| 灰色Verhulst模型的参数特征研究 |
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| 引用本文： | 熊萍萍,党耀国,束慧,崔杰.灰色Verhulst模型的参数特征研究[J].长春光学精密机械学院学报,2012(1):105-108,111. |
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| 作者姓名： | 熊萍萍 党耀国 束慧 崔杰 |
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| 作者单位： | [1]南京航空航天大学经济与管理学院,南京210016 [2]南京信息工程大学数理学院,南京210044 [3]南京邮电大学数理学院,南京210003 |
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| 基金项目： | 国家自然科学基金项目（71071077,71171116）; 江苏省普通高校研究生科研创新计划资助项目（CXZZ11_0226）; 中国博士后科学基金（20100481137）; 全国教育科学规划教育部重点课题（DFA090215）; 南京航空航天大学基本科研业务费专项科研项目资助（NZ2010006）; 教育部人文社会科学青年基金资助项目（11YJC630032） |
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| 摘 要： | 对灰色Verhulst模型的建模数据序列作数乘变换,利用最小二乘法求出数乘变换后的参数序列,经过一系列的数学公式推导,分析了模型参数特征在数乘变换作用下的变化,讨论了数乘变换对模型的模拟预测值及相对误差的影响。研究结果表明,对建模序列作数乘变换,灰色Verhulst模型的模拟和预测效果不变,同时缩小建模数据的量级,简化建模过程,该结果对灰色Verhulst模型的进一步系统研究有着重要意义。最后,通过实例验证Verhulst模型特性研究的有效性和实用性。
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| 关 键 词： | 灰色Verhulst模型 数乘变换 最小二乘法 参数特征 |
Research on Characteristics of Grey Verhulst Model Based on Multiple Transformation |
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| XIONG Pingping,DANG Yaoguo,SHU Hui,CUI Jie.Research on Characteristics of Grey Verhulst Model Based on Multiple Transformation[J].Journal of Changchun Institute of Optics and Fine Mechanics,2012(1):105-108,111. |
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| Authors: | XIONG Pingping DANG Yaoguo SHU Hui CUI Jie |
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| Affiliation: | 1. College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 210016 ; 2. College of Mathematics and Physics, Nanjing University of Information Science and Technology, Nanjing 210044; 3. College of Mathematics and Physics, Nanjing University of Posts and Telecommunications, Nanjing 210003) |
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| Abstract: | Multiple transformation is made for the data series of grey Verhulst model. The least square estimate method is used in order to get parameters series of multiple transformation. Through a series of mathematical formula caculation, the change of muhiple transformation on parameters characteristics of the model is analyzed, and the effect of sire ulation and prediction values and the relative error of the transformed model are discussed.Research results show that the model simulative and predicative results do not change, while the magnitude of the datas is also reduced and the modeling process is simplified, when the original data series is transformed by multiple transformation.The results for the further system study of grey Verhulst model are of great significance. Finally, the validity and the practicality of characteristics research on the Verhulst model is proved by a real project. |
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| Keywords: | grey Verhulst model multiple transformation the least square estimate parameter characteristics |
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