Nonlinear multi independent variables in quantifying river bank erosion using Neural Network AutoRegressive eXogenous (NNARX) model

Abstract

This study proposed a novel application of Neural Network AutoRegressive eXogenous (NNARX) model in predicting nonlinear behaviour of riverbank erosion rates which is difficult to be achieved with good accuracy using conventional approaches. This model can estimate complex river bank erosion rates with flow variations. The NNARX model analysed to a set of primary data, 60% (203 data for training) and 40% (135 data for testing), which were collected from Sg. Bernam, Malaysia. A set of nondimensional parameters, known as functional relationship, used as an input to the NNARX model has been established using the method of repeating variables. The One-Step-Ahead time series prediction plots are used to assess the accuracy of all developed models. Model no. 6 (5 independent variables with 10 hidden layers) gives good predictive performance, supported by the graphical analysis with discrepancy ratio of 94% and 90% for training and testing datasets. This finding is consistent with model accuracy result, where Model no. 6 achieved R2 of 0.932 and 0.788 for training and testing datasets, respectively. Result shows that bank erosion is maximized when the near-bank velocity between 0.2 and 0.5 m/s, and the riverbank erosion is between 1.5 and 1.8 m/year. On the other hand, higher velocities ranging from 0.8 to 1.3 m/s induces erosion at a rate between 0.1 and 0.4 m/year. Sensitivity analysis shows that the highest accuracy of 91% is given by the ratio of shear velocity to near-bank velocity followed by boundary shear stress to near-bank velocity ratio (88.5%) and critical shear stress to near-bank velocity ratio (88.2%). It is concluded that the developed model has accurately predicted non-linear behaviour of riverbank erosion rates with flow variations. The study's findings provide valuable insights in advanced simulations and predictions of channel migration, encompassing both lateral and vertical movements, the repercussions on the adjacent river corridor, assessing the extent of land degradation and in formulating plans for effective riverbank protection and management measures.