Railway freight volume forecast using an ensemble model with optimised deep belief network

Forecasting freight traffic contributes to the improvement of traffic facilities and making industrial policy, so it is significant to predict freight volume accurately. Extensive works had proved that ensemble model performed better than single model, so an ensemble model, combining seasonal autoregressive integrated moving average (SARIMA) with deep belief network (DBN), is proposed here. SARIMA, a linear model, is used to find the regularities of railway freight traffic. DBN, a non‐linear model, is taken to mine the complex relationships between indexes and railway freight. In order to decide appropriate architecture of DBN, including the number of network layers and neurons in each hidden layer, Gaussian particle swarm optimisation algorithm is designed to decide appropriate architecture of DBN, including the number of network layers and neurons in each hidden layer. Besides, Spearman rank correlation analysis is used for selecting indexes related to freight volume. Experimental results show that, compared with SARIMA, DBN, back propagation neural network, Elman neural network, and radial basis function neural network, the proposed ensemble model obtains best performance, and the mean absolute error is 5.5159 million t and the mean absolute percentage error is 1.9657%.