改进的GM(1,1)模型在滑坡变形预测中的应用

Application of improved GM(1,1) models to prediction of landslide deformation

为了提高GM(1,1)模型在滑坡变形预测中的预测精度和普遍适用性,论文首先分析了GM(1,1)模型的数学特点,并根据建模机理所存在的固有缺陷探讨了几种合理实用的改进方法。在此基础上,结合呈对数型曲线的链子崖危岩体变形监测数据和呈指数型曲线的黄龙西村滑坡变形监测数据,分别了建立了传统GM(1,1)、无偏GM(1,1)、中心逼近式GM(1,1)、重构背景值的GM(1,1)和灰色神经网络组合等预测模型。预测结果表明:针对不同数学特点的滑坡变形数据,特定改进的GM(1,1)模型较传统模型预测精度更高,适用性更强。

For the purpose of heightening prediction precision and general applicability of GM （ 1,1 ） models to prediction of landslide deformation, mathematical characteristics of GM （ 1,1 ） model were analyzed and several practical improved methods that aimed at inherent limitation of conventional GM （ 1,1 ） model were discussed in this paper. With referenced typical deformation monitoring data of the Lianziya hazard rock mass （logarithmic） and the Huanglongxi landslide （exponential）, prediction models of conventional GM （ 1, 1） , unbiased GM （ 1, 1 ）, center approach GM （1, 1 ）, reconstruct ground value GM （1, 1 ） and gray-neutral network were established to study deformation prediction. The prediction results show that, aimed at different monitoring data sequence in mathematical natures of slope deformation, compared with conventional GM （1, 1 ） model, some improved GM （1, 1） models have higher prediction accuracy and general applicability.