Estimation of scour depth around cross-vane structures using a novel non-tuned high-accuracy machine learning approach

Abstract

Due to the vital role of rivers and canals, the protection of their banks and beds is critically important. There are various methods for protecting beds and banks of rivers and canals in which “cross-vane structures” is one of them. In this paper, the scour hole depth at the downstream of cross-vane structures with different shapes (i.e., J, I, U, and W) is simulated utilizing a modern artificial intelligence method entitled “Outlier Robust Extreme Learning Machine (ORELM)”. The observational data are divided into two groups: training (70%) and test (30%). After that, the most optimal activation function for simulating the scour depth at the downstream of cross-vane structures is selected. Then, using the input parameters including the ratio of the structure length to the channel width (b/B), the densimetric Froude number (Fd), the ratio of the difference between the downstream and upstream depths to the structure height (Δy/hst) and the structure shape factor $$ \left( \phi \right) $$, eleven different ORELM models are developed for estimating the scour depth. Subsequently, the suitable model and also the most effective input parameters are identified through the conduction of an uncertainty analysis. The suitable model simulates the scour values by the dimensionless parameters b/B, Fd, Δy/hst. For this model, the values of the correlation coefficient (R), Variance accounted for (VAF) and the Nash-Sutcliffe efficiency (NSC) for the suitable model in the test mode are obtained 0.956, 91.378 and 0.908, respectively. Also, the dimensionless parameters b/B, Δy/hst. are detected as the most effective input parameters. Furthermore, the results of the suitable model are compared with the extreme learning machine model and it is concluded that the ORELM model is more accurate. Moreover, an uncertainty analysis exhibits that the ORELM model has an overestimated performance. Besides, a partial derivative sensitivity analysis (PDSA) model is performed for the suitable model.