Forecasting of landslide displacements using a chaos theory based wavelet analysis-Volterra filter model

Landslide displacement time series can directly reflects landslide deformation and stability characteristics. Hence, forecasting of the non-linear and non-stationary displacement time series is necessary and significant for early warning of landslide failure. Traditionally, conventional machine learning methods are adopted as forecasting models, these forecasting models mainly determine the input and output variables experientially and does not address the non-stationary characteristics of displacement time series. However, it is difficult for these conventional machine learning methods to obtain appropriate input-output variables, to determine appropriate model parameters and to acquire satisfied prediction performance. To deal with these drawbacks, this study proposes the wavelet analysis (WA) to decompose the displacement time series into low- and high-frequency components to address the non-stationary characteristics; then proposes thee chaos theory to obtain appropriate input-output variables of forecasting models, and finally proposes Volterra filter model to construct the forecasting model. The GPS monitoring cumulative displacement time series, recorded on the Shuping and Baijiabao landslides, distance measuring equipment monitoring displacements on the Xintan landslide in Three Gorges Reservoir area of China, are used as test data of the proposed chaotic WA-Volterra model. The chaotic WA-support vector machine (SVM) model and single chaotic Volterra model without WA method, are used as comparisons. The results show that there are chaos characteristics in the GPS monitoring displacement time series, the non-stationary characteristics of landslide displacements are captured well by the WA method, and the model input-output variables are selected suitably using chaos theory. Furthermore, the chaotic WA-Volterra model has higher prediction accuracy than the chaotic WA-SVM and single chaotic Volterra models.