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中文摘要：
针对具有时滞特征的输入输出系统,建立了灰色时滞GDM（1,2）模型。并结合三次样条插值和粒子群优化算法,求解出模型的3个参数[a,b,τ]。相对于先利用灰关联分析确定出时滞参数τ再求解灰预测模型的方法,把时滞参数τ融入模型中求解,避免了参数求解过程中的误差传递;并且还消除了时滞参数τ必须为整数的限制,使模型更加贴合现实中滞后期数不一定为整数的实际情况。最后将模型应用于公路旅客周转量的预测问题,实例表明该模型在具有时滞特征的输入输出系统预测中具有较高的精度。
英文摘要：
Considering the time-delay characteristics of input-output systems, a GDM（1,2） model is es- tablished. Combining the cubic spline interpolation with the particle swarm optimization（PSO）, the pa- rameters [a,b, τ] of the model are obtained by the intelligent optimization algorithm. Compared with the traditional method in which the grey relational model is used to estimate the time-delay r before sol- ving the grey prediction model, this method can avoid the error transfer in the process of solving param- eters and remove the limitation that time-delay r must be an integer, which is more fit to the actual. Then parameters are substituted into time response formula to conclude the solution of the model. Fi- nally, last the model is applied to the prediction of highway passenger turnover in China. Result shows that the model has high accuracy in input-output systems with time-delay characteristics.
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