A DES-BDNN based probabilistic forecasting approach for step-like landslide displacement

Accurate and reliable displacement prediction is very important for landslide early warning. However, various uncertainties contained in landslide displacement prediction will greatly affect the prediction accuracy, and reduce the credibility of prediction results. Probability prediction is an efficient way to assess the uncertainties associated landslide displacement and improve the reliability of prediction. This paper proposes a new probabilistic forecasting framework for landslide displacement based on exponential smoothing (DES) and Bayesian deep neural networks (BDNN), which can clearly distinguish the aleatoric uncertainty covered by the evolution of data itself and the epistemic uncertainty reflecting the unsteadiness of intelligent model. Therein, DES predicts the linear part contained in the total displacement, and BDNN predicts the residual nonlinear part. The optimal input features of BDNN model are determined by the maximum information coefficient and Pearson correlation coefficient. The Baishuihe landslide in the Three Gorges Reservoir area was selected to test the effectiveness of the proposed framework with three BDNN models, including Bayesian recurrent neural network (BRNN), Bayesian gated recurrent unit network (BGRU) and Bayesian long short-term memory network (BLSTM). The results suggest that the proposed framework can obtain considerable prediction effect, especially DES-BLSTM and DES-BGRU model. The variational mode decomposition (VMD) and interpolation are used to further optimize the DES-BDNN model from the perspective of reducing the complexity of nonlinear displacement and increasing training datasize. The comparison results show that the improved model can not only obtain high-precision point prediction results, but also accurately infer the total/aleatoric/epistemic uncertainty associated with landslide displacement prediction.