Application of a Hybrid Model Based on an Attention-Mechanism-Enhanced Esn and Woa in Water Level Forecasting

Abstract

In the hydrological domain, owing to the ubiquity of time series data such as precipitation, runoff, and water levels, echo state networks (ESNs) have been extensively researched and adopted. We initially established an ESN model fused with a soft attention mechanism, termed A-ESN. By applying attention weights to the generation of the output weight matrix, the ESN can more effectively adapt to key reservoir states during the prediction process. Thus, during the training process, the network is continually adjusted based on the current state and historical information, enhancing the forecasting accuracy. Subsequently, we designed a composite model based on variational mode decomposition (VMD), A-ESN, and the whale optimization algorithm (WOA), termed VMD-VMD-WOA-A-ESN. After extracting the historical data that are highly correlated with the prediction days using hierarchical clustering, the original sequences were subjected to two rounds of VMD. The decomposed subsequences were then input into the A-ESN model for forecasting. The WOA was employed to optimize the hyperparameters of the A-ESN model, thereby obtaining the final predictions. For model training, four water level datasets from the runoff encryption observation sites located in the middle reaches of the Heihe River in Zhangye City, Gansu Province, China, were selected. The predictive performance was evaluated using five assessment metrics. The experimental results, when compared with those of eleven other benchmark models, demonstrated that the proposed hybrid model achieved satisfactory performance across all four datasets.

Keywords: Water level prediction；Echo state networks；Soft attention mechanism；Hierarchical clustering；Whale optimization algorithm；Hybrid model