基于模糊模型的结构和参数的一体化辨识

基于模糊集合的模糊建模捕述复杂、病态、非线性系统的特性是一种有效方法．文中讨论了从样本数据中通过正交变换和模糊聚类获取模糊规则的方法．利用正交最小二乘对模糊聚类的结果进行变换,采用CGS（Classical Gram—Schmidt）方法确定对建模贡献大的规则,删除对建模贡献小的规则,并对模型中的参数进行估计,能够同时模对糊模型的结构和参数进行辨识．仿真结果表明,提出的方法能够对非线性系统进行模糊建模．     

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.     

一种基于精简的模糊规则库的分类算法*

结合模糊聚类和粗糙集提出了一种基于精简的模糊规则库分类算法.对于数值型样本数据,首先采用模糊聚类生成模糊规则库,然后运用粗糙集理论对样本属性进行约简,删除冗余规则,即可得到精简的模糊规则库,以方便进行分类决策.通过对IRIS的仿真测试表明,本算法所产生的模糊规则不仅简单易懂,而且分类效果很好.     

基于论域空间模糊划分的粗集神经网络

针对粗集神经网络构建过程中的论域空间划分问题,提出一种基于模糊聚类的论域划分方法。将带交叉变异算子的粒子群优化算法(PSO)与模糊C-均值聚类算法(FCM)相结合,给出一种新的模糊聚类算法CMPSO-FCM,该算法具有良好的搜索能力和聚类效果。提出一种基于信息熵的模糊粗糙集决策规则获取方法,并用获取的规则指导粗集神经网络的构建。实验结果表明,该方法构造的神经网络具有更精简的结构、较好的分类精度和泛化能力。     

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.     

基于聚类的迭代双向最近点机器人位姿估计

针对迭代最近点（ICP）算法在存在严重遮挡的情况下容易陷入局部最小值的问题,对最近点规则（CP） 进行了修改,提出双向最近点规则（DCP）．DCP 规则包含两次CP 规则对应,使计算量增加了一倍．为了降低算法 的复杂度,继而提出基于聚类的迭代双向最近点（IDCP BoC）算法．IDCP BoC 对扫描数据进行聚类,在聚类的基础 上进行数据精简．在相邻两次迭代的残差之差小于某个阈值之前,用精简数据进行迭代以提高计算速度,之后再改 用非精简数据以保证精度．实验结果表明,IDCP BoC 算法能够有效避免陷入局部最小值的问题且其实时性也是可 接受的．     

基于在线聚类的模糊建模方法及其应用

针对复杂非线性动态系统的模糊建模问题,提出了一种基于在线聚类的模糊建模方法。该方法首先采用在线聚类算法辨识T-S模型的前提参数,然后采用递推最小二乘算法辨识结论参数。根据系统过程中新的数据信息,模糊规则可以自动增加、修改和删除,实现了模型结构和参数的在线辨识和更新。最后将提出的方法应用于Box-Jenkin煤气炉建模和二自由度机器人建模两个例子。仿真结果表明,基于该方法辨识的T-S模糊模型具有很高的精度,而且模型结构简单、建模速度快,便于工程应用。     

一种基于GA优化模糊推理神经网络的新方法

通过对已有的一些基于遗传算法（GA）优化模糊系统方法的分析，指出了它们存在的一些缺陷，提出了一种新颖的基于GA优化模型推理神经网络的方法，并给出了相应的优化算法，这种方法可以对模糊推理系统中的所有结构和参数同时或分别进行优化。在此基础上，还讨论了模糊推理神经网络的精简问题，如无用模糊规则的删除，最后通过实例验证了该方法是一种很有效的方法，具有易理解，精度高，收敛快，泛化能力好且能全局收敛的优点。     

基于客观满意聚类的pH中和过程建模方法

针对一类生产中存在严重非线性的复杂工业过程——p H中和过程,基于客观聚类思想,并结合Gustafson-Kessel聚类,提出一种新的T-S模糊建模方法。根据用户对建模性能的满意度要求,通过迭代模糊聚类,进行模型前提结构和参数的辨识。仿真结果表明,与传统的模糊聚类等方法相比,该方法不依赖于系统的先验知识和预先定义的模糊隶属度函数,具有较为精简的结构和更好的逼近性能,对数据中的噪声具有一定的鲁棒性。     

基于聚类和SVD算法的模糊逻辑系统结构辨识

为了研究模糊逻辑系统新的结构辨识方法, 提出采用基于山峰函数的减法聚类算法构造模糊逻辑系统的初始结构, 并利用奇异值分解(SVD)算法分析了模糊规则与奇异值、累积贡献率以及索引向量的关系, 从而实现了模糊逻辑结构的优化. 最后, 对该算法的可行性和有效性进行了仿真验证和性能比较, 取得了较好的效果.     

基于聚类和SVD算法的解释性模糊建模方法

提出了一种基于减法聚类算法构造解释性模糊模型的方法。首先指出模糊模型解释性的重要地位,分析影响解释性的主要因素;然后利用减法聚类算法辨识初始模糊模型,SVD算法和集合非冗余度约简初始模糊模型,从而提高其解释性;最后采用约束优化算法整体优化模型,提高其精度。PH值中和过程的模糊建模验证了该方法的有效性。     

A fuzzy clustering method for generating fuzzy models

A systematic fuzzy approach considering both accuracy and interpretability is developed in the paper. First, a fuzzy modeling method based on a new objective function is proposed. The proposed method can deal with the problem where the input variables have an affect on the input space of the fuzzy system while the output variables do not exert any influence on input space of fuzzy system. Then rule reduction is performed to obtain the model structure of the fuzzy system by QR decomposition of the fuzzy reference matrix. According to analysis of the rank loss of the matrix, the important rules and unimportant rules can be confirmed in this paper. Simulation results demonstrate that the proposed approach can be used to build fuzzy models of nonlinear systems. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

一种基于多目标进化算法的模糊关联分类方法

准确率和解释性是模糊关联分类模型的两个相互制约的优化目标.目前已有的研究方法中,有的只考虑了分类模型的准确率,有的把模型两个目标转化为单目标问题求解,在模型解释性目标上的优化策略较简单.为此提出一种基于Apriori和NSGA-II多目标进化算法的模糊关联分类模型(MOEA-FACM),采用基于概率独立性的模糊确认指标筛选生成高质量的模糊关联规则集,以Pittsburgh式的编码方式构建准确率和解释性折中的模糊关联分类模型.标准数据集上的实验表明,该方法所建模型分类准确率比同类模型高,分类模型具有较好的泛化能力,而其所含模糊关联规则的数目和规则前件总的模糊项的个数却较少,模型的解释性较好.     

基于SVD 方法的简约型区间二型模糊模型构建

针对奇异值-QR分解方法存在有效奇异值难以确定的问题,采用奇异值分解方法分析从区间二型模糊模型抽取的两个激活强度矩阵,提出了奇异值归一化差值的概念以描述相邻奇异值的变化情况,从而反映了重要规则和冗余规则在奇异值变化上的本质差异;进而根据其临界点确定有效奇异值个数,并利用QR分解得到有效奇异值所对应的重要规则构建简约型区间二型模糊结构。仿真实例验证了所提出方法的有效性和可行性。     

Simplifying fuzzy rule-based models using orthogonal transformationmethods

An important issue in fuzzy-rule-based modeling is how to select a set of important fuzzy rules from a given rule base. Even though it is conceivable that removal of redundant or less important fuzzy rules from the rule base can result in a compact fuzzy model with better generalizing ability, the decision as to which rules are redundant or less important is not an easy exercise. In this paper, we introduce several orthogonal transformation-based methods that provide new or alternative tools for rule selection. These methods include an orthogonal least squares (OLS) method, an eigenvalue decomposition (ED) method, a singular value decomposition and QR with column pivoting (SVD-QR) method, a total least squares (TLS) method, and a direct singular value decomposition (D-SVD) method. A common attribute of these methods is that they all work on a firing strength matrix and employ some measure index to detect the rules that should be retained and eliminated. We show the performance of these methods by applying them to solving a nonlinear plant modeling problem. Our conclusions based on analysis and simulation can be used as a guideline for choosing a proper rule selection method for a specific application.     

Extracting Takagi-Sugeno Fuzzy Rules with Interpretable Submodels via Regularization of Linguistic Modifiers

In this paper, a method for constructing Takagi-Sugeno (TS) fuzzy system from data is proposed with the objective of preserving TS submodel comprehensibility, in which linguistic modifiers are suggested to characterize the fuzzy sets. A good property held by the proposed linguistic modifiers is that they can broaden the cores of fuzzy sets while contracting the overlaps of adjoining membership functions (MFs) during identification of fuzzy systems from data. As a result, the TS submodels identified tend to dominate the system behaviors by automatically matching the global model (GM) in corresponding subareas, which leads to good TS model interpretability while producing distinguishable input space partitioning. However, the GM accuracy and model interpretability are two conflicting modeling objectives, improving interpretability of fuzzy models generally degrades the GM performance of fuzzy models, and vice versa. Hence, one challenging problem is how to construct a TS fuzzy model with not only good global performance but also good submodel interpretability. In order to achieve a good tradeoff between GM performance and submodel interpretability, a regularization learning algorithm is presented in which the GM objective function is combined with a local model objective function defined in terms of an extended index of fuzziness of identified MFs. Moreover, a parsimonious rule base is obtained by adopting a QR decomposition method to select the important fuzzy rules and reduce the redundant ones. Experimental studies have shown that the TS models identified by the suggested method possess good submodel interpretability and satisfactory GM performance with parsimonious rule bases.     

Nature-inspired optimal tuning of input membership functions of Takagi-Sugeno-Kang fuzzy models for Anti-lock Braking Systems

This paper suggests a synergy of fuzzy logic and nature-inspired optimization in terms of the nature-inspired optimal tuning of the input membership functions of a class of Takagi-Sugeno-Kang (TSK) fuzzy models dedicated to Anti-lock Braking Systems (ABSs). A set of TSK fuzzy models is proposed by a novel fuzzy modeling approach for ABSs. The fuzzy modeling approach starts with the derivation of a set of local state-space models of the nonlinear ABS process by the linearization of the first-principle process model at ten operating points. The TSK fuzzy model structure and the initial TSK fuzzy models are obtained by the modal equivalence principle in terms of placing the local state-space models in the rule consequents of the TSK fuzzy models. An operating point selection algorithm to guide modeling is proposed, formulated on the basis of ranking the operating points according to their importance factors, and inserted in the third step of the fuzzy modeling approach. The optimization problems are defined such that to minimize the objective functions expressed as the average of squared modeling errors over the time horizon, and the variables of these functions are a part of the parameters of the input membership functions. Two representative nature-inspired algorithms, namely a Simulated Annealing (SA) algorithm and a Particle Swarm Optimization (PSO) algorithm, are implemented to solve the optimization problems and to obtain optimal TSK fuzzy models. The validation and the comparison of SA and PSO and of the new TSK fuzzy models are carried out for an ABS laboratory equipment. The real-time experimental results highlight that the optimized TSK fuzzy models are simple and consistent with both training data and validation data and that these models outperform the initial TSK fuzzy models.     

基于奇异值分解的非均匀采样非线性系统的模糊模型辨识

针对复杂、不确定、非均匀采样数据的非线性系统,提出一种基于矩阵奇异值分解(SVD)的模型结构辨识和参数估计的建模方法.首先,利用矩阵奇异值(SVD)分解算法分析各局部模型与奇异值、积累贡献率的关系,确定模糊模型的规则数,从而实现模型的结构优化;然后,为了克服递推最小二乘出现的误差积累、传递现象,采用奇异值分解的递推最小二乘估计模型的结论参数;最后,通过仿真实例验证所提出算法的有效性.     

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．