Innovative modeling of discharge coefficients for rectangular C-type piano key side weirs using GPR-POA and LSTM techniques

The rectangular piano key side weirs (RPKSW) usually use and install in the outer arch of the channels, which is a convenient location for side weirs. As well, the calculation of the discharge coefficient (C_d) in the weirs is of particular importance in their proper design. Accordingly, in the present study, first, the number of 239 experiments were performed on C-Type RPKSW at two arc angles of 30 and 120°. First, two data-mining models of Gaussian Process Regression (GPR) and Long Short-Term Memory (LSTM) were utilized for modelling. Then, the data-mining models were developed using the Pelican Optimization Algorithm (POA) to enhance the discharge coefficient predictions of basic models. By evaluating these models, it was found that the optimization (POA) performed on GPR was effective and caused a reduction in the prediction error of the weir discharge coefficient. The parameters of α, p_d/B, L/R_c, P/h₁, L/b, and F₁ were identified as effective parameters on the weir discharge coefficient. Due to data normalization, the range of all data was set between 0 and 1. In this study, the best model was the GPR-POA model with RMSE = 0.0486, R² = 0.9388, and KGE = 0.9533. The GPR and LSTM models were ranked after the GPR-POA model. By evaluating the results of different combinations in modeling, it was determined that P/h₁ and p_d/B ratios had a greater effect in providing correct results. Unlike three parameters of L/b, Fr, and L/R, three parameters of α, p_d/B, and P/h₁ had a great impact on the accuracy of the model, so without these parameters, the model accuracy decreased significantly.