基于模糊聚类的非线性系统辨识研究
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摘要
在控制工程领域中,非线性系统的建模与辨识是控制、管理和故障诊断系统设计的重要环节。由于传统方法不能有效地对复杂和不确定系统进行建模,因此需要一种能够描述非线性系统的全局函数或者解析结构。Zadeh提出一种有效的方法来描述不能用精确数学模型表达的复杂或者病态系统。近年来模糊逻辑理论在非线性系统辨识中的应用以及在基本理论方面的研究工作已经取得了一定的进展并形成了较为完整的理论框架。
模糊集合理论和模糊逻辑的概念应用在系统建模中有许多方式,其中应用最广泛的是系统变量之间的关系通过if-then规则来描述的基于模糊规则的系统。而在基于模糊规则的系统中研究较多的是T-S模糊模型。本文利用模糊聚类算法对T-S模糊模型进行模糊划分。
基于目标函数的模糊C均值(Fuzzy C-Mean, FCM)算法是当前研究较为成熟的模糊聚类算法。本文首先利用G-K聚类算法和FCM聚类算法进行模糊空间划分,并将之用于T-S模糊模型的辨识过程中。针对FCM算法本身的缺陷利用一种改进的模糊划分聚类算法应用于T-S模糊模型的辨识过程中,仿真结果表明,该算法在一定程度上提高了辨识精度。
模糊C回归模型(Fuzzy C-Regression Model, FCRM)是对系统的输入-输出数据进行超平面分类,把输入-输出数据分成若干类,每一类的输入-输出数据对应一个回归模型,可以很好地描述T-S模糊模型的数据空间结构。本文在FCRM聚类算法的基础上,对其目标函数增加FCM算法的目标函数,利用一种改进模糊划分方法,提高了辨识精度。
基于模糊函数的模糊系统建模方法利用一些模糊函数表达式来描述模糊系统,而不是if-then规则。基于模糊函数的模糊系统用一组线性或者非线性函数来表示。其输入变量在包括了系统输入变量的同时,还包含了当前输入变量的隶属度,或者隶属度的一些转换形式。输入变量的模糊聚类个数,即为该模糊函数系统的函数个数。本文通过在FCM样本距离中加入了FCRM距离,提高了系统的辨识精度。
本文的主要工作和创新点包括：
1.对T-S模糊模型的两种表示形式,分别利用G-K聚类算法和FCM聚类算法进行辨识研究；
2.利用一种改进的模糊划分聚类算法对T-S模糊模型进行辨识研究；
3.提出了一种基于改进模糊C回归模型聚类算法的T-S模糊模型辨识算法；
4.提出了一种基于混合聚类算法的模糊函数系统辨识方法。
In the field of control engineering, the nonlinear system's modeling and identification is an important part of control, management and fault diagnosis system design. Considering the defect of the traditional methods in modeling the complex and uncertain systems, a global function or an analytic structure that can describe the nonlinear systems becomes a necessity. Zadeh proposed an effective method to describe the complex or pathological systems which can not be expressed by a precise mathematical model. In recent years, the application of the fuzzy logic theory in the basic theory research of nonlinear system identification has made some progress and has formed a relatively complete theoretical framework.
In the system modeling, there are many ways to apply the theory of fuzzy set and the concept of fuzzy logic, with the following one being the most widely used----the fuzzy rule based systems in which the relation between system variables is through if-then rules. As to this type of systems, most of the in-depth studies focus on the T-S fuzzy model. Thus, fuzzy clustering algorithm is applied for fuzzy partion of T-S fuzzy model in this article.
The Fuzzy C-Mean (FCM) that is based on objective functions is a fuzzy clustering algorithm of great maturity. At first, the paper makes the space partition for the identification of the T-S Fuzzy Model by using the G-K and the FCM clustering algorithms. Then an improved fuzzy partion clustering algorithm is used to make up the defects of the FCM algorithm itself. At last, the simulation results show that this algorithm can improve the recognition accuracy to a certain extent.
The Fuzzy C-Regression Model (FCRM) serves as a hyperplane classification of the input-output datum. It divides the datum into several classes, each of which is corresponding to a regression model. Therefore, the data spatial structure of the T-S Fuzzy Model is precisely described. Basing on the FCRM algorithm, an improved fuzzy partition method to the objective functions of FCM algorithm so as to improve the accuracy of identification is proposed in this article.
In fuzzy systems that are based on fuzzy functions, the modeling methods use some fuzzy functions rather than the if-then rules to describe the system characteristics----a set of linear or nonlinear function in concrete. The input variables also include the current membership of input variable, or the conversion of some form of membership apart from the system input variables. The number of the fuzzy clustering in the input variables equals to the number of functions in the fuzzy function system. In this paper, the FCRM distance is added into the distance among the FCM samples in order to improve the identification accuracy of the system.
The main work and innovations are as follows:
1. By using G-K and the FCM clustering algorithms, two T-S fuzzy models has been described, identified and studied respectively.
2. An improved fuzzy partion clustering is applied for T-S fuzzy model identification.
3. Propoed an improved fuzzy c-regression model clustering algorithm for T-S fuzzy model identification.
4. Propoed a fuzzy function system identification method based on hybrid clustering algorithm.
模糊集合理论和模糊逻辑的概念应用在系统建模中有许多方式,其中应用最广泛的是系统变量之间的关系通过if-then规则来描述的基于模糊规则的系统。而在基于模糊规则的系统中研究较多的是T-S模糊模型。本文利用模糊聚类算法对T-S模糊模型进行模糊划分。
基于目标函数的模糊C均值(Fuzzy C-Mean, FCM)算法是当前研究较为成熟的模糊聚类算法。本文首先利用G-K聚类算法和FCM聚类算法进行模糊空间划分,并将之用于T-S模糊模型的辨识过程中。针对FCM算法本身的缺陷利用一种改进的模糊划分聚类算法应用于T-S模糊模型的辨识过程中,仿真结果表明,该算法在一定程度上提高了辨识精度。
模糊C回归模型(Fuzzy C-Regression Model, FCRM)是对系统的输入-输出数据进行超平面分类,把输入-输出数据分成若干类,每一类的输入-输出数据对应一个回归模型,可以很好地描述T-S模糊模型的数据空间结构。本文在FCRM聚类算法的基础上,对其目标函数增加FCM算法的目标函数,利用一种改进模糊划分方法,提高了辨识精度。
基于模糊函数的模糊系统建模方法利用一些模糊函数表达式来描述模糊系统,而不是if-then规则。基于模糊函数的模糊系统用一组线性或者非线性函数来表示。其输入变量在包括了系统输入变量的同时,还包含了当前输入变量的隶属度,或者隶属度的一些转换形式。输入变量的模糊聚类个数,即为该模糊函数系统的函数个数。本文通过在FCM样本距离中加入了FCRM距离,提高了系统的辨识精度。
本文的主要工作和创新点包括：
1.对T-S模糊模型的两种表示形式,分别利用G-K聚类算法和FCM聚类算法进行辨识研究；
2.利用一种改进的模糊划分聚类算法对T-S模糊模型进行辨识研究；
3.提出了一种基于改进模糊C回归模型聚类算法的T-S模糊模型辨识算法；
4.提出了一种基于混合聚类算法的模糊函数系统辨识方法。
In the field of control engineering, the nonlinear system's modeling and identification is an important part of control, management and fault diagnosis system design. Considering the defect of the traditional methods in modeling the complex and uncertain systems, a global function or an analytic structure that can describe the nonlinear systems becomes a necessity. Zadeh proposed an effective method to describe the complex or pathological systems which can not be expressed by a precise mathematical model. In recent years, the application of the fuzzy logic theory in the basic theory research of nonlinear system identification has made some progress and has formed a relatively complete theoretical framework.
In the system modeling, there are many ways to apply the theory of fuzzy set and the concept of fuzzy logic, with the following one being the most widely used----the fuzzy rule based systems in which the relation between system variables is through if-then rules. As to this type of systems, most of the in-depth studies focus on the T-S fuzzy model. Thus, fuzzy clustering algorithm is applied for fuzzy partion of T-S fuzzy model in this article.
The Fuzzy C-Mean (FCM) that is based on objective functions is a fuzzy clustering algorithm of great maturity. At first, the paper makes the space partition for the identification of the T-S Fuzzy Model by using the G-K and the FCM clustering algorithms. Then an improved fuzzy partion clustering algorithm is used to make up the defects of the FCM algorithm itself. At last, the simulation results show that this algorithm can improve the recognition accuracy to a certain extent.
The Fuzzy C-Regression Model (FCRM) serves as a hyperplane classification of the input-output datum. It divides the datum into several classes, each of which is corresponding to a regression model. Therefore, the data spatial structure of the T-S Fuzzy Model is precisely described. Basing on the FCRM algorithm, an improved fuzzy partition method to the objective functions of FCM algorithm so as to improve the accuracy of identification is proposed in this article.
In fuzzy systems that are based on fuzzy functions, the modeling methods use some fuzzy functions rather than the if-then rules to describe the system characteristics----a set of linear or nonlinear function in concrete. The input variables also include the current membership of input variable, or the conversion of some form of membership apart from the system input variables. The number of the fuzzy clustering in the input variables equals to the number of functions in the fuzzy function system. In this paper, the FCRM distance is added into the distance among the FCM samples in order to improve the identification accuracy of the system.
The main work and innovations are as follows:
1. By using G-K and the FCM clustering algorithms, two T-S fuzzy models has been described, identified and studied respectively.
2. An improved fuzzy partion clustering is applied for T-S fuzzy model identification.
3. Propoed an improved fuzzy c-regression model clustering algorithm for T-S fuzzy model identification.
4. Propoed a fuzzy function system identification method based on hybrid clustering algorithm.
引文
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