灰色预测模型的系统动力学仿真

摘要

针对灰色预测模型的仿真拟合问题展开研究,运用系统动力学方法,针对GM（1,1）模型、DGM模型、NDGM模型等3种灰色预测模型进行系统动力学分析,研究了这3种模型的拟合预测效果。结果表明,GM（1,1）模型的白化形式在拟合预测原序列时偏差较大;DGM模型是齐次指数序列的精确模拟,NDGM模型是非齐次指数序列的精确模拟;在对近似非齐次指数序列进行拟合时,NDGM模型的拟合效果明显优于其他模型。此外,将反馈的观点引入灰色模型,使得系统动力学仿真方法成为灰色预测建模的辅助工具,有利于灰色预测模型的拓展与完善。%To study predictive effects and fitting results of grey models,this paper analyses four basic grey forecasting models under homogeneous exponential sequences,non-homogeneous exponential sequences and approximate non-homogeneous exponential sequences by means of system dynamics.Results indicate that the whitenization model of grey model is not satisfactory for sequences＇ prediction;NDGM is a model that precisely fits and forecasts non-homogeneous exponential sequences.Furthermore,dynamic analysis software can become grey modeling procedure＇s aiding tool by introducing feedback into grey model,which also facilitates the research and development of grey models.