Estimation of Mean Velocity Upstream and Downstream of a Bridge Model Using Metaheuristic Regression Methods

Abstract This study compares four data-driven methods, Gaussian process regression (GPR), multivariate adaptive regression spline (MARS), M5 model tree (M5Tree), and multilinear regression (MLR), in estimating mean velocity upstream and downstream of bridges. Data were obtained through multiple experiments in a rectangular laboratory flume with glass walls 9.5 m long, 0.6 m wide, and 0.6 m deep. Four different bridge models were placed at the 6th meter of the channel to determine the average velocities upstream and downstream. Different data-driven models were implemented with different combinations of effective parameters as input. They were evaluated and compared using root mean square error (RMSE), mean absolute relative error (MARE), and Nash–Sutcliffe efficiency (NSE). The results showed that the MARS had the best efficiency in estimating the mean velocity upstream of the bridge model. At the same time, the M5Tree provided the highest performance in estimating the mean velocity downstream. The MARS method improved the estimation accuracy of GPR, M5Tree, and MLR in the test phase by 23.8%, 45.1%, and 47.4% concerning the RMSE at the upstream. The M5Tree provided better RMSE accuracy of 31.8%, 70.4%, and 75.5% at the downstream compared to MARS, GPR, and MLR, respectively. The study recommends the MARS and M5Tree for estimating mean velocities upstream and downstream of the bridge.