广义输出误差模型的两阶段最小二乘递推辨识

在有色噪声干扰系统中有一类系统, 它具有广义输出误差模型(OEARMA), 本文提出一类广义输出误差模型的 两阶段递推最小二乘参数估计算法. 该算法基本思想是结合辅助模型辨识思想和分解技术, 将系统分解成两个子系统, 每个子系统包含一个参数向量. 借助基于辅助模型和递推最小二乘理论, 用辅助模型的输出代替辨识模型信息向量中未 知中间变量, 用估计残差代替信息向量中不可测噪声项, 从而可以运用递推辨识思想来估计系统所有参数. 该算法具有 较高的计算效率, 仿真例子说明提出算法的有效性.     

Interval analysis using least squares support vector fuzzy regression

A least squares support vector fuzzy regression model(LS-SVFR) is proposed to estimate uncertain and imprecise data by applying the fuzzy set principle to weight vectors.This model only requires a set of linear equations to obtain the weight vector and the bias term,which is different from the solution of a complicated quadratic programming problem in existing support vector fuzzy regression models.Besides,the proposed LS-SVFR is a model-free method in which the underlying model function doesn’t need to be predefined.Numerical examples and fault detection application are applied to demonstrate the effectiveness and applicability of the proposed model.     

基于辅助模型的递推增广最小二乘辨识方法

针对有色噪声干扰的输出误差滑动平均系统, 将辅助模型与递推增广最小二乘算法相结合: 用辅助模型的输出代替辨识模型信息向量中的未知真实输出项, 用估计残差代替信息向量中的不可测噪声项, 从而提出了基于辅助模型的递推增广最小二乘辨识方法. 为了展示所提方法的特点, 文中还给出了经过模型变换的递推增广最小二乘算法. 理论分析和仿真研究表明, 提出的方法原理简单、计算量小, 可以给出高精度参数估计, 且能够用于在线辨识.     

Fuzzy least squares regression model based of weighted distance between fuzzy numbers

A new distance ND1 between fuzzy numbers based on an averaged representative of a fuzzy number (Weighting Average Based on Levels, WABL) is proposed. Based on this distance a new least squares regression model is proposed. The proposed model is studied for a broad class of fuzzy numbers and class of functions the membership of which is formed on the basis of the template μ_[.](x) = max(0.1 ? |x|^s).     

Asymptotic properties of least squares estimation with fuzzy observations

This paper deals with the asymptotic properties of the least squares estimators for fuzzy linear regression models with fuzzy triangular input-output and random error terms. The asymptotic normality and strong consistency of the fuzzy least squares estimator (FLSE) are investigated; a confidence region based on a class of FLSEs is proposed; the asymptotic relative efficiency of FLSEs with respect to the crisp least squares estimators is also provided and a numerical example is given. Some simulation results are also presented to illustrate the behavior of FLSEs.     

Approximate aggregation of Markovian models using alternating least squares

State based analysis of Markovian models is faced with the problem of state space explosion. To handle huge state spaces often compositional modeling and aggregation of components are used. Exact aggregation resulting in exact transient or stationary results is only possible in some cases, when the Markov process is lumpable. Therefore approximate aggregation is often applied to reduce the state space. Several approximate aggregation methods exist which are usually based on heuristics.This paper presents a new aggregation approach for Markovian components which computes aggregates that minimize the difference according to some algebraically defined function which describes the difference between the component and the aggregate. If the difference becomes zero, aggregation is exact, which means that component and aggregate are indistinguishable in the sense that transient and stationary results in any environment are identical. For the computation of aggregates, an alternating least squares approach is presented which tries to minimize the norm-wise difference between the original component and the aggregate. Algorithms to compute aggregates are also introduced and the quality of the approximation is evaluated by means of several examples.     

Decomposition-based recursive least squares identification methods for multivariate pseudo-linear systems using the multi-innovation

This paper studies the parameter estimation algorithms of multivariate pseudo-linear autoregressive systems. A decomposition-based recursive generalised least squares algorithm is deduced for estimating the system parameters by decomposing the multivariate pseudo-linear autoregressive system into two subsystems. In order to further improve the parameter accuracy, a decomposition based multi-innovation recursive generalised least squares algorithm is developed by means of the multi-innovation theory. The simulation results confirm that these two algorithms are effective.     

一种改进的加权最小二乘相位展开方法研究

相位展开是光栅投影廓术中的一个关键步骤。对加权最小二乘相位展开算法的原理进行了介绍,利用小波多分辨率特性对Picard迭代算法进行了改进。改进的算法将误差分解为低频和高频成分,对它们分别进行Picard迭代来提高收敛速度。实验结果证明：改进后的算法具有收敛速度快,抗噪能力强等优点。     

The Koul-Susarla-Van Ryzin and weighted least squares estimates for censored linear regression model: A comparative study

The Koul-Susarla-Van Ryzin (KSV) and weighted least squares (WLS) methods are simple to use techniques for handling linear regression models with censored data. They do not require any iterations and standard computer routines can be employed for model fitting. Emphasis has been given to the consistency and asymptotic normality for both estimators, but the finite sample performance of the WLS estimator has not been thoroughly investigated. The finite sample performance of these two estimators is compared using an extensive simulation study as well as an analysis of the Stanford heart transplant data. The results demonstrate that the WLS approach performs much better than the KSV method and is reliable for use with censored data.     

基于最小二乘和最小投影距离的车牌倾斜校正

在车牌图像的采集过程中,经常会有车牌倾斜的现象发生,这种倾斜给后续的字符分割和字符识别造成了很多不利影响。为此,文中提出了一种基于最小二乘和最小投影距离的车牌倾斜校正方法。该方法将车牌倾斜分成水平倾斜和垂直倾斜两部分:对于水平倾斜,首先对二值化后的车牌去边框和铆钉,再对车牌利用最小二乘拟合直线求取倾斜角;而对于垂直倾斜,则引入分块查找法来降低查找最小投影距离的执行次数,从而提高算法的执行效率。实验结果表明:该算法简单实用,能够准确地对车牌进行校正。     

PLS模糊多模型建模方法在航煤干点估计中的应用研究

针对常压塔复杂工况下的航煤干点估计困难的问题,本文提出一种基于PLS模糊多模型软测量建模方法:(FuzzyMulti-model based on PLS,FMM-PLS)。该方法:采用减法c-均值聚类进行数据划分,按隶属度最大原则,合理划分子空间,确定予空间个数为3个,然后利用PLS方法:建立3个子模型,并对各子模型的输出进行隶属度加权预测输出值。同时,也建立PLS、QPLS、RBF-PLS单模型,并与提出的FMM-PLS方法:相比较。PLS、QPLS、RBF-PLS和FMM-PLS的最大误差分别为4.9541、4.6282、4.7517、3.8040;均方根误差分别为1.8599、1.7025、1.7381、1.5327。研究结果:表明,与PLS、QPLS、RBF-PLS相比,在航煤干点的估计中本文提出的FMM-PLS方法:预测精度更高,泛化性能更好。     

Algorithms for recursive/semi-recursive bias-compensating least squares system identification within the errors-in-variables framework

Algorithms for the recursive/semi-recursive estimation of the system parameters as well as the measurement noise variances for linear single-input single-output errors-in-variables systems are considered. Approaches based on three offline techniques are presented: namely, the bias eliminating least squares, the Frisch scheme and the extended bias compensating the least squares method. Whilst the underlying equations used within these approaches are identical under certain design choices, the performances of the recursive/semi-recursive algorithms are investigated via simulation, in order to determine the most suitable technique for practical applications.     

基于非线性最小二乘原理的原木端面识别算法

为了更好地进行原木端面识别,研究了一种基于非线性最小二乘原理的椭圆拟合算法。椭圆拟合的精度在很大程度上受初始值的影响,该方法通过对目标图像的边界点进行距离计算,得到了适当的初始值;之后运用最小二乘原理,计算边界点到拟合椭圆之间欧式距离的最小值,确定最优拟合椭圆的长短轴参数。实验结果表明,提出的算法在原木端面的识别中,具有良好的拟合精度和适用性。     

基于最小二乘模糊支持向量机的基因分类研究*

随着大量基因表达数据的涌现,把海量的数据划分成数量相对较少的组,有助于提取对生理学和医药学等有价值的生物信息。基因分类技术能够很好地处理和分析这些基因数据。提出了一种应用于基因分类的模糊最小二乘支持向量机方法,通过设置模糊隶属度改变分类中样本的贡献属性。该方法不仅考虑了样本与类中心点的距离关系,还充分考虑样本与样本之间的关系,减弱噪声或野值样本对分类的影响。采用美国威斯康星乳腺癌数据和皮马印第安人糖尿病数据进行实验检测,均取得了很好的效果。     

An iterative algorithm for a least squares solution of a matrix equation

In this article, we propose an iterative algorithm to compute the minimum norm least-squares solution of AXB+CYD=E, based on a matrix form of the algorithm LSQR for solving the least squares problem. We then apply this algorithm to compute the minimum norm least-squares centrosymmetric solution of min _X ‖AXB?E‖ _F . Numerical results are provided to verify the efficiency of the proposed method.     

利用偏最小二乘法的一种变量筛选法

根据偏最小二乘法(PLS)建模中的回归系数等一些信息,筛选原始自变量,在不损失模型预报能力的前提下,除去冗余的或影响不大的一些原始自变量,使模型更简单。本研究中找到了用于删除变量的一种新判据,计算简单,使用效果好。研究结果表明,利用PL3法得到的删除变量的新判据筛选变量是一种非常实用和有效的变量筛选方法,该法非常适合处理海量数据或变量数很大的建模问题,可使最终所得的模型中变量数大大减少,使模型大大简化,因而便于分析和解决实际问题。在处理中药指纹图谱数据时,与传统的算法比较,模型得到了大大简化。     

A simple method for identification of singleton fuzzy models

This article presents a simple method for constructing a singleton fuzzy model from a given set of input/output data. The method consists of three computational steps: the initial phase, the growth phase, and the optional refining phase. The universe of discourse and two linguistic terms for each input variable and a rule base are established during the initial phase. Additional linguistic terms and rules are then appended sequentially during the growth phase to modify the model structure and to elevate the performance. During the optional refining phase the overall modelling performance can be further improved by adjusting the singleton outputs of the rule set in the sense of least squares. The proposed identification method can simultaneously provide an appropriate model structure and parameters without any time-consuming optimisation. Several numerical examples demonstrate the effectiveness of the proposed identification method.     

基于空间距离的快速模糊C均值聚类算法

针对传统的模糊C均值聚类算法在进行图像分割时对孤立点、噪声点敏感性较强,聚类耗时随图像变大而快速增长等缺陷,基于临近元素空间距离的模糊C均值聚类算法即SFGFCM算法,采用核化的空间距离公式,计算出空间临近像素与考察像素的相似度Sij,然后用邻近像素灰度加权和计算出邻近信息制约图像,并进一步在邻近信息制约图像的灰度级统计的基础上进行聚类。该算法考察了临近像素灰度和位置等信息,并且它们之间取得了很好的平衡;不仅表现出较强的鲁棒性且很好地保留了原图像边缘等细节信息,提高了聚类精度,同时大大缩短了大幅图像的聚类时间。通过在合成图像、医学图像及自然图像上的大量实验,与传统算法对比该算法聚类性能明显提高,在图像分割上体现出了较好的分割效果。     

l1鲁棒辨识: 最小二乘算法及试验设计

现有的l¹鲁棒辨识方法依赖于观测数据自的起始时刻因而不能用来辨识时变系统, 针对该问题基于最小二乘法提出了一种l¹鲁棒辨识算法. 该算法与观测窗的起始时刻无关, 可用于时变系统的辨识, 证明了当试验输入为持续激励信号时所提出的算法为本质最优算法, 进一步证明了周期持续激励序列为最优试验信号, 并给出了辨识误差紧界的计算公式. 最后利用提出的算法研究了慢时变系统的l¹鲁棒辨识问题.     

总体最小二乘辨识陀螺加速度计误差模型研究

开展了陀螺加速度计在三轴转台上的测试试验,由于三轴转台给陀螺加速度计提供的输入加速度引入设备误差,需采用总体最小二乘法对试验数据进行辨识。将最小二乘法应用于辨识陀螺加速度计在三轴台上的测试试验,主要是消除了测试设备的误差对陀螺加速度计精度的影响,与最小二乘法辨识结果进行比较,总体二乘法的辨识结果要优于最小二乘法,提高了陀螺加速度计的辨识精度。