This study focuses on the use of deep neural network (DNN) to predict the soil friction angle, one of the crucial parameters in geotechnical design. Besides, particle swarm optimization (PSO) algorithm was used to improve the performance of DNN by selecting the best structural DNN parameters, namely, the optimal numbers of hidden layers and neurons in each hidden layer. For this aim, a database containing 245 laboratory tests collected from a project in Ho Chi Minh city, Vietnam, was used for the development of the proposed hybrid PSO-DNN model, including seven input factors (soil state, standard penetration test value, unit weight of soil, void ratio, thickness of soil layer, top elevation of soil layer, and bottom elevation of soil layer) and the friction angle was considered as the target. The data set was divided into three parts, namely, the training, validation, and testing sets for the construction, validation, and testing phases of the model. Various quality assessment criteria, namely, the coefficient of determination (R²), mean absolute error (MAE), and root mean square error (RMSE), were used to estimate the performance of PSO-DNN models. The PSO algorithm showed a remarkable ability to find out an optimal DNN architecture for the prediction process. The results showed that the PSO-DNN model using 10 hidden layers outperformed the DNN model, in which the average correlation improvement increased R² by 1.83%, MAE by 5.94%, and RMSE by 8.58%. Besides, a global sensitivity analysis technique was used to detect the most important inputs, and it showed that, among the seven input variables, the elevation of top and bottom of soil played an important role in predicting the friction angle of soil.

中文翻译：

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基于粒子群算法的深层神经网络体系结构改进，提高了确定土壤摩擦角的性能

这项研究的重点是利用深层神经网络（DNN）预测土壤摩擦角，这是岩土工程设计中的关键参数之一。此外，通过选择最佳的结构DNN参数，即最优的隐层数和每个隐层中的神经元数量，采用粒子群优化（PSO）算法提高了DNN的性能。为此，使用了一个数据库，该数据库包含从越南胡志明市的一个项目中收集的245个实验室测试，用于开发拟议的PSO-DNN混合模型，包括七个输入因子（土壤状态，标准渗透测试值，单位以土的重量，空隙率，土层的厚度，土层的最高海拔，土层的最低海拔和摩擦角为目标。数据集分为三个部分，即 模型的构建，验证和测试阶段的培训，验证和测试集。各种质量评估标准，即确定系数（R ²），平均绝对误差（MAE）和均方根误差（RMSE）用于估计PSO-DNN模型的性能。PSO算法具有出色的能力，可以为预测过程找到最佳的DNN架构。结果表明，使用10个隐藏层的PSO-DNN模型优于DNN模型，其中平均相关性改进使R ²增长了1.83％，MAE增长了5.94％，RMSE增长了8.58％。此外，采用全局敏感性分析技术检测最重要的输入，结果表明，在七个输入变量中，土壤顶部和底部的高度在预测土壤摩擦角方面起着重要作用。