【作者】 何海；

【导师】 陈绵云；

【作者基本信息】 华中科技大学 ， 控制理论与控制工程， 2004， 硕士

【摘要】 灰色系统理论的研究对象是“部分信息已知,部分信息未知”的“小样本”、“贫”信息不确定系统,它通过对“部分”已知信息的生成、开发去了解、认识现实世界,实现对系统运行行为和演化规律的正确把握和描述。灰色动态建模是灰色系统理论的核心,也是灰色系统理论与实际相结合的桥梁。因此,本文主要讨论和研究灰色动态建模技术,通过对现有建模方法的研究与分析,全面展现目前学界的研究成果和发展动态。论文以“灰色动态建模技术”为背景,对灰色动态建模原理,特别是对GM(n,h)和SCGM(n,h)两类模型的建模机理进行了深入的分析和研究。在此基础上,对GM(1,1)模型、SCGM(1,1)a0模型提出了新的改进方法。以“电视机”问题为范例,详细演示了灰色动态建模的实现过程,并对新陈代谢模型的应用方法进行了深入研究。论文的主要新成果如下:通过分析GM(1,1)模型的构造原理,指出GM(1,1)模型预测公式的系数选取存在缺陷。对此作者提出了一种新的系数选取方法,并在考虑理想绝对误差的情况下对新方法作了进一步拓展;在考虑误差扰动的情况下建立了一种拓广的SCGM(1,1)a0模型;首次用GM(1,1) 新陈代谢模型来预测“电视机问题”,取得了良好的建模效果。文章末尾提出分段建模构想,为解决实际问题提供了新思路。更多还原

【Abstract】 Grey System Theory (GST) studies on the indeterminate system with “a few samples” and “poor” information, which is in the situation of “part of information known, part of information unknown”. By generating and developing the “part of information known”, GST can help us understand and recognize the real world, and help us rightly master and describe the operational behavior and evolutional law of the investigated system. Grey Dynamic Modeling Technique (GDMT) is the core of GST, and is also the bridge between the GST and practice. Therefore, this paper mainly discusses the GDMT. By investigating and analyzing the presented gray modeling methods, this paper details the research results and evolutional situation of GDMT.Firstly this paper deeply analyzes and investigates the principle of GDMT, especially that of GM(n,h) model and SCGM(n,h) model. Then some new improved methods are proposed for GM(1,1) model and SCGM(1,1)a0 model. In the end the process and realization methods of GDMT are displayed in detail based on the example of famous “TV problem”. There are such new research results as follows:Analyze the structure principle of GM(1,1) , and point out that there exists defect at the coefficient’s choice of its prediction formula. Based on the principle that the total of errors equals to zero, a novel calculating method is proposed for this problem. Then the new method is further extended according to the criteria of absolute errors under ideal situation. A novel extended SCGM(1,1)a0 model is set up in the background of considering the error disturbances. Use GM(1,1) metabolism model to predict the output of TV and get satisfactory effects. This is the first time for scholars to use such way to resolve this problem. The thought of subsection modeling is also put forward, which provides a new idea for resolving realistic problems.更多还原