基于混合核函数SVM水文时序模型及其应用

核函数的选取与构造是SVM应用的关键所在. 传统SVM在水文时序分析方面的应用多是默认选取单一径向基核函数，而忽略了核函数的选择对模型精度和预测结果的影响. 本文基于Mercer核理论，将多项式核与径向基核进行线性组合，构造出混合 核函数，并植入SVM中，对水文时序建立自回归预测模型. 基于武山站和南河川站的月径流预测结果表明，预测序列的相对误差及 均方误差明显优于任一单一核函数. 这是由于混合核函数能够更好地适应并处理复杂的水文时序变化，因此提高了预测精度. 该研究为利用SVM解决复杂多变的非线性水文时序提供了新的探索模式.

Hydrological time series model based on SVM with mixed kernel function and its application

Kernel function plays an important role in the application of SVM model. Radial basis function (RBF) is used as the most common one in hydrological series analysis and prediction. However, the influence of the selection of kernel function and its structure has been neglected. Therefore, an improved SVM model is developed and used for hydrological predication in this paper. Based on Mercer theorem, polynomial kernel and radial basis kernel are combined to construct the mixed kernel function. Then, auto regression SVM model of mixed kernel function is set up for hydrological series prediction. The model is applied in Wushan and Nanhechuan hydrological station, and the result of monthly runoff prediction shows that the RE and MSE of the improved model are lower than the single kernel function model. This is mainly because mixed kernel function can meet the needs of complex hydrological time series changes, which makes the forecast precision increased. This may also provide a new exploration method for SVM model on research of the non-linear hydrological series.