半参数GM(1,1)模型参数辨识及滑坡变形预测

Identification of parameters of semi-parametric GM(1, 1) and its application in landslide deformation prediction

针对利用传统GM(1,1)模型进行滑坡变形预测时存有较大的局限性及模型误差的问题,引入半参数理论对其进行改进.构建基于半参数模式的GM(1,1)滑坡预测模型,以补偿最小二乘为约束条件,对半参数GM(1,1)模型的灰参数a和b进行辨识;并对影响半参数模型求解的关键参数正则矩阵R和平滑参数α进行优选,最后将半参数GM(1,1)模型用于茅坪和古树屋滑坡变形预测.研究结果表明:基于半参数的GM(1,1)模型拟合精度较高,预测结果正确可靠,能够反映滑坡变形位移的发展趋势.

Aiming at that the conventional GM（1,1） model is highly limited and prone to accumulate systematic error in landslide deformation forecast, this paper traces its error sources and introduces a nonlinear semi-parametric model in the compensation of GM（1,1） model＇s limtations. The semi-parametric model based compensation equation of the landslide deformation is established. According to penalized least squares, the estimators of grey parameters a and b are then derived, and at the same time, the selection of regular matrix R and smoothing parameter α upon solving are further discussed. Lastly, the model is applied to predicting the deformation time series data monitored at the Maoping landslide and Gushuwu landslide. The case studies show that the fitting precision is high and the prediction is reliable. The proposed model is of a certain theoretical and practical significance.