A Multivariable Grey Model Based on Optimized Background Value and its Application to Subgrade Settlement Prediction

Abstract

Subgrade settlement is a complex process system. Commonly used single-point prediction models can’t consider the correlation between the discrete deformation monitoring points, which doesn’t adequately reflect the overall deformation law of subgrade. A multivariable grey model (MGM(1,n)), which is an expansion of the single-point GM(1,1) model for multiple variables, is introduced to resolve the above problem. Aiming at the drawback of background value in the traditional MGM(1,n) model, the functions with non-homogeneous exponential law are used to fit the accumulated sequences for every variable, reconstruct the calculating formula of background value, and gets a new MGM(1,n) model based on optimized background value (OMGM(1,n)). A case study shows that the forecast result of the proposed model is more precise and effective than these of the single-point GM(1,1) model and the traditional MGM(1,n) model for predicting subgrade settlement.