基于数据挖掘技术的模糊推理系统设计
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摘要
模糊推理系统由模糊规则集和模糊推理算法组成。通常模糊推理算法都是固定的标准算法,对系统的整体性能影响不大。因此,模糊系统建模成功的关键取决于模糊规则的质量。
而模糊规则的生成由模糊系统的结构辨识和隶属度函数的参数优化两步组成。模糊系统的结构辨识旨在为每个输入变量定义适合的模糊分区以及确定对应的模糊IF-THEN规则。结构辨识的方法分为两种：基于先验知识的方法和数据驱动的方法。基于先验知识的方法依据专业知识估计输入输出模糊集的数量,总结IF-THEN规则。尽管该方法有过一些成功的应用,但基于先验知识的方法十分耗时,需要进行复杂的经验总结才能归纳出最终的模糊规则。而数据驱动的方法运用数据挖掘技术或者其他计算机智能方法,能够直接从数据中提取适合的模糊规则。T-S模糊模型和模糊基函数模型是两种广泛应用的模糊模型。已经证明模糊模型能够全局逼近非线性映射函数。为确定模糊基函数模型,王立新和孟德尔提出了一种简单实用的方法从数值数据中抽取模糊规则,并命名为WM算法。由于WM算法简单有效,各领域的研究人员和工程师已经广泛运用该方法进行模糊建模。但对WM算法的进一部研究表明,可以改进WM算法生成模糊规则的鲁棒性。
本文提出了一种利用数据挖掘技术构建模糊推理系统的新方法。在模糊规则的结构辨识方面,引入数据挖掘中支持度和信任度的概念改进模糊规则提取算法,使架构的模糊系统对异常值和噪声数据具有更好的鲁棒性。在隶属度函数的参数优化方面,本文通过调整模糊隶属度函数的中心位置以及增减模糊集的数量,使模糊系统的拓扑结构与输入输出数据分布相适应。并且优化算法能够从程序生成的不同系统结构中,选择系统近视精度与模糊规则复杂度最好折衷的系统架构。
最后,针对时间序列问题分别对经典的Mackey-Glass混沌时间序列和实船操纵运动时间序列进行了仿真建模。在对Mackey-Glass混沌时间序列建模中,通过全面的仿真对比分析,证明了本文所提出的数据挖掘算法确实比现有的WM算法有更强的鲁棒性。在对船舶操纵运动时间预报中,运用本文提出的数据挖掘方法处理实船Z型试验收集数据。数据挖掘算法通过提取模糊规则搭建模糊推理系统,对船舶操纵运动进行系统辨识。相比传统的建模方法,模糊推理系统的架构不必依据固有的框架确定船舶动态系数,避免了生成不匹配模型的情况。另外,由于在船舶航行的海况复杂,存在的风、浪、流等外部环境干扰,所收集的船舶操纵数据中经常混入噪声影响系统建模。而基于数据挖掘算法所生成的模糊推理系统具有良好的鲁棒性,因而能够满足实际情况要求,进行较精确的系统辨识和数据预测。
Fuzzy inference systems are composed of a set of fuzzy rules and a fuzzy inference engine. Fuzzy inference algorithms are standard and usually have little impact on the system's performance. Therefore, the success of fuzzy modeling relies heavily on the quality of fuzzy rule base.
The generation of fuzzy rules generally involves two steps:structure identification of fuzzy rules and parameter optimization of membership functions. Structure identification aims to construct a basic system with a given space partitioning and the corresponding set of fuzzy If-Then rules. The structure identification methods can be grouped into two categories:apriori knowledge-based approaches and data-driven approaches. Apriori knowledge-based approaches employ domain experts to estimate the numbers of fuzzy sets of input/output variables and then summarize the IF-THEN rules. Some successful applications show that this approach works favorably, although it is time-consuming, and some empirical studies have to be carried out before the finalization of the fuzzy rulebase. Data-driven approaches can employ data mining or other computational intelligence techniques to extract fuzzy rules from numerical data directly. Two popular and widely used fuzzy models are the Takagi-Sugeno fuzzy model and the fuzzy basis function model. It has been proved that these fuzzy models have universal approximation power as regards nonlinear maps. To identify the fuzzy basis function model, Wang and Mendel proposed a simple and practical algorithm, termed the WM algorithm, for the extraction of fuzzy rules from numerical data. This algorithm for fuzzy modeling have been highly cited and widely used by researchers and engineers in various domains due to their simplicity and effectiveness. A further study of this WM algorithm revealed that there is further opportunity to improve robustness of the fuzzy rule base.
In this paper, a novel method based on data mining technique is proposed to construct fuzzy inference system. In structure identification of fuzzy rules, the conceptions of support degree and confidence degree defined in data mining are introduced to improve the fuzzy rule extraction algorithm, which make the resulting fuzzy inference system more robust with respect to the noises or outliers. In parameter optimization of membership functions, the fuzzy inference system is optimized with a partition refining strategy, adjusting the center locations of the membership functions and adding fuzzy sets, so that the structure is more suitable for the input-output data. In addition, the optimization program can select from the different structures obtained to construct a fuzzy system the one providing the best compromise between the accuracy of the approximation and the complexity of the rule set.
At last, aiming at time series forecasting problems, the classical Mackey-Glass chaotic time series and the actual ship maneuvering time series is simulated. With comprehensive robustness analysis, the fuzzy inference system constructed by data mining algorithm is proved to be more robust than the system constructed by the WM method in the Mackey-Glass chaotic time series modeling. In the ship maneuvering time series modeling, our data mining algorithm is used to deal with the data information generated by an actual ship zig-zag test. The ship maneuvering model is constructed by a fuzzy inference system using fuzzy rule extracting algorithm. Compared with the traditional modeling method, the construction of a fuzzy inference system does not have to characterize the ship manoeuvrability in a unified framework, which avoids constructing a mismatched model. In addition, ship maneuvering characteristics are often interfered by the complex flow, wind and wave on the actual voyage. Lots of unavoidable noise and outliers are mixed in ship maneuvering time series records. The fuzzy inference system based on data mining technology itself is a robust system. Therefore, the system generated by data mining algorithm could meet the actual demand to make an accurate system modeling and data forecasting.
而模糊规则的生成由模糊系统的结构辨识和隶属度函数的参数优化两步组成。模糊系统的结构辨识旨在为每个输入变量定义适合的模糊分区以及确定对应的模糊IF-THEN规则。结构辨识的方法分为两种：基于先验知识的方法和数据驱动的方法。基于先验知识的方法依据专业知识估计输入输出模糊集的数量,总结IF-THEN规则。尽管该方法有过一些成功的应用,但基于先验知识的方法十分耗时,需要进行复杂的经验总结才能归纳出最终的模糊规则。而数据驱动的方法运用数据挖掘技术或者其他计算机智能方法,能够直接从数据中提取适合的模糊规则。T-S模糊模型和模糊基函数模型是两种广泛应用的模糊模型。已经证明模糊模型能够全局逼近非线性映射函数。为确定模糊基函数模型,王立新和孟德尔提出了一种简单实用的方法从数值数据中抽取模糊规则,并命名为WM算法。由于WM算法简单有效,各领域的研究人员和工程师已经广泛运用该方法进行模糊建模。但对WM算法的进一部研究表明,可以改进WM算法生成模糊规则的鲁棒性。
本文提出了一种利用数据挖掘技术构建模糊推理系统的新方法。在模糊规则的结构辨识方面,引入数据挖掘中支持度和信任度的概念改进模糊规则提取算法,使架构的模糊系统对异常值和噪声数据具有更好的鲁棒性。在隶属度函数的参数优化方面,本文通过调整模糊隶属度函数的中心位置以及增减模糊集的数量,使模糊系统的拓扑结构与输入输出数据分布相适应。并且优化算法能够从程序生成的不同系统结构中,选择系统近视精度与模糊规则复杂度最好折衷的系统架构。
最后,针对时间序列问题分别对经典的Mackey-Glass混沌时间序列和实船操纵运动时间序列进行了仿真建模。在对Mackey-Glass混沌时间序列建模中,通过全面的仿真对比分析,证明了本文所提出的数据挖掘算法确实比现有的WM算法有更强的鲁棒性。在对船舶操纵运动时间预报中,运用本文提出的数据挖掘方法处理实船Z型试验收集数据。数据挖掘算法通过提取模糊规则搭建模糊推理系统,对船舶操纵运动进行系统辨识。相比传统的建模方法,模糊推理系统的架构不必依据固有的框架确定船舶动态系数,避免了生成不匹配模型的情况。另外,由于在船舶航行的海况复杂,存在的风、浪、流等外部环境干扰,所收集的船舶操纵数据中经常混入噪声影响系统建模。而基于数据挖掘算法所生成的模糊推理系统具有良好的鲁棒性,因而能够满足实际情况要求,进行较精确的系统辨识和数据预测。
Fuzzy inference systems are composed of a set of fuzzy rules and a fuzzy inference engine. Fuzzy inference algorithms are standard and usually have little impact on the system's performance. Therefore, the success of fuzzy modeling relies heavily on the quality of fuzzy rule base.
The generation of fuzzy rules generally involves two steps:structure identification of fuzzy rules and parameter optimization of membership functions. Structure identification aims to construct a basic system with a given space partitioning and the corresponding set of fuzzy If-Then rules. The structure identification methods can be grouped into two categories:apriori knowledge-based approaches and data-driven approaches. Apriori knowledge-based approaches employ domain experts to estimate the numbers of fuzzy sets of input/output variables and then summarize the IF-THEN rules. Some successful applications show that this approach works favorably, although it is time-consuming, and some empirical studies have to be carried out before the finalization of the fuzzy rulebase. Data-driven approaches can employ data mining or other computational intelligence techniques to extract fuzzy rules from numerical data directly. Two popular and widely used fuzzy models are the Takagi-Sugeno fuzzy model and the fuzzy basis function model. It has been proved that these fuzzy models have universal approximation power as regards nonlinear maps. To identify the fuzzy basis function model, Wang and Mendel proposed a simple and practical algorithm, termed the WM algorithm, for the extraction of fuzzy rules from numerical data. This algorithm for fuzzy modeling have been highly cited and widely used by researchers and engineers in various domains due to their simplicity and effectiveness. A further study of this WM algorithm revealed that there is further opportunity to improve robustness of the fuzzy rule base.
In this paper, a novel method based on data mining technique is proposed to construct fuzzy inference system. In structure identification of fuzzy rules, the conceptions of support degree and confidence degree defined in data mining are introduced to improve the fuzzy rule extraction algorithm, which make the resulting fuzzy inference system more robust with respect to the noises or outliers. In parameter optimization of membership functions, the fuzzy inference system is optimized with a partition refining strategy, adjusting the center locations of the membership functions and adding fuzzy sets, so that the structure is more suitable for the input-output data. In addition, the optimization program can select from the different structures obtained to construct a fuzzy system the one providing the best compromise between the accuracy of the approximation and the complexity of the rule set.
At last, aiming at time series forecasting problems, the classical Mackey-Glass chaotic time series and the actual ship maneuvering time series is simulated. With comprehensive robustness analysis, the fuzzy inference system constructed by data mining algorithm is proved to be more robust than the system constructed by the WM method in the Mackey-Glass chaotic time series modeling. In the ship maneuvering time series modeling, our data mining algorithm is used to deal with the data information generated by an actual ship zig-zag test. The ship maneuvering model is constructed by a fuzzy inference system using fuzzy rule extracting algorithm. Compared with the traditional modeling method, the construction of a fuzzy inference system does not have to characterize the ship manoeuvrability in a unified framework, which avoids constructing a mismatched model. In addition, ship maneuvering characteristics are often interfered by the complex flow, wind and wave on the actual voyage. Lots of unavoidable noise and outliers are mixed in ship maneuvering time series records. The fuzzy inference system based on data mining technology itself is a robust system. Therefore, the system generated by data mining algorithm could meet the actual demand to make an accurate system modeling and data forecasting.
引文
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