Prediction of discharge coefficient of submerged gates using a stacking ensemble model

Abstract Improving the precision of discharge coefficient (Cd) prediction is crucial for effective agricultural water management. However, existing methods for Cd calculation are often complex and dependent on specific assumptions. Therefore, there is a critical need for robust and automated models for Cd estimation. This study introduces a dual-stage ensemble model called EnsembleCNN, for Cd prediction using two distinct gate types under submerged flow conditions. The EnsembleCNN framework uniquely integrates machine learning (ML) models with a recurrent convolutional neural network (CNN) model to capture higher-order interactions and non-linearities. Five base ML models are employed to generate initial predictions. These predictions are subsequently processed by a CNN model embedded with long short-term memory (LSTM) layer, residual connection (RC) and an attention mechanism (ATM). This setup effectively manages the complexity of the combined predictions, seamlessly integrating the outputs from the base models. LSTM is exploited to aggregate the best features for prediction. ATM effectively prioritized high-performing base model outputs, while RC improved the gradient flow, collectively reducing the impact of irrelevant features. The proposed approach strategically weights the contributions of each base model, resulting in accurate Cd estimations. The proposed model achieved root mean square errors of 0.0552 and 0.0173 on vertical sluice gates and radial gates datasets, respectively. Additionally, EnsembleCNN outperformed the base and existing models in terms of prediction accuracy. The proposed system provides a robust tool for optimizing water resource management. Moreover, the adaptability to two field datasets further underscores the practical utility of our model in diverse irrigation scenarios.