用小波分析与灰色支持向量机预测高铁变形

针对高铁变形监测数据的非线性特征，构建一种基于小波与灰色支持向量机的高铁变形预测组合模型。利用小波分析获取不同时频尺度上的随机序列和近似序列，通过嵌入维数的确定和高低频数据的相关性分析，将重构后的随机序列作为遗传算法优化SVR模型的输入，对近似序列则采用灰色支持向量机来描述其演变特征，最后将二者预测结果进行耦合叠加，得到小波灰色支持向量机的组合模型预测结果。以贵广高铁实测数据为例，将均方差、平均绝对误差、平均绝对相对误差作为评判指标对预测效果进行评价，结果表明该模型较好地拟合了近似分量，同时避免了细节分量的过拟合，为高铁变形预测提供了新途径。

High Speed Rail Deformation Prediction Based on Wavelet Analysis and Grey-Support Vector Machine

According to the nonlinear characteristics of the deformation monitoring data of high speed railways, a combined forecasting model based on wavelet and gray support vector machine is proposed.Using wavelet analysis to obtain the random sequence and approximate sequence of different time-frequency scales,through the determination of embedding dimension and the correlation analysis of high and low frequency data,the reconstructed random sequence is used as the genetic algorithm to optimize the input of the SVR model.The grey support vector machine is then used to describe the evolution of the approximate sequence. Finally, the two prediction results are coupled and superimposed,and the result of the combined model of wavelet-gray-support vector machine (SVM) is obtained.Taking the measured data of Guizhou-Guangzhou high-speed railway as an example, the mean square error, the mean absolute error and the mean absolute relative error are used to evaluate the prediction results.The example shows that the model fits the approximate component well, and avoids the over fitting of the detail components.