灰色系统与神经网络分析方法及其应用研究
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摘要
系统科学是20世纪人类最伟大的科学成就之一。一般系统理论是系统科学的基础理论,它由L.V.Bertranffy提出,并经Klir、Mesarovic、Takahara以及Lin、Ma等学者发展,已经有许多极具指导意义的成果。其中,由Mesarovic、Takahara提出的数学一般系统理论致力于对输入输出系统的控制、决策等的研究,并提供了相当完善和精确的概念、结构及相关定理。灰色系统理论作为一种重要的一般系统理论形式,得到了广泛应用,特别是陈绵云提出的趋势关联分析理论和系统云建模理论为一般系统论在“贫”信息系统中的应用提供了新的途径。本文在这两者的基础上,利用人工神经网络作为主要手段,研究了控制系统中的建模、预测、聚类、智能控制和分布式计算等相关问题,论文的主要内容和成果如下:
在集中对一般系统论、“贫”信息系统理论的研究现状及发展趋势进行较为系统的综述基础上,探讨了一般系统论、“贫” 信息系统理论和控制系统三者之间的关系,对人工神经网络,特别是动态神经网络的发展状况进行了系统的概述,论证了“贫”信息与人工神经网络结合的可能性和必要性。为将一般系统理论、“贫” 信息系统理论和人工神经网络方法应用于控制系统奠定了基础。
提出了滞后系统的灰色预测及神经网络控制方法。针对小滞后的伺服系统提出了基于SCGM预测模型的误差预测控制方法,有效的改善了系统跟踪性能。讨论了GM(1,1) 预测模型和SCGM(1,1) 预测模型的特点,指出两者都是对能量系统建模的方法,其中GM(1,1) 模型要求发展系数较小,而SCGM(1,1) 模型则无此要求,两者对于扰动和突变都相当敏感。在此基础上,对于大滞后系统,提出了几种在不同情况下应用的灰色预测控制方案,特别是其中提出的的变步数灰色预测控制模型,能有效降低灰色预测带来的预测误差,而神经元控制器则提高了系统的自适应性能。
介绍了高阶神经网络的优越性所在,并提出了基于高阶动态神经网络对非线性动态系统建模的方法,研究了其收敛性,在此基础上给出了滤波回归算法、滤波误差算法以及动态BP算法这三种训练算法。进而利用数学一般系统理论中对一般动态系统规范表达式的论述将动态系统分为动态部分和静态部分,相应的提出了利用混合神经网络对一般动态系统建模的方法,论述了其优点,并讨论了分别学习方法和整体学习方法这两种在不同情况下应用的训练算法。
研究了趋势关联度的性质,指出其满足灰关联四公理,并体现了在“接近性”和“相似性”两方面的整体相关性。在此基础上提出了用趋势关联度指导遗传算法实现非线性系统参数辨识的方法和利用趋势关联距离公式进行时间序列聚类的方法,包括了用于定类别数的趋势关联K-Means聚类方法和用于定类别数且定类规模的基于单亲遗传算法的趋势关联聚类算法。
就灰色系统与神经网络融合的方法进行了探讨。首先,讨论了灰色预测方法和人工神经网络的互补性,提出了将灰色预测与人工神经网络的并联的灰色-神经网络混合预测模型。并在此基础上,就数据库规划、神经网络关联、自适应学习以及故障诊断等方面提出了模型的改进方案,以使其能应用于不同的环境。然后提出了利用系统云灰色模型指导建立神经网络和利用神经网络学习实现系统云灰色模型参数白化的模型和模型。从两个不同的层次上研究了灰色系统与神经网络互补的方法。
研究了一般寻优过程的特点,指出了其对分布式计算的需求和实现的可能性。然后基于一般系统理论中的信息系统开发方法提出了一般寻优过程的分解方法,将一般寻优过程分成了与问题相关的自动机和与问题无关的优化过程。在分布式软件架构方面,充分论述了CORBA体系的优越性,在此基础上提出了用CORBA架构在控制网络中实现分布式优化算法的软件方法。最后就并行遗传算法这一具体实例讨论了其在控制网络中的实现,并就并行遗传算法的特点提出了多项改进方案。从而从各方面论证了控制网络中实现分布式优化计算的方法,为实现分布式智能控制系统创造了条件。
System science is one of the most grandeur achievements of the 20th century. General system theory proposed by L.V.Bertranffy, Klir is the basic theory of system science. Mesarovic, Takahara and Lin developed general system theory and got many instructive results. The mathematical general system theory proposed by Mesarovic and Takahara does commit to the control and decision-making problems of input-output system and gives a series of concepts, structures and theorems in quit perfect and precision format. Meaning while, as an important part of general system theory, the gray system theory is widespread availability, especially the trend associate analyzing theory and system cloud modeling theory proposed by Prof. M.Y. Chen gives a novel way to apply general system theory in “poor” information system. This dissertation is based on the both theories, by using neural network methods, researches on the modeling, forecasting, clustering, intelligent control and distributed computing problems of control system. The main results of the dissertation is as follows:
By summarizing present state and perspectives of the researches on general system theory and “poor” information system, this dissertation discusses the relationship of general system theory, “poor” information system and control system. More over, the development status of artificial neural networks, especially the dynamic neural networks is introduced, as well the possibility and necessity of the combination of “poor” information system and neural network is proofed. These works give the feasibility of the application of general system theory, “poor” information system theory and neural network in control system.
The gray forecast and neural network control mode on lag system is proposed. Firstly, an error-forecast method for little lag servo systems is given in order to improve the tracing performance. Secondly, we discuss the features of prediction models GM(1,1) and SCGM(1,1), and indicate that both are modeling methods for energy system, in which GM(1,1) model requires a tiny develop coefficient while SCGM(1,1) model not, while both are sensitive to disturbances and mutations. The article proposes several gray predicted methods for great lag systems in variable circumstance, especially the step-varying gray
predicted control model that can abate prediction errors, and the neural controller that can improve the adaptability of control system.
By indicating the superiority of high-order neural networks, this dissertation proposes a modeling method for nonlinear dynamical system based on high-order neural networks and discusses its convergence property. More over, three training algorithms including filter regression algorithm, filter error algorithm and dynamical BP algorithm are given based on this network. With further discussing, the dynamical system is divided into dynamic part and static part using mathematic general system theory. The modeling method for general dynamical system is proposed with combined neural network with its merits indicated. Two training methods, partial learning method and global learning method, are discussed with certain circumstance.
Several features of trend relational grade are studied, which satisfied the four axioms of gray correlation, and externalized the integer correlation of approachability and comparability. A parameter identification method of nonlinear system based on genetic algorithm is proposed using trend relational grade as indication. A clustering method of temporal series is proposed by applying distance formula of trend relational grade, including the trend relational K-Means clustering for constant categories, trend relational clustering for constant categories and constant dimensions based on Partheno-Genetic algorithm.
The methods of coalescence of gray system and neural network are discussed. First of all, the complementation of gray predicted method and neural network is discussed, and proposes a gray-neural network prediction model combined both gray predicted method and neural netwo
在集中对一般系统论、“贫”信息系统理论的研究现状及发展趋势进行较为系统的综述基础上,探讨了一般系统论、“贫” 信息系统理论和控制系统三者之间的关系,对人工神经网络,特别是动态神经网络的发展状况进行了系统的概述,论证了“贫”信息与人工神经网络结合的可能性和必要性。为将一般系统理论、“贫” 信息系统理论和人工神经网络方法应用于控制系统奠定了基础。
提出了滞后系统的灰色预测及神经网络控制方法。针对小滞后的伺服系统提出了基于SCGM预测模型的误差预测控制方法,有效的改善了系统跟踪性能。讨论了GM(1,1) 预测模型和SCGM(1,1) 预测模型的特点,指出两者都是对能量系统建模的方法,其中GM(1,1) 模型要求发展系数较小,而SCGM(1,1) 模型则无此要求,两者对于扰动和突变都相当敏感。在此基础上,对于大滞后系统,提出了几种在不同情况下应用的灰色预测控制方案,特别是其中提出的的变步数灰色预测控制模型,能有效降低灰色预测带来的预测误差,而神经元控制器则提高了系统的自适应性能。
介绍了高阶神经网络的优越性所在,并提出了基于高阶动态神经网络对非线性动态系统建模的方法,研究了其收敛性,在此基础上给出了滤波回归算法、滤波误差算法以及动态BP算法这三种训练算法。进而利用数学一般系统理论中对一般动态系统规范表达式的论述将动态系统分为动态部分和静态部分,相应的提出了利用混合神经网络对一般动态系统建模的方法,论述了其优点,并讨论了分别学习方法和整体学习方法这两种在不同情况下应用的训练算法。
研究了趋势关联度的性质,指出其满足灰关联四公理,并体现了在“接近性”和“相似性”两方面的整体相关性。在此基础上提出了用趋势关联度指导遗传算法实现非线性系统参数辨识的方法和利用趋势关联距离公式进行时间序列聚类的方法,包括了用于定类别数的趋势关联K-Means聚类方法和用于定类别数且定类规模的基于单亲遗传算法的趋势关联聚类算法。
就灰色系统与神经网络融合的方法进行了探讨。首先,讨论了灰色预测方法和人工神经网络的互补性,提出了将灰色预测与人工神经网络的并联的灰色-神经网络混合预测模型。并在此基础上,就数据库规划、神经网络关联、自适应学习以及故障诊断等方面提出了模型的改进方案,以使其能应用于不同的环境。然后提出了利用系统云灰色模型指导建立神经网络和利用神经网络学习实现系统云灰色模型参数白化的模型和模型。从两个不同的层次上研究了灰色系统与神经网络互补的方法。
研究了一般寻优过程的特点,指出了其对分布式计算的需求和实现的可能性。然后基于一般系统理论中的信息系统开发方法提出了一般寻优过程的分解方法,将一般寻优过程分成了与问题相关的自动机和与问题无关的优化过程。在分布式软件架构方面,充分论述了CORBA体系的优越性,在此基础上提出了用CORBA架构在控制网络中实现分布式优化算法的软件方法。最后就并行遗传算法这一具体实例讨论了其在控制网络中的实现,并就并行遗传算法的特点提出了多项改进方案。从而从各方面论证了控制网络中实现分布式优化计算的方法,为实现分布式智能控制系统创造了条件。
System science is one of the most grandeur achievements of the 20th century. General system theory proposed by L.V.Bertranffy, Klir is the basic theory of system science. Mesarovic, Takahara and Lin developed general system theory and got many instructive results. The mathematical general system theory proposed by Mesarovic and Takahara does commit to the control and decision-making problems of input-output system and gives a series of concepts, structures and theorems in quit perfect and precision format. Meaning while, as an important part of general system theory, the gray system theory is widespread availability, especially the trend associate analyzing theory and system cloud modeling theory proposed by Prof. M.Y. Chen gives a novel way to apply general system theory in “poor” information system. This dissertation is based on the both theories, by using neural network methods, researches on the modeling, forecasting, clustering, intelligent control and distributed computing problems of control system. The main results of the dissertation is as follows:
By summarizing present state and perspectives of the researches on general system theory and “poor” information system, this dissertation discusses the relationship of general system theory, “poor” information system and control system. More over, the development status of artificial neural networks, especially the dynamic neural networks is introduced, as well the possibility and necessity of the combination of “poor” information system and neural network is proofed. These works give the feasibility of the application of general system theory, “poor” information system theory and neural network in control system.
The gray forecast and neural network control mode on lag system is proposed. Firstly, an error-forecast method for little lag servo systems is given in order to improve the tracing performance. Secondly, we discuss the features of prediction models GM(1,1) and SCGM(1,1), and indicate that both are modeling methods for energy system, in which GM(1,1) model requires a tiny develop coefficient while SCGM(1,1) model not, while both are sensitive to disturbances and mutations. The article proposes several gray predicted methods for great lag systems in variable circumstance, especially the step-varying gray
predicted control model that can abate prediction errors, and the neural controller that can improve the adaptability of control system.
By indicating the superiority of high-order neural networks, this dissertation proposes a modeling method for nonlinear dynamical system based on high-order neural networks and discusses its convergence property. More over, three training algorithms including filter regression algorithm, filter error algorithm and dynamical BP algorithm are given based on this network. With further discussing, the dynamical system is divided into dynamic part and static part using mathematic general system theory. The modeling method for general dynamical system is proposed with combined neural network with its merits indicated. Two training methods, partial learning method and global learning method, are discussed with certain circumstance.
Several features of trend relational grade are studied, which satisfied the four axioms of gray correlation, and externalized the integer correlation of approachability and comparability. A parameter identification method of nonlinear system based on genetic algorithm is proposed using trend relational grade as indication. A clustering method of temporal series is proposed by applying distance formula of trend relational grade, including the trend relational K-Means clustering for constant categories, trend relational clustering for constant categories and constant dimensions based on Partheno-Genetic algorithm.
The methods of coalescence of gray system and neural network are discussed. First of all, the complementation of gray predicted method and neural network is discussed, and proposes a gray-neural network prediction model combined both gray predicted method and neural netwo
引文
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