传统灰色GM(1,1)模型 ,多适用于等间距和低增长序列监测数据的模拟预测 ;对非等间距和高增长序列 ,一般经过等间距处理或经过复杂的变换建立非等间距模型进行预测 ,且往往产生较大的滞后误差。在时间序列 [k ,k + 1]区间上 ,用n个小区间的梯形面积代替 [k ,k + 1]区间上GM(1,1)函数曲线对应的面积 ,以优化提高背景值z( 1) (k + 1)的精度。这种以优化灰色模型背景值为基础构建的灰色优化模型 ,普遍适用于隧道围岩位移等间距或非等间距以及低、高增长监测数据序列的位移预测 ,能很好地模拟预测隧道围岩位移的Ⅰ型、Ⅱ型、Ⅲ型时序变化特征 ,且都能获得很高的模拟和预测精度 The traditional gray GM (1,1) model is mostly suitable for the simulation prediction of monitoring data with equidistant and low-growth sequences. For non-equidistant and high-growth sequences, it is usually processed with equidistance or complex transformation to establish non-equidistant model Predict, and often produce larger lag errors. In the time series [k, k + 1], the area of ​​the GM (1,1) function curve on the interval [k, k + 1] is replaced by the trapezoidal area between n cells to optimize the background value z 1) (k + 1) accuracy. This gray optimization model based on the optimized gray model background value is generally applicable to the displacement prediction of equidistant or non-equidistant intervals of the surrounding rock displacement and low and high growth monitoring data series, which can well predict the tunnel surrounding rock Displacement type Ⅰ, type Ⅱ, type Ⅲ timing characteristics of changes, and can obtain high simulation and prediction accuracy