What question did this study set out to answer?

The aim is to enhance seepage flow prediction in earth–rock dams by addressing limitations of traditional models.

February 12, 2026Open Access

Interval Prediction Model for Seepage Flow in Earth–Rock Dams Based on Time Series Characteristics

Key Points

The aim is to enhance seepage flow prediction in earth–rock dams by addressing limitations of traditional models.
Utilized temporal convolutional network (TCN) for feature extraction from seepage monitoring data.
Employed bidirectional gated recurrent unit (BiGRU) to capture historical dependencies in time series.
Implemented self-attention mechanism (SATT) to assign dynamic weights to extracted features.
Applied adaptive bandwidth kernel density estimation (ABKDE) for uncertainty quantification in predictions.
Constructed prediction intervals based on statistical analysis of point prediction error distributions.
The TCN–BiGRU–SATT model outperformed benchmark models in predictive accuracy and stability.
At confidence intervals of 85%, 90%, and 95%, the integrated evaluation index F improved by 9.02%, 9.59%, and 4.05%, respectively.
Demonstrated effective uncertainty quantification compared to conventional kernel density estimation methods.

Abstract

To address challenges posed by insufficient feature extraction, difficulties in capturing complex patterns, limited prediction accuracy, and unquantified uncertainty inherent in traditional point prediction models for complex time series data, this study proposes a novel interval prediction framework based on temporal convolutional network (TCN)–bidirectional gated recurrent unit (BiGRU)–self‐attention mechanism (SATT)–adaptive bandwidth kernel density estimation (ABKDE), specifically tailored for earth–rock dam seepage flow prediction. Initially, the TCN is employed to extract essential temporal features from seepage monitoring data. Subsequently, these extracted features are input into a BiGRU, effectively capturing both historical dependencies and future‐oriented information. Following this, a SATT dynamically assigns weights to critical features, thereby enhancing the predictive relevance and forming a high‐accuracy point prediction model. Finally, utilizing point prediction error distributions combined with ABKDE and bootstrap methodology, statistically robust intervals at multiple confidence levels are constructed. This integrated approach comprehensively addresses feature extraction, complex time series modeling, and uncertainty quantification. The case conducted demonstrates that the proposed TCN–BiGRU–SATT model consistently outperforms both benchmark models and the simpler BiGRU–SATT in evaluation metrics, indicating superior accuracy and stability. Leveraging residuals derived from point predictions, the ABKDE component adaptively adjusts bandwidths, effectively capturing and quantifying the uncertainty inherent in predictions. Performance metrics at distinct confidence intervals surpass those obtained using conventional kernel density estimation (KDE), confirming greater adaptability and responsiveness to variations in data. Specifically, at confidence levels of 85%, 90%, and 95%, the integrated evaluation index F attains values of 1.6447, 1.5821, and 1.3885, respectively, corresponding to improvements of 9.02%, 9.59%, and 4.05% over the KDE method. These findings underscore the practical value and potential applicability of the proposed methodology in engineering contexts.

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