Combining Radial Basis Function Neural Network Models and Inclusive Multiple Models for Predicting Suspended Sediment Loads

An important issue in water engineering is predicting suspended sediment load (SSL). For the Telar River and its tributaries, this study employs an inclusive multiple model (IMM) to predict SSL. Telar River branches into two main branches: Telar and Kasilian. The modeling process consisted of two levels: 1) creating hybrid models and 2) creating ensemble models. At the first level, the Honeybadger optimization algorithm (HBOA), salp swarm algorithm (SSA), and particle swarm optimization (PSO) were applied to set the parameters of the radial basis function neural network (RBFNN) models. The IMM model was used to integrate the outputs of the RBFNN-HBOA, RBFNN-SSA, RBFNN-PSO, and RBFNN models into the RBFNN model at the second level. Inputs to the models included lagged rainfall, discharge, and SSL. Several new ideas have been introduced in the current paper, including hybrid RBFNN models, a gamma test for selecting optimal input combinations, an analysis of output uncertainty, and an advanced IMM for SSL prediction. Various performance evaluation criteria, including root mean square error (RMSE), Nash Sutcliffe Efficiency (NSE), mean absolute error (MAE), and percentage bias (PBIAS), were used to evaluate the models. The comparative results indicated high accuracy of IMM with an MAE of 0.983, NSE of 0.254, PBIAS of 0.991 at Telar station. The training MAE of the IMM model was 4.4%, 4.8%, 6.7%, 52%, and 9.2% lower than that of the RBFNN-HBOA, RBFNN-SSA, RBFNN-PSO, and RBFNN models at Kasilian station. The study results revealed that the IMM and RBFNN-HBOA provided lower uncertainty than the other RBFNN models. Thus, the IMM model represents the most accurate estimation of SSL.