Improved Neural Network Model and Its Application in Hydrological Simulation

When applying a back-propagation neural network (BPNN) model in hydrological simulation, researchers generally face three problems. The first one is that real-time correction mode must be adopted when forecasting basin outlet flow, i.e., observed antecedent outlet flows must be utilized as part of the inputs of the BPNN model. Under this mode, outlet flow can only be forecasted one time step ahead, i.e., continuous simulation cannot be implemented. The second one is that topology, weights, and biases of BPNN cannot be optimized simultaneously by traditional training methods. Topology designed by the trial-and-error method and weights and biases trained by back-propagation (BP) algorithm are not always global optimal and the optimizations are experience-based. The third one is that simulation accuracy for the validation period is usually much lower than that for the calibration period, i.e., generalization property of BPNN is not good. To solve these problems, a novel coupled black-box model named BK (BP-KNN) and a new methodology of calibration are proposed in this paper. The BK model was developed by coupling BPNN model with $K$-nearest neighbor (KNN) algorithm. Unlike the traditional BPNN model previously reported, the BK model implemented continuous simulation under nonreal-time correction mode. Observed antecedent outlet flows were substituted by simulated values. The simulated values were calculated by the BPNN model first and then corrected based on the KNN algorithm, historical simulation error, and other relevant factors. According to the calculation process, parameters of the BK model were divided into three hierarchies and each hierarchy was calibrated respectively by the NSGA-II multiobjective optimization algorithm. This new methodology of calibration ensured higher accuracy and efficiency, and enhanced the generalization property of the BPNN. The accuracy of flow concentration module of Xinanjiang model is not always high enough, in order to combine advantages of conceptual and black-box models, XBK and XSBK models were proposed. The XBK model was constituted by coupling runoff generation module of Xinanjiang model with BK flow concentration model and the XSBK model was constituted by coupling runoff generation and separation module of Xinanjiang model with BK flow concentration model. BK, XBK, XSBK, and Xinanjiang models were applied in Chengcun, Dongwan, and Dage watersheds. The simulation results indicated that improved models obtained higher accuracies than Xinanjiang model and can overcame limitations of traditional BPNN model.