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.