模袋砂堤防沉降量预测的分数阶灰色模型

A fractional-order grey model for prediction of settlement of dykes with fabric form sand

为获得更优的模袋砂堤防沉降预测结果,基于灰色模型,提出一种分数阶灰色模型。运用MATLAB语言编写了相关程序,实现微分阶次到分数阶的改变,并运用该模型对模袋砂滩涂围垦测试的沉降结果进行实例分析。分数阶灰色模型与灰色Verhulst模型、残差GM模型、GM(1,1)模型对比分析表明:(a)分数阶灰色模型预测结果更精确,其不仅具有GM(1,1)模型前期预测效果好的优点,而且具有灰色Verhulst模型后期预测效果好的优点;(b)分数阶灰色模型的中长期预测结果稳定性比残差GM模型好。

In order to acquire better forecast results for settlements of dykes with fabric form sand,a fractionalorder grey model is presented based on the grey model. The program was established using MATLAB to change the differential-order derivative into a fractional-order one. This model was used to predict the settlement of dykes with fabric form sand. Comparative analysis of the grey Verhulst model,residual GM model,and proposed model was performed. The results show that the predicted results of the fractional-order grey model are more accurate,and the fractional-order grey model not only has the reliable previous forecast effect of the GM（ 1,1） model,but also the reliable later forecast effect of the Grey Verhulst model. Moreover,the long-term forecast results of the fractionalorder grey model show a higher degree of stability than those of the GM model.