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| 灰色Verhulst 拓展模型的病态性问题 | |
| 引用本文： | 崔杰 刘思峰. 灰色Verhulst 拓展模型的病态性问题[J]. 控制与决策, 2014, 29(3): 567-571 |
| 作者姓名： | 崔杰 刘思峰 |
| 作者单位： | 1. 南京航空航天大学灰色系统研究所，南京210016 2. 淮阴工学院经济管理学院，江苏淮安223001 |
| 基金项目： | 国家自然科学基金项目(71301060, 71271226, 71171113, 71171116)；国家统计局科研计划项目(2011LY008)；教育部人文社会科学青年基金项目(11YJC630032, 13YJC630109); 中国博士后科学基金项目(20100481137)；江苏省高校社会科学基金项目(2013SJB6300009)；江苏省博士后科研计划项目(1101094C)；江苏省青蓝工 |
| 摘 要： | 有效判定灰色模型的病态性是进行灰预测建模的关键. 为了揭示灰色Verhulst 拓展模型建模参数在原始序列存在微小扰动下的变化规律, 以矩阵谱条件数为工具对该模型灰导数的背景值进行分类证明. 结果表明, 灰色Verhulst 拓展模型不存在严重病态性. 采用灰色Verhulst 拓展模型进行预测建模, 模型的解不会因系统原始数据在收集过程中存在微小误差而产生显著漂移现象. |
| 关 键 词： | 灰色预测理论|灰色Verhulst 拓展模型|病态|条件数 |
| 收稿时间： | 2012-10-09 |
| 修稿时间： | 2012-12-18 |
Morbid property of grey extended Verhulst model |
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| CUI Jie LIU Si-feng. Morbid property of grey extended Verhulst model[J]. Control and Decision, 2014, 29(3): 567-571 | |
| Authors: | CUI Jie LIU Si-feng |
| Abstract: | It is essential to effectively judge the morbidity of grey model in constructing grey predictive models. Aiming to reveal the change law of modeling parameters of grey Verhulst extended model resulted from a small perturbation of primitive sequence, the spectrum condition number of matrix is taken as a tool of measuring the morbidity of this model, and the values of condition of coefficient matrix with the background value of this model in different case are analyzed. Research result shows that grey Verhulst extended model has no unusually severe morbidity. The research conclusion suggests that, in the grey prediction modeling process, while using the grey extended Verhulst model, the solution of this model will not occur significant drift for the original data series of systems exist minor errors in collecting process. |
| Keywords: | grey forecasting theory|grey derived Verhulst model|morbidity|condition number |
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