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.
Retraction: Yuan, N., et al. Laplacian Eigenmaps Feature Conversion and Particle Swarm Optimization-Based Deep Neural Network for Machine Condition Monitoring. Appl. Sci. 2018, 8, 2611, doi:10.3390/app8122611