A novel method of nonuniform phase space reconstruction for multivariate prediction of daily runoff

Abstract

Phase space reconstruction is crucial for predicting chaotic hydrological time series. However, traditional multivariate phase space reconstruction methods, such as high-dimensional and low-dimensional phase space reconstruction (HDPSR and LDPSR) neglect variable interdependence, resulting in redundant information in the reconstructed phase space and affecting the model prediction accuracy. To address this limitation, this study proposes a new nonuniform phase space reconstruction (NUPSR) method that combines the minimum redundancy maximum relevance criterion and conditional entropy. Then, using HDPSR, LDPSR, NUPSR, particle swarm optimization (PSO), support vector regression (SVR), and bidirectional long- and short-term memory neural networks (BiLSTM), the models HDPSR-PSO-SVR, LDPSR-PSO-SVR, NUPSR-PSO-SVR, HDPSR-PSO-BiLSTM, LDPSR-PSO-BiLSTM, and NUPSR-PSO-BiLSTM are built to evaluate the performance of the NUPSR method. To demonstrate the effectiveness of the NUPSR method in multistep daily runoff prediction, the models PSO-NUPSR-BiLSTM, LDPSR-PSO-BiLSTM, and HDPSR-PSO-BiLSTM are also built. The multifactor daily runoff data from five hydrological stations in the Weihe River Basin are used to evaluate the prediction performance of all models. The results show that the state variables obtained by NUPSR are more independent and less redundant than those obtained by HDPSR and LDPSR, as evidenced by the embedded state variables and lower embedding dimension of NUPSR and the performance of the model based on NUPSR outperforms based on HDPSR and LDPSR. Particularly, the PSO-NUPSR-BiLSTM model exhibits a slower decrease in prediction accuracy compared to the other two models as the number of prediction steps increases. In summary, the NUPSR method effectively selects and reconstructs predictors, significantly improves the prediction accuracy of the coupled models, and has broad application prospects in multivariate prediction in fields such as hydrology.