基于小波分解的非线性系统多模型自适应控制

提出了一种改进的基于小波分解的非线性系统辨识算法,利用小波函数的逼近能力在线辨识被控对象的非线性项.针对基于小波分解的辨识算法缺乏预测能力,提出了根据线性鲁棒自适应控制器提供的当前控制信息预测未来的非线性项值新方法,并结合多模型方法,根据所定义的切换指标自动切换到当前最优控制器.仿真结果表明,改进的基于小波分解的辨识算法能够有效逼近非线性系统,基于小波分解的非线性系统多模型自适应控制方法改善了系统性能,随着系统运行跟踪误差明显减小,说明了该方法的有效性和可行性.     

非线性系统辨识方法研究

讨论了利用小波神经网络对非线性系统辨识的新方法。在辨识过程中,为了提高小波神经网络对非线性系统的辨识性能,使用一种改进粒子群优化算法对BP小波神经网络参数进行训练,求得最优值,达到对非线性系统辨识目的。在数值仿真中,与采用标准粒子群优化算法相比,结果显示了提出的方法在收敛性和稳定性等方面均得到了明显的改善。     

一种非线性模型的在线辨识方法

提出一种用于非线性模型在线辨识的模糊算法。该算法将非线性输入输出系统用时变线性系统模型来拟和。并把此非线性系统模型表示成模糊模型的形式，用在线调节模糊模型的方法来辨识时变线性模型的相关参数。在以往的模糊辨识方法中，均未给出在线调整非线性系统的模糊辨识算法。将递推模糊聚类方法与卡尔曼滤波法用于在线调整模糊模型参数，仿真算例表明了此算法的有效性与良好的实用价值。     

基于正交小波网络的非线性系统辨识

本文介绍了一种基于正交小波网络(OWN)的非线性系统的辨识方法。阐述了正交小波网络理论，提供了用正交小波网络进行辨识的方法．并对高炉煤粉喷吹系统的非线性系统进行了动态辨识，结果表明此方法是可行的。     

基于神经网络的非线性气动弹性系统辨识

由于气动弹性系统的非线性和不确定性的存在,传统的辨识方法在工程中难以满足。针对这种情况提出了一种模糊小波神经网络(FWNN)辨识方法。首先,采用区间2型模糊逻辑系统和小波神经网络结合构建FWNN网络结构,能够较好地逼近具有不确定性的非线性AE系统;然后,考虑到辨识的快速性和准确性,系统采用一组模糊IF-THEN规则,对模糊后件采用单隐层小波神经网络结构;参数学习采用基于Lyapunov稳定性的滑模学习算法,保证系统存在参数不确定的情况下,辨识误差能更快地收敛。最后,对结构非线性二元翼段进行仿真研究,验证了该模型的有效性。     

时变非线性分布参数控制系统的小波辨识算法

基于正交函数逼近理论,在Haar小波正交规范基的基础上,总结并推导出了其积分运算矩阵、微分运算矩阵、乘积运算矩阵及其运算性质,并应用于一类时变非线性分布参数系统的辨识.借助于正交小波函数逼近方法对分布参数系统进行辨识,经正交小波逼近变换转化为代数矩阵方程,因此该方法可以不考虑初始条件和边界条件,较其他辨识方法要简单得多.该算法简单、计算量小、简化了分布参数系统辨识的求解过程,应用在分布参数系统辨识中不失为一种有效的分析方法.     

小波神经网络学习的结构风险最小化方法

针对大噪声、小样本情形下神经网络学习的外推能力弱这一突出的问题，根据统计学习理论中结构风险最小化准则的基本原理，提出了一种基于小波神经基元频率谱分布的小波神经网络阵列结构和基于小波多分辨逼近、综合风险分析的小波网络学习算法．该方法充分发挥了小波神经网络的优点，理论基础可靠，实际意义明确，算法实现简便，自适应性强．仿真实验结果和应用实例说明了该方法对于非线性系统在线辨识的有效性，同时也为统计学习理论的工程应用提供了新的途径．     

基于模糊分类的模糊神经网络辨识方法及应用

基于改进的T-S模型，提出一种自适应模糊神经网络模型(AFNN)，给出了网络的连接结构和学习算法。基于竞争学习算法的模糊分类器确定系统的模糊空间和模糊规则数，并得出每个样本对每条规则的适用程度。利用卡尔曼滤波算法在线辨识删的后件参数。AFNN结构简洁，逼近能力强，能够显著提高辨识精度，并且在线辨识的模糊模型简单有效。将该AFNN用于非线性系统的模糊辨识和化工过程连续搅拌反应器(CSTR)的建模中，仿真结果验证了该方法的有效性，表明该网络能够实现复杂非线性系统的建模，而且建模精度高、收敛速度快。可当作复杂系统建模的一种有效手段。     

多模型小波网络非线性动态系统辨识

由于许多复杂的工业系统具有非线性特性，难以建立确切的数学模型，因此提出用 多模型小波网络辨识非线性动态系统，并给出了辨识结构和训练算法．仿真实验比较了多模型小波网络与单小波网络在辨识非线性系统时性能上的差异，验证了该方法收敛速度快，抗干扰能力强，具有较高的逼近精度．     

用非均匀分布样本训练多分辨小波网络的新方法

本文基于小波网格系提出一种用非均匀分布样本训练MN的新方法,避免了当样本分布不均匀时难以发挥MWN优点的缺陷;同时给出了该算法的逼近精度分析.该方法的最大特点是:计算简单,便于在线应用.最后用于辨识非线性动态系统,仿真结果验证了该方法的可行性和有效性.     

Wavelet networks for nonlinear system modeling

This study presents a nonlinear systems and function learning by using wavelet network. Wavelet networks are as neural network for training and structural approach. But, training algorithms of wavelet networks is required a smaller number of iterations when the compared with neural networks. Gaussian-based mother wavelet function is used as an activation function. Wavelet networks have three main parameters; dilation, translation, and connection parameters (weights). Initial values of these parameters are randomly selected. They are optimized during training (learning) phase. Because of random selection of all initial values, it may not be suitable for process modeling. Because wavelet functions are rapidly vanishing functions. For this reason heuristic procedure has been used. In this study serial-parallel identification model has been applied to system modeling. This structure does not utilize feedback. Real system outputs have been exercised for prediction of the future system outputs. So that stability and approximation of the network is guaranteed. Gradient methods have been applied for parameters updating with momentum term. Quadratic cost function is used for error minimization. Three example problems have been examined in the simulation. They are static nonlinear functions and discrete dynamic nonlinear system.     

Two Types of Haar Wavelet Neural Networks for Nonlinear System Identification

Since wavelet transform uses the multi-scale (or multi-resolution) techniques for time series, wavelet transform is suitable for modeling complex signals. Haar wavelet transform is the most commonly used and the simplest one. The Haar wavelet neural network (HWNN) applies the Harr wavelet transform as active functions. It is easy for HWNN to model a nonlinear system at multiple time scales and sudden transitions. In this paper, two types of HWNN, feedforward and recurrent wavelet neural networks, are used to model discrete-time nonlinear systems, which are in the forms of the NARMAX model and state-space model. We first propose an optimal method to determine the structure of HWNN. Then two stable learning algorithms are given for the shifting and broadening coefficients of the wavelet functions. The stability of the identification procedures is proven.     

非线性系统辨识方法的新进展

对现有的非线性系统辨识方法进行了简要综述。介绍了多层递阶辨识方法，以及把神经网络、模糊逻辑、遗传算法等知识应用于非线性系统辨识而得到的一些新型辨识方法，最后慨括了非线性系统辨识未来的发展方向。     

Using wavelet network in nonparametric estimation

Wavelet networks are a class of neural networks consisting of wavelets. In this paper, algorithms for wavelet network construction are proposed for the purpose of nonparametric regression estimation. Particular attentions are paid to sparse training data so that problems of large dimension can be better handled. A numerical example on nonlinear system identification is presented for illustration.     

基于能量密度的小波神经网络

本文提出了基于能量密度构造单隐层前向小波网络用以逼近复杂非线性函数。在时频定位分析的基础上，引入了能量密度的概念，用其作为选择小波元的标准。在本文中给出了网络构造算法及相应的学习算法，并与其它小波网及ＢＰ网进行了比较。实验结果证明了该方法是可行的，且具有小波元数目相对较少、学习收敛速度快等特点，并就其在实际应用中应注意的问题提出了我们的观点。     

A modified adaptive IIR filter design via wavelet networks based on Lyapunov stability theory

In this paper, we present a wavelet network IIR filtering system satisfying asymptotic stability in the sense of Lyapunov unlike many other gradient descent algorithms based adaptive filtering systems. The proposed system also carries the advantages of the time-frequency specific properties of wavelet networks embedded into the proposed filter dynamics. Two experiments for system identification problems corresponding to the infinite impulse response filter design are proposed. The results verified that the proposed wavelet network infinite impulse response adaptive filtering system not only performs better than gradient descent based algorithms but also performs as good as other stability theory based optimization algorithms.     

NARX model based nonlinear dynamic system identification using low complexity neural networks and robust H∞ filter

This paper proposes NARX (nonlinear autoregressive model with exogenous input) model structures with functional expansion of input patterns by using low complexity ANN (artificial neural network) for nonlinear system identification. Chebyshev polynomials, Legendre polynomials, trigonometric expansions using sine and cosine functions as well as wavelet basis functions are used for the functional expansion of input patterns. The past input and output samples are modeled as a nonlinear NARX process and robust H_∞ filter is proposed as the learning algorithm for the neural network to identify the unknown plants. H_∞ filtering approach is based on the state space modeling of model parameters and evaluation of Jacobian matrices. This approach is the robustification of Kalman filter which exhibits robust characteristics and fast convergence properties. Comparison results for different nonlinear dynamic plants with forgetting factor recursive least square (FFRLS) and extended Kalman filter (EKF) algorithms demonstrate the effectiveness of the proposed approach.     

An expert system based on wavelet decomposition and neural network for modeling Chua’s circuit

This paper presents an expert system based on wavelet decomposition and neural network for modeling and simulation of Chua’s circuit which is used for chaos studies. The problems which arise in modeling Chua’s circuit by neural networks are high structural complexity and slow and difficult training. With this proposed method a new solutions is produced to solve these problems. Wavelet decomposition is used for new useful feature extracting from input signal and neural network is used for modeling. Test results of proposed wavelet decomposition and neural network model are compared with test results of neural network model. Desired performance is provided by this new model. Test results showed that the suggested method can be used efficiently for modeling nonlinear dynamical systems.     

基于鲁棒小波网络的非线性系统辨识

分析了传统小波网络的不足,同时考虑到实际中学习样本可能被非高斯白噪声干扰的情况,提出用于辨识非线性系统的鲁棒正交小波网络,并对辨识精度和收敛性进行了分析。理论分析和仿真研究表明,该文提出的方法是有效的。     

基于小波网络的实时稳定器研究

提出一种应用小波神经网络进行动态实时调整侍统电力系统稳定器参数的设计方法。由于小波神经网络所具有的非线性逼近能力及良好的时频分析能力，系统能精确地辨识动态特性，映射更复杂的控制策略。仿真结果表明小波网络电力系统稳定器比传统电力系统稳定器更有效。