顾及邻近点变形因素的高斯过程建模及预测

针对传统的变形监测建模方法一般针对单一监测点的变形预测模型,未考虑到监测点间相互作用的变形特点,该文分析了变形监测点间的相互关联性,通过相关系数法对监测点进行分类,并将邻近监测点的观测序列值作为和时间因素等同的影响因子应用到建模过程中,利用高斯过程算法进行训练,建立预测模型。为提高高斯过程算法的模型预测精度,应选择适合工程案例最优协方差函数。通过实例分析,比较GM(1,1)、多点灰色预测模型和顾及邻近点变形因素的高斯过程等3种模型在基坑围岩、滑坡等变形监测数据处理中的预测精度,表明该文算法考虑到监测点间的变形关联性,充分利用高斯过程在针对小样本、非线性数据建模时的高自适应性等优点,具有较高的预测精度。

Modeling and prediction of Gaussian process considering the deformation factors of adjacent points

Aiming at the problem that traditional deformation monitoring models are generally built based on the data only with a single monitoring point,without taking the deformation characteristics of the interaction between the monitoring points into account,this paper analyzed the mutual association of the deformation monitoring and classified monitoring points using the method of correlation coefficient,then the observed sequence values of adjacent monitoring points were taken as the same as time factors and applied to the modeling process.Finally,Gaussian process algorithm was used for training to establish the prediction model.The optimal covariance function of the engineering case was selected in order to improve the prediction accuracy of the GP algorithm.By comparing the prediction accuracy of three models which contained the GM(1,1)、M-GM(1,1)and the GP model with two examples of surrounding rock and landslide of foundation pit.Experimental results showed that the algorithm considering the monitoring point deformation relationship made full use of the the high self adaptability of Gaussian process in the small sample and nonlinear data modeling with higher prediction accuracy.