Development of a new hybrid technique for estimating of relative uplift force in gravity dams based on whale optimization algorithm

A numerical model is developed in this study using the finite element method (FEM) to estimate relative total uplift force for different positions of holes of drainage gallery in the foundation of Guangzhao gravity dam, located in China. The data of the relative total uplift force generated for different input combinations using the FEM were used to develop machine learning (ML) models. A three-layer Artificial Neural Network (ANN) and a new hybrid model known as ANN-Whale Optimization Algorithm (ANN-WOA) were used for this purpose. The results showed that R2, RMSE, NSE, KGE and RE% for ANN-WOA model in estimation of the relative total uplift forces were 0.998, 0.021, 0.989, 0.964 and 3.3% respectively and those for ANN model were 0.980, 0.023, 0.982, 0.953 and 4.67% respectively, which indicate the higher accuracy of ANN-WOA model compared to ANN model. The new hybrid model, ANN-WOA with the less RMSE and RE% and high KGE and NSE is a more appropriate model for the estimation of the relative total uplift force. The extracted metrics of violin plots indicated that the probability distribution of the relative total uplift force estimated using ANN-WOA model was very similar to that obtained using the FEM.