背景值是影响GM(1,1)模型精度的关键因素之一。当前背景值优化的改进模型均取得较好的效果,但优化后的背景值公式多数比较繁琐,并且部分优化模型不适用于高增长型序列。本文根据模型的指数性质以及积分特点,分析背景值的构造原理,利用黎曼积分的核心思想,提出以不规则梯形面积取代传统梯形面积构造法,对传统GM(1,1)模型背景值进行优化。通过实验验证了新模型具有白指数律重合性,不仅适用于低增长指数序列,亦适用于高增长指数序列,并且优化公式简单,具有较高的实用性与可靠性。
The background value is one of the key factors influencing the accuracy of GM(1,1) model.The improved models by optimizating background value are effective at present.But a lot of the optimized formulas are complicated and part of them are also not suitable for the high growth series.According to the exponential properties and intergral characteristics of model, the structure principle of background value is analyzed, and a new construction method is proposed in this paper using the irregular trapezoid to replace the traditional one based on the core idea of Riemann integral,so as to achieve optimizing model.The test results showed that the optimized model possessed white exponential law coincidence property,it could be applied to low-rising exponential series,and also could be the same with high-rising one.Thus,the test verified the improved GM(1,1) model with simpler formula was higher in practicality and reliability.
[1] 刘思峰,党耀国,方志耕,等.灰色系统理论及其应用[M].北京:科学出版社,2010.
[2] 谭冠军.GM(1,1)模型的背景值构造方法和应用(I)[J].系统工程理论与实践,2000,20(5): 98-103.
[3] 王义闹,刘光珍,刘开第. GM(1,1)的一种逐步优化直接建模方法[J],系统工程理论与实践,2000,20(9):99-104.
[4] 罗党,刘思峰,党耀国. 灰色模型GM(1,1)优化[J].中国工程科学,2003,5(8): 50-53.
[5] Yang Jinxian, Zhang Ying. Micro-mechanical Gyro Drift modeling based on GM(1,1) of reconstruction of background value//Proceedings of the 2009 IEEE International Conference on Grey Syestems and Intelligent Services,2009,11, Nanjing,China.
[6] 张彬,西桂权.基于背景值和边值修正的GM(1,1)模型优化[J].系统工程理论与实践,2013,33(3):682-688.
[7] 李俊峰,戴文战.基于插值和Newton-Cores公式的GM(1,1)模型的背景值构造新方法与应用[J].系统工程理论与实践, 2004,(10): 122-126.
[8] 阮春旺,肖新平.基于复化梯形公式的GM(1,1)改进模型及其应用.第16届全国灰色系统学术会议论文,April,2008.
[9] Li Bo, Zhao Shengli, Fang Ling. Optimized GM(1,1) based on Romberg algorithm and quadratic interpolation method . International Conference on Apperceiving Computing and Intelligence Analysis (ICACIA), Chengdu,October 23-25,2009.
[10] 王晓佳,杨善林.基于组合插值的GM(1,1)模型预测方法的改进与应用[J].中国管理科学,2012, 20(2): 129-134.
[11] 徐宁,党耀国,丁松. 基于误差最小化的GM(1,1)模型背景值优化方法[J].控制与决策,2015,30(2):283-288.
[12] 曾波,刘思峰.近似非齐次指数增长序列的DGM(1,1)直接建模法[J].系统工程理论与实践,2011,31(2):297-301.
[13] 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): 2874-2878.
[14] 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.
[15] 肖新平,王欢欢.GM(1,1,a)模型背景值的变化对相对误差的影响[J].系统工程理论与实践,2014,34(2):408-415.
[16] Li Junfeng,Yang,A.P., Dai Wenzhan. Modeling mechanism of the ameliorating GM(1,1) model and application//Proceedings of 2007 IEEE International Conference on Grey Systems and Intelligent Services, Nanjing, China,2007.
[17] Zhai Zhenjie, Liu Sifeng, Liu Bin, et al. Study on the optimum prediction model for GM//Proceedings of 2007 IEEE International Conference on Grey Systems and Intelligent Services, Nanjing, November,18-20, 2007.
[18] Wang Zhengxin, Dang Yaoguo, Liu Sifeng. Optimization of background value in GM(1,1) model [J]. Systems Engineering—Theory & Practice. 2008, 28(2) : 61-67.
[19] Zhang Yi, Wei Yong,Xiong Changwei.A new method to find the original value of various GM(1,1) with optimum background value //Proceedings of 2008 IEEE International Conference on Systems,Man and Cybernetics, Singapore,October 12-15,2008.
[20] Zeng Xiangyan, Xiao Xinping. A new method of building grey forecasting model//Proceedings of 2009 Chinese Control and Decision Conference, Guilion,June 17-19,2009.
[21] Li Hongwei, Liu Qingyou, Mao Weijin.An optimized GM(1,1) model based on the modified construction method of background value//Proceedings of International Conference on Computational and Information Sciences, Chengdu, 2010.
[22] 王正新,党耀国,刘思峰.无偏GM(1,1)模型的混沌特性分析[J].系统工程理论与实践,2007,27(11):153-158.
