灰色Verhulst模型背景值优化的建模方法研究

Abstract

Abstract: In this study, the error sources of background value of traditional grey Verhulst model and optimizes the background value of the model are analyzed, in order to improve the simulation and prediction accuracy of the model. Based on the Logistic function structure of the time response formula in the grey Verhulst model, the Logistic function is used to fit the accumulated sequence, three parameters in Logistic function are solved through a series of mathematical derivation and the idea of accumulated generating operation in opposite direction, and then the optimal formula of background value of grey Verhulst model is got and the optimal grey Verhulst model is constructed. Finally, the optimization effect in this paper is verified by an example and an application example respectively. The result shows that it can effectively improve the simulation and prediction accuracy of the traditional grey Verhulst model to use the optimization background value.

Key words: grey Verhulst model, logistic function, background value, optimization

CLC Number:

N491.5

XIONG Ping-ping, DANG Yao-guo, YAO Tianxiang, CUI Jie. The Research on the Modeling Method of Background Value Optimization in Grey Verhulst Model[J]. Chinese Journal of Management Science, 2012, 20(6): 154-159.

References

[1] 邓聚龙.灰理论基础[M].武汉: 华中理工大学出版社,2002.
[2] 刘思峰,党耀国,方志耕.灰色系统理论及其应用(第三版)[M].北京:科学出版社, 2004.
[3] 罗战友,龚晓南,杨晓军.全过程沉降量的灰色verhulst预测方法[J]水利学报,2003,(3): 29-31.
[4] 毛承雄,高翔.灰参数Verhulst模型在电力期货价格预测中的应用[J].水电能源科学, 2005, 23(3): 80-82.
[5] 刘玉成.改进的灰色VerhulstGM(1,1)建筑物沉降模型[J].中国地质灾害与防治学报, 2006, 17(4): 61-63.
[6] 李秀珍,孔纪名,王成华.最优加权组合模型在滑坡变形预测中的应用[J].自然灾害学报, 2008, 17(2): 53-57.
[7] Peleg M, Corradini M G, Normand M D.The logistic (Verhulst) model for sigmoid microbial growth curves revisited[J].Food Research International, 2007, 40(7): 808-818.
[8] Strzalka D, Grabowski F.Towards possible q-generalizations of the Malthus and Verhulst growth models [J].Physica A: Statistical Mechanics and its Applications, 2008, 387(11): 2511-2518.
[9] Gross T J, Abrao T, Jeszensky P J E.Distributed power control algorithm for multiple access systems based on Verhulst model [J].AEU-International Journal of Electronics and Communications, 2011, 65(4): 361-372.
[10] 党耀国,刘思峰.以x⁽¹⁾(n)为初始条件的GM模型[J].中国管理科学, 2005, 13(1): 132-135.
[11] 何文章,吴爱弟.估计Verhulst模型中参数线性规划方法及其应用[J].系统工程理论与实践, 2006,(8): 141-144.
[12] 王正新,党耀国,刘思峰.无偏灰色Verhulst模型及其应用[J].系统工程理论与实践,2009,29(10):138-144.
[13] Xiong Pingping, Dang Yaoguo, Qian Wuyong.The optimization of time response function in non-equidistant Verhulst model [J].The Journal of Grey System, 2010, 22(3): 249-256.
[14] 王正新, 党耀国,刘思峰.基于离散指数函数优化的GM(1,1)模型[J].系统工程理论与践,2008, 28(2): 61-67.
[15] 王叶梅, 党耀国, 王正新.非等间距GM(1,1)模型背景值的优化[J].中国管理科学,2008,16(4):159-162.
[16] 宋中民,邓聚龙.反向累加生成及灰色GOM(1,1)模型[J].系统工程, 2001, 19(1): 66-69.

The Research on the Modeling Method of Background Value Optimization in Grey Verhulst Model

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