边坡可靠度分析的支持向量机法

提出了基于支持向量机（SVM）的边坡可靠度分析新算法。该方法采用均匀设计确定样本点，通过一定数量的确定性计算来训练SVM，拟合边坡的功能函数；采用一阶可靠度方法（FORM）和迭代算法优化SVM模型，获得可靠度指标和验算点信息；在SVM模型基础上进一步通过二阶可靠度方法（SORM）和蒙特卡罗模拟（MCS）计算边坡的失稳概率。以两个典型边坡为例，通过与其他方法比较，证明了该方法的准确性和高效性。结果表明：提出的在标准正态空间（U空间）中取样并构建SVM，在原始空间（X空间）中计算功能函数的算法，有效地解决了具有相关非正态分布变量的可靠度分析问题，并且可很容易扩展到SORM的计算。算例结果证明，该方法的精度高于FORM；而效率优于MCS。分析过程中，边坡安全系数计算和可靠度分析相互独立。因此，该方法既适用于具有显式功能函数的简单问题，也适用于需要软件计算安全系数的实际边坡问题。

Slope reliability analysis using support vector machine

A new methodology for slope reliability analysis using support vector machine (SVM) is proposed. The presented method fits the actual performance function of slope via SVM, by performing deterministic computations at some sampling points designed with uniform design method for training SVM. Then, the reliability index and the design point are obtained using first-order reliability method (FORM) and iterative algorithm. Based on SVM model, the failure probability of slope is calculated using second-order reliability method (SORM) and Monte Carlo simulation (MCS). The accuracy and efficiency of the method are demonstrated by comparing with other methods for two illustrative examples. The results show that sampling and constructing SVM in U-space and evaluating performance function in X-space make the procedure easy to perform reliability analysis involving correlated abnormal distribution variables and ready to do SORM. Comparisons among different methods for two example slopes show that the proposed method is more accurate than FORM and has higher efficiency than MCS. In the proposed algorithm, computations of factor of safety and reliability analysis are separate, which makes the method adaptive for both simple problems having explicit performance function and complicated applications requiring commercial software to calculate the factor of safety.