灰色Verhulst模型优化的新方法  

New Method of Grey Verhulst Model Optimization

作　　者：曾柯方 魏勇[1] 

机构地区：[1]西华师范大学数学与信息学院,南充637009

出　　处：《应用泛函分析学报》2015年第2期177-182,共6页Acta Analysis Functionalis Applicata

基　　金：四川省应用基础研究资助项目(2008JY0112);四川省高等教育人才培养质量和教学改革资助项目(P09264);四川省留学人员科技活动择优资助项目(川人社函2010年32号)

摘　　要：通过分析传统灰色Verhulst模型利用倒数变换求解白化方程发现了灰色微分方程与白化方程不匹配而导致误差的根源,提出了直接对原始序列的一次累加序列作倒数变换后建立与倒数替换后的白化方程相匹配的灰色微分方程来估计参数a和b,并在此基础上将优化灰导数以改造灰色方程与利用平均相对误差最小为指标确定响应系数的方法相结合对模型进行了优化.结果表明,该优化模型对其本身的时间响应函数所表达的曲线进行模拟和预测具有重合性.通过实例分析说明了优化模型使得传统模型的模拟预测精度得到明显的提高.Through the analysis of the traditional grey Verhulst model by using the reciprocal transformation to solve the whitening equation,it is found that the mismatch of the grey differential equation with whitening equation is the root of model errors.The method of directly using the reciprocal transformation sequence of the 1-AGO sequence to establish the grey differential equation that matches with the whitening equation by reciprocal transformation to estimate parameters is proposed.And the methods of optimizing the grey derivative to transform the gray equation and regarding the minimum of average relative error as index to determining the response coefficient are combined to optimize the model.The result shows that the optimization model is simulated and predicted with coincidence to the time response function expressed by the curve.Through the analysis of an example,it shows that the simulation forecasting accuracy in traditional model has been improved obviously by the optimization model.

关 键 词：灰色VERHULST模型 灰色微分方程 白化方程 倒数变换 灰导数 响应系数 

分 类 号：N941.5[自然科学总论—系统科学]