Landslide displacement prediction method based on DLNM lag effect analysis: A case study of a certain landslide in the Yangtze River

Landslide displacement prediction is crucial for geological hazard early warning and prevention. Landslide deformation is driven by external factors such as rainfall and reservoir water level fluctuations, and its response process exhibits complex lag and nonlinear characteristics, posing significant challenges for accurate prediction. Taking the Outang landslide in the Three Gorges Reservoir Area as a case study, this paper proposes a landslide displacement prediction method based on the Distributed Lag Nonlinear Model (DLNM), aiming to enhance the accuracy and interpretability of displacement predictions by quantifying the lag effects of triggering factors. The study utilizes DLNM to reveal the exposure-lag-response relationships between rainfall/reservoir water level and surface displacement, identifying key lag periods: the maximum lag times for rainfall at the front (FJOT02) and rear (FJOT05) sections of the primary sliding mass are 35 days and 36 days, respectively. For reservoir water level changes, the impact of the drawdown phase can last up to 11 days, while the impoundment phase lasts 14 days. Based on these lag characteristics, a multi-dimensional input dataset is constructed. The Variational Mode Decomposition (VMD) method is applied to adaptively decompose the displacement series into trend and periodic components. These components are then separately predicted using the Triple Exponential Smoothing (ES) method and the Long Short-Term Memory (LSTM) network, ultimately constructing a VMD-ES-LSTM prediction model that integrates the lag mechanism. Empirical analysis using monitoring points FJOT05 and FJOT02 at the Outang landslide demonstrates that the proposed model achieves an R² of 0.9865 and an RMSE of 1.1722 mm on the test set. Its prediction accuracy is significantly superior to that of comparative models that do not consider lag effects. By coupling lag effect analysis with machine learning modeling, this method enables high-precision and interpretable landslide displacement prediction, providing reliable technical support for risk early warning and prevention of reservoir landslide hazards.