Abstract It is known that uncertainties in geotechnical engineering are unavoidable. Slope reliability analysis is vital because the failure of a slope may cause great loss. In the reliability analysis of slopes, the stochastic response surface method (SRSM) provides an effective way to address the non-convergence of calculation results and has the advantage of high accuracy for highly nonlinear problems. However, multicollinearity, defined as the existence of exact correlations or highly correlated relationships among the explanatory variables, is not considered in the SRSM, leading to local solutions. To address the multicollinearity existing in slope reliability analysis, the least absolute shrinkage and selection operator (Lasso)-based SRSM, the ridge regression-based SRSM, the elastic net regression-based SRSM, and the stepwise regression-based SRSM are proposed in this paper. Monte Carlo simulations and the traditional SRSM are used to validate the accuracy of the proposed methods. It is found from the numerical results that the stepwise regression-based SRSM is the most competitive among the four proposed methods in addressing the uncertainties of slope stability due to its accuracy and efficiency.

中文翻译：

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使用改进的具有多重共线性的随机响应面方法的边坡可靠性分析

摘要 众所周知，岩土工程中的不确定性是不可避免的。边坡可靠性分析至关重要，因为边坡的破坏可能会造成巨大的损失。在边坡可靠度分析中，随机响应面法(SRSM)为解决计算结果的不收敛问题提供了一种有效的方法，对高度非线性问题具有精度高的优点。然而，多重共线性定义为解释变量之间存在精确相关或高度相关的关系，在 SRSM 中没有考虑，导致局部解。为了解决边坡可靠性分析中存在的多重共线性，基于最小绝对收缩和选择算子 (Lasso) 的 SRSM、基于岭回归的 SRSM、基于弹性网回归的 SRSM，本文提出了基于逐步回归的SRSM。Monte Carlo 模拟和传统的 SRSM 用于验证所提出方法的准确性。从数值结果中发现，基于逐步回归的 SRSM 因其准确性和效率而在解决边坡稳定性不确定性的四种方法中最具竞争力。