A hybrid intelligent approach for constructing landslide displacement prediction intervals

Abstract

Accurate and reliable landslide displacement predictions are important for providing early warning regarding the occurrence of landslides. Machine learning methods are widely used for point predictions of landslide displacement because of their powerful nonlinear processing ability. However, due to the uncertainties involved in landslide systems, prediction errors are unavoidable in traditional point prediction methods. To quantify the uncertainties associated with point forecasting, we apply prediction intervals (PIs) to predict landslide displacement rather than using point predictions. A hybrid double exponential smoothing (DES) and lower and upper bound estimation (LUBE) model is proposed to construct the PIs of landslide displacement. In LUBE, an extreme machine learning (ELM) model with two outputs optimized by the particle swarm optimization (PSO) algorithm (PSO-ELM) is applied to directly estimate the lower and upper bounds of future displacement. The proposed DES-PSO-ELM method consists of three steps. First, DES is applied to predict the linear component of the cumulative displacement of the landslide. Second, the partial autocorrelation function (PACF) and maximum information coefficient (MIC) are used to select the optimal variables that influence the nonlinear component (residuals from the first step); then, these variables are used as inputs for the PSO-ELM method to construct the PIs of the nonlinear component. An ensemble technique is also applied to improve the stability and accuracy of PSO-ELM. Finally, the PIs of cumulative displacement are obtained by adding the predicted linear component and the PIs of the nonlinear component. The Baishuihe landslide and Shuping landslide in the Three Gorges Reservoir area were selected to test the effectiveness of the proposed method. A comparison of the results shows that the proposed method performs better and can provide high-quality PIs of landslide displacement.