基于组合核函数的高斯过程边坡角智能设计

高斯过程(GP)是近年来发展迅速的一种全新学习机。与支持向量机(SVM)相比，该方法有着容易实现、超参数可自适应获取及预测输出具有概率意义等优点。结合边坡工程中的边坡角设计，编写了在多种因素影响下边坡角设计的GP程序，为克服单一核函数预测精度和网络泛化能力差的缺点，采用单一核函数相加作为GP的组合核函数，将自动关联性测定参数（ARD）引入其中，建立了关于超参数的GP回归网络模型，使用共轭梯度下降算法导出最优超参数，用ARD超参数进行输入属性相关性分析和特征选取，并以此网络对测试样本进行学习预测，结合支持向量回归方法给出了在回归问题上的应用和对比分析。结果表明：在边坡角智能设计应用中，采用组合核函数的GPR网络ARD参数具有明确的物理意义，预测回归性能优于SVM，且预测输出的概率解释能更好的体现预测值的代表性，为边坡角设计开辟新径。

Slope angle intelligent design based on Gaussian process with combinatorial kernel function

The Gaussian process (GP) is a high and new machine learning way developed rapidly in recent years. It embodies the characteristics of programming easily, self-adaptive acquisition of hyper-parameters and prediction with probability interpretation which are superior to those of SVM. Aiming at the slope angle design influenced by many factors in slope engineering, the Gaussian process with the combinatorial kernel function obtained by combination of squared exponential and rational quadratic covariance function is implemented by learning machine routine in Matlab for overcoming poor predictive precision and network generalization ability of single kernel function. Then the automatic relevant determination (ARD) is introduced into combinatorial Gaussian kernel function in the programme and a GP regression model with regard to hyper-parameters is established; meanwhile the correlation and characteristics selection about inputs and prediction for testing samples on the basis of the net are completed respectively. The results show that compared with support vector regression method, the prediction precision of GP is not only slightly better about all error indexes; and the prediction results reflect well uniformity of predictive precision and dispersion between predictive value and measured value, but also the physical meaning of ARD parameters are distinct; so it can be served as a new tool in slope angle design.