An STL–attention-TFT ensemble for multi-horizon time series forecasting with application to dam deformation

Accurate multi-horizon forecasting of dam deformation is critical for proactive structural health monitoring and early warning in large hydraulic infrastructures. However, long-term displacement responses exhibit interacting trend, seasonal, and irregular components driven by hydrostatic, thermal, and aging effects, which challenge both classical statistical models and end-to-end deep learning approaches. This study proposes an STL–attention-TFT (STL–ATFT) ensemble framework that integrates seasonal–trend decomposition using LOESS (STL) with attention-enhanced temporal fusion transformers (ATFTs) for probabilistic multi-point dam deformation. The original multivariate time series is first decomposed into trend, seasonal, and residual components using STL; separate TFT sub-models are then trained for each component, and their forecasts are subsequently integrated through additive ensemble reconstruction to recover the final predictive distribution. This component-wise design allows the model to learn slow trend evolution, periodic deformation, and irregular residual fluctuations separately, thereby reducing interference among different temporal patterns. Methodologically, the STL–ATFT framework is tailored to multi-horizon, multi-output forecasting with calibrated uncertainty. It leverages TFT’s variable selection and interpretable multi-head attention to capture nonlinear dependencies across covariates, while decomposition reduces nonstationary and separates slow and fast dynamics, improving long-range predictive accuracy. A real-world case study on multi-point deformation of a concrete gravity dam demonstrates that STL–ATFT consistently outperforms benchmark models, including AutoARIMA, LSTM-based architectures, and a baseline TFT, in terms of error metrics and quantile-based coverage, achieving root mean squared error of up to 15% compared with the best-performing benchmark and R ² values frequently exceeding 0.95. The decomposed components and attention weights further provide physically meaningful insights into the relative contributions of hydrostatic, thermal, and aging factors. Although evaluated on dam deformation data, the proposed framework is applicable to other long-horizon forecasting tasks with pronounced trend–seasonal structure. Overall, the STL–ATFT ensemble offers a flexible, interpretable, and broadly deployable methodology for multi-horizon time series forecasting in safety-critical settings.