Improved explicit formulation of bedload transport using a novel multi-level multi-model data-driven ensemble approach

Abstract

AbstractEstimation of bedload transport in rivers is a very complex and important river engineering challenge needs substantial additional efforts in pre-processing and ensemble modeling to derive the desired level of prediction accuracy. This paper aims to develop a new framework for the formulation of bedload transport in rivers using multi-level Multi-Model Ensemble (MME) approach to derive improved explicit formulations hybridized with multiple pre-processed-based models. Three pre-processing techniques of feature selection by Gamma Test (GT), dimension reduction by principal component analysis (PCA), and data clustering by subset selection of maximum dissimilarity (SSMD) are utilized at level 0. The multi-linear regression (MLR), MLR-PCA, artificial neural network (ANN), ANN-PCA, Gene expression programming (GEP), GEP-PCA, Group method of data handling (GMDH) and GMDH-PCA are used to develop individual explicit formulations at level 1, and the inferred formulas are hybridized with the MME approach at level 2 by Pareto optimality. A newly revised discrepancy ratio (RDR) for error distributions in conjunction with several statistical and graphical indicators were used to evaluate the strategy's performance. Results of MME showed that the proposed framework acted as an efficient tool in explicit equation induction for bedload transport (i.e., 33–96% reduction of RMSE; 2–29% increase of R2, 2-138% increase of NSE and 38–98% reduction of RAE in testing step in comparison with the best individual model) and clearly outperformed estimations made by other models. The current study highlights the importance of pre-processing and multi-modelling techniques in deep learning models to encounter the challenges of function finding for complex bedload transport estimations in multiple observed datasets.