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.     

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.     

Fuzzy identification using fuzzy neural networks with stable learning algorithms

In general, fuzzy neural networks cannot match nonlinear systems exactly. Unmodeled dynamic leads parameters drift and even instability problem. According to system identification theory, robust modification terms must be included in order to guarantee Lyapunov stability. This paper suggests new learning laws for Mamdani and Takagi-Sugeno-Kang type fuzzy neural networks based on input-to-state stability approach. The new learning schemes employ a time-varying learning rate that is determined from input-output data and model structure. Stable learning algorithms for the premise and the consequence parts of fuzzy rules are proposed. The calculation of the learning rate does not need any prior information such as estimation of the modeling error bounds. This offer an advantage compared to other techniques using robust modification.     

NeuroFAST: on-line neuro-fuzzy ART-based structure and parameterlearning TSK model

NeuroFAST is an on-line fuzzy modeling learning algorithm, featuring high function approximation accuracy and fast convergence. It is based on a first-order Takagi-Sugeno-Kang (TSK) model, where the consequence part of each fuzzy rule is a linear equation. Structure identification is performed by a fuzzy adaptive resonance theory (ART)-like mechanism, assisted by fuzzy rule splitting and adding procedures. The well known delta rule continuously performs parameter identification on both premise and consequence parameters. Simulation results indicate the potential of the algorithm. It is worth noting that NeuroFAST achieves a remarkable performance in the Box and Jenkins gas furnace process, outperforming all previous approaches compared.     

Fuzzy rule-base driven orthogonal approximation

In this study, orthogonal approximation concept is applied to fuzzy systems. We propose a new useful model adapted from the well-known Sugeno type fuzzy system. The proposed fuzzy model is a generalization of the zero-order Sugeno fuzzy system model. Instead of linear functions in standard Sugeno model, we use nonlinear functions in the consequent part. The nonlinear functions are selected from a trigonometric orthogonal basis. Orthogonal function parameters are trained along with the Sugeno fuzzy system. The proposed model is demonstrated using three simulations—a nonlinear piecewise-continuous scalar function modeling and filtering, nonlinear dynamic system identification, and time series prediction. Finally some performance comparisons are carried out.     

基于移动率的T-S模糊模型的结构辨识方法

为了提高现行模糊辨识方法的有效性,提出了基于移动率的T-S模糊模型的结构辫识方法。主要工作如下: 首先,定义I=S模糊模型的S型、Z型和梯形隶属函数的移动率,将此移动率与现行的隶属度相比较可以看出,提出的 方法比较有效;然后,定义基于移动率的T-S模糊推理方法,并且提出基于移动率的前提和结论部分的子S模型的辫 识方法;最后,将提出的识别方法应用于降水量和安全形势的预测模糊建模。测试结果表明,与现行方法和模糊神经 网络算法相比,该方法明显提高了模糊辨识的有效性,减少了规则数目,并降低了辫识误差。     

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。     

基于神经模糊方法的复杂系统建模

本文提出一种基于模糊模型同径向基函数网络相结合的复杂系统建模方法．该方法表 明具有确定后件结构的MTS模糊模型与径向基函数网络之间有一种直接对应关系,基于这种 对应,我们可把MTS模型的前件结构确定和后件结构辨识分开,利用径向基函数网络的学习 特性和其它学习算法相结合来得到模糊模型．该方法简单且能达到较高精度．仿真实例说明 了所提方法的有效性．     

Hybrid learning-based neuro-fuzzy inference system: a new approach for system modeling

In this article, a hybrid learning neuro-fuzzy inference system (HLNFIS) with a new inference mechanism is proposed for system modeling. In the HLNFIS, the incoming signal is fuzzified by the proposed improved Gaussian membership function (IGMF), which is derived from two standard Gaussian functions. With the premise construction with IGMFs, the system inference ability can be upgraded. The fuzzy inference processor, which involves both numerical and linguistic reasoning, is introduced in rule base construction. For effective parameter learning, the hybrid algorithm of random optimization (RO) and least square estimation (LSE) is exploited, where the premise and the consequence parameters of are updated by RO and LSE, respectively. To validate the feasibility and the potential of the proposed approach, three examples of system modeling are conducted. Through experimental results and comparisons the proposed HLNFIS shows excellent performance for complex modeling.     

The fuzzy crystallization algorithm: a new approach to complexsystems modeling

A new identification method for fuzzy modeling is introduced. Since the method has some analogy with the process of material crystallization in nature, the name of fuzzy crystallization algorithm (FCA) is given to this novel approach. This method accomplishes structure identification and parameter identification at the same time, and possesses the properties of simplicity, flexibility, and high calculation speed. Compared with other modeling strategies, it is easier to construct a model with a specific accuracy. Numerical examples are provided to demonstrate the performance of this approach.