The wavelet-NARMAX representation: A hybrid model structure combining polynomial models with multiresolution wavelet decompositions

A new hybrid model structure combing polynomial models with multiresolution wavelet decompositions is introduced for nonlinear system identification. Polynomial models play an important role in approximation theory and have been extensively used in linear and nonlinear system identification. Wavelet decompositions, in which the basis functions have the property of localization in both time and frequency, outperform many other approximation schemes and offer a flexible solution for approximating arbitrary functions. Although wavelet representations can approximate even severe nonlinearities in a given signal very well, the advantage of these representations can be lost when wavelets are used to capture linear or low-order nonlinear behaviour in a signal. In order to sufficiently utilize the global property of polynomials and the local property of wavelet representations simultaneously, in this study polynomial models and wavelet decompositions are combined together in a parallel structure to represent nonlinear input–output systems. As a special form of the NARMAX model, this hybrid model structure will be referred to as the WAvelet-NARMAX model, or simply WANARMAX. Generally, such a WANARMAX representation for an input–output system might involve a large number of basis functions and therefore a great number of model terms. Experience reveals that only a small number of these model terms are significant to the system output. A new fast orthogonal least-squares algorithm, called the matching pursuit orthogonal least squares (MPOLS) algorithm, is also introduced in this study to determine which terms should be included in the final model.     

Fuzzy wavelet neural network based on fuzzy clustering and gradient techniques for time series prediction

This paper presents the development of fuzzy wavelet neural network system for time series prediction that combines the advantages of fuzzy systems and wavelet neural network. The structure of fuzzy wavelet neural network (FWNN) is proposed, and its learning algorithm is derived. The proposed network is constructed on the base of a set of TSK fuzzy rules that includes a wavelet function in the consequent part of each rule. A fuzzy c-means clustering algorithm is implemented to generate the rules, that is the structure of FWNN prediction model, automatically, and the gradient-learning algorithm is used for parameter identification. The use of fuzzy c-means clustering algorithm with the gradient algorithm allows to improve convergence of learning algorithm. FWNN is used for modeling and prediction of complex time series and prediction of foreign-exchange rates. Exchange rates are dynamic process that changes every day and have high-order nonlinearity. The statistical data for the last 2 years are used for the development of FWNN prediction model. Effectiveness of the proposed system is evaluated with the results obtained from the simulation of FWNN-based systems and with the comparative simulation results of previous related models.     

On the series expansion approach to the identification ofHammerstein systems

A polynomial identification algorithm for recovering a nonlinearity in the Hammerstein system is proposed. The estimate employs the Legendre orthogonal system with adaptively selected number of terms. The global consistency along with rates of convergence are established. No assumptions concerning continuity of the nonlinearity or its functional form are made. A data-driven method using the cross-validation technique for selecting the number of terms in the estimate is presented     

具有预负载非线性特性的双率系统递推最小二乘估计算法

针对具有预负载非线性特性的双率系统, 提出一种新的辨识方法. 借助切换函数简化系统模型, 通过损失数据模型估计系统损失的输出数据, 进而利用系统所有输入和输出数据, 提出相应双率系统递推最小二乘算法. 与多项式转换方法相比, 该方法能够直接辨识出系统参数. 仿真结果验证了所提出方法的有效性.

     

基于多模型和SVM逆系统单元机组解耦控制

火力单元机组协调控制系统是一个多变量、强耦合的控制系统,具有非线性、耦合和延迟等特性,其性能直接影响单元机组运行的安全性和经济性.为了有效解决火力单元机组协调控制系统的耦合特性和动态非线性,设计了基于多模型和支持向量机(SVM)逆系统的解耦控制方法,并进行了相应实验研究.针对一个300 MW单元机组的试验仿真模型,得到单元机组在5个典型工作点的线性化模型,然后对每个线性化模型分别设计SVM逆模型及其动态PID控制器,进而用模型线性组合成多模型全局控制系统.通过加权多项式选取合成的多模型控制方法,可以解决负荷大范围变化引起的非线性问题;支持向量机与逆系统的结合能很好地解决非线性系统的强耦合问题.仿真研究证明了这种控制算法设计的有效性和优越性.     

A nonparametric polynomial identification algorithm for theHammerstein system

Almost all existing Hammerstein system nonparametric identification algorithms can recover the unknown system nonlinear element up to an additive constant, and one functional value of the nonlinearity is usually assumed to be known to make the constant solvable. To overcome this defect, in this paper, a new nonparametric polynomial identification algorithm for the Hammerstein system is proposed which extends the idea in the author's previous work (1993, 1994) on the Hammerstein system identification to a more general and practical case, where no functional value of the system nonlinearity is known a priori. Convergence and convergence rates in both uniform and global senses are established, and simulation studies demonstrate the effectiveness and advantage of the new algorithm     

Robust control of uncertain systems with polynomial nonlinearity by output feedback

The problem of global robust stabilization by output feedback is investigated for two classes of uncertain systems with polynomial nonlinearity—one is with controllable/observable linearization and the other is not. The uncertainties in the systems are assumed to be dominated by both lower‐ and higher‐order nonlinearities multiplying by an output‐dependent growth rate. There are two ingredients in this study. One is to exploit the idea of how to handle polynomial growth conditions via homogeneity and domination without introducing an observer gain updated law. The other is the development of a recursive design algorithm for the construction of reduced‐order observers, which is not only interesting in its own right but also has a valid counterpart, capable of dealing with strongly nonlinear systems, even lack of uniform observability and smooth stabilizability. Copyright © 2008 John Wiley & Sons, Ltd.     

Control of a direct internal reforming molten carbonate fuel cell system using wavelet network-based Hammerstein models

Inspired by a direct internal reforming molten carbonate fuel cell (DIR-MCFC) coupled with complicated nonlinear dynamics, the identification and control design of the Hammerstein model is presented. Through the sequential identification procedure, the static nonlinearity block is considered as the wavelet network which is trained and validated by the on-line learning algorithm, and the linear dynamic block is described by the state-space model in which parameters are estimated by the recursive least square algorithm. Using the numerical interpolation technique to approximate the implicit nonlinear function, we present a composite control framework consists of a nonlinear inversion and linear control. Through the closed-loop simulation tests, the nonlinear inversion design for the nonlinearity cancellation of a class of nonlinear systems is validated.     

Identification of IIR Wiener systems with spline nonlinearities that have variable knots

An algorithm is developed for the identification of Wiener systems, linear dynamic elements followed by static nonlinearities. In this case, the linear element is modeled using a recursive digital filter, while the static nonlinearity is represented by a spline of arbitrary but fixed degree. The primary contribution in this note is the use of variable knot splines, which allow for the use of splines with relatively few knot points, in the context of Wiener system identification. The model output is shown to be nonlinear in the filter parameters and in the knot points, but linear in the remaining spline parameters. Thus, a separable least squares algorithm is used to estimate the model parameters. Monte-Carlo simulations are used to compare the performance of the algorithm identifying models with linear and cubic spline nonlinearities, with a similar technique using polynomial nonlinearities.     

Modeling and identification of a PEM fuel cell humidification system

A theoretical model of a humidifier of proton exchange membrane （PEM） fuel cell systems is developed and analyzed first in this paper. The model shows that there exists a strong nonlinearity in the system. Then, the system is identified using a wavelet networks method. To avoid the curse-of-dimensionality problem, a class of wavelet networks proposed by Billings is employed. The experimental data acquired from the test bench are used for identification. The one-step-ahead predictions and the five-step-ahead predictions are compared with the real measurements, respectively. It shows that the identified model can effectively describe the real system.     

基于MPSoC平台小波变换并行算法研究

快速小波变换是数字信号处理面临的一个重要问题,针对并行小波算法展开研究,缩减小波变换中卷积运算的规模,提高小波变换过程中的并行效能,以实现小波变换的快速并行计算。通过FFT矩阵代入计算,消去了并行计算过程中的同步通信,降低了乘法运算次数。对算法思想进行了理论分析,说明新算法在短小数据分段情况下能够减少50%~75%的乘法操作;通过搭建两种不同平台进行了对比测试,证明了算法的先进性与有效性。基于FFT矩阵的并行小波变换算法是一种稳定有效的经典小波并行算法。     

Identification of time-varying pH processes using sinusoidal signals

This paper presents an approach to the identification of time-varying, nonlinear pH processes based on the Wiener model structure. The algorithm produces an on-line estimate of the titration curve, where the shape of this static nonlinearity changes as a result of changes in the weak-species concentration and/or composition of the process feed stream. The identification method is based on the recursive least-squares algorithm, a frequency sampling filter model of the linear dynamics and a polynomial representation of the inverse static nonlinearity. A sinusoidal signal for the control reagent flow rate is used to generate the input-output data along with a method for automatically adjusting the input mean level to ensure that the titration curve is identified in the pH operating region of interest. Experimental results obtained from a pH process are presented to illustrate the performance of the proposed approach. An application of these results to a pH control problem is outlined.     

Time-varying parametric system multiresolution identification by wavelets

In this paper, the problem of time-varying parametric system identification by wavelets is discussed. Employing wavelet operator matrix representation, we propose a new multiresolution least squares (MLS) algorithm for time-varying AR (ARX) system identification and a multiresolution least mean squares (MLMS) algorithm for the refinement of parameter estimation. These techniques can achieve the optimal tradeoff between the over-fitted solution and the poorly represented identification. The main features of time-varying model parameters are extracted in a multiresolution way, which can be used to represent the smooth trends as well as track the rapidly changing components of time-varying parameters simultaneously and adaptively. Further, a noisy time-varying AR (ARX) model can also be identified by combining the total least squares algorithm with the MLS algorithm. Based on the proposed AR (ARX) model parameter estimation algorithm, a novel identification scheme for time-varying ARMA (ARMAX) system is presented. A higher-order time-varying AR (ARX) model is used to approximate the time-varying ARMA (ARMAX) system and thus obtain an initial parameter estimation. Then an iterative algorithm is applied to obtain the consistent and efficient estimates of the ARMA (ARMAX) system parameters. This ARMA (ARMAX) identification algorithm requires linear operations only and thus greatly saves the computational load. In order to determine the time-varying model order, some modified AIC and MDL criterions are developed based on the proposed wavelet identification schemes. Simulation results verify that our methods can track the rapidly changing of time-varying system parameters and attain the best balance between parsimonious modelling and accurate identification.     

Classification of masses in mammographic image using wavelet domain features and polynomial classifier

Breast cancer is the most common cancer among women. In CAD systems, several studies have investigated the use of wavelet transform as a multiresolution analysis tool for texture analysis and could be interpreted as inputs to a classifier. In classification, polynomial classifier has been used due to the advantages of providing only one model for optimal separation of classes and to consider this as the solution of the problem. In this paper, a system is proposed for texture analysis and classification of lesions in mammographic images. Multiresolution analysis features were extracted from the region of interest of a given image. These features were computed based on three different wavelet functions, Daubechies 8, Symlet 8 and bi-orthogonal 3.7. For classification, we used the polynomial classification algorithm to define the mammogram images as normal or abnormal. We also made a comparison with other artificial intelligence algorithms (Decision Tree, SVM, K-NN). A Receiver Operating Characteristics (ROC) curve is used to evaluate the performance of the proposed system. Our system is evaluated using 360 digitized mammograms from DDSM database and the result shows that the algorithm has an area under the ROC curve Az of 0.98 ± 0.03. The performance of the polynomial classifier has proved to be better in comparison to other classification algorithms.     

Digital estimation and compensation method for nonlinearity mismatches in time-interleaved analog-to-digital converters

Channel mismatches in time-interleaved analog-to-digital converters (TIADCs) typically result in significant degradation of the ADC's dynamic performance. Offset, gain, and timing mismatches have been widely investigated whereas nonlinearity mismatches have not. In this work, we analyze the influence of nonlinearity mismatches by using a polynomial model. As a cost measure we use the signal-to-noise and distortion ratio (SNDR) and then derive a compact formula describing the dependency on nonlinearity mismatches. Based on the spectral characteristics of the TIADCs, we propose a foreground estimation method and a compensation method using a cascaded structure of adders and multipliers. Through behavioral-level simulations, we prove the validity of the derivations and demonstrate that the proposed estimation and compensation method can bring a considerable amount of improvement in the combined TIADCs dynamic performance. The proposed method is efficient assuming that a smooth approximation of the nonlinearity mismatches is sufficient.     

基于遗传算法的WANN的加速器故障诊断分析

利用基于遗传算法的全局优化能力,小波分析具有数据压缩和特征提取的特性,神经网络具有非线性映射和学习推理的优点.将遗传算法(GA)、小波(WA)与概率神经网络(PNN)算法相结合,用于加速器故障.实例证明,利用GA-WANN模型进行故障,故障诊断速度快,鲁棒性好,正确率高.     

Structured system models Part 3. An application to feedback compensator design

The controllability and observability indices are studied and applied to the feedback compensator design. The compensator design method uses polynomial matrices as system models. As the main result, a new algorithm is introduced for the construction of a first candidate for the feedback compensator. A new algorithm is also given for constructing a state-space model from polynomial matrix models. Such a realization is needed if there is originally only a polynomial matrix model for the system.     

基于小波变换的非线性广义预测控制

提出了基于小波变换的非线性广义预测控制算法。预测模型采用Hammerstein模型,对于其静态非线性部分采用小波网络来辨识,动态线性部分用最小二乘法来辨识。这种辨识方法比传统的多项式拟合的模型误差要小得多。基于这种预测模型广义预测控制器弥补了传统广义预测控制的模型失配问题。以CSTR为例对所设计的控制器进行仿真研究,结果表明控制器能够取得良好的控制效果。     

基于小波多尺度的图像增强新算法

传统图像增强算法在增强对比度的同时,也很大地提升图像噪声,需要对图像进行降噪处理。小波增强方法兼顾图像信号的空域和频域特性,但没有充分考虑到视觉的非线性特性。针对现有图像增强技术的这一缺陷,在分析小波变换对噪声影响规律的基础上,结合小波多尺度的特性,提出了一种基于小波多尺度的图像增强新算法,利用不同尺度上的小波系数间的相关性和小波分析的时频局部化特性来有效区分噪声和图像信息,有效改善了图像增强过程中的噪声放大问题。