Landslide displacement prediction based on variational mode decomposition and WA-GWO-BP model

Many models have been widely used in landslide displacement prediction. However, few studies have proposed quantitative prediction formulas. Thus, the variational mode decomposition (VMD) theory was applied to decompose the step-like displacement of landslides into trend displacement, periodic displacement, and random displacement. Then, a novel prediction model based on wavelet analysis (WA) and a back-propagation neural network (BPNN) optimized by the grey wolf optimizer (GWO) algorithm was proposed (the GWO-BP model) to obtain a prediction formula. In this model, a polynomial function was first used to predict the trend displacement. All the hidden periods of periodic displacement were calculated using the WA method, and a trigonometric function was applied to predict the periodic displacement. In addition, based on an analysis of the grey relational degree (GRD), the main triggering factors, which can affect the random displacement, were determined. Then, the mathematical connection between random displacement and triggering factors was obtained with the GWO-BP model. Finally, all the predicted values were superposed to achieve the prediction cumulative displacement based on the time series model. The Outang landslide in the Three Gorges Reservoir area, China, was taken as an example, and the displacement data of monitoring sites MJ01 and MJ02 from December 2010 to December 2016 were selected for analysis. The results indicated that the root mean square errors (RMSE) between the real displacement values and the prediction values obtained using the formula were 14.79 mm and 12.59 mm, respectively. The correlation coefficient R values were 0.99 and 0.93, respectively. This model can be used to obtain the landslide displacement formula and provide a solid basis for developing early warning systems for landslides.