Neuro-f uzzy system modeling based on automatic f uzzy clustering

A neuro-fuzzy system model based on automatic fuzzy clustering is proposed. A hybrid model identification algorithm is also developed to decide the model structure and model parameters. The algorithm mainly includes three parts :1) Automatic fuzzy C-means (AFCM) , which is applied to generate fuzzy rules automatically , and then fix on the size of the neuro-fuzzy network , by which the complexity of system design is reducesd greatly at the price of the fitting capability; 2)Recursive least square estimation ( RLSE) . It is used to update the parameters of Takagi-Sugeno model , which is employed to describe the behavior of the system;3) Gradient descent algorithm is also proposed for the fuzzy values according to the back propagation algorithm of neural network. Finally ,modeling the dynamical equation of the two- link manipulator with the proposed approach is illustrated to validate the feasibility of the method.     

Neuro-fuzzy system modeling based on automatic fuzzy clustering

A neuro-fuzzy system model based on automatic fuzzy dustering is proposed. A hybrid model identification algorithm is also developed to decide the model structure and model parameters. The algorithm mainly includes three parts：1） Automatic fuzzy C-means （AFCM）, which is applied to generate fuzzy rttles automatically, and then fix on the size of the neuro-fuzzy network, by which the complexity of system design is reducesd greatly at the price of the fitting capability; 2） R.ecursive least square estimation （RLSE）. It is used to update the parameters of Takagi-Sugeno model, which is employed to describe the behavior of the system;3） Gradient descent algorithm is also proposed for the fuzzy values according to the back propagation algorithm of neural network. Finally,modeling the dynamical equation of the two-link manipulator with the proposed approach is illustrated to validate the feasibility of the method.     

An efficient compensatory neuro-fuzzy system and its applications

In this study, a compensatory neuro-fuzzy system (CNFS) is proposed. The compensatory fuzzy reasoning method uses adaptive fuzzy operations of a neuro-fuzzy system to make the fuzzy logic system more adaptive and effective. Furthermore, an online learning algorithm that consists of structure learning and parameter learning is proposed to automatically construct the CNFS. The structure learning is based on the fuzzy similarity measure to determine the number of fuzzy rules, and the parameter learning is based on backpropagation algorithm to adjust the parameters. The simulation results have shown that (1) the CNFS model converges quickly and (2) the CNFS model has a lower root mean square (RMS) error than other models.     

A systematic neuro-fuzzy modeling framework with application tomaterial property prediction

A systematic neural-fuzzy modeling framework that includes the initial fuzzy model self-generation, significant input selection, partition validation, parameter optimization, and rule-base simplification is proposed in this paper. In this framework, the structure identification and parameter optimization are carried out automatically and efficiently by the combined use of a sell-organization network, fuzzy clustering, adaptive back-propagation learning, and similarity analysis-based model simplification. The proposed neuro-fuzzy modeling approach has been used for nonlinear system identification and mechanical property prediction in hot-rolled steels from construct composition and microstructure data. Experimental studies demonstrate that the predicted mechanical properties have a good agreement with the measured data by using the elicited fuzzy model with a small number of rules.     

An efficient quantum neuro-fuzzy classifier based on fuzzy entropy and compensatory operation

In this paper, a quantum neuro-fuzzy classifier (QNFC) for classification applications is proposed. The proposed QNFC model is a five-layer structure, which combines the compensatory-based fuzzy reasoning method with the traditional Takagi–Sugeno–Kang (TSK) fuzzy model. The compensatory-based fuzzy reasoning method uses adaptive fuzzy operations of neuro-fuzzy systems that can make the fuzzy logic system more adaptive and effective. Layer 2 of the QNFC model contains quantum membership functions, which are multilevel activation functions. Each quantum membership function is composed of the sum of sigmoid functions shifted by quantum intervals. A self-constructing learning algorithm, which consists of the self-clustering algorithm (SCA), quantum fuzzy entropy and the backpropagation algorithm, is also proposed. The proposed SCA method is a fast, one-pass algorithm that dynamically estimates the number of clusters in an input data space. Quantum fuzzy entropy is employed to evaluate the information on pattern distribution in the pattern space. With this information, we can determine the number of quantum levels. The backpropagation algorithm is used to tune the adjustable parameters. The simulation results have shown that (1) the QNFC model converges quickly; (2) the QNFC model has a higher correct classification rate than other models.     

神经模糊系统中模糊规则的优选

提出一种基于两级聚类算法的自组织神经模糊系统，该系统采用两级聚类算法（改进的最近邻域聚类算法和Gustafson-Kessel模糊聚类算法）对输入／输出数据进行模糊聚类，并由模糊聚类的划分熵确定最优划分，建立模糊模型，模型精度可由梯度下降法进一步提高。仿真结果表明，这种神经模糊系统具有结构简单、规则数少、学习速度快以及建模精度高等特点。     

A method for design of a hybrid neuro-fuzzy control system based onbehavior modeling

It is known that control signals from a fuzzy logic controller are determined by a response behavior of a controlled object rather than its analytical models. That implies that the fuzzy controller could yield a similar control result for a set of plants with a similar dynamic behavior. This idea lends to modeling of a plant with unknown structure by defining several types of dynamic behaviors. On the basis of dynamic behavior classification, a new method is presented for the design of a neuro-fuzzy control system in two steps: 1) we model a plant with unknown structure by choosing a set of simplified systems with equivalent behavior as “templates” to optimize their fuzzy controllers off-line; and 2) we use an algorithm for system identification to perceive dynamic behavior and a neural network to adapt fuzzy logic controllers by matching the “templates” online. The main advantage of this method is that convergence problem can be avoided during adaptation process. Finally, the proposed method is used to design neuro-fuzzy controllers for a two-link manipulator     

有混合数据输入的自适应模糊神经推理系统

现有数据建模方法大多依赖于定量的数值信息,而对于数值与分类混合输入的数据建模问题往往根据分类变量组合建立多个子模型,当有多个分类变量输入时易出现子模型数据分布不均匀、训练耗时长等问题.针对上述问题,提出一种具有混合数据输入的自适应模糊神经推理系统模型,在自适应模糊推理系统的基础上,引入激励强度转移矩阵和结论影响矩阵,采用基于高氏距离的减法聚类辨识模型结构,通过混合学习算法训练模型参数,使数值与分类混合数据对模糊规则的前后件参数同时产生作用,共同影响模型输出.仿真实验分析了分类数据对模型规则后件的作用以及结构辨识算法对模糊规则数的影响,与其他几种混合数据建模方法对比表明本文所提出的模型具有较高的预测精度和计算效率.     

基于自组织神经网络的非线性系统建模

针对基于T-S模糊模型的非线性系统建模问题,提出了一种基于自组织神经网络的新方法.在T-S模糊模型的建模中,目前常用的模糊C均值聚类算法存在迭代次数多,计算耗时的缺点.首先,利用竞争学习算法对输入空间进行聚类,基于此结果,借助于模糊C均值聚类算法进一步优化聚类结果,提取T-S模糊模型的规则前件隶属函数参数.然后,采用最小二乘法求得T-S模糊模型的规则后件参数,从而建立起非线性系统的T-S模糊模型.最后,仿真结果表明,该方法可以为模糊建模提供好的模型结构,并且有较高的计算效率和精度.     

An IV-QR Algorithm for Neuro-Fuzzy Multivariable Online Identification

In this paper, a new algorithm for neuro-fuzzy identification of multivariable discrete-time nonlinear dynamic systems, more specifically applied to consequent parameters estimation of the neuro-fuzzy inference system, is proposed based on a decomposed form as a set of coupled multiple input and single output (MISO) Takagi-Sugeno (TS) neuro-fuzzy networks. An on-line scheme is formulated for modeling a nonlinear autoregressive with exogenous input (NARX) recurrent neuro-fuzzy structure from input-output samples of a multivariable nonlinear dynamic system in a noisy environment. The adaptive weighted instrumental variable (WIV) algorithm by QR factorization based on the numerically robust orthogonal Householder transformation is developed to modify the consequent parameters of the TS multivariable neuro-fuzzy network     

Enhanced Fuzzy System Models With Improved Fuzzy Clustering Algorithm

Although traditional fuzzy models have proven to have high capacity of approximating the real-world systems, they have some challenges, such as computational complexity, optimization problems, subjectivity, etc. In order to solve some of these problems, this paper proposes a new fuzzy system modeling approach based on improved fuzzy functions to model systems with continuous output variable. The new modeling approach introduces three features: i) an improved fuzzy clustering (IFC) algorithm, ii) a new structure identification algorithm, and iii) a nonparametric inference engine. The IFC algorithm yields simultaneous estimates of parameters of c-regression models, together with fuzzy c-partitioning of the data, to calculate improved membership values with a new membership function. The structure identification of the new approach utilizes IFC, instead of standard fuzzy c-means clustering algorithm, to fuzzy partition the data, and it uses improved membership values as additional input variables along with the original scalar input variables for two different choices of regression methods: least squares estimation or support vector regression, to determine ldquofuzzy functionsrdquo for each cluster. With novel IFC, one could learn the system behavior more accurately compared to other FSM models. The nonparametric inference engine is a new approach, which uses the alike -nearest neighbor method for reasoning. Empirical comparisons indicate that the proposed approach yields comparable or better accuracy than fuzzy or neuro-fuzzy models based on fuzzy rules bases, as well as other soft computing methods.     

Neuro-fuzzy control of antilock braking system using sliding mode incremental learning algorithm

A neuro-fuzzy adaptive control approach for nonlinear dynamical systems, coupled with unknown dynamics, modeling errors, and various sorts of disturbances, is proposed and used to design a wheel slip regulating controller. The implemented control structure consists of a conventional controller and a neuro-fuzzy network-based feedback controller. The former is provided both to guarantee global asymptotic stability in compact space and as an inverse reference model of the response of the controlled system. Its output is used as an error signal by an incremental learning algorithm to update the parameters of the neuro-fuzzy controller. In this way the latter is able to gradually replace the conventional controller from the control of the system. The proposed new learning algorithm makes direct use of the variable structure systems theory and establishes a sliding motion in terms of the neuro-fuzzy controller parameters, leading the learning error toward zero. In the simulations and in the experimental studies, it has been tested on the control of antilock breaking system model and the analytical claims have been justified under the existence of uncertainty and large nonzero initial errors.     

基于UKF的自适应模糊推理神经网络

如何生成最优的模糊规则数及模糊规则的自动生成和修剪是模糊神经网络训练算法研究的重点。针对这一问题,本文提出了基于UKF的自适应模糊推理神经网络(UKF-ANFIS)。首先,通过减法聚类确定UKF-ANFIS的模糊规则及其高斯隶属函数的中心和宽度参数;其次,分析了模糊神经网络的非线性动力系统表示,并用LLS和UKF分别学习线性和非线性的参数;然后,用误差下降率方法作为模糊规则修剪的策略,删除作用不大的规则;最后,通过典型的函数逼近和系统辨识实例,表明本文算法得到的模糊神经网络的结构更为紧凑,泛化性能也更佳。     

基于增广输入变量的T-S 模糊模型建模

针对现有T-S 模糊模型建模精度与计算效率之间的矛盾, 提出一种利用增广输入变量进行T-S 模糊模型建模的方法. 对输入变量进行多项式增广处理后, 以核模糊?? 均值聚类算法配合聚类评价指标自适应获得最佳聚类数及相应的模糊划分, 并通过递推最小二乘计算得出T-S 模糊模型的后件参数. 提出可利用后件参数反推断前件结构的方法来快速有效地确定前件结构. 最后通过仿真验证了上述方法的有效性.

     

Adaptive extended fuzzy basis function network

The structure of the extended fuzzy basis function network (EFBFN) is firstly proposed, and the least squares (LS) method is used to design it by fixing the widths of the hidden units in EFBFN. Then, to enhance the performance of the obtained EFBFN ulteriorly, a novel evolutionary algorithm based on LS and the hybrid of evolutionary programming and particle swarm optimization (LS-EPPSO) is proposed, in which we use EPPSO to tune the parameters of the premise part in EFBFN, and the LS algorithm to decide the consequent parameters in it simultaneously. The enhanced EFBFN whose parameters are refined automatically using LS-EPPSO is thus called adaptive EFBFN. In the simulation part, the proposed method to construct AEFBFN is employed to model a three input nonlinear function and to predict a chaotic time series. Comparisons with some typical fuzzy modeling methods and artificial neural networks are presented and discussed.     

基于F-SVMs的多模型建模方法

针对全局模型难以精确描述复杂工业过程的问题,提出一种基于模糊支持向量机(F-SVMs)的多模型(F-SVMs MM)建模方法。用模糊支持向量分类算法(F-SVC)对输入数据进行预处理,得到多模型模糊隶属度;用模糊支持回归算法(F-SVR)建立多模型(MM)估计器。应用该方法对pH中和滴定过程进行建模,仿真结果表明,F-SVMs MM跟踪性能好、泛化能力强,比USOCPN方法和标准支持向量机(SVMs)方法具有更好的性能和推广能力。     

发酵过程的多模型融合建模算法

提出了利用多模型融合技术进行发酵过程建模的新方法， 该方法能够将在线参数和离线参数同时用于建模中． 首先给出了多模型融合建模算法框架， 并描述了基于自适应模糊神经网络和模糊推理技术两个参与融合的子模型的建立方法. 采用三个非线性函数分别运用GMDH-PTSV算法、傅里叶神经网络和多模型融合建模算法进行建模精度比较. 最后给出了多模型融合建模算法在青霉素发酵过程中应用的结果．     

Self-organized fuzzy system generation from training examples

In the synthesis of a fuzzy system two steps are generally employed: the identification of a structure and the optimization of the parameters defining it. The paper presents a methodology to automatically perform these two steps in conjunction using a three-phase approach to construct a fuzzy system from numerical data. Phase 1 outlines the membership functions and system rules for a specific structure, starting from a very simple initial topology. Phase 2 decides a new and more suitable topology with the information received from the previous step; it determines for which variable the number of fuzzy sets used to discretize the domain must be increased and where these new fuzzy sets should be located. This, in turn, decides in a dynamic way in which part of the input space the number of fuzzy rules should be increased. Phase 3 selects from the different structures obtained to construct a fuzzy system the one providing the best compromise between the accuracy of the approximation and the complexity of the rule set. The accuracy and complexity of the fuzzy system derived by the proposed self-organized fuzzy rule generation procedure (SOFRG) are studied for the problem of function approximation. Simulation results are compared with other methodologies such as artificial neural networks, neuro-fuzzy systems, and genetic algorithms     

A novel parametric fuzzy CMAC network and its applications

This paper shows fundamentals and applications of the novel parametric fuzzy cerebellar model articulation controller (P-FCMAC) network. It resembles a neural structure that derived from the Albus CMAC algorithm and Takagi–Sugeno–Kang parametric fuzzy inference systems. The Gaussian basis function is used to model the hypercube structure and the linear parametric equation of the network input variance is used to model the TSK-type output. A self-constructing learning algorithm, which consists of the self-clustering method (SCM) and the backpropagation algorithm, is proposed. The proposed the SCM scheme is a fast, one-pass algorithm for a dynamic estimation of the number of hypercube cells in an input data space. The clustering technique does not require prior knowledge of things such as the number of clusters present in a data set. The backpropagation algorithm is used to tune the adjustable parameters. Illustrative examples were conducted to show the performance and applicability of the proposed model.     

Parameter identification of PWARX models using fuzzy distance weighted least squares method

PieceWise AutoRegressive eXogenous (PWARX) models represent one of the broad classes of the hybrid dynamical systems (HDS). Among many classes of HDS, PWARX model used as an attractive modeling structure due to its equivalence to other classes. This paper presents a novel fuzzy distance weight matrix based parameter identification method for PWARX model. In the first phase of the proposed method estimation for the number of affine submodels present in the HDS is proposed using fuzzy clustering validation based algorithm. For the given set of input–output data points generated by predefined PWARX model fuzzy c-means (FCM) clustering procedure is used to classify the data set according to its affine submodels. The fuzzy distance weight matrix based weighted least squares (WLS) algorithm is proposed to identify the parameters for each PWARX submodel, which minimizes the effect of noise and classification error. In the final phase, fuzzy validity function based model selection method is applied to validate the identified PWARX model. The effectiveness of the proposed method is demonstrated using three benchmark examples. Simulation experiments show validation of the proposed method.