A grey-based clustering algorithm and its application on fuzzy system design

A grey-based clustering method was proposed and applied on fuzzy system design. A new grey-clustering algorithm using grey relational analysis as the similarity measure was developed for data clustering. It was more effective and accurate than C-Means like algorithms when dealing with data clustering issue, when the compact and complete separate data were considered. Some data clustering examples are presented to illustrate the effectiveness of the proposed clustering algorithm. Next, an application of the proposed method on fuzzy system design is presented. The procedure of fuzzy system design can be separated into two parts. In the first procedure, the grey-clustering algorithm was employed to form a rough fuzzy system only from gathered input-output data. Then, the gradient descent method was used to determine a suitable parameter set of the formed fuzzy system. A nonlinear system modelling and an inverted pendulum control problem were then used to illustrate the validity of the proposed fuzzy system design procedure.     

Fuzzy modeling of fluidized catalytic cracking unit

The paper deals with the fuzzy system identification of reactor–regenerator–stripper–fractionator's (RRSF) section of a fluidized catalytic cracking unit (FCCU). The fuzzy system identification based on the data collected from an operating refinery of FCCU of capacity, 1.2 MMPTA, with a sample time of 10 min. A generalized fuzzy model (GFM) and identification of structure and model parameter for multi-input/single output is presented. The GFM has the capability of representing both the CRI model and TS model under certain conditions. The structure identification and the parameter estimation are carried out using hybrid learning approach comprising modified mountain clustering and gradient descent learning with least square estimation (LSE) for the identification of a fuzzy model. The modified mountain clustering considers every data point as a potential cluster center in x × y hyperspace. The optimum number of clusters, which leads to an optimum number of rules, is determined with the help of validity function that guides the search. The obtained result from the modified mountain clustering initializes the GFM. Further hybrid of the gradient descent technique and LSE is aimed at learning of the GFM parameters in two phases. In the first phase of an epoch of learning gradient descent tunes the premise parameter and index of fuzziness of each rule. In second phase, LSE utilizes the results of first phase for evaluating the coefficient of local linear model of corresponding rules.     

A new approach to fuzzy modeling

This paper proposes a new approach to fuzzy modeling. The suggested fuzzy model can express a given unknown system with a few fuzzy rules as well as Takagi and Sugeno's model (1985), because it has the same structure as that of Takagi and Sugeno's model. It is also as easy to implement as Sugeno and Yasukawa's model (1993) because its identification mimics the simple identification procedure of Sugeno and Yasukawa's model. The suggested algorithm is composed of two steps: coarse tuning and fine tuning. In coarse tuning, fuzzy C-regression model (FCRM) clustering is used, which is a modified version of fuzzy C-means (FCM). In fine tuning, gradient descent algorithm is used to precisely adjust parameters of the fuzzy model instead of nonlinear optimization methods used in other models. Finally, some examples are given to demonstrate the validity of this algorithm     

Structure identification of generalized adaptive neuro-fuzzy inference systems

This paper presents a method to identify the structure of generalized adaptive neuro-fuzzy inference systems (GANFISs). The structure of GANFIS consists of a number of generalized radial basis function (GRBF) units. The radial basis functions are irregularly distributed in the form of hyper-patches in the input-output space. The minimum number of GRBF units is selected based on a heuristic using the fuzzy curve. For structure identification, a new criterion called structure identification criterion (SIC) is proposed. SIC deals with a trade off between performance and computational complexity of the GANFIS model. The computational complexity of gradient descent learning is formulated based on simulation study. Three methods of initialization of GANFIS, viz., fuzzy curve, fuzzy C-means in x/spl times/y space and modified mountain clustering have been compared in terms of cluster validity measure, Akaike's information criterion (AIC) and the proposed SIC.     

T–S fuzzy model identification based on a novel fuzzy c-regression model clustering algorithm

This paper proposes a novel approach for identification of Takagi–Sugeno (T–S) fuzzy model, which is based on a new fuzzy c-regression model (FCRM) clustering algorithm. The clustering prototype in fuzzy space partition is hyper-plane, so FCRM clustering technique is more suitable to be applied in premise parameters identification of T–S fuzzy model. A new FCRM clustering algorithm (NFCRMA) is presented, which is deduced from the fuzzy clustering objective function of FCRM with Lagrange multiplier rule, possessing integrative and concise structure. The proposed approach consists mainly of two steps: premise parameter identification and consequent parameter identification. The NFCRMA is utilized to partition the input–output data and identify the premise parameters, which can discover the real structure of the training data; on the other hand, orthogonal least square is exploited to identify the consequent parameters. Finally, some examples are given to verify the validity of the proposed modeling approach, and the results show the new approach is very efficient and of high accuracy.     

一种新的基于神经模糊推理网络的复杂系统模糊辨识方法

针对基于输入输出数据的复杂系统的模糊辨识问题,提出了一种新的神经模糊推理网络及相应的学习算法．学习算法被应用于系统的结构辨识与参数辨识．在结构辨识阶段,介绍了一种新的直接从输入输出数据中抽取和优化模糊规则的学习算法;在参数辨识阶段,提出和推导了一种非监督学习和监督学习相结合的混合式学习算法,实现模糊隶属函数的初步调整和优化．仿真结果表明,本文的方法可以同时满足对辨识精度、收敛速度、可读性和规则数的要求．     

基于模糊ARMAX模型的模糊建模

提出了一种利用MGS(modified Gram-Schmidt)算法建立模糊ARMAX模型的方法, 给出了基于MGS算法的模型结构和参数辨识的一体化方法. 利用MGS正交变换对通过GK模糊聚类的聚类结果进行变换, 确定对模型贡献大的规则, 删除对模型贡献小的规则, 同时对模型中的参数进行估计. 本文提出的方法能够实现模糊模型的结构和参数的优化. 仿真结果表明, 本文提出的方法能够建立非线性系统的模糊ARMAX模型.     

一种基于模糊规则融合的模糊建模方法及其应用

为了有效地利用经验知识,弥补训练数据覆盖范围不足的问题,提出一种将经验知识以TSK (Takagi-Sugeno-Kang)型模糊规则引入模糊模型的建模方法.在结构辨识中,提出了模糊规则融合方法,用以确定初始模糊规则.在参数辨识中,改进了原梯度下降方法中的目标函数,并引入了经验知识准确性评价参数,用以平衡样本数据和经验知识对模型的影响.数值仿真和工程实例应用结果表明,所提出的方法可以有效地利用经验知识和样本数据,使预报结果更可靠、更精确.     

一种基于模糊聚类的模糊辨识方法

介绍一种基于模糊聚类的模糊辨识方法。首先利用含有聚类准则函数的模糊聚类方法来确定模糊规则数和模型前提参数,然后利用最小二乘法来辨识模型的结论参数,最后采用梯度下降法来调整模型的参数。该方法应用于Box-Jenkins数据仿真实例,仿真结果表明该方法简单有效。     

A Fuzzy Modelling Approach Using Hierarchical Neural Networks

A simple and effective fuzzy modelling approach is presented in this paper. A three-layer hierarchical clustering neural network is developed to build fuzzy rule-based models from numerical data. Differing from existing clustering-based methods, in this approach the structure identification of the fuzzy model is implemented on the basis of a class of sub-clusters created by a self-organising network instead of on raw data. By combined use of unsupervised and supervised learning, both structure identification and parameter optimisation of the fuzzy model can be carried out automatically. The simulation results show that the proposed method can provide good model structure for fuzzy modelling and has high computing efficiency.     

Identification of complex systems based on neural and Takagi-Sugeno fuzzy model

The paper describes a neuro-fuzzy identification approach, which uses numerical data as a starting point. The proposed method generates a Takagi-Sugeno fuzzy model, characterized with transparency, high accuracy and a small number of rules. The process of self-organizing of the identification model consists of three phases: clustering of the input-output space using a self-organized neural network; determination of the parameters of the consequent part of a rule from over-determined batch least-squares formulation of the problem, using singular value decomposition algorithm; and on-line adaptation of these parameters using recursive least-squares method. The verification of the proposed identification approach is provided using four different problems: two benchmark identification problems, speed estimation for a dc motor drive, and estimation of the temperature in a tunnel furnace for clay baking.     

A neuro-fuzzy system modeling with self-constructing rule generationand hybrid SVD-based learning

We propose an approach for neuro-fuzzy system modeling. A neuro-fuzzy system for a given set of input-output data is obtained in two steps. First, the data set is partitioned automatically into a set of clusters based on input-similarity and output-similarity tests. Membership functions associated with each cluster are defined according to statistical means and variances of the data points included in the cluster. Then, a fuzzy IF-THEN rule is extracted from each cluster to form a fuzzy rule-base. Second, a fuzzy neural network is constructed accordingly and parameters are refined to increase the precision of the fuzzy rule-base. To decrease the size of the search space and to speed up the convergence, we develop a hybrid learning algorithm which combines a recursive singular value decomposition-based least squares estimator and the gradient descent method. The proposed approach has advantages of determining the number of rules automatically and matching membership functions closely with the real distribution of the training data points. Besides, it learns faster, consumes less memory, and produces lower approximation errors than other methods.     

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.     

On-line fuzzy modeling via clustering and support vector machines

In this paper, we propose a novel approach to identify unknown nonlinear systems with fuzzy rules and support vector machines. Our approach consists of four steps which are on-line clustering, structure identification, parameter identification and local model combination. The collected data are firstly clustered into several groups through an on-line clustering technique, then structure identification is performed on each group using support vector machines such that the fuzzy rules are automatically generated with the support vectors. Time-varying learning rates are applied to update the membership functions of the fuzzy rules. The modeling errors are proven to be robustly stable with bounded uncertainties by a Lyapunov method and an input-to-state stability technique. Comparisons with other related works are made through a real application of crude oil blending process. The results demonstrate that our approach has good accuracy, and this method is suitable for on-line fuzzy modeling.     

一种基于数据挖掘的模糊建模方法

为提高非线性系统模糊建模的速度和精确度,提出一种快速有效的基于数据挖掘的非线性系统模糊建模方法.该方法先采用改进的减法聚类结合模糊C-均值聚类进行结构辨识,在解决初始化问题的同时减少计算量,进而提高建模速度;然后利用带动态遗忘因子的递推最小二乘法进行后件参数辨识,减小动态误差,提高建模精度.将提出的方法应用于Box-J...     

A design and analysis of objective function-based unsupervised neural networks for fuzzy clustering

Fuzzy clustering has played an important role in solving many problems. In this paper, we design an unsupervised neural network model based on a fuzzy objective function, called OFUNN. The learning rule for the OFUNN model is a result of the formal derivation by the gradient descent method of a fuzzy objective function. The performance of the cluster analysis algorithm is often evaluated by counting the number of crisp clustering errors. However, the number of clustering errors alone is not a reliable and consistent measure for the performance of clustering, especially in the case of input data with fuzzy boundaries. We introduce two measures to evaluate the performance of the fuzzy clustering algorithm. The clustering results on three data sets, Iris data and two artificial data sets, are analyzed using the proposed measures. They show that OFUNN is very competitive in terms of speed and accuracy compared to the fuzzy c-means algorithm.     

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.     

蚁群聚类算法的T-S模糊模型辨识

基于T-S模型,提出一种非线性系统的模型辨识方法。利用蚁群聚类算法来进行结构辨识,确定系统的模糊空间和模糊规则数。在聚类的基础上,利用遗传算法辨识模糊模型的后件加权参数,得到一个精确的模糊模型,从而实现参数辨识。仿真结果验证了该方法的有效性,表明该方法能够实现非线性系统的辨识,辨识精度高,可当作复杂系统建模的一种有效手段。     

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.