Reliability and sensitivity analysis of robust learning machine in prediction of bank profile morphology of threshold sand rivers

Abstract

This paper investigates how to achieve an equilibrium or stable state in a channel by taking into account widening and variations in its cross-section geometry dimensions. The current proposal is carried out by using an artificial intelligence technique, a Feed-Forward Neural Network (FFNN), which is trained by Extreme Learning Machine (ELM) algorithm to predict the banks profile morphology or shape profile characteristics of banks after stability. Moreover, the performance of proposed FFNN-ELM model is compared with eight famous previous traditional models and also a designed Non-Linear Regression (NLR). The analyses have been validated using a large number of experimental studies at different flow discharge rates. The results of ELM in comparison with NLR and traditional methods shows that the FFNN-ELM model has the best performance with lower error index values of Root Mean Squared Error (RMSE) equal to 5.6E−5 and Mean Absolute Relative Error (MARE) equal to 0.016, compared to NLR (RMSE = 2.2E−4 and MARE = 0.1225) and the most accurate traditional model which is related to Cao and Knight’s (1997) model (RMSE = 0.119 and MARE = 0.1095). Therefore, the FFNN-ELM model proposed in this paper maintains a suitable computational efficiency, as second-degree polynomial, for its performance compared to NLR and previous traditional models in estimating shape profile of stable channels banks. Furthermore, the uncertainty of proposed FFNN-ELM is calculated by Monte-Carlo based simulation method to assess the reliability of model to predict bank profile shape. The uncertainty result shows the less uncertainty of the FFNN-ELM model in shape simulation with the percentage of observed data bracketed by 95 percentage prediction uncertainties (95PPU) equal to 81.35% and d-factor value equal to 1.26 in test stage. Furthermore, the sensitivity of FFNN-ELM model relative to input parameters (flow discharge, Q, and lateral distance from the centreline of the channel, x) represents that in nearly all discharges, the sensitivity value is negative, indicates that by increasing the value of x parameter, the predicted value for the vertical level of the bank’s by model decreases. Moreover, by increasing the flow discharge, the sensitivity of the FFNN-ELM model to the two effective parameters of Q and x on the estimation of vertical level of the stable channels bank is increased.