基于回归分析和小波变换的边坡变形组合预测研究

Combinatorial Forecasting of Slope Deformation Based on Regression Analysis and Wavelet Transform

为有效地判断边坡变形的发展趋势,基于边坡变形的现场数据,首先利用回归分析和小波变换分解边坡变形数据的趋势项和误差项,并选取若干最优的分解数据进行组合确定边坡变形数据的趋势项和误差项,再利用BP和RBF神经网络对趋势项和误差项序列进行预测,得到单项预测的结果,最后研究分析了定权组合预测和非定权组合预测的效果。结果表明:在趋势项和误差项的分离过程中,不同分离方法的分离结果具有一定的差异,以6次多项式回归、5次及7次傅里叶回归和sym2小波变换的结果较好;同时,在单项预测中,分项预测的效果要优于传统的单项预测,验证了分项预测的有效性,并由组合预测的结果可知,2种组合预测的效果均较好,均很大程度上提高了预测精度,且非定权组合的预测精度要优于定权组合预测的精度。上述研究为边坡的变形预测提供一种新的思路。

In order to effectively estimate the variation trend of slope deformation,we employed regression analysis and wavelet transform to decompose the trend term and error term of slope deformation. In subsequence we selected data of optimal decomposition and predicted series of trend term and error term by using BP and RBF neural network. Then,we obtained the forecast results of single term and analyzed the forecast results of fixed weight combination and non-fixed weight combination. Results showed that the results of decomposing trend term and error term by different methods are different. Among the methods,polynomial regression with power of six. Fourier regression with power of five and seven and wavelet transform of sym2 have better results. Moreover,partial prediction is prior to conventional prediction of single term,which verifies the effectiveness of partial prediction in the present research. According to combinatorial forecasting results,fixed weight and non-fixed weight both obviously improved prediction accuracy,and the prediction accuracy of the latter is better than that of the former.