Developing Extended and Unscented Kalman Filter-Based Neural Networks to Predict Cluster-Induced Roughness in Gravel Bed Rivers

Flow resistance in natural gravel-bed rivers must be precisely predicted in order for water-related infrastructure to be designed effectively. Cluster microforms are significant factors in determining the resistance of flow in rivers with gravel beds. To precisely estimate the cluster microform-induced Darcy-Weisbach roughness coefficient, the current study utilized two novel and robust data-intelligence paradigms: Unscented Kalman Filter (UKF) and Extended Kalman Filter (EKF) -based Artificial Neural Networks (UKF-ANN and EKF-ANN), in addition to Response Surface Methodology (RSM) and Multi-layer Perceptron Neural Network (MLPNN). A total of 128 sets of laboratory data were used to develop the models, which encompassed a range of geometric and hydraulic scenarios. Various performance metrics, including, Mean Absolute Percentage Error (MAPE) Root Mean Square Error (RMSE) and Correlation Coefficient (R) were employed to assess the models' performance. The results showed that the implemented machine learning methods (i.e., MLPNN, UKF-ANN, EKF-ANN) had a good performance. Comparison of machine learning models showed that the EKF-ANN (R = 0.9747, MAPE = 7.73, RMSE = 0.0041) and UKF-ANN (R = 0.9617, MAPE = 8.17, RMSE = 0.0050) models provided higher accuracy compared to MLPNN (R = 0.940, MAPE = 11.38, RMSE = 0.0064,) and RSM (R = 0.957, MAPE = 11.02, RMSE = 0.0057). Moreover, the sensitivity analysis demonstrates that the roughness coefficient is primarily affected by the hydraulic radius to the longitudinal distance of clusters (R/λ).