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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 ›› 2019, Vol. 36 ›› Issue (2): 138-154.doi: 10.3969/j.issn.1005-3085.2019.02.002

• • 上一篇    下一篇

非等间距NGM$(1,1,k)$模型的改进算法及其应用

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:2016-12-21 接受日期:2017-06-26 出版日期:2019-04-15 发布日期:2019-06-15
  • 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)；湖北省教育厅科学研究计划指导性项目(B2017347).

Improved Algorithm for Non-equidistant NGM$(1,1,k)$ Model and Its Applications

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:2016-12-21 Accepted:2017-06-26 Online:2019-04-15 Published:2019-06-15
  • Contact: L. He. E-mail address: 23518427@qq.com
  • Supported by:
    The National Natural Science Foundation of China (71371066); the  Science and Technology Foundation of Education Commission of Hubei Province (B2017347).

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摘要： 针对观测数据的非等间距性以及NGM$(1,1,k)$\,模型建立的不足，本文构建了灰作用量优化的非等间距NGM$(1,1,k)$模型．基于数值积分原理，推导出模型背景值改进算法的非等间距Simpson数值积分公式．然后利用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，构建新的效用函数作为求解新模型的时间响应函数中的最优常数表达式，从而形成了完整的非等间距NGM$(1,1,k)$模型的改进算法．最后，通过两个算例验证了所提出模型的有效性和实用性，表明了优化模型可以有效地提高预测精度．

关键词: 非等间距序列, NGM$(1,1,k)$模型, 背景值, 时间响应函数

Abstract: According to the non-equidistance of observation data and the deficiency of NGM$(1,1,k)$ model, a modeling approach for the grey action quantity with non-equidistant NGM$(1,1,k)$ model is established in this paper. A new model's background value optimization method is proposed based on the principle of numerical integration by using non-equidistance Simpson numerical integration formula. Then the desirability function is construsted by the minimizing the square sum of relative error between the raw sequence and the simulative sequence, which is used to determine the optimal constant value in the time response function. Moreover, a complete improved algorithm for non-equidistance NGM$(1,1,k)$ model is proposed. Finally, the efficiency and applicability of the proposed optimization model are demonstrated by two examples. The results show that the optimal model is able to significantly improve the simulation and prediction accuracy.

Key words: non-equidistant sequence, NGM$(1,1,k)$ model, background value, the time res-ponse function

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