非等间距NGM(1,1,k)模型的改进算法及其应用
|
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.
According to the non-equidistance of observation data and the de?ciency 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 e?ciency and applicability of the proposed optimization model are demonstrated by two examples. The results show that the optimal model is able to signi?cantly improve the simulation and prediction accuracy.
According to the non-equidistance of observation data and the de?ciency 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 e?ciency and applicability of the proposed optimization model are demonstrated by two examples. The results show that the optimal model is able to signi?cantly improve the simulation and prediction accuracy.
引文
[1]刘思峰,党耀国,方志耕.灰色系统理论及其应用[M].北京:科学出版社,2010Liu S F, Dang Y G, Fang Z G. Grey System and Its Applications[M]. Beijing:Science Press, 2010
[2] Lian R J. Enhanced adaptive grey-prediction self-organizing fuzzy sliding-mode controller for robotic systems[J]. Information Sciences, 2012, 236(1):186-204
[3] Chang T S, Ku C Y, Fu H P. Grey theory analysis of online population and online game industry revenue in Taiwan[J]. Technological Forecasting&Social Change, 2013, 80(1):175-185
[4] Xia M, Wong W K. A seasonal discrete grey forecasting model for fashion retailing[J]. Knowledge-Based Systems, 2014, 57(2):119-126
[5]崔杰,党耀国,刘思峰.一种新的灰色预测模型及其建模机理[J].控制与决策,2009, 24(11):1702-1706Cui J, Dang Y G, Liu S F. Novel grey forecasting model and its modeling mechanism[J]. Control and Decision, 2009, 24(11):1702-1706
[6]崔杰,党耀国,刘思峰.基于矩阵条件数的NGM(1, 1, k)模型病态性研究[J].控制与决策,2010, 25(7):1050-1054Cui J, Dang Y G, Liu S F. Morbidity of NGM(1, 1, k)model based on conditions of matrix[J]. Control and Decision, 2010, 25(7):1050-1054
[7]陈芳,魏勇.近非齐次指数序列GM(1, 1)模型灰导数的优化[J].系统工程理论与实践,2013, 33(11):2874-2878Chen F, Wei Y. Approximate non-homogeneous index sequence GM(1, 1)model of grey derivative optimization[J]. Systems Engineering–Theory&Practice, 2013, 33(11):2874-2878
[8]童明余,周孝华,曾波.基于直接估计法的NGM(1, 1)模型拓展[J].控制与决策,2015, 30(10):1841-1846Tong M Y, Zhou X H, Zeng B. Expand of NGM(1, 1)model based on the direct estimation method[J].Control and Decision, 2015, 30(10):1841-1846
[9]江艺羡,张岐山.近似非齐次无偏GM(1, 1)模型的递推解法及应用[J].控制与决策,2015, 30(12):2199-2204Jiang Y X, Zhang Q S. Recursive solution to approximate non-homogeneous unbiased GM(1, 1)model and its application[J]. Control and Decision, 2015, 30(12):2199-2204
[10]鲁宝春,赵深,田盈,等.优化系数的NGM(1, 1, k)模型在中长期电量预测中的应用[J].电力系统保护与控制,2015, 43(12):98-103Lu B C, Zhao S, Tian Y, et al. Mid-long term electricity consumption forecasting based on improved NGM(1, 1, k)gray model[J]. Power System Protection and Control, 2015, 43(12):98-103
[11]王钟羡,吴春笃,史雪荣.非等间距序列的灰色模型[J].数学的实践与认识,2003, 33(10):16-20Wang Z X, Wu C D, Shi X R. A grey model for non-equidistant sequence[J]. Mathematics in Practice and Theory, 2003, 33(10):16-20
[12] Li Q Y, Wang N C, Yi D Y. Numerical Analysis[M]. Wuhan:Huazhong University of Science and Technology Press, 2000:126-127
[13]曾祥艳,曾玲.非等间距GM(1, 1)模型的改进与应用[J].数学的实践与认识,2011, 41(2):90-95Zeng X Y, Zeng L. Improvement of non-equidistance GM(1, 1)model and its application[J]. Mathematics in Practice and Theory, 2011, 41(2):90-95
[14]吴清海.非等间距模型在沉降预测中的应用研究[J].工程勘测,2007, 35(12):57-60Wu Q H. The application of the non-equidistant model on subsidence predicting[J]. Geotechnical Investigation&Surveying, 2007, 35(12):57-60
[15]熊萍萍,党耀国,姚天祥.基于初始条件优化的一种非等间距GM(1, 1)建模方法[J].控制与决策,2015, 11(30):2097-2102Xiong P P, Dang Y G, Yao T X. Modeling method of non-equidistant GM(1, 1)model based on optimization initial condition[J]. Control and Decision, 2015, 11(30):2097-2102
[2] Lian R J. Enhanced adaptive grey-prediction self-organizing fuzzy sliding-mode controller for robotic systems[J]. Information Sciences, 2012, 236(1):186-204
[3] Chang T S, Ku C Y, Fu H P. Grey theory analysis of online population and online game industry revenue in Taiwan[J]. Technological Forecasting&Social Change, 2013, 80(1):175-185
[4] Xia M, Wong W K. A seasonal discrete grey forecasting model for fashion retailing[J]. Knowledge-Based Systems, 2014, 57(2):119-126
[5]崔杰,党耀国,刘思峰.一种新的灰色预测模型及其建模机理[J].控制与决策,2009, 24(11):1702-1706Cui J, Dang Y G, Liu S F. Novel grey forecasting model and its modeling mechanism[J]. Control and Decision, 2009, 24(11):1702-1706
[6]崔杰,党耀国,刘思峰.基于矩阵条件数的NGM(1, 1, k)模型病态性研究[J].控制与决策,2010, 25(7):1050-1054Cui J, Dang Y G, Liu S F. Morbidity of NGM(1, 1, k)model based on conditions of matrix[J]. Control and Decision, 2010, 25(7):1050-1054
[7]陈芳,魏勇.近非齐次指数序列GM(1, 1)模型灰导数的优化[J].系统工程理论与实践,2013, 33(11):2874-2878Chen F, Wei Y. Approximate non-homogeneous index sequence GM(1, 1)model of grey derivative optimization[J]. Systems Engineering–Theory&Practice, 2013, 33(11):2874-2878
[8]童明余,周孝华,曾波.基于直接估计法的NGM(1, 1)模型拓展[J].控制与决策,2015, 30(10):1841-1846Tong M Y, Zhou X H, Zeng B. Expand of NGM(1, 1)model based on the direct estimation method[J].Control and Decision, 2015, 30(10):1841-1846
[9]江艺羡,张岐山.近似非齐次无偏GM(1, 1)模型的递推解法及应用[J].控制与决策,2015, 30(12):2199-2204Jiang Y X, Zhang Q S. Recursive solution to approximate non-homogeneous unbiased GM(1, 1)model and its application[J]. Control and Decision, 2015, 30(12):2199-2204
[10]鲁宝春,赵深,田盈,等.优化系数的NGM(1, 1, k)模型在中长期电量预测中的应用[J].电力系统保护与控制,2015, 43(12):98-103Lu B C, Zhao S, Tian Y, et al. Mid-long term electricity consumption forecasting based on improved NGM(1, 1, k)gray model[J]. Power System Protection and Control, 2015, 43(12):98-103
[11]王钟羡,吴春笃,史雪荣.非等间距序列的灰色模型[J].数学的实践与认识,2003, 33(10):16-20Wang Z X, Wu C D, Shi X R. A grey model for non-equidistant sequence[J]. Mathematics in Practice and Theory, 2003, 33(10):16-20
[12] Li Q Y, Wang N C, Yi D Y. Numerical Analysis[M]. Wuhan:Huazhong University of Science and Technology Press, 2000:126-127
[13]曾祥艳,曾玲.非等间距GM(1, 1)模型的改进与应用[J].数学的实践与认识,2011, 41(2):90-95Zeng X Y, Zeng L. Improvement of non-equidistance GM(1, 1)model and its application[J]. Mathematics in Practice and Theory, 2011, 41(2):90-95
[14]吴清海.非等间距模型在沉降预测中的应用研究[J].工程勘测,2007, 35(12):57-60Wu Q H. The application of the non-equidistant model on subsidence predicting[J]. Geotechnical Investigation&Surveying, 2007, 35(12):57-60
[15]熊萍萍,党耀国,姚天祥.基于初始条件优化的一种非等间距GM(1, 1)建模方法[J].控制与决策,2015, 11(30):2097-2102Xiong P P, Dang Y G, Yao T X. Modeling method of non-equidistant GM(1, 1)model based on optimization initial condition[J]. Control and Decision, 2015, 11(30):2097-2102