The accuracy of medium- and long-term runoff forecasting plays a significant role in several applications involving the management of hydrological resources, such as power generation, water supply and flood mitigation. Numerous studies that adopted combined forecasting models to enhance runoff forecasting accuracy have been proposed. Nevertheless, some models do not take into account the effects of different lag periods on the selection of input factors. Based on this, this paper proposed a novel medium- and long-term runoff combined forecasting model based on different lag periods. In this approach, the factors are initially selected by the time-delay correlation analysis method of different lag periods and further screened with stepwise regression analysis. Next, an extreme learning machine (ELM) is adopted to integrate each result obtained from the three single models, including multiple linear regression (MLR), feed-forward back propagation-neural network (FFBP-NN) and support vector regression (SVR), which is optimized by particle swarm optimization (PSO). To verify the effectiveness and versatility of the proposed combined model, the Lianghekou and Jinping hydrological stations from the Yalong River basin, China, are utilized as case studies. The experimental results indicate that compared with MLR, FFBP-NN, SVR and ridge regression (RR), the proposed combined model can better improve the accuracy of medium- and long-term runoff forecasting in the statistical indices of MAE, MAPE, RMSE, DC, U95 and reliability.
In the application of medium and long-term runoff forecasting, machine learning has some problems, such as high learning cost, limited computing cost, and difficulty in satisfying statistical data assumptions in some regions, leading to difficulty in popularization in the hydrology industry. In the case of a few data, it is one of the ways to solve the problem to analyze the data characteristics consistency. This paper analyzes the statistical hypothesis of machine learning and runoff data characteristics such as periodicity and mutation. Aiming at the effect of data characteristics inconsistency on three representative machine learning models (multiple linear regression, random forest, back propagation neural network), a simple correction/improvement method suitable for engineering was proposed. The model results were verified in the Danjiangkou area, China. The results show that the errors of the three models have the same distribution as the periodic characteristics of the runoff periods, and the correction/improvement based on periodicity and mutation characteristics can improve the forecasting accuracy of the three models. The back propagation neural network model is most sensitive to the data characteristics consistency.INDEX TERMS Danjiangkou reservoir, data characteristics consistency, machine learning, medium and long-term runoff forecasting, mutation, characteristics, periodicity characteristics.
Accuracy in monthly runoff forecasting is of great significance in the full utilization of flood and drought control and of water resources. Data-driven models have been proposed to improve monthly runoff forecasting in recent years. To effectively promote the prediction effect of monthly runoff, a novel hybrid data-driven model using particle swarm optimization coupled with flower pollination algorithm-based deep belief networks (PSO-FPA-DBNs) was proposed, which selected the optimal network depth via PSO and searched for the optimum hyper parameters (the number of neurons in the hidden layer and the learning rate of the RBMs) in the DBN using FPA. The methodology was divided into three steps: (i) the Comprehensive Basin Response (COM) was constructed and calculated to characterize the hydrological state of the basin, (ii) the information entropy algorithm was adopted to select the key factors, and (iii) the novel model was proposed for monthly runoff forecasting. We systematically compared the PSO-FPA-DBN model with the traditional prediction models (i.e., the backpropagation neural network (BPNN), support vector machines (SVM), deep belief networks (DBN)), and other improved models (DBN-PLSR, PSO-GA-DBN, and PSO-ACO-DBN) for monthly runoff forecasting by using an original dataset. Experimental results demonstrated that our PSO-FPA-DBN model outperformed the peer models, with a mean absolute percentage error (MAPE) of 18.23%, root mean squared error (RMSE) of 230.45 m3/s, coefficient of determination (DC) of 0.9389, and qualified rate (QR) of 64.2% for the data from the Yalong River Basin. Also, the stability of our PSO-FPA-DBN model was evaluated. The proposed model might adapt effectively to the nonlinear characteristics of monthly runoff forecasting; therefore, it could obtain accurate and reliable runoff forecasting results.
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