优化背景值的非等间距线性时变参数GM(1,1)幂模型在变形监测中的应用

为弥补传统GM(1,1)幂模型背景值等权构造的缺陷，针对原始变形序列的非等距振荡特征构建背景值加权优化的非等间距线性时变参数GM(1,1)幂模型，并采用具有全局优化特性、收敛速度快的粒子群算法求解模型的幂指数和背景值权重。以2组矿区监测点累积沉降观测数据为例进行沉降分析与预测，结果表明，本文模型的平均绝对百分比误差分别为2.33%和4.70%，预测误差分别为2.10%和6.38%，计算结果均优于其他3种模型。工程应用表明，优化模型在小样本非等距振荡序列应用中具有优越性，适用于地表沉陷的短期预测与时变分析。

Application of Non-Equidistant Linear Time-Varying Parameter GM(1,1) Power Model with Optimized Background Value in Deformation Monitoring

In order to fill in the gaps of the traditional GM(1,1) power model with equal-weight construction for background values, a non-equidistance linear time-varying parametric GM(1,1) power model with weighted optimization of background values is constructed for the non-equidistance spaced oscillation characteristics of the original deformation sequences. In addition, we use the particle swarm optimization(PSO) algorithm with fast convergence and high precision to solve the power exponent and background value weight. Taking the cumulative settlement observation data of monitoring points in two mining areas as examples, we use the constructed model for settlement analysis and prediction. The results show that average absolute percentage fitting errors of the model in this paper are 2.33% and 4.70% respectively, and the prediction errors are 2.10% and 6.38% respectively, which are better than other three GM(1,1) power models. The engineering application shows that the proposed optimization model has applicability and superiority to deal the small-sample non-equidistant oscillation sequences, and that it is suitable for short-term prediction and time-varying analysis in coal mining deformation monitoring engineering.