In this study, we employed various machine learning-based techniques in predicting factor of safety against slope failures. Different regression methods namely, multi-layer perceptron (MLP), Gaussian process regression (GPR), multiple linear regression (MLR), simple linear regression (SLR), support vector regression (SVR) were used. Traditional methods of slope analysis (e.g., first established in the first half of the twentieth century) used widely as engineering design tools. Offering more progressive design tools, such as machine learning-based predictive algorithms, they draw the attention of many researchers. The main objective of the current study is to evaluate and optimize various machine learning-based and multilinear regression models predicting the safety factor. To prepare training and testing datasets for the predictive models, 630 finite limit equilibrium analysis modelling (i.e., a database including 504 training datasets and 126 testing datasets) were employed on a single-layered cohesive soil layer. The estimated results for the presented database from GPR, MLR, MLP, SLR, and SVR were assessed by various methods. Firstly, the efficiency of applied models was calculated employing various statistical indices. As a result, obtained total scores 20, 35, 50, 10, and 35, respectively for GPR, MLR, MLP, SLR, and SVR, revealed that the MLP outperformed other machine learning-based models. In addition, SVR and MLR presented an almost equal accuracy in estimation, for both training and testing phases. Note that, an acceptable degree of efficiency was obtained for GPR and SLR models. However, GPR showed more precision. Following this, the equation of applied MLP and MLR models (i.e., in their optimal condition) was derived, due to the reliability of their results, to be used in similar slope stability problems.

In this paper, a neuro particle-based optimization of the artificial neural network (ANN) is investigated for slope stability calculation. The results are also compared to another artificial intelligence technique of a conventional ANN and adaptive neuro-fuzzy inference system (ANFIS) training solutions. The database used with 504 training datasets (e.g., a range of 80%) and testing dataset consists of 126 items (e.g., 20% of the whole dataset). Moreover, variables of the ANN method (for example, nodes number for each hidden layer) and the algorithm of PSO-like swarm size and inertia weight are improved by utilizing a total of 28 (i.e., for the PSO-ANN) trial and error approaches. The key properties were fed as input, which were utilized via the analysis of OptumG2 finite element modelling (FEM), containing undrained cohesion stability of the baseline soil (C_u), angle of the original slope (β), and setback distance ratio (b/B) where the target is selected factor of safety. The estimated data for datasets of ANN, ANFIS, and PSO-ANN models were examined based on three determined statistical indexes. Namely, root mean square error (RMSE) and the coefficient of determination (R²). After accomplishing the analysis of sensitivity, considering 72 trials and errors of the neurons number, the optimized architecture of 4 × 6 × 1 was determined to the structure of the ANN model. As an outcome, the employed methods presented excellent efficiency, but based on the ranking method, the PSO-ANN approach might have slightly better efficiency in comparison to the algorithms of ANN and ANFIS. According to statistics, for the proper structure of PSO-ANN, the indexes of R² and RMSE values of 0.9996, and 0.0123, as well as 0.9994 and 0.0157, were calculated for the training and testing networks. Nevertheless, having the ANN model with six neurons for each hidden layer was formulized for further practical use. This study demonstrates the efficiency of the proposed neuro model of PSO-ANN in estimating the factor of safety compared to other conventional techniques.