Hybridization of multivariate adaptive regression splines and random forest models with an empirical equation for sediment deposition prediction in open channel flow

It has been known that the channel cross-section shape impacts on flow velocity at sediment deposition condition; however, existing models only apply to specific cross-section shapes and there has been a lack of a general incipient deposition model applicable for all types of cross-section shapes. To this end, this study is designed to generalize incipient deposition models by including of a cross-section shape factor into the model parameters. Experimental data collected from channels of five different cross-sectional shapes namely; trapezoidal, rectangular, circular, U-shape and V-bottom are used for the modeling. Two machine-learning models, multivariate adaptive regression splines (MARS) and random forest (RF); and an empirical multi non-linear regression (MNLR) model, are developed. The accuracy of the stand-alone models is improved by hybridizing the MARS and RF models with the MNLR equation to generate robust models of MARS-MNLR and RF-MNLR. Comparison of these models with those existing in the literature indicates that cross-section-specific models may have poor performances on varied cross-section channels. MARS, RF and MNLR models as general incipient deposition models outperform cross-section-specific models, which may be attributed to the considering of shape factor as an input parameter. Hybridization of the MARS and RF models with the MNLR equation results in improving their performances in MARS-MNLR and RF-MNLR models by a factor of 25% in contrast to MNLR model. Although the MARS-MNLR model gives better results than MNLR-RF model, they both perform better than their stand-alone counterparts in terms of different statistical indices. Explicit formulae are suggested which may be applied as practical tools for channel design.