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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2017, Vol. 34 ›› Issue (2): 124-134.doi: 10.3969/j.issn.1005-3085.2017.02.002

• • 上一篇    下一篇

一类改进的非等间距灰色模型及应用

张  锴1,   王成勇2,   贺丽娟1   

  1. 1- 文华学院数学科学系，武汉  430074
    2- 湖北文理学院数学与计算机科学学院，襄阳  441053
  • 收稿日期:2015-12-09 接受日期:2016-11-26 出版日期:2017-04-15 发布日期:2017-06-15
  • 通讯作者: 贺丽娟 E-mail: 23518427@qq.com
  • 基金资助:
    国家自然科学基金(71371066).

An Improved Non-equidistant Grey Model and Its Application

ZHANG Kai1,   WANG Cheng-yong2,   HE Li-juan1   

  1. 1- Department of Mathematics Science, Wenhua College, Wuhan 430074
    2- College of Mathematics & Computer Science, Hubei University of Arts of Science, Xiangyang 441053
  • Received:2015-12-09 Accepted:2016-11-26 Online:2017-04-15 Published:2017-06-15
  • Contact: L. He. E-mail address: 23518427@qq.com
  • Supported by:
    The National Natural Science Foundation of China (71371066).

PDF (PC)

254

被引次数

1

摘要： 现实中存在着大量近似非齐次指数增长规律的数据序列．根据非等间距灰色模型建模机理，本文构造了一个用非齐次指数序列来拟合原始数据序列的非等间距灰色模型，以原始数据序列的观测值与模拟值的相对误差平方和最小为目标，推导出新模型参数的最小二乘解及其时间响应函数的表达式．最后通过两个实例，将改进模型与经典模型对比，取得了良好的效果，进而验证了所提出模型的有效性和实用性．

关键词: 非等间距, 非齐次, GM(1,1)模型, 预测

Abstract: There exists a lot of non-homogenous exponential incremental sequence in real life. According to the non-equidistant GM(1,1) modeling mechanism, an improved grey model which uses non-homogenous exponential sequence to fit the original data sequence is proposed. In order to minimize the square sum of relative error between observed values and simulated values, the model's parameters are deduced by means of the least square method as well as the time response function. Finally, the improved model is compared with the classical model by two examples, and the results show that the effectiveness and practicality of the new proposed model.

Key words: non-equidistant, non-homogenous, GM(1,1) model, forecasting

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