Application of Grey Majorized Model in Tunnel Surrounding Rock Displacement Forecasting

Abstract

Source grey GM(1,1) model usually be used simulation and prediction of equidistant monitoring data sequent. But to non-equidistant and high growth data sequent, had to build the grey GM(1,1) model through equidistant treatment of non-equidistant data or to build directly non-equidistant grey model through complex transfermation , and usually had larger lagging error. In time sequent [k,k+1] interval, in order to majorize and increase accuracy of background value z ⁽¹⁾ (k+1), the area of [k,k+1] interval and GM(1,1) function curve envelope had been replaced by n small interval trapezoidal area.The GM(1,1) grey majorized model was built based on majorized grey model background value generally be used simulation and prediction of equidistant or non-equidistant and low or high growth data sequent of surrounding rock displacement in tunnel. Data sequent characters of I,II and III shape of surrounding rock displacement can be simulated and predicted better by the grey majorized model, and the model had higher simulation and prediction accuracy.