A predictive equation for residual strength using a hybrid of subset selection of maximum dissimilarity method with Pareto optimal multi-gene genetic programming

摘要

More accurate and reliable estimation of residual strength friction angle(/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/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/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/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/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/r significantly outperformed other existing machine learning methods,including the ANN,BRNN,LMNN,and DENN equations。