中文摘要：

针对相关向量机与差分进化优化算法的特点,通过将两种算法有机融合提出进化相关向量机模型E-RVM,并应用于边坡安全系数估算.以留一交叉验证法构建差分进化算法的适应度函数,基于差分优化算法确定相关向量机的最优参数,可有效提高算法预测精度及可靠性.根据模型计算得到的预测均值及预测方差建立预测变量置信区间,分析预测结果的不确定性.以两个边坡数据为例建立基于E-RVM 的边坡安全系数估算模型,并与GA-BP、V-SVM、GP 方法对比.分析结果表明：E-RVM 方法的平均绝对误差、平均相对误差与均方根误差精度指标均明显优于GA-BP、V-SVM、GP.通过95%置信度的置信区间分析,理论安全系数均在置信区间内,并且E-RVM 方法具有比GP 方法更短的置信区间长度.分析证实E-RVM 模型是一种精度高、可靠性强的边坡安全系数预测新方法.

英文摘要：

According to the characteristics of the relevance vector machine and the differential evolution optimization algorithm, the evolutionary relevance vector machine model ( E?RVM ) was put forward by combining the two algorithms and applied to the estimation of slope safety factor. The fitness function was built based on leave?one?out cross validation. Then the optimal parameters of the relevance vector machine were determined based on the differential evolution optimization algorithm and the new method could effectively improve the accuracy and reliability of algorithm. Confidence interval of prediction variables were determined based on the mean and variance. This paper analyzed the uncertainty of prediction results. With two side slope as an example to establish the slope safety factor prediction model based on E?RVM, and it compared the new method with GA?BP, V?SVM and GP in terms of accuracy. The analysis results show that MAE, MRE and RMSE of E?RVM method are significantly superior to GA?BP , V?SVM and GP . The analysis of the confidence interval of 95% confidence level shows that the actual safety factor of test data is within the scope of the confidence interval. And E?RVM method is shorter than GP methods in terms of confidence interval length. The above analysis shows that E?RVM model is a kind of new prediction method of Slope Safety Factor with high precision and reliability.