基于递归最小二乘支持向量机的动态系统建模研究

针对递归最小二乘支持向量机的递归性易导致建模中偏微分方程组求解困难的问题,提出用解析法求解偏微分方程组,实现了完整的递归最小二乘支持向量机模型．首先分析了各参数的相关性,然后推导出偏微分方程的解析表达式并求解．仿真实例表明,在动态系统建模中,该模型的性能比常用的串并联模型以及现有不完整递归最小二乘支持向量机模型的精度更高、性能更好．     

Applying a novel extended Kalman filter to missile–target interception with APN guidance law: A benchmark case study

This paper considers the estimation of the target acceleration with unknown dynamics along with other states of a benchmark example of a nonlinear 2D missile–target engagement system in presence of model uncertainties and measurement noises. The objective is to implement the augmented proportional navigation (APN) guidance law for the missile–target interception to minimize the distance between the missile and the target. The estimated target acceleration can be treated as an unknown input to the nonlinear 2D missile–target engagement system. A novel analytical recursive approach referred to as extended Kalman filter with unknown inputs without direct feedthrough (EKF-UI-WDF) is derived with the weighted least squares estimation for an extended state vector including states and unknown inputs which can be any type of signals without prior information. By applying the proposed EKF-UI-WDF approach to a 2D missile–target interception control system, simulation results demonstrate that this approach is capable of (i) estimating the states and unknown input (target acceleration) well, and (ii) achieving more reasonable interception performance comparing with the traditional extended Kalman filter (EKF) approach.     

基于最小二乘支持向量机的函数拟合的研究

函数拟合通常要在有限的训练样本下对函数变量之间的关系做出预测,在实践中由于训练样本有限,并且训练样本本身存在噪音和孤立点,用传统的方法进行函数拟合的结果往往不能满足要求.本文主要利用最小二乘支持向量机对函数进行拟合.首先介绍了最小二乘支持向量机的工作原理,并对参数选择方法进行了研究,然后通过仿真实验对利用最小二乘支持向量机进行函数拟合的效果加以对比说明.     

基于模糊最小二乘支持向量机的软测量建模

将模糊隶属度概念引入最小二乘支持向量机,提出一种基于支持向量数据域描述的模蝴隶属度函数模型,将输入空间中的样本映射到一个高维的特征空间;然后根据其偏离数据域的程度赋予不同的隶属度．该方法提高了最小二乘支持向量机的抗噪声能力,尤其适用于未能完全揭示输入样本特性的情况．将提出的方法用于催化裂化分馏塔轻柴油凝固点的软测量建模,仿真结果表明,该模糊隶属度函数模型能够提高最小二乘支持向量机的预测精度．     

基于LSSVM的混沌时间序列的多步预测

结合相空间重构理论和统计学习理论，实现混沌时间序列的多步预测．采用擞熵率法求得最优嵌入维数和时延参数，重构系统相空间，用最小二乘支持向量机建立渑沌时间序列的多步预测模型，并与径向基函数网络预测模型比较．结果表明，所建立的模型能够捕捉到原混沌系统的动力学特征．前者的归一化均方根预测误差远小于径向基函数网络预测模型的预测误差，泛化能力较强．其预测效果较好．     

基于遗传算法和最小二乘支持向量机可靠性分配*

为了提高系统可靠性的精确快速分配,采用支持向量机对系统可靠性进行建模,采用逆向思维对系统可靠性进行分配;为了提高求解速度和鲁棒性,用最小二乘法对支持向量机进行算法优化,并用遗传算法对最小二乘支持向量机进行参数优化;为了提高分配精度,用三角模糊数进行模糊处理;最后针对某系统的可靠性,采用遗传算法优化和模糊处理的最小二乘支持向量机进行分配,并与神经网络和普通遗传算法优化的最小二乘支持向量机进行对比。结果表明,用遗传算法优化和模糊数处理的最小二乘支持向量机具有分配精度高,泛化能力强等优点。     

基于支持向量机的大样本回归算法比较研究

支持向量机的研究是当前人工智能领域的研究热点。基于支持向量机的大样本回归问题一直是一个非常具有挑战性的课题。最近,基于递归最小二乘算法,Engel等人提出了核递归最小二乘算法。文中基于块增量学习和逆学习过程,提出了自适应迭代回归算法。为了说明两种方法的性能,论文在训练速度、精度和支持向量数量等方面,对它们做了比较。模拟结果表明:核递归最小二乘算法所得到的支持向量个数比自适应迭代回归算法少,而训练时间比自适应迭代回归算法的训练时间长,训练和测试精度也比自适应迭代回归算法差。     

Internal model control based on a novel least square support vector machines for MIMO nonlinear discrete systems

To improve the robustness of the traditional inverse system method, the internal model control based on a novel least square support vector machines (LS-SVM) is proposed. The novel LS-SVM considers general errors that include noises of input variables and output variables as empirical errors. The data of original MIMO discrete system is exploited to approximate its inverse model by the novel LS-SVM. By cascading the inverse model and the original system to constitute a decoupling pseudo-linear system, the internal model control strategy is carried out to the pseudo-linear system to realize the effective control. Simulation validates that the novel LS-SVM used in the inverse system identification is effective and shows that the internal model control of nonlinear discrete systems has better robustness of anti-interference and parameters varying than that of the open-loop system only based on inverse control.     

回归型支持向量机的简化算法

针对支持向量机应用于函数估计时支持向量过多所引起的计算复杂性,提出一种简化算法,可以大幅度地减少支持向量的数量,从而简化其应用.采用简化算法还可以将最小平方支持向量机算法和串行最小化算法结合起来,达到学习效率高且生成的支持向量少的效果.     

A prior-knowledge input LSSVR metamodeling method with tuning based on cellular particle swarm optimization for engineering design

Engineering design is usually a daunting optimization task which often involving time-consuming, even computation-prohibitive process. To reduce the computational expense, metamodels are commonly used to replace the actual expensive simulations or experiments. In this paper, a new and efficient metamodeling method named prior-knowledge input least square support vector regression (PKI-LSSVR) is developed, in which samples from different levels of fidelity are incorporated to gain an accurate approximation with limited times of the high-fidelity (HF) expensive simulations. The low-fidelity (LF) output serves as a prior-knowledge of the real response function, and then is used as the input variables of least square support vector regression (LSSVR). When the corresponding HF response is gained, a function that maps the LF outputs to HF outputs is constructed via LSSVR. The predictive accuracy of LSSVR models is highly dependent on their learning parameters. Therefore, a novel optimization method, cellular particle swarm optimization (CPSO), is exploited to seek the optimal hyper-parameters for PKI-LSSVR in order to improve its generalization capability. To get a better optimization performance, a new neighborhood function is developed for CPSO where the global and local search is efficiently balanced by adaptively varied neighbor radius. Several numerical experiments and one engineering case verify the efficiency of the proposed PKI-LSSVR method. Sample quality merits including sample sizes and noise, and metamodel performance evaluation measures incorporating accuracy, robustness, and efficiency are considered.     

Support vector machines models for surface roughness prediction in CNC turning of AISI 304 austenitic stainless steel

In the present investigation, three different type of support vector machines (SVMs) tools such as least square SVM (LS-SVM), Spider SVM and SVM-KM and an artificial neural network (ANN) model were developed to estimate the surface roughness values of AISI 304 austenitic stainless steel in CNC turning operation. In the development of predictive models, turning parameters of cutting speed, feed rate and depth of cut were considered as model variables. For this purpose, a three-level full factorial design of experiments (DOE) method was used to collect surface roughness values. A feedforward neural network based on backpropagation algorithm was a multilayered architecture made up of 15 hidden neurons placed between input and output layers. The prediction results showed that the all used SVMs results were better than ANN with high correlations between the prediction and experimentally measured values.     

在线稀疏最小二乘支持向量机回归的研究

现有最小二乘支持向量机回归的训练和模型输出的计算需要较长的时间,不适合在线实时训练.对此,提出一种在线稀疏最小二乘支持向量机回归,其训练算法采用样本字典,减少了训练样本的计算量.训练样本采用序贯加入的方式,适合在线获取,并且该算法在理论上是收敛的.仿真结果表明,该算法具有较好的稀疏性和实时性,可进一步用于建模与实时控制等方面的研究.     

基于边界近邻的最小二乘支持向量机实现

最小二乘支持向量机采用最小二乘线性系统代替传统的支持向量即采用二次规划方法解决模式识别问题,能够有效地减少计算的复杂性。但最小二乘支持向量机失去了对支持向量的稀疏性。文中提出了一种基于边界近邻的最小二乘支持向量机,采用寻找边界近邻的方法对训练样本进行修剪,以减少了支持向量的数目。将边界近邻最小二乘支持向量机用来解决由1-a-r(one-against-rest)方法构造的支持向量机分类问题,有效地克服了用1-a-r(one-against-rest)方法构造的支持向量机分类器训练速度慢、计算资源需求比较大、存在拒分区域等缺点。实验结果表明,采用边界近邻最小二乘支持向量机分类器,识别精度和识别速度都得到了提高。     

Interest rate prediction: a neuro-hybrid approach with data preprocessing

The following research implements a differential evolution-based fuzzy-type clustering method with a fuzzy inference neural network after input preprocessing with regression analysis in order to predict future interest rates, particularly 3-month T-bill rates. The empirical results of the proposed model is compared against nonparametric models, such as locally weighted regression and least squares support vector machines, along with two linear benchmark models, the autoregressive model and the random walk model. The root mean square error is reported for comparison.     

基于- 范数约束的LSSVR 多核学习算法

针对核函数选择对最小二乘支持向量机回归模型泛化性的影响, 提出一种新的基于????- 范数约束的最小二乘支持向量机多核学习算法. 该算法提供了两种求解方法, 均通过两重循环进行求解, 外循环用于更新核函数的权值, 内循环用于求解最小二乘支持向量机的拉格朗日乘数, 充分利用该多核学习算法, 有效提高了最小二乘支持向量机的泛化能力, 而且对惩罚参数的选择具有较强的鲁棒性. 基于单变量和多变量函数的仿真实验表明了所提出算法的有效性.

     

A weighted LS-SVM approach for the identification of a class of nonlinear inverse systems

In this paper, a weighted least square support vector machine algorithm for identification is proposed based on the T-S model. The method adopts fuzzy c-means clustering to identify the structure. Based on clustering, the original input/output space is divided into several subspaces and submodels are identified by least square support vector machine (LS-SVM). Then, a regression model is constructed by combining these submodels with a weighted mechanism. Furthermore we adopt the method to identify a class of inverse systems with immeasurable state variables. In the process of identification, an allied inverse system is constructed to obtain enough information for modeling. Simulation experiments show that the proposed method can identify the nonlinear allied inverse system effectively and provides satisfactory accuracy and good generalization. Supported by the National Natural Science Foundation of China (Grant No. 60874013) and the Doctoral Project of the Ministry of Education of China (Grant No. 20070286001)     

A normal least squares support vector machine (NLS-SVM) and its learning algorithm

Least squares support vector machine (LS-SVM) is a successful method for classification or regression problems, in which the margin and sum square errors (SSEs) on training samples are simultaneously minimized. However, LS-SVM only considers the SSEs of input variable. In this paper, a novel normal least squares support vector machine (NLS-SVM) is proposed, which effectively considers the noises on both input and response variables. It introduces a two-stage learning method to solve NLS-SVM. More importantly, a fast iterative updating algorithm is presented, which reaches the solution of NLS-SVM with lower computational complexity instead of directly adopting the two-stage learning method. Several experiments on artificial and real-world datasets are simulated, in which the results show that NLS-SVM outperforms LS-SVM.     

新型SVM对时间序列预测研究

In this paper, we present a new support vector machines-least squares support vector machines (LS-SVMs). While standard SVMs solutions involve solving quadratic or linear programming problems, the least squaresversion of SVMs corresponds to solving a set of linear equations, due to equality instead of inequality constraints in the problem formulation. In LS-SVMs, Mercer condition is still applicable. Hence several type of kernels such aspolynomial, RBF's and MLP's can be used. Here we use LS-SVMs to time series prediction compared to radial basisfunction neural networks. We consider a noisy (Gaussian and uniform noise)Mackey-Glass time series. The resultsshow that least squares support vector machines is excellent for time series prediction even with high noise.     

惯性导航系统非线性初始对准的LS-SVM方法研究

由陀螺仪和加速度计等惯性传感器组成的惯性导航系统,在进入导航状态之前必须进行初始对准.根据支持向量机强大的非线性映射能力,建立了基于最小二乘支持向量机(LS-SVM)的捷联惯导系统非线性初始对准方法.LS-SVM避开了经典支持向量机求解时的复杂优化运算,通过求解一组线性方程组就可以得到唯一的全局最优解,所以算法的复杂度大大降低,能更好的满足工程应用中的实时性要求.针对方位初始失准角为大角度时的捷联惯导系统非线性误差模型进行仿真分析,并在相同条件下与卡尔曼滤波方法作比较,结果表明LS-SVM在初始对准中的有效性和可行性.     

变元可分离核函数对非线性支持向量分类机的影响

证明了变元可分离函数在Hilbert空间中满足Mercer定理的条件，为构造新的非线性支持向量分类机时选定核函数提供了一种新方法，并通过新方法构造的核函数与其它核函数构造的非线性支持向量分类机比较，得出了较好的结果。