Online fuzzy modeling with structure and parameter learning

This paper describes a novel nonlinear modeling approach with fuzzy rules and support vector machines. Structure identification is realized by an online clustering method and fuzzy support vector machines, the fuzzy rules are generated automatically. Time-varying learning rates are applied for updating 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 an application of gas furnace process. The results demonstrate that our approach has good accuracy, and this method is suitable for online fuzzy modeling.     

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.     

A PSO-BASED METHOD FOR EXTRACTING FUZZY RULES DIRECTLY FROM NUMERICAL DATA

In this paper, a PSO-based method is proposed for automatically constructing a fuzzy system with an appropriate number of rules to approach the identified system. In the PSO-based method, each individual in the population is constructed to determine the number of fuzzy rules and the premise part of the fuzzy system, and then the recursive least-squares method is used to determine the consequent part of the fuzzy system constructed by the corresponding individual. Consequently, an individual corresponds to a fuzzy system. Subsequently, a fitness function is defined to guide the searching procedure to select an appropriate fuzzy system with the desired performance. Finally, two identification problems of nonlinear systems are utilized to illustrate the effectiveness of the proposed method for fuzzy modeling.     

Interval Fuzzy Model Identification Using$l_infty$-Norm

In this paper, we present a new method of interval fuzzy model identification. The method combines a fuzzy identification methodology with some ideas from linear programming theory. We consider a finite set of measured data, and we use an optimality criterion that minimizes the maximum estimation error between the data and the proposed fuzzy model output. The idea is then extended to modeling the optimal lower and upper bound functions that define the band which contains all the measurement values. This results in lower and upper fuzzy models or a fuzzy model with a set of lower and upper parameters. The model is called the interval fuzzy model (INFUMO). We also showed that the proposed structure uniformly approximates the band of any nonlinear function. The interval fuzzy model identification is a methodology to approximate functions by taking into account a finite set of input and output measurements. This approach can also be used to compress information in the case of large amount of data and in the case of robust system identification. The method can be efficiently used in the case of the approximation of the nonlinear functions family. If the family is defined by a band containing the whole measurement set, the interval of parameters is obtained as the result. This is of great importance in the case of nonlinear circuits' modeling, especially when the parameters of the circuits vary within certain tolerance bands     

基于特征选择和协同模糊聚类的模糊建模研究

为了提高模糊模型辨识效率,提出了一种新的模糊模型建摸方法,该方法由两步组成：（1）采用基于特征相似性的特征选择方法,去除原始数据的冗余;（2）利用协同模糊聚类与G-K相结合的算法初始化模糊模型,使其前件和后件参数得到优化。采用该算法对有效的特征进行协同模糊聚类,模型参数得到改善,提高了模糊模型辨识的效率。模糊建模的实验结果表明了该方法的有效性。     

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.     

A robust design criterion for interpretable fuzzy models with uncertain data

We believe that nonlinear fuzzy filtering techniques may be turned out to give better robustness performance than the existing linear methods of estimation (H/sup 2/ and H/sup /spl infin// filtering techniques), because of the fact that not only linear parameters (consequents), but also the nonlinear parameters (membership functions) attempt to identify the uncertain behavior of the unknown system. However, the fuzzy identification methods must be robust to data uncertainties and modeling errors to ensure that the fuzzy approximation of unknown system's behavior is optimal in some sense. This study presents a deterministic approach to the robust design of fuzzy models in the presence of unknown but finite uncertainties in the identification data. We consider online identification of an interpretable fuzzy model, based on the robust solution of a regularized least-squares fuzzy parameters estimation problem. The aim is to resolve the difficulties associated with the robust fuzzy identification method due to lack of a priori knowledge about upper bounds on the data uncertainties. The study derives an optimal level of regularization that should be provided to ensure the robustness of fuzzy identification strategy by achieving an upper bound on the value of energy gain from data uncertainties and modeling errors to the estimation errors. A time-domain feedback analysis of the proposed identification approach is carried out with emphasis on stability, robustness, and steady-state issues. The simulation studies are provided to show the superiority of the proposed fuzzy estimation over the classical estimation methods.     

A fuzzy modeling method via Enhanced Objective Cluster Analysis for designing TSK model

This paper proposes a fuzzy modeling method via Enhanced Objective Cluster Analysis to obtain the compact and robust approximate TSK fuzzy model. In our approach, the Objective Cluster Analysis algorithm is introduced. In order to obtain more compact and more robust fuzzy rule prototypes, this algorithm is enhanced by introducing the Relative Dissimilarity Measure and the new consistency criterion to represent the similarity degree between the clusters. By these additional criteria, the redundant clusters caused by iterations are avoided; the subjective influence from human judgment for clustering is weakened. Moreover the clustering results including the number of clusters and the cluster centers are considered as the initial condition of the premise parameters identification. Thus the traditional iteration modeling procedure for determining the number of rules and identifying parameters is changed into one-off modeling, which significantly reduces the burden of computation. Furthermore the decomposition errors and the approximation errors resulted from premise parameters identification by Fuzzy c-Means clustering are decreased. For the consequence parameters identification, the Stable Kalman Filter algorithm is adopted. The performance of the proposed modeling method is evaluated by the example of Box–Jenkins gas furnace. The simulation results demonstrate the power of our model.     

模糊时间序列挖掘在复杂系统模糊建模中的应用

针对于复杂工业过程领域模糊建模问题, 提出了一种基于时间序列的模糊定量数据挖掘方法, 并讨论了其在复杂系统模糊逻辑推理模型结构辨识中的应用. 该方法建立在系统历史采集数据库基础之上, 较好的解决了多入多出 (MIMO)非线性复杂工业过程模糊建模时初始模型的建立问题. 文章最后讨论了该方法在氧化铝熟料烧结回转窑建模中的应用, 取得了良好的现场运行效果.     

Hydraulic turbine governing system identification using T–S fuzzy model optimized by chaotic gravitational search algorithm

Hydraulic turbine governing system (HTGS) is a complicated nonlinear system that controls the frequency and power output of hydroelectric generating unit (HGU). The modeling of HTGS is an important and difficult task, because some components, like hydraulic turbine and governor actuator, are with strong nonlinearity. In this paper, a novel Takagi–Sugeno (T–S) fuzzy model identification method based on chaotic gravitational search algorithm (CGSA) is proposed and applied in the modeling of HTGS. In the proposed method, fuzzy c-regression model clustering algorithm is used to partition the input space and identify the coarse antecedent membership function (MF) parameters at first. And then, a novel CGSA is proposed to search better MF parameters around the coarse results, in which chaotic search has been embedded in the iteration of basic GSA to search and replace the current best solution of GSA. The performance of the proposed fuzzy model identification method is validated by benchmark problems, and the results show that the accuracies of identified models have been improved significantly compared with the other existing models. Finally, the proposed approach has been applied to approximate the dynamic behaviors of HTGS of a HGU in a hydropower station of Jiangxi Province of China. The experimental results show that our approach can identify the HTGS satisfactorily with acceptable accuracy.     

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.     

用模糊模型在线辨识非线性系统

讨论用模糊方法实现非线性系统在线辨识问题.首先给出了简化的模糊规则表达 方法及其相应的自适应模糊推理,在此基础上给出了模糊模型参数在线辨识算法.最后对 非线性模型进行在线辨识,验证了本文提出的模糊模型及其在线辨识算法.     

/spl epsiv/-insensitive fuzzy c-regression models: introduction to /spl epsiv/-insensitive fuzzy modeling

This paper introduces a new epsilon-insensitive fuzzy c-regression models (epsilonFCRM), that can be used in fuzzy modeling. To fit these regression models to real data, a weighted epsilon-insensitive loss function is used. The proposed method make it possible to exclude an intrinsic inconsistency of fuzzy modeling, where crisp loss function (usually quadratic) is used to match real data and the fuzzy model. The epsilon-insensitive fuzzy modeling is based on human thinking and learning. This method allows easy control of generalization ability and outliers robustness. This approach leads to c simultaneous quadratic programming problems with bound constraints and one linear equality constraint. To solve this problem, computationally efficient numerical method, called incremental learning, is proposed. Finally, examples are given to demonstrate the validity of introduced approach to fuzzy modeling.     

基于改进遗传算法的非线性系统模糊辨识新方法

提出一种基于改进遗传算法和递推最小二乘的非线性模糊辨识新算法.该辨识方法包含结构辨识辨出和参数辨识,结构辨识即输入空间的模糊划分,采用具有自适应性的广义高斯隶属函数;参数辨识包含前提参数和结论参数,用基于动态比例变换的改进遗传算法优化高斯函数的前提参数,用递推最小二乘辨识模糊模型的结论参数.最后通过著名的Box-Jenkins煤气炉数据仿真(仿真环境:MATLAB 6.5,计算机主频2.4 GHz,内存512 MB),并根据输入变量个数和模糊规则数,得到均方误差以证明本文方法的辨识精度,将该文辨识方法与其他方法进行比较,验证了该方法辨识精度更高.     

Identification of evolving fuzzy rule-based models

An approach to identification of evolving fuzzy rule-based (eR) models is proposed. eR models implement a method for the noniterative update of both the rule-base structure and parameters by incremental unsupervised learning. The rule-base evolves by adding more informative rules than those that previously formed the model. In addition, existing rules can be replaced with new rules based on ranking using the informative potential of the data. In this way, the rule-base structure is inherited and updated when new informative data become available, rather than being completely retrained. The adaptive nature of these evolving rule-based models, in combination with the highly transparent and compact form of fuzzy rules, makes them a promising candidate for modeling and control of complex processes, competitive to neural networks. The approach has been tested on a benchmark problem and on an air-conditioning component modeling application using data from an installation serving a real building. The results illustrate the viability and efficiency of the approach.     

Chattering-free fuzzy variable structure control for multivariable nonlinear systems

In this paper, a fuzzy logic controller (FLC) based variable structure control (VSC) with guaranteed stability for multivariable systems is presented. It is aimed at obtaining an improved performance of nonlinear multivariable systems. The main contribution of this work is firstly developing a generic matrix formulation of the FLC-VSC algorithm for nonlinear multivariable systems, with a special attention to non-zero final state. Secondly, ensuring the global stability of the controlled system. The multivariable nonlinear system is represented by T-S fuzzy model. The identification of the T-S model parameters has been improved using the well known weighting parameters approach to optimize local and global approximation and modeling capability of T-S fuzzy model. The main problem encountered is that T-S identification method cannot be applied when the membership functions (MFs) are overlapped by pairs. This in turn restricts the application of the T-S method because this type of membership function has been widely used in control applications. In order to overcome the chattering problem a switching function is added as an additional fuzzy variable and will be introduced in the premise part of the fuzzy rules together with the state variables. A two-link robot system and a mixing thermal system are chosen to evaluate the robustness, effectiveness, accuracy and remarkable performance of proposed FLC-VSC method.     

Fuzzy bounded least-squares method for the identification of linearsystems

This paper presents the fuzzy bounded least-squares method which uses both linguistic information and numerical data to identify linear systems. This method introduces a new type of fuzzy system, i.e., a fuzzy interval system. The steps in the method are as follows: 1) to utilize all the available linguistic information to obtain a fuzzy interval system and then to use the fuzzy interval system to give the admissible model set (i.e., the set of all models which are acceptable and reasonable from the point of view of linguistic information); 2) to find a model in the admissible model set which best fits the available numerical data. It is shown that such a model can be obtained by a quadratic programming approach. By comparing this method with the least-squares method, it is proved that the model obtained by this method fits a real system better than the model obtained by the least-squares method. In addition, this method also checks the adequacy of linear models for modeling a given system during the identification process and can help one to decide whether it is necessary to use nonlinear models     

Building Sugeno-type models using fuzzy discretization andorthogonal parameter estimation techniques

This paper develops a new approach to building Sugeno-type models. The essential idea is to separate the premise identification from the consequence identification, while these are mutually related in the previous methods. A fuzzy discretization technique is suggested to determine the premise of the model, and an orthogonal estimator is provided to identify the consequence of the model. The orthogonal estimator can provide information about the model structure, or which terms to include in the model, and final parameter estimates in a very simple and efficient manner. The well-known gas furnace data of Box and Jenkins is used to illustrate the proposed modeling approach and to compare its performance with other statistical and fuzzy modeling approaches. It shows that the performance of the new approach compares favorably with these existing techniques     

A hybrid clustering and gradient descent approach for fuzzymodeling

In this paper, a hybrid clustering and gradient descent approach is proposed for automatically constructing a multi-input fuzzy model where only the input-output data of the identified system are available. The proposed approach is composed of two steps: structure identification and parameter identification. In the process of structure identification, a clustering method is proposed to provide a systematic procedure to determine the number of fuzzy rules and construct an initial fuzzy model from the given input-output data. In the process of parameter identification, the gradient descent method is used to tune the parameters of the constructed fuzzy model to obtain a more precise fuzzy model from the given input-output data. Finally, two examples of nonlinear system are given to illustrate the effectiveness of the proposed approach.