Weighted error-output recurrent Xavier echo state network for concept drift handling in water level prediction

Water level holds utmost significance in maritime domains. Precise water level predictions furnish indispensable insights for safe maritime navigation, guiding ships and vessels through passages, harbors, and waterways. This paper introduces a novel approach: the Weighted Error-Output Recurrent Xavier Echo State Network with Adaptive Forgetting Factor (WER-XESN-AFF). One of the contributions of this study is the introduction of the Xavier weights selection method, which replaces random weight selection from the Echo State Network (ESN). This method not only enhances forecasting performance but also reduces uncertainty in predictions. Additionally, two modified concept drift detectors, the Early Drift Detection Method and the Adaptive Forgetting Factor, are employed to address concept drift challenges. Another notable contribution is the introduction of a novel weighted error-output recurrent multi-step algorithm. This algorithm successfully overcomes the error accumulation problem by using past forecast errors to update current output weights. This study performs extensive experiments to evaluate the effectiveness of our approach in multi-step prediction in synthetic and real datasets. It compares the performance between the conventional randomization-based models and the ESN with the new weights selection approach and also tests the ability of concept drift detectors and the weighted error-output multi-step algorithm. Empirical findings and statistical analyses demonstrate that our proposed methods achieve expected effects, and the proposed model has better prediction ability than baselines. A significant improvement rate of 75.39% in Mean Squared Error is evident within the Jiujiang water level dataset when contrasting the performance of WER-XESN-AFF against the baseline model R-ESN across the 1–5 period.