Integrating hippopotamus optimization algorithm into machine learning frameworks for predicting suspended sediment concentrations

Abstract The vertical distribution of sediment concentration is a fundamental component of sediment transport hydraulics, directly impacting the estimation of sediment loads in riverine and channel systems. Therefore, accurate characterization of this distribution remains a critical challenge in hydraulic engineering. To address this, advanced intelligent modeling techniques offer a robust pathway for reliable prediction. This study evaluates the performance of six distinct modeling approaches—ORELM, ORELM-HOA, GPR, GPR-HOA, GMDH-ANFIS, and GMDH-ANFIS-HOA—to predict the relative sediment concentration distribution (C/C a ​). Results indicated that the integration of meta-heuristic optimization significantly enhances the predictive precision of the GMDH-ANFIS, ORELM, and GPR frameworks. Comparative analysis reveals that the GMDH-ANFIS-HOA model achieved the highest predictive accuracy, yielding an RMSE of 0.0434 and R 2 of 0.9747 during the training phase, and an RMSE of 0.0424 and R 2 of 0.9727 during the testing phase. The GPR-HOA model followed as the second-best performer. Furthermore, sensitivity analysis identified the relative depth (y/D) as the most dominant factor influencing model accuracy. These findings demonstrate that the optimized GMDH-ANFIS-HOA model provides a reliable and efficient computational tool for engineers and hydrologists, facilitating improved design and management of irrigation canals, river engineering projects, and sediment-related environmental assessments.