地基沉降预测的两种灰色模型与Asaoka法

Asaoka法、GM(1,1)模型和灰色Verhulst模型都是地基沉降预测中的常用模型。通过分析Asaoka方程与两种灰色模型之间的联系,指出灰色模型理论与Asaoka法一阶微分方程具有一致性,可以利用GM(1,1)模型代替Asaoka法进行沉降预测;灰色Verhulst模型是参数收敛的时变参数Asaoka方程。分析指出三种方法都存在两点不足,即只能应用于等时距沉降数据分析以及参数求解精度还可以进一步提高,从而建立了改进的GM(1,1)模型和改进的灰色Verhulst模型,最后通过工程实例说明了改进灰色模型的具体应用。

Asaoka Method and Two Grey Models in the Forecast of Groundsill Settlement

Asaoka formula, GM (1, 1) model and grey Verhulst model are commonly used in the forecast of groundsill settlement. According to the analysis of the relationship between Asaoka equation and two grey models, it is indicated that the first-order differential equation of grey model is equivalent to that of Asaoka method. So GM (1, 1) model can be a substitute for Asaoka method in the forecast of groundsill settlement. It is also indicated that the grey Verhulst model is an Asaoka equation with time-dependent parameter considering parameter convergence. There are two defects for these three models. Firstly, because of the modeling mechanism, the three methods can only be applied in forecast of equal interval settlement data. Secondly, the precision of the parameters can be improved. Thus, this paper proposed an improved grey Verhulst model and an improved GM (1, 1) model. Finally, the improved grey models are applied in an engineering example.