Machine learning-based estimation of discharge coefficient for semicircular labyrinth weirs.

Area of Science:

• Hydraulics and Fluid Mechanics
• Computational Engineering
• Artificial Intelligence

Background:

• Accurate discharge coefficient (Cd) prediction is vital for hydraulic structure design.
• Semicircular Labyrinth Weirs (SCLWs) require precise hydraulic performance estimation.
• Traditional methods for Cd estimation have limitations.

Purpose of the Study:

• To develop and evaluate advanced Machine Learning (ML) models for estimating Cd in SCLWs.
• To compare the performance of various ML models including TabNet-MFO, ELM-JFO, LightGBM, and DT.
• To identify key factors influencing Cd predictions in SCLWs.

Main Methods:

• Exploration of ML models: Tabular Neural Network (TabNet) with Moth Flame Optimization (MFO), Extreme Learning Machine (ELM) with Jaya and Firefly Algorithms (JFO), Decision Tree (DT), and Light Gradient Boosting Machine (LightGBM).
• Sensitivity analysis using Explainable Boosting Machine (EBM) and SHapley Additive exPlanations (SHAP) to determine influential parameters.
• Performance evaluation using statistical indicators: R², RMSE, sMAPE, SI, WMAPE, Taylor diagrams, and Performance Index (PI).

Main Results:

• The ratio of upstream flow depth to weir height (h/P) was identified as the most significant factor influencing Cd.
• In training, ELM-JFO showed the best performance (PI=166, E'=0.0052), followed closely by TabNet-MFO (PI=142, E'=0.0068).
• In testing, TabNet-MFO achieved the highest accuracy (PI=81.92, E'=0.0118), outperforming ELM-JFO, LightGBM, and DT.

Conclusions:

• Hybrid and interpretable ML techniques, particularly TabNet-MFO, offer a reliable alternative for Cd estimation in SCLWs.
• The developed ML models significantly improve flow prediction accuracy compared to traditional methods.
• This research supports enhanced hydraulic structure design through advanced computational approaches.