时滞累积TDAGM($1,N,t)$模型及其在粮食生产中的应用

考虑到社会经济系统中广泛存在时滞因果关系,通过分析驱动因素对系统主行为的时滞累积作用效果以及系统行为线性发展趋势,构建了含时间趋势项的时滞累积型多变量灰色TDAGM($1,N,t$)模型,论证了GM(1, 1)、GM(1,N)、OGM(1,N)、时滞GM(1,N)、TDDGM(1,N)模型均是该模型在不同参数取值下的特殊形式;为避免模型求解过程中微分形式与差分形式转换而产生误差,通过定义TDAGM($1,N,t$)模型的派生形式,给出了TDAGM($1,N,t$)模型时间响应式的直接求解方法;针对模型时滞效应参数的识别和优化问题,基于粒子群优化算法,给出了TDAGM($1,N,t$)模型参数估计的算法框架.时滞系统的数值实验结果表明,TDAGM($1,N,t$)模型能够较好地解决含时滞特征的多变量系统预测问题.将该模型应用于河南省粮食产量预测的实例中,拟合精度较高且预测结果符合河南省粮食生产发展趋势,验证了模型的有效性.

Time-delayed accumulative TDAGM(${bm 1,N,t

Considering the widely existed time-delayed causalities in economic realities, this paper constructs a time-delay accumulative multivariable grey mode with the time trend TDAGM($1,N,t$) based on the analysis of the linear trend of system behaviors and the time-delayed accumulative mode of driving factors. It is proved that the prediction model GM(1,1), GM(1,N), OGM(1,N), time-delay GM(1,N), and TDDGM(1,N) are all special forms of TDAGM($1,N,t$) with different coefficients. Furthermore, the direct solution method of the time response formula of TDAGM($1,N,t$) is proposed, in order to avoid the error in the transformation of differential form and difference form in the process of model solving. Aiming at the problem of identification and optimization of the time-delay parameters, the algorithm framework of model parameter estimation is presented based on the particle swarm optimization algorithm. The numerical experiments of the time-delay system show that TDAGM($1,N,t$) can solve the problem of predictive modeling for multivariable systems with time-delay characteristics. To verify the effectiveness of the development, the proposed model is applied to prediction of grain yield production in Henan Province. The result of the model is consistent with the development trend of grain production, and shows the effectiveness of the proposed model.