粗集在系统辨识中的应用研究

【作者】 李成栋；

【导师】 史开泉；

【作者基本信息】 山东大学 ， 系统理论， 2007， 硕士

【摘要】 系统辨识的目的是在输入输出观测的基础上，在指定的一类系统中，确定一个与被识别的系统等价的系统。系统辨识是建立系统数学模型的重要途径之一，而模型化方法是进行系统分析、设计、控制、决策的前提和基础。但是，对一些复杂系统或过程建立精确的数学模型是很困难的，因此，需要采用其他方法，从系统的输入输出量测值来辨识系统规律，构造系统近似模型。尽管这些模型可能比较粗糙，但是它们也能对复杂系统的基本特征给出严格的定量描述。近年来发展起来的粗集理论提供了这么一种手段。粗集理论仅利用数据本身提供的信息，无须任何先验知识就可以对数据进行分析，发现数据中隐藏的模式，因此，它可以用来辨识系统规律，进行系统分析。本文将讨论粗集在系统辨识中的应用，主要包括系统规则的获取和系统模糊建模；系统规则的获取是指由系统的输入输出观测数据得到反映系统输入输出特性的规则，系统模糊建模是指基于系统规则库构建系统模糊模型，以模拟系统的输入输出特性。首先，文章简要给出了粗集、决策表、决策规则和决策规则库的一些基本概念和结论，为后面的应用提供了理论基础。然后，在第三章中先讨论了基于粗集的规则获取步骤和算法，由此可以得到反映系统输入输出规律的基本规则库，但在基本规则库中，可能存在不一致规则，而不一致规则在应用中会引起不必要的麻烦，是不受欢迎的，为将不一致规则库一致化，文章先讨论基本规则库的概率性质，在此基础上，创新性地提出了最小损失规则库及最小错误率规则库的概念，并得出了相应的规则获取方法和应用该规则库时的理论错误率。接下来，在第四章，文章先讨论了系统模糊建模方法，指出了其不足，为弥补这些不足，提出了基于粗集的系统模糊建模方法。该法利用了粗集在属性约简和规则提取上的强大功能，采用第三章中的方法进行输入输出规则库的提取，自动生成一致的模糊规则库，并利用该模糊规则库建立系统的模糊模型。在第四章第三节，将文中的基于粗集的辨识方法用在了时间序列预测问题上并进行了仿真试验，仿真结果表明了该法的有效性。更多还原

【Abstract】 System identification aims to find out a system which is equivalent to the system being identified. System identification is one of the important approaches for system modeling, and modeling method provides a basis for systems analysis、 design、 control and decision-making. But for some complex systems, building accurate mathematic model is very difficult, so other methods are needed to build approximate models.Alt-hough these approximate models are not accurate, but they can reflect the basic laws of complex systems. Rough set theory which is developing rapidly in recent years provides such a tool.Without any prior knowledge, only based on the information provided in the data itself, Rough set theory can be used for data analysis and pattern recognition to find useful information hidden in the data .Therefore , it can be used for system identification and system analysis. Based on rough sets, this paper will mainly discuss system identification which includes rule acquisition and fuzzy system modeling. Here, rule acquisition intends to obtain the rules which reflect the input-output characteristics of complex systems. System modeling aims to construct a rule-based system to simulate the input-output characteristics of the complex system.First of all, some basic concepts, such as rough sets, decision table, decision rule and decision rule base, are given concisely. All these make a great theoretical preparation for the following applications. Then, in the third chapter, rule acquisition and the algorithm are discussed firstly. So the rule base (knowledge base) which reflects the input-output regulation can be obtained. But in this rule base, there maybe some inconsistent rules which will cause great trouble in our application. So in order to make these inconsistent rules consistent, the probability properties of basic rule base arediscu-ssed firstly, and then, the concepts of minimum-loss rule base and minimum-error-rate rule base are proposed innovatively. Through the discussion, the corresponding methods of consistent rule acquisition and the error-rate are obtained. Further more, in the fourth chapter, one method for fuzzy system modeling is discussed and its deficiency is analyzed firstly. In order to resolve its deficiency, a new method for fuzzy system modeling based on rough set is proposed. Based on the powerful ability of rough set on attribute reduction and rule acquisition, the fuzzy rules can be obtained automatically from the data. On the basis of the fuzzy rule base, a fuzzy system is designed. In chapter 4, the discussed method for system identification is used in the area of time series prediction, and simulating results indicates that this method is efficient.更多还原