Hydrological time series prediction by extreme machine learning and sparrow search algorithm

In general, accurate hydrological time series prediction information is of great significance for the rational planning and management of water resource system. Extreme learning machine (ELM) is an effective tool proposed for the single-layer feedforward neural network in the regression and classification problems. However, the standard ELM model falls into local minimum with a high probability in hydrological prediction problems since the randomly assigned parameters (like input-hidden weights and hidden biases) often remain unchanged at the learning process. For effectively improving the prediction accuracy, this paper develops a hybrid hydrological forecasting model where the emerging sparrow search algorithm (SSA) is firstly used to determine the satisfying parameter combinations of the ELM model, and then the Moore-Penrose generalized inverse method is chosen to analytically obtain the weight matrix between the hidden layer and output layer. The proposed method is used to forecast the long-term daily runoff series collected from three real-world hydrological stations in China. Based on several performance evaluation indexes, the results show that the proposed method outperforms several ELM variants optimized by other evolutionary algorithms in both training and testing phases. Hence, an effective evolutionary machine learning tool is developed for accurate hydrological time series forecasting.