A hybrid model for water quality prediction based on two-layer modal decomposition and long short-term memory neural networks optimized by chaos sparrow search optimization algorithm

Abstract Accurate water quality prediction is essential for water resource protection. For the complex water quality change mechanism is difficult to grasp, the water quality time series of long-term and short-term information affect each other and lead to poor prediction accuracy, this study proposes a hybrid prediction model based on quadratic decomposition, the chaos sparrow search optimization algorithm (CSSOA), and the combination of long short-term memory neural network (LSTM). The original data is first decomposed using complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) to obtain several subsequences, and then the features in the high frequency subsequences are further extracted using variation mode decomposition (VMD) to further extract the features in the high frequency subsequences. Finally, the CSSOA-optimized LSTM is applied to predict each sequence, and the prediction results of each sequence are summed to yield the final prediction results. Experimental results show that the proposed model achieves significant improvements compared to benchmark models. For example, on the Gui River dataset (Dataset A), the mean square error (MSE) is reduced by 89% compared to the single LSTM model (0.005 vs. 0.046). On the Xun River dataset (Dataset B), the MSE is 0.003, which is 83% lower than the single LSTM model (0.018). Meanwhile, the results of extreme value and Diebold-Mariano (DM) test as well as multi-step prediction similarly confirm the superiority of the proposed model. So, the combined prediction method proposed in this study has enhanced prediction generalizability and accuracy, and it can be used to predict water quality in complex water environments.