基于小波去噪的高斯过程回归模型在面板堆石坝沉降预测中的应用研究

Application of Gaussian process regression model based on wavelet denoising in settlement prediction of CFRD

引起面板堆石坝沉降变形的环境因素复杂,观测数据呈现出明显的噪声干扰特性,限制了数学模型拟合及预测的精度。对原始信号进行小波变换可有效分解其中的有用信号和噪声,因此,引入小波变换理论建立了基于小波阈值去噪的数学模型,并对面板堆石坝(CFRD)的沉降变形实测数据实施去噪,再对去噪后的数据进行高斯过程回归(GPR),建立了预测堆石坝沉降变形的模型。依托CFRD的实测沉降变形资料,采用Wavelet-GPR模型对大坝沉降进行了拟合与预测,并与未进行去噪的GPR模型计算结果进行对比。结果表明:Wavelet-GPR模型观测值与预测值的残差符合正态分布,去噪后学习段的均方根误差(RMSE)由0.9287 mm减小至0.4577 mm,平均绝对误差(MAE)由0.4850 mm减小至0.3306 mm;预测段的RMSE由1.3089 mm减小至0.9176 mm,MAE由0.9263 mm减小至0.7303 mm;且去噪后模型的样本观测值个数在其预测值95%置信范围内的占比有明显提升。因此,利用小波阈值去噪对实测沉降数据进行降噪处理能够降低噪声导致的数据观测值与真实值之间的误差,Wavelet-GPR模型用于预测面板堆石坝的沉降变形具有实用性与可靠性。

The settlement and deformation of CFRD are caused by multiple complicated environmental factors,and the observed deformation data show obvious characteristics of noise interference,which has a great influence on the fitting and prediction accuracy of mathematical models;however,the useful signal and noise in the original signal can be decomposed effectively by wavelet transform theory.Therefore,the wavelet transform theory is introduced to establish a mathematical model based on wavelet threshold denoising,which is then applied to the denoising of the measured settlement data of a CFRD,and the denoised data is processed by Gaussian process regression(GPR)to establish a model for predicting settlement deformation of CFRD.Based on the measured settlement deformation data of a certain CFRD,the Wavelet-GPR model is used to fit and predict the dam settlement,and the calculation results are compared with those of the GPR model without denoising.The results show that the residual difference between predicted values and observed values of the Wavelet-GPR model is in accord with normal distribution.The RMSE of the learning segment decreased from 0.9287 mm to 0.4577 mm,and the MAE decreased from 0.4850 mm to 0.3306 mm after denoising.Furthermore,the RMSE of the prediction segment decreased from 1.3089 mm to 0.9176 mm,and the MAE decreased from 0.9263 mm to 0.7303 mm after denoising.After denoising,the proportion of sample observed values that fall in the 95%confidence range of the predicted values of the model is significantly increased.Therefore,the application of wavelet threshold denoising to the measured settlement data can reduce the error between the observed values and the actual values caused by noise,and the Wavelet-GPR model is practical and reliable in predicting the settlement deformation of CFRD.