单易行.算例结果表明,拟合结果和原文数据吻合较好.     

回归函数的速归LS─权估计的强收敛性

本文讨论了把传统的最小二乘方法与非参数的权函数法结合起来所得回归函数的递归最小二乘—权估计（简记为ＬＳ—权估计）的强收敛性。     

Instructions for Authors

<正>Submission Authors must use LaTeX for typewriting,and visit our website www.actamath.com to submit your paper.Our address is Editorial Office of Acta Mathematica Sinica,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,P.R.China.     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

正August 10-14,2015Beijin,China The International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

FRACTIONAL INTEGRALS OF THE WEIERSTRASS FUNCTIONS： THE EXACT BOX DIMENSION

The present paper investigates the fractal structure of fractional integrals of Weierstrass functions. The ezact box dimension for such functions many important cases is established. We need to point out that, although the result itself achieved in the present paper is interesting, the new technique and method should be emphasized. These novel ideas might be useful to establish the box dimension or Hausdorff dimension (especially for the lower bounds) for more general groups of functions.     

English Series

正1 Aims and Scope Acta Mathematicae Applicatae Sinica(English Series)is a quarterly journal established by the Chinese Mathematical Society.The journal publishes high quality research papers from all branches of applied mathematics,particularly welcomes those from partial differential equations,computational mathematics,applied probability,mathematical finance,statistics,dynamical systems,optimization and management science.     

CHINESE ANNALS OF MATHEMATICS SERIES B Volume 35 · 2014 TOTAL CONTENTS

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Congruences,ideals and annihilators in standard QBCC-algebras

We characterize congruence lattices of standard QBCC-algebras and their connection with the congruence lattices of congruence kernels. Work on the paper was supported by Council of Czech Government No J14/98:153100011.     

A decomposition of continuity via ideals

A new class of sets in ideal topological spaces is introduced and using these sets, a decomposition of continuity is given.      

When a compact (countably compact) set is closed. II

We obtain (a) necessary and sufficient conditions and (b) sufficient conditions for a compact (countably compact) set to be closed in products (sequential products) and subspaces (sequential subspaces) of normal spaces. As a consequence of these, sufficient conditions are obtained for (i) the closedness of arbitrary (countable) union of closed sets and (ii) the equality of the union of the closures and the closure of the union of arbitrary (countable) families of sets in these spaces. It is also shown that these results do not hold for quotients of even T ₄,-spaces.     

ASYMPTOTIC BEHAVIOR OF ECKHOFF＇S METHOD FOR FOURIER SERIES CONVERGENCE ACCELERATION

The current paper considers the problem of recovering a function using a limited number of its Fourier coefficients. Specifically, a method based on Bernoulli-like polynomials suggested and developed by Krylov, Lanczos, Gottlieb and Eckhoff is examined. Asymptotic behavior of approximate calculation of the so-called ＂jumps＂ is studied and asymptotic L2 constants of the rate of convergence of the method are computed.