Uncertainty elevation of landslide displacement prediction based on LSTM and Mixture Density Network

Abstract

Considering monitoring noise and complexity of landslide movement, quantify the uncertainty of landslide displacement prediction is crucial and challenging. Traditional data-driven models such as long short-term memory networks (LSTM), support vector regression, and extrema learning machines, etc, give the predicted displacement without considering the uncertainty of the predictions. Moreover, the loss function of the data-driven model is mainly taken as mean square error, which may lead to a worse performance when the training data follows non-normal distribution and thus reduces the robustness of the model. This study tends to propose a novel hybrid model based on LSTM and mixture density network to quantify each data point’s probability density distribution. By introducing the mixture density network and the maximum likelihood loss function, this model can get rid of the limitation that the data needs to obey the normal distribution. The mixed probability density parameters of each data point were predicted accurately due to the dynamic learning process in time series by LSTM. Moreover, we introduce the ensemble prediction to consider the uncertainty of model parameters. The performance of the model was validated based on a typical landslide in the Three Gorges Reservoir Area (TGRA), the Baishuihe landslide. Application results demonstrate that the proposed model provides accurate mean predictions and reasonable confidence displacement intervals.