基于灰作用量优化的分数阶灰色预测模型研究  

Optimum Grey Action Quantity for GM(1,1) Model with Fractional Order Accumulate and Its Research

作　　者：许泽东 柳福祥[1] 刘军[1] XU Ze-dong LIU Fu-xiang LIU Jun(Science College, China Three Gorges University, Yichang 443002, Chin)

机构地区：[1]三峡大学理学院,湖北宜昌443002

出　　处：《数学的实践与认识》2016年第19期235-242,共8页Mathematics in Practice and Theory

基　　金：三峡大学科学基金(KJ2013B030;KJ2013B031)

摘　　要：针对小样本振荡型数据序列的灰建模预测问题,提出基于灰作用量优化的分数阶GM(1,1|sin+cos)预测模型.在已有经典GM(1,1|sin)的基础上,一方面,将一阶累加灰生成拓展为分数阶累加灰生成,使得构建的模型更加符合新信息优先原理.另一方面,将灰作用量b_1 sin pk+b_2改进为b_1 sin pk+b_2 cos qk+b_3,其作用是通过增加余弦函数项cos qk,使得具有两个不同周期的运动项cos qk与b_1 sin pk+b_2叠加复合之后,能够生成更加贴近于振荡原始序列趋势和特征的时间响应序列,从而得到拟合精度较高的灰色模型.其次,对建模过程的时间响应式、模型参数p和q的最优估计问题进行了研究,构造了最优累加阶数r、参数p和q的粒子群优化算法,得到的优化模型实现了某些类型振荡序列较高精度的预测.实际数据例子结果表明,所建立的模型能够较好地模拟常见振荡型数据序列的波动趋势和特征,具有较强的适用性和拟合性能.Aiming at the problems of grey modeling and prediction of small sample oscillation data,this papers puts forward a modeling approach for the grey action quantity in fractional order accumulation grey model,that is fractional order GM（1,1｜ sin ＋ cos） model.On the basis of classical GM（1,1 ｜ sin） model,on the one hand,it is extended to the fractional order accumulation grey generation,which makes the model more consistent with the new information priority principle.On the other hand,the grey action quantity b_1 sin pk ＋ b_2improves to b_1 sin pk ＋ b_2 cos qk ＋ b_3.Its purpose is by adding the item of cos qk,which makes the two different cycles of sport items cos qk and b_1 sin pk＋b_2 superposition and compound can generate more close to original sequence oscillation trend and characteristics of the time response sequence.So the grey model with high fitting accuracy is obtained.Secondly,the modeling process,parameter estimation,time response function,the range of p and q are studied,and using the particle swarm optimization algorithm,we determine the optimal cumulative order and parameters of model,and the optimization model of certain types of oscillatory sequence with high precision is achieved.The results of real data show that the model can better simulate the fluctuation trends and characteristics of the common oscillation data sequences,and has strong applicability and fitting performance.

关 键 词：振荡序列 灰作用量 分数阶累加GM(1 1|sin+cos)模型 优化 

分 类 号：N941.5[自然科学总论—系统科学]