分数阶反向累加非等间距GM(1,1)模型及应用

曾亮

doi:10.21656/1000-0887.380252

分数阶反向累加非等间距GM(1,1)模型及应用

doi: 10.21656/1000-0887.380252

曾亮

广东理工学院基础教学部, 广东肇庆 526100

基金项目: 国家自然科学基金(61472089)；广东省普通高校特色创新项目(2016KTSCX164)

详细信息

作者简介:
曾亮(1982—)，男，副教授(E-mail: zengliang19820809@126.com).

中图分类号: O29
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- 被引次数: 0
出版历程
- 收稿日期: 2017-09-07
- 修回日期: 2017-11-09
- 刊出日期: 2018-07-15

Non-Equidistant GM(1,1) Models Based on Fractional-Order Reverse Accumulation and the Application

ZENG Liang

Department of Basic Courses, Guangdong Polytechnic College, Zhaoqing, Guangdong 526100, P.R.China

Funds: The National Natural Science Foundation of China(61472089)

摘要

摘要: 针对非等间距递减序列的预测问题，首先构建了一阶反向累加非等间距GM(1,1)模型(简称为非等间距GOM(1,1)模型)，并给出了模型参数的最小二乘解和可用于预测的离散时间响应式.为进一步提高模拟预测精度，利用分数阶累加思想，提出了分数阶非等间距GOM(1,1)模型.以平均模拟相对误差最小化为目标，建立非线性规划模型可求解得到最优阶数.最后，以数值模拟和钛合金疲劳强度随温度变化预测为例，证实了该文提出模型的有效性和实用性.
- 灰色预测模型 /
- 反向累加 /
- 非等间距 /
- GOM(1,1)模型 /
- 分数阶
Abstract: For the prediction of non-equidistant decreasing series, a non-equidistant GM(1,1) model based on the 1st-order reverse accumulation was constructed, and the least square solutions of the model parameters and the discrete time response functions applicable to prediction were given. In order to further improve the prediction accuracy, a fractional-order reverse accumulation non-equidistant GM(1,1) model was proposed. With the objective of minimizing the average relative error of simulation, a nonlinear programming model was established to obtain the optimal order. Finally, numerical simulation and an example of the prediction of the fatigue strength of Ti alloy were given to verify the validity and practicability of the proposed model.
- grey prediction model /
- reverse accumulation /
- non-equidistant /
- GOM(1,1) model /
- fractional order

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参考文献(22)

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