Soft computing approaches for forecasting discharge over symmetrical piano key weirs

Piano Key Weir (PKW) is an advanced hydraulic structure that enhances water discharge efficiency and flood control through its innovative design, which allows for higher flow rates at lower upstream levels. Accurate discharge prediction is crucial for PKW performance within various water management systems. This study assesses the efficacy of Artificial-Neural-Network (ANN) and Gene-Expression-Programming (GEP) models in improving discharge prediction for symmetrical PKWs. A comprehensive dataset comprising 476 experimental records from previously published studies was utilized, considering a range of geometric and fluid parameters (PKW key widths, PKW height, and upstream head). In the training stage, the ANN model demonstrated a superior determination coefficient (R²) of 0.9997 alongside a lower Mean Absolute Percentage Error (MAPE) of 0.74%, whereas the GEP model yielded an R² of 0.9971 and a MAPE of 2.36%. In the subsequent testing stage, both models displayed a high degree of accuracy in comparison to the experimental data, attaining an R² value of 0.9376. Furthermore, SHapley-Additive-exPlanations and Partial-Dependence-Plot analyses were incorporated, revealing that the upstream head exerted the greatest influence on the discharge prediction, followed by PKW height and PKW key width. Therefore, these models are recommended as reliable, robust, and efficient tools for forecasting the discharge of symmetrical PKWs. Additionally, the mathematical expressions and associated script codes developed in this study are made accessible, thus providing hydraulic engineers and researchers with the means to perform rapid and accurate discharge predictions.