A new hybrid method for establishing point forecasting, interval forecasting, and probabilistic forecasting of landslide displacement

In addition to its inherent evolution trend, landslide displacement contains strong fluctuation and randomness, and omni-directional landslide displacement prediction is more scientific than single point prediction or interval prediction. In this study, a new hybrid approach composed of double exponential smoothing (DES), variational mode decomposition (VMD), long short-term memory network (LSTM), and Gaussian process regression (GPR) is proposed for the point, interval, and probabilistic prediction of landslide displacement. The proposed model includes two parts: (i) predicting the inherent evolution trend of landslide displacement through DES-VMD-LSTM; (ii) evaluating the uncertainty in the first prediction based on the GPR model. In the first part, DES is used to predict the trend displacement, and the periodic and stochastic displacement in the residual displacement is extracted by VMD and predicted by the LSTM. The triggering factors of the periodic and stochastic displacement are screened by the maximum information coefficient (MIC), and the screened factors are decomposed into low- and high-frequency components by VMD to predict the periodic and stochastic displacements, respectively. The first cumulative displacement prediction results are achieved by adding the predicted trend and the periodic and stochastic displacements. By setting the first predicted displacement as the input and the actual displacement as the expected output, the point, interval, and probabilistic predictions of landslide displacement are achieved through the GPR model. The plausibility of the proposed model is validated with data from the Bazimen (BZM) and Baishuihe (BSH) landslides in the Three Gorges Reservoir area. This model has the potential to achieve the deterministic prediction of landslide displacement and quantify the uncertainty contained in the displacement. A comparative study shows that this method has a high performance for the point, interval, and probabilistic prediction of landslide displacement.