More accurate and reliable estimation of residual strength friction angle (ϕ_r) of clay is crucial in many geotechnical engineering applications, including riverbank stability analysis, design, and assessment of earthen dam slope stabilities. However, a general predictive equation for ϕ_r, with applicability in a wide range of effective parameters, remains an important research gap. The goal of this study is to develop a more accurate equation for ϕ_r using the Pareto Optimal Multi-gene Genetic Programming (POMGGP) approach by evaluating a comprehensive dataset of 290 experiments compiled from published literature databases worldwide. A new framework for integrated equation derivation proposed that hybridizes the Subset Selection of Maximum Dissimilarity Method (SSMD) with Multi-gene Genetic Programming (MGP) and Pareto-optimality (PO) to find an accurate equation for ϕ_r with wide range applicability. The final predictive equation resulted from POMGGP modeling was assessed in comparison with some previously published machine learning-based equations using statistical error analysis criteria, Taylor diagram, revised discrepancy ratio (RDR), and scatter plots. Base on the results, the POMGGP has the lowest uncertainty with U95 = 2.25, when compared with Artificial Neural Network (ANN) (U95 = 2.3), Bayesian Regularization Neural Network (BRNN) (U95 = 2.94), Levenberg-Marquardt Neural Network (LMNN) (U95 = 3.3), and Differential Evolution Neural Network (DENN) (U95 = 2.37). The more reliable results in estimation of ϕ_r derived by POMGGP with reliability 59.3%, and resiliency 60% in comparison with ANN (reliability = 30.23%, resiliency = 28.33%), BRNN (reliability = 10.47%, resiliency = 10.39%), LMNN (reliability = 19.77%, resiliency = 20.29%) and DENN (reliability = 27.91%, resiliency = 24.19%). Besides the simplicity and ease of application of the new POMGGP equation to a broad range of conditions, using the uncertainty, reliability, and resilience analysis confirmed that the derived equation for ϕ_r significantly outperformed other existing machine learning methods, including the ANN, BRNN, LMNN, and DENN equations.

残余强度摩擦角（更准确和可靠的估算φ _ř粘土）在许多岩土工程应用，包括河岸稳定性分析，设计，和土坝斜率稳定性的评价是至关重要的。然而，对于一般的预测方程φ _{- [R} ，具有在宽范围内的有效参数的适用性，仍然是一个重要的研究间隙。这项研究的目的是为ϕ _r建立一个更精确的方程。使用帕累托最优多基因遗传规划（POMGGP）方法，通过评估从全球已出版文献数据库汇编的290个实验的综合数据集。提出了一种新的积分方程推导框架，该框架将最大相似度法（SSMD）的子集选择与多基因遗传规划（MGP）和帕累托最优（PO）混合，以找到ϕ _r的精确方程具有广泛的适用性。使用统计误差分析标准，泰勒图，修正的差异比（RDR）和散点图，将POMGGP建模产生的最终预测方程与一些以前发布的基于机器学习的方程进行了比较。根据结果​​，与人工神经网络（ANN）（U95 = 2.3），贝叶斯正则化神经网络（BRNN）（U95 = 2.94），Levenberg-Marquardt神经网络（PONN）相比，POMGGP的不确定度最低（U95 = 2.25） LMNN）（U95 = 3.3）和差分进化神经网络（DENN）（U95 = 2.37）。估计ϕ _r的结果更可靠由POMGGP衍生，与ANN（可靠性= 30.23％，弹性= 28.33％），BRNN（可靠性= 10.47％，弹性= 10.39％），LMNN（可靠性= 19.77％，弹性= 20.29％）和DENN（可靠性= 27.91％，弹性= 24.19％）。除了简单和容易的新POMGGP方程的应用到宽范围的条件下，利用不确定性，可靠性和弹性分析证实派生方程φ _ř显著优于其它现有的机器学习方法，包括人工神经网络，BRNN， LMNN和DENN方程。