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．     

基于小波网络的动态系统辨识方法及应用*

本文介绍了一种多输入非线性动态系统辨识算法，基于该算法的非线性辨识系统成功用于局部地区短时暴雨的预报。在这个系统中我们采用一种小波网络来追踪非线性系统的动态性，用一种基于小波逼近的非参数估计方法用于系统的状态空间模型的辨识中。从实验结果可看出，与传统的神经网络方法相比，该系统在速度、可靠性以及精确度上都有了很大的提高。     

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.     

基于小波逼近和尺度变换的非参数辨识方法

提出一种以非正交小波为基函数并应用小波多尺度分析的系统脉冲响应辨识方法，该方法以小波级数的形式逼近脉冲响应过程．从理论上证明了经小波尺度变换后系统随机噪声的方差值减小，即噪声得到有效的抑制，从而大大提高了辨识精度．应用实例验证了所得结果的正确性和算法的实用性．     

多自由度非线性系统动态参数化模型建模方法研究

针对多自由度非线性系统的动态模型辨识问题,基于NARX(Non-linear Autoregressive with Exogenous inputs)模型的建模方法,考虑系统的物理设计参数,建立非线性系统动态参数化模型.首先,根据系统输入、输出数据建立系统不同参数下的NARX模型,并通过EFOR(Extended Forward Orthogonal Regression)算法对不同参数下NARX模型进行修正,以统一辨识得到的系统模型结构.随后,建立NARX模型系数与物理设计参数间的函数关系,得到多自由度非线性系统的动态参数化模型.以单输入、单输出两自由度非线性系统为例,根据数值仿真结果,对系统的动态参数化模型建模过程进行说明.最后,以带非线性涂层阻尼的悬臂梁作为试验对象,建立其动态参数化模型以反映其动力学特性.试验结果表明,非线性系统动态参数化模型能准确预测多自由度非线性系统的输出响应,为非线性系统的分析与优化设计提供了理论基础.     

基于小波网络的一类非线性系统稳定最小方差控制

研究一类非线性系统的最小方差控制．将非线性系统等价表示为时变线性系统，利用小波网络的非线性逼近特性在线辨识时变系数，利用改进的投影算法在线调整小波网络的权值；在此基础上设计了非线性系统的最小方差控制器，并分析了闭环控制系统的稳定性．仿真结果表明了该算法的有效性．     

离散非线性系统Worst-Case辨识--小波逼近法

利用小波逼近的软阈（Ｓｏｆｔ－Ｔｈｒｅｓｈｏｌｄｉｎｇ）方法，研究了离散非线性系统的Ｗｏｒｓｔ－Ｃａｓｅ辨识问题．证明了该算法在Ｗｏｒｓｔ－Ｃａｓｅ误差下的拟最优性和光滑性；估计了该算法的Ｗｏｒｓｔ－Ｃａｓｅ误差：给出了存在鲁棒收敛的辨识算法的充要条件；最后，证明了小波网逼近算法是鲁棒收敛的．     

一种基于小波的模糊建模方法

为克服一般Takagi-Sugeno模糊模型的局限性,提出了一种新的用于复杂系统建模的模糊模型．理论分析表明该模型可表示任何一个紧集上的连续函数．该模型的一个显著特点是,模糊模型的输入输出关系与使用特殊母波函数的小波变换的形式相同．基于该性质,可方便地运用小波变换理论确定模糊模型的结构并初始化模型参数．本文详细地介绍了辨识该模糊模型的算法．通过对一个复杂非线性系统的建模并与以前的结果进行比较,验证了本文方法的有效性．     

非整数阶系统频域辨识的递推最小二乘算法

非整数阶系统辨识方法是建立非整数阶系统模型的一种重要工具．本文提出了一种非整数阶系统频域辨识的最小二乘递推算法．给出了算法的详细推导，并用已知系统验证了算法的有效性．结果表明该算法是整数阶系统辨识的最小二乘递推算法的推广．使用此算法，不但能辨识整数阶系统，还能辨识非整数阶系统．     

基于非线性多参数模型的软件老化检测

提出了一种软件系统的非线性有源自回归(Nonlinear AutoRegressive models with eXogenous Inputs,NARX)网络模型的老化检测方法。解决了目前软件老化方法未考虑多变量间关联性及历史数据的延迟影响的问题。该方法首先通过对实验采集的HelixServer-VOD服务器性能数据进行主成分分析,确定网络的输入维数,根据AIC准则确定最佳模型阶数,最终选取合理的网络模型结构;使用已知的未老化状态样本对NARX网络进行训练,建立系统的辨识模型;然后运用序贯概率比检验(Sequential Probability Ratio Test,SPRT)对NARX辨识模型的残差进行假设检验,判断系统的老化状态。实验分析表明,基于NARX网络模型的故障检测方法能够有效地应用于软件老化的检测。     

A unified wavelet-based modelling framework for non-linear system identification: the WANARX model structure

A new unified modelling framework based on the superposition of additive submodels, functional components, and wavelet decompositions is proposed for non-linear system identification. A non-linear model, which is often represented using a multivariate non-linear function, is initially decomposed into a number of functional components via the well-known analysis of variance (ANOVA) expression, which can be viewed as a special form of the NARX (non-linear autoregressive with exogenous inputs) model for representing dynamic input–output systems. By expanding each functional component using wavelet decompositions including the regular lattice frame decomposition, wavelet series and multiresolution wavelet decompositions, the multivariate non-linear model can then be converted into a linear-in-the-parameters problem, which can be solved using least-squares type methods. An efficient model structure determination approach based upon a forward orthogonal least squares (OLS) algorithm, which involves a stepwise orthogonalization of the regressors and a forward selection of the relevant model terms based on the error reduction ratio (ERR), is employed to solve the linear-in-the-parameters problem in the present study. The new modelling structure is referred to as a wavelet-based ANOVA decomposition of the NARX model or simply WANARX model, and can be applied to represent high-order and high dimensional non-linear systems.     

Intelligent non-linear modelling of an industrial winding process using recurrent local linear neuro-fuzzy networks

This study deals with the neuro-fuzzy (NF) modelling of a real industrial winding process in which the acquired NF model can be exploited to improve control performance and achieve a robust fault-tolerant system. A new simulator model is proposed for a winding process using non-linear identification based on a recurrent local linear neuro-fuzzy (RLLNF) network trained by local linear model tree (LOLIMOT), which is an incremental tree-based learning algorithm. The proposed NF models are compared with other known intelligent identifiers, namely multilayer perceptron (MLP) and radial basis function (RBF). Comparison of our proposed non-linear models and associated models obtained through the least square error (LSE) technique (the optimal modelling method for linear systems) confirms that the winding process is a non-linear system. Experimental results show the effectiveness of our proposed NF modelling approach.     

Non-linear system modelling based on non-parametric identification and linear wavelet estimation of SDP models

This paper describes a data-based approach to the identification and estimation of non-linear dynamic systems which exploits the concept of a state dependent parameter (SDP) model structure. The major attractive features of the proposed approach are: (1) the initial non-parametric identification of the non-linear system structure using an SDP algorithm based on recursive fixed interval smoothing; (2) a compact parameterization of this initially identified model structure via a linear wavelet functional approximation; and (3) final optimized model structure selection using the predicted residual sums of squares (PRESS) statistic, prior to final parametric optimization using this optimized, parsimonious structure. Two simulation examples are used to demonstrate the proposed approach.     

Non-linear system identification using wavelet multiresolution models

A new methodology for identifying non-linear NARMAX models, from noise corrupted data, is introduced based on semi-orthogonal wavelet multiresolution approximations. An adaptive model sequencing strategy is introduced to infer model complexity from the data while reducing computational costs. This is used in conjunction with an iterative orthogonal-forward-regression routine coupled with model validity tests to identify sparse but accurate wavelet series representations of non-linear processes. Experimental data from two real systems, a liquid level system and from a civil engineering structure are used to illustrate the effectiveness of the new identification procedure.     

A new class of wavelet networks for nonlinear system identification

A new class of wavelet networks (WNs) is proposed for nonlinear system identification. In the new networks, the model structure for a high-dimensional system is chosen to be a superimposition of a number of functions with fewer variables. By expanding each function using truncated wavelet decompositions, the multivariate nonlinear networks can be converted into linear-in-the-parameter regressions, which can be solved using least-squares type methods. An efficient model term selection approach based upon a forward orthogonal least squares (OLS) algorithm and the error reduction ratio (ERR) is applied to solve the linear-in-the-parameters problem in the present study. The main advantage of the new WN is that it exploits the attractive features of multiscale wavelet decompositions and the capability of traditional neural networks. By adopting the analysis of variance (ANOVA) expansion, WNs can now handle nonlinear identification problems in high dimensions.     

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。     

Term and variable selection for non-linear system identification

The purpose of variable selection is to pre-select a subset consisting of the significant variables or to eliminate the redundant variables from all the candidate variables of a system under study prior to model term detection. It is required that the selected significant variables alone should sufficiently represent the system. Generally, not all the model terms, which are produced by combining different variables, make an equal contribution to the system output and terms, which make little contribution, can be omitted. A parsimonious representation, which contains only the significant terms, can often be obtained without the loss of representational accuracy by eliminating the redundant terms. Based on these observations, a new variable and term selection algorithm is proposed in this paper. The term detection algorithm can be applied to the general class of non-linear modelling problems which can be expressed as a linear-in-the-parameters form. The variable selection procedure is based on locally linear and cross-bilinear models, which are used together with the forward orthogonal least squares (OLS) and error reduction ratio (ERR) approach to determine the significant terms and to pre-select the important variables for both time series and input–output systems. Several numerical examples are provided to illustrate the applicability and effectiveness of the new approach.     

Intelligent non-linear modelling of an industrial winding process using recurrent local linear neuro-fuzzy networks

This study deals with the neuro-fuzzy (NF) modelling of a real industrial winding process in which the acquired NF model can be exploited to improve control performance and achieve a robust fault-tolerant system. A new simulator model is proposed for a winding process using non-linear identification based on a recurrent local linear neuro-fuzzy (RLLNF) network trained by local linear model tree (LOLIMOT), which is an incremental tree-based learning algorithm. The proposed NF models are compared with other known intelligent identifiers, namely multilayer perceptron (MLP) and radial basis function (RBF). Comparison of our proposed non-linear models and associated models obtained through the least square error (LSE) technique (the optimal modelling method for linear systems) confirms that the winding process is a non-linear system. Experimental results show the effectiveness of our proposed NF modelling approach.     

Application of bacterial foraging technique trained artificial and wavelet neural networks in load forecasting

A new load forecasting (LF) approach using bacterial foraging technique (BFT) trained wavelet neural network (WNN) is proposed in this paper. Artificial neural network (ANN) is combined with wavelet transform called wavelet neural network is applied for LF. The parameters of translation and dilation in the wavelet nodes and the weighting factors in the weighting nodes are tuned using BFT optimization. With the advantages of global search abilities of BFT as well as the multiresolution and localizing natures of wavelets, the networks are constructed which identifies the inherent non-linear characteristics of power system loads. The proposed approach is validated with Tamil Nadu Electricity Board (TNEB) system, India. The comparison of Delta Rule and BFT-based LF for different periods are depicted with their mean absolute percentage errors (MAPE).     

Classification of parameter changes in a dynamic system with the use of wavelet analysis and neural networks

In this paper a neural detector of internal parameter changes in a stationary, non-linear SISO dynamic system is considered. A dynamic system is usually described by an input-output relation or by a set of state equations. Each change of parameter values creates a new non-nominal model of a dynamic system (sometimes with different values of parameters, sometimes with different structure and different values of parameters). Thus the detection of parameter changes can be formulated as a multi-model classification. The LVQ (Learning Vector Quantisation) neural network has been proposed as a classifier. Selected aggregated properties of discrete wavelet decomposition coefficients of the system output have been chosen as the inputs of the LVQ classifier. The output of the classifier points out the current model. The proposed approach to classification can be adopted as a fault detection method where faults are represented by changes of values of internal parameters of a system. The algorithm has been evaluated on the example of a non-linear fluid system with a non-ideal pipe which internal state is characterised by one value of a parameter, chosen from the known set.