背景值优化的多变量灰色模型在路基沉降预测中的应用

路基沉降是一个复杂的系统过程，常用的单点预测模型不能考虑各沉降监测点间的相关性，不足以反映路基整体的变形规律。多变量灰色模型MGM(1, n)是单点GM(1, 1)模型在多元变量条件下的拓展，可以实现对路基中相互影响的多个监测点变形预测模型的建模和预测。针对传统多变量灰色模型背景值取值存在的误差，利用非齐次指数函数拟合模型中各变量的一次累加生成序列重构了背景值计算公式，提出了背景值优化的多变量灰色模型。对路基横断面上3个监测点进行了灰色关联分析，建立了相应的背景值优化的MGM(1,3)模型，采用新陈代谢方法预测路基沉降值。实例计算表明，与传统MGM (1, n)模型以及GM(1, 1)模型相比，背景值优化的多变量灰色模型具有更高的预测精度，显示了该方法进行路基沉降预测的有效性。

A multivariable grey model based on background value optimization and its application to subgrade settlement prediction

Subgrade settlement is a complex systematic process. Frequently used single point forecasting models can’t consider the correlation of settlement between the discrete monitoring points, so that it can’t represent the integrated deformation regularity of subgrade. A multivariable grey model named MGM(1,n), which is an extension of the single point model named GM(1,1), is introduced to solve the problem. According to the error of background value in the traditional multivariable grey model, this paper uses the functions with non-homogeneous exponential law to fit the accumulated sequences for every variable, reconstruct the calculating formula of background value, and gets a new multivariable grey model with optimized background value. Three monitoring points on the subgrade cross-section are analyzed by grey relational analysis theory. The corresponding MGM (1,3) model based on optimized background value is established; and the metabolism method is applied to predict subgrade settlement value. A case study shows that the forecast result of the proposed model is more precise and effective than these of the single-point grey model and the traditional multivariable grey model for predicting subgrade settlement.