Prediction Interval Estimation of Landslide Displacement Using Bootstrap, Variational Mode Decomposition, and Long and Short-Term Time-Series Network

Using multi-source monitoring data to model and predict the displacement behavior of landslides is of great significance for the judgment and decision-making of future landslide risks. This research proposes a landslide displacement prediction model that combines Variational Mode Decomposition (VMD) and the Long and Short-Term Time-Series Network (LSTNet). The bootstrap algorithm is then used to estimate the Prediction Intervals (PIs) to quantify the uncertainty of the proposed model. First, the cumulative displacements are decomposed into trend displacement, periodic displacement, and random displacement using the VMD with the minimum sample entropy constraint. The feature factors are also decomposed into high-frequency components and low-frequency components. Second, this study uses an improved polynomial function fitting method combining the time window and threshold to predict trend displacement and uses feature factors obtained by grey relational analysis to train the LSTNet networks and predict periodic and random displacements. Finally, the predicted trend, periodic, and random displacement are summed to the predicted cumulative displacement, while the bootstrap algorithm is used to evaluate the PIs of the proposed model at different confidence levels. The proposed model was verified and evaluated by the case of the Baishuihe landslide in the Three Gorges reservoir area of China. The case results show that the proposed model has better point prediction accuracy than the three baseline models of LSSVR, BP, and LSTM, and the reliability and quality of the PIs constructed at 90%, 95%, and 99% confidence levels are also better than those of the baseline models.