Mid- to long-term runoff prediction by combining the deep belief network and partial least-squares regression

Data representation and prediction model design play an important role in mid- to long-term runoff prediction. However, it is challenging to extract key factors that accurately characterize the changes in the runoff of a river basin because of the complex nature of the runoff process. In addition, the low accuracy is another problem for mid- to long-term runoff prediction. With an aim to solve these problems, two improvements are proposed in this paper. First, the partial mutual information (PMI)-based approach was employed for estimating the importance of various factors. Second, a deep learning architecture was introduced by using the deep belief network (DBN) with partial least-squares regression (PLSR), together denoted as PDBN, for mid- to long-term runoff prediction, which solves the problem of parameter optimization for the DBN using PLSR. The novelty of the proposed method lies in the key factor selection and a novel forecasting method for mid- to long-term runoff. Experimental results demonstrated that the proposed method can significantly improve the effect of mid- to long-term runoff prediction. Also, compared with the results obtained by current state-of-the-art prediction methods, i.e., DBN, backpropagation neural networks, and support vector machine models, our prediction results demonstrate the performance of the proposed method.