离散卡尔曼滤波法在滑坡变形预测中的应用

Application of discrete Kalman filter method in landslide deformation forecast

讨论了树坪滑坡的基本特征及其形成机制,介绍该滑坡的监测系统。变形监测表明树坪滑坡的变形主要与滑坡体的地形地貌及土层结构有关,而大气降雨及三峡水库库水位的影响是导致树坪滑坡产生变形的外界因素。使用泰勒级数建立滑坡变形与时间的函数关系,并将泰勒级数的余项及时间变化的2次方及3次方的系数变化量看作数学期望为零的动态噪声,建立卡尔曼滤波模型,应用于滑坡变形的预测预报。算例计算结果表明卡尔曼滤波模型的拟合效果和预测效果良好。

The fundamental features and the formation mechanism of the Shuping landshde are discussed. The monitoring system of the Shuping landslide is introduced. The deformation monitoring shows that the deformation of the Shuping landslide is related to the topography and geomorphology and the soil layer construction of the landslide. The atmospheric rainfall and the water level of the Three Gorges reservoir are the external factors causing the deformation of the Shuping landslide. The Taylor series is used to establish the functional relationship between the deformation of the landslide and the time. The renminder term of the Taylor series and the variation of coefficients of the square or cube of the time are regarded as dynamic noises whose expected value is 0. The Kalman filter model is described and used to predict the deformation of the landslide. A numerical example shows that the fitted effect and the forecast effect of the model are good.