累积时滞非线性ATNDGM(1,N)模型构建及应用

Construction of accumulative time-delay nonlinear ATNDGM(1,N) model and its application

针对多变量时滞非线性系统的预测建模问题,引入时滞驱动项和幂指数,构建了累积时滞非线性多变量离散灰色ATNDGM(1,N)模型,给出了模型参数求解方法.基于累积时滞灰色关联模型确定了驱动因素和时滞期数,并探讨了时滞期与时滞权重的关系;利用粒子群算法确定了模型的最优幂指数;论证了 DGM(1,N)、DGPM(1,N)和ATDGM(1,N)模型均是ATNDGM(1,N)模型的特殊形式,研究了数乘变换对模型参数取值的影响;数值实验验证了模型的可行性.将ATNDGM(1,N)模型应用于河南省农业产值的预测中,结果表明该模型具有较高的拟合和预测精度,能够有效处理具有时滞非线性特征的小样本多变量系统预测问题.

As to the problem of prediction modelling for multivariable time-delay and nonlinear systems,a new multivariable grey prediction model,called the accumulative time-delay nonlinear multivariable discrete grey model(ATNDGM(1,N)),is proposed by adding time-delay driving term and power exponent,and its parameters calculation method is given.The accumulative time-delay grey incidence model is put forward to determine the driving factors and time-delay parameters,and the relationship between the time-delay period and the time-delay weight is discussed.In addition,the optimal power exponent is determined by particle swarm optimization.It is proved to be that the DGM(1,N)、DGPM(1,N)and ATDGM(1,N) models are all the special cases of ATNDGM(1,N) model,and the affections of multiplication transformation caused to this model is studied.The numerical examples are carried out to assess the modeling feasibility in comparison with other models.Finally,the ATNDGM(1,N) model is employed to predict the agricultural output value in Henan Province.The results show that this model has high fitting and forecasting accuracy,which can effectively deal with the prediction problem of small sample multivariable systems with time-delay and nonlinear characteristics.