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)

[1]	DENG Julong. Control problem of grey systems[J]. Systems & Control Letters,1982,1(5): 288-294.
[2]	ZHAO Huiru, GUO Sen. An optimized grey model for annual power load forecasting[J]. Energy,2016,107: 272-286.
[3]	LIU Li, WANG Qianru, WANG Jianzhou, et al. A rolling grey model optimized by particle swarm optimization in economic prediction[J]. Computational Intelligence,2016,32(3): 391-419.
[4]	WU Chengmau, WEN Jetchau, CHANG Kouchiang. Evaluation of the gray model GM(1,1) applied to soil particle distribution[J]. Soil Science Society of America Journal,2009,73(6): 1775-1785.
[5]	LI Cuiping, QIN Jiexuan, LI Jiajie, et al. The accident early warning system for iron and steel enterprises based on combination weighting and grey prediction model GM(1,1)[J]. Safety Science,2016,89: 19-27.
[6]	宋中民, 肖新平. 反向累加生成及灰色GOM(1,1)模型[J]. 武汉理工大学学报(交通科学与工程版), 2002,26(4): 531-533.(SONG Zhongmin, XIAO Xinping. The accumulated generating operation in opposite direction and its use in grey model GOM(1,1)[J]. Journal of Wuhan University of Technology(Transportation Science & Engineering),2002,26(4): 531-533.(in Chinese))
[7]	关叶青, 刘桦. 递减序列的灰色建模方法[J]. 系统工程, 2015,33(4): 154-158.(GUAN Yeqing, LIU Hua. Grey model based on descending sequence[J]. Systems Engineering,2015,33(4): 154-158.(in Chinese))
[8]	杨知, 任鹏, 党耀国. 反向累加生成与灰色GOM(1,1)模型的优化[J]. 系统工程理论与实践, 2009,29(8): 160-164.(YANG Zhi, REN Peng, DANG Yaoguo. Grey opposite-direction accumulated generating and optimization of GOM(1,1) model[J]. Systems Engineering: Theory & Practice,2009,29(8):160-164.(in Chinese))
[9]	何霞, 刘卫锋. 两个初值修正灰色GOM(1,1)模型及其等价性研究[J]. 杭州师范大学学报(自然科学版), 2011,10(3): 217-222.(HE Xia, LIU Weifeng. Two grey GOM(1,1) models based on modified initial value and its equivalence[J].Journal of Hangzhou Normal University(Natural Science Edition),2011,10(3): 217-222.(in Chinese))
[10]	练郑伟, 党耀国, 王正新. 反向累加生成的特性及GOM(1,1)模型的优化[J]. 系统工程理论与实践, 2013,33(9): 2306-2312.(LIAN Zhengwei, DANG Yaoguo, WANG Zhengxin. Properties of accumulated generating operation in opposite-direction and optimization of GOM(1,1) model[J]. Systems Engineering: Theory & Practice,2013,33(9): 2306-2312.(in Chinese))
[11]	MONJE C A, CHEN Y Q, VINAGRE B M, et al. Fractional-Order Systems and Controls: Fundamentals and Applications[M]. London: Springer, 2010.
[12]	张玮玮, 吴然超. 基于线性控制的分数阶混沌系统的对偶投影同步[J]. 应用数学和力学, 2016,37(7): 710-717.(ZHANG Weiwei, WU Ranchao. Dual projective synchronization of fractional-order chaotic systems with a linear controller[J]. Applied Mathematics and Mechanics,2016,37(7): 710-717.(in Chinese))
[13]	WU Lifeng, LIU Sifeng, YAO Ligen, et al. Grey system model with the fractional order accumulation[J]. Communications in Nonlinear Science and Numerical Simulation,2013,18(7): 1775-1785.
[14]	吴利丰, 刘思峰, 姚立根. 基于分数阶累加的离散灰色模型[J]. 系统工程理论与实践, 2014,34(7): 1822-1827.(WU Lifeng, LIU Sifeng, YAO Ligen. Discrete grey model based on fractional order accumulate[J]. Systems Engineering: Theory & Practice,2014,34(7): 1822-1827.(in Chinese))
[15]	刘解放, 刘思峰, 吴利丰, 等. 分数阶反向累加离散灰色模型及其应用研究[J]. 系统工程与电子技术, 2016,38(3): 719-724.(LIU Jiefang, LIU Sifeng, WU Lifeng, et al. Fractional order reverse accumulative discrete grey model and its application[J]. Systems Engineering and Electronics,2016,38(3): 719-724.(in Chinese))
[16]	刘解放, 刘思峰, 吴利丰, 等. 分数阶反向累加NHGM(1,1, k )模型及其应用研究[J]. 系统工程理论与实践, 2016,36(4): 1033-1041.(LIU Jiefang, LIU Sifeng, WU Lifeng, et al. Research on fractional order reverse accumulative NHGM(1,1,k) model and its application[J]. Systems Engineering: Theory & Practice,2016,36(4): 1033-1041.(in Chinese))
[17]	战立青, 施化吉. 近似非齐次指数数据的灰色建模方法与模型[J]. 系统工程理论与实践, 2013,33(3): 689-694.(ZHAN Liqing, SHI Huaji. Methods and model of grey modeling for approximation non-homogenous exponential data[J]. Systems Engineering: Theory & Practice,2013,33(3): 689-694.(in Chinese))
[18]	于丽亚, 王丰效. 基于粒子群算法的非等距GOM(1,1)模型[J]. 纯粹数学与应用数学, 2011,27(4): 472-476.(YU Liya, WANG Fengxiao. Non-equidistant GOM(1,1) model based on particle swarm optimization algorithm[J]. Pure and Applied Mathematics,2011,27(4): 472-476.(in Chinese))
[19]	屈婉玲. 组合数学[M]. 北京: 北京大学出版社, 1989: 48-51.(QU Wanling. Combinatorial Mathematics [M]. Beijing: Peking University Press, 1989: 48-51.(in Chinese))
[20]	罗佑新, 周继荣. 非等间距GM(1,1)模型及其在疲劳试验数据处理和疲劳试验在线监测中的应用[J]. 机械强度, 1996,18(3): 60-63.(LUO Youxin, ZHOU Jirong. Nonequidistance GM(1,1) model and its application in fatigue experimental data processing and on-line control[J]. Journal of Mechanical Strength,1996,18(3): 60-63.(in Chinese))
[21]	王正新, 党耀国, 赵洁珏. 优化的GM(1,1)幂模型及其应用[J]. 系统工程理论与实践, 2012,32(9): 1973-1978.(WANG Zhengxin, DANG Yaoguo, ZHAO Jiejue. Optimized GM(1,1) power model and its application[J]. Systems Engineering: Theory & Practice,2012,32(9): 1973-1978.(in Chinese))
[22]	韩晋, 杨岳, 陈峰, 等. 基于非等时距加权灰色模型与神经网络的组合预测算法[J]. 应用数学和力学, 2013,34(4): 408-419.(HAN Jin, YANG Yue, CHEN Feng, et al. Combination forecasting algorithm based on non-equal interval weighted grey model and neural network[J]. Applied Mathematics and Mechanics,2013,34(4): 408-419.(in Chinese))