基于遗传–组合核函数高斯过程回归算法的边坡非线性变形时序分析智能模型

 与支持向量机相比，高斯过程有着容易实现、灵活的非参数推断及预测输出具有概率意义等优点。将高斯过程回归引入边坡非线性变形时序分析，采用单一核函数之和作为高斯过程回归的组合核函数以提高其泛化性能。目前通常采用共轭梯度法求取训练样本对数似然函数的极大值以自适应地获得最优超参数，但共轭梯度法存在优化效果初值依赖性强、迭代次数难以确定、易陷入局部最优解的缺陷。改用十进制遗传算法在训练过程中搜索最优超参数，形成遗传–组合核函数高斯过程回归算法，并编制了相应的计算程序。卧龙寺新滑坡变形时序分析结果表明，与遗传–单一核函数高斯过程回归算法和遗传–支持向量回归算法相比，所提出的遗传–组合核函数高斯过程回归算法显著提高预测精度，可以应用于边坡变形的时序分析，并为类似工程提供借鉴。

INTELLIGENT ANALYSIS MODEL OF SLOPE NONLINEAR DISPLACEMENT TIME SERIES BASED ON GENETIC-GAUSSIAN PROCESS REGRESSION ALGORITHM OF COMBINED KERNEL FUNCTION

Compared with support vector machines(SVM)，Gaussian process(GP) holds many advantages such as easy coding，self-adaptive acquisition of hyper-parameters and prediction with probability interpretation. Herein，the Gaussian process regression(GPR) is adopted to analyze the slope displacement time series. A combined kernel function of GPR(CKGPR) obtained by additive single standard covariance functions is putted forward to overcome poor generalization ability of single kernel function. At present，the hyper-parameters of GPR are achieved by maximizing likelihood function of training samples based on conjugate gradient algorithm. However，the conjugate gradient algorithm has the shortcomings of too strong dependence on initial value in optimization effect，showing the difficultly in determination of iteration steps and easily falling into local optimum. On the basis of above-mentioned results，genetic algorithm(GA) coded in decimal system is used to optimize the hyper- parameters of GPR with the combined kernel function，and then the GA-CKGPR algorithm can be formed；and the corresponding code is programmed in Matlab. From the analytical results of Wolongsi slope displacement time series，it can be concluded that the GA-CKGPR algorithm can obviously improve the prediction precision than those of GA-SVR and standard GA-GPR algorithms，so it can be utilized in slope displacement analysis and meanwhile can be served as a reference for similar projects.