Accurate discharge coefficient prediction of streamlined weirs by coupling linear regression and deep convolutional gated recurrent unit

Streamlined weirs, which are a nature-inspired type of weir, have gained tremendous attention among hydraulic engineers, mainly owing to their established performance with high discharge coefficients. Computational fluid dynamics (CFD) is considered as a robust tool to predict the discharge coefficient. To bypass the computational cost of CFD-based assessment, the present study proposes data-driven modeling techniques, as an alternative to CFD simulation, to predict the discharge coefficient based on an experimental dataset. To this end, after splitting the dataset using a k-fold cross-validation technique, the performance assessment of classical and hybrid machine learning-deep learning (ML-DL) algorithms is undertaken. Among ML techniques, linear regression (LR), random forest (RF), support vector machine (SVM), k-nearest neighbor (KNN) and decision tree (DT) algorithms are studied. In the context of DL, long short-term memory (LSTM), convolutional neural network (CNN) and gated recurrent unit (GRU), and their hybrid forms, such as LSTM-GRU, CNN-LSTM and CNN-GRU techniques, are compared using different error metrics. It is found that the proposed three-layer hierarchical DL algorithm, consisting of a convolutional layer coupled with two subsequent GRU levels, which is also hybridized with the LR method (i.e. LR-CGRU), leads to lower error metrics. This paper paves the way for data-driven modeling of streamlined weirs.