Simulation of monthly river flow using SVR neural network improved with population-based optimization algorithms

Since the measurement of river discharge has always been one of the crucial challenges in the river management, the utilization of accurate tools to compute it becomes necessary. Numerical, analytical, artificial intelligence and experimental methods are the most common methods for measuring the monthly flow of the river. The objective of the current research is to enhance the efficiency of the support vector regression (SVR) as a neural network model for monthly river flow simulation and improve it’s performance useing Harris Hawks optimization (HHO), Grey Wolf Optimization (GWO) and grasshopper optimization (GOA) population-based optimization algorithms. To this end, monthly data related to river flow, precipitation and temperature during 21 years (from 2000 to 2021) are used. To choose the best input variables in developing the HHO-SVR, GWO-SVR and GOA-SVR models, the trial and error procedure is carried out. Based on the acquired results, \({Q}_{t-1}{, R}_{t-1},{T}_{t-1}\) $Q_{t-1}{,R}_{t-1},T_{t-1}$ are the best variables for modeling the variable  \({Q}_{t}\) $Q_t$ . For developing all models, 80% of the data are implemented for training and 20% for testing. Moreover, the indices R², RMSE and NSE are implemented for evaluating the efficiency of the models. Also, Linear, polynomial, RBF, and Sigmoid kernel functions are used to build the SVR model. Then, the performance of the SVR model is examined with each kernel function.First, the HHO-SVR model is developed. Based on the results, this model with the polynomial kernel function has the best performance in the training and testing phases (Train: RMSE: 0.1647, NSE: 0.8945,:  \({R}^{2} :\) $R^2:$ 0.8997, Test: RMSE: 0.1575, NSE: 0.8948, \({R}^{2}:0.8998\) $R^2:0.8998$ ). Then, the GWO-SVR model is developed, based on the results of this model with the polynomial kernel function, it has the best performance in the training and testing phases (Train: RMSE: 0.1920, NSE: 0.8878,: 0.8978, Test: RMSE: 0.1863, NSE: 0.8928, \({R}^{2}:0.8985\) $R^2:0.8985$ ). Finally, the performance of the GOA-SVR model is examined, based on the outcomes, this model with the polynomial kernel function has the best performance in the training and testing phases (Train: RMSE: 0.2067, NSE: 0.8760, \({R}^{2}:0.8958\) $R^2:0.8958$ , Test: RMSE: 0.2028, NSE: 0.8788, \({R}^{2}:0.8966\) $R^2:0.8966$ ). After that, the performance of these three models is compared with each other. According to the results acquired from this research and the type of the kernel function, the HHO, GWO and GOA algorithms can be utilized to improve the efficiency of the SVR model as well as accurate simulation of the monthly flow rate. After developing different models, their sensitivity to various variables are evaluated. Based of the sensitivity analysis outcomes, all models show most sensitivity to the variable \({Q}_{t-1}\) $Q_{t-1}$ and the least sensitivity to the variable \({T}_{t-1}\) $T_{t-1}$ .