Development of riverbank erosion rate predictor for natural channels using NARX-QR Factorization model: a case study of Sg. Bernam, Selangor, Malaysia

This study presents a novel and comprehensive model development technique to predict the riverbank erosion rate for a natural channel using a Nonlinear AutoRegressive model with eXogenous inputs and QR factorization parameter estimation, known as the NARX-QR Factorization model. The model was developed based on a 12-month extensive field measurement at Sg. Bernam. This study established the governing factors and derived dependent and independent variables for riverbank erosion using dimensional analysis, based on the Buckingham PI theorem. Two functional relationships were derived from dimensional analysis incorporating the factors governing riverbank erosion. The functional relationships include parameters of hydraulic characteristics of the channel, riverbank geometry and soil characteristics. Parameter estimation was conducted using a linear least squares technique to quantify riverbank erosion rates. The significant independent variables and fourteen models with several numbers of hidden layers were set as the input parameters to the NARX-QR Factorization model. The model performance analysis shows that Models 1 and 9, developed based on the proposed NARX-QR Factorization model, have the highest R² at 75% and 91%, respectively. Model 1 performed the best with accuracies for training and testing datasets of 75% and 73%, respectively. Additionally, the scatter plot of Model 1 is uniformly distributed along the line of perfect agreement. Therefore, it is concluded that the NARX-QR Factorization model developed in this study performed well in estimating the riverbank erosion rate, particularly for a natural river similar to Sg. Bernam.