An ensemble genetic programming approach to develop incipient sediment motion models in rectangular channels

•Sediment incipient motion in rectangular channel with a bed deposit is investigated.•Two new ensemble genetic programming models (PEGP and QPEGP) are suggested.•Fluid, flow, sediment and channel characteristics are incorporated into the models.•Deposited bed thickness is of importance in sediment incipient motion.•The new PEGP and QPEGP models outperform the conventional regression models. Assimilating unique features of genetic programming (GP) and gene expression programming (GEP), this study introduces a hybrid algorithm which results in promising incipient non-cohesive sediment motion models. The new models use the dimensionless input parameters including relative particle size, relative deposited bed thickness, channel friction factor and channel bed slope to estimate particle Froude number in rectangular channels. The models’ accuracy is tested using different error measures and cross-validated through comparison with that of five empirical models available in the relevant literature. The results showed enhanced accuracy of the proposed models in comparison to the existing ones with concordance correlation coefficient of 0.92 and 0.94 for parsimonious and quasi-parsimonious ensemble GP models, respectively. Such superiority is attributed to the integrated use of flow, fluid, sediment and channel characteristics in the modeling of incipient motion. Although the new algorithm is hybrid, the proposed models are explicit and precise, and thus, motivating to be used in practice.