Failure probability assessment of step-like landslide using a hybrid interval prediction method under uncertain conditions

To address prediction errors and limited information extraction in machine learning (ML)-based interval prediction, a hybrid model was proposed for interval estimation and failure assessment of step-like landslides under uncertainty. The model decomposed displacements into trend and periodic components via Variational Mode Decomposition (VMD) and K-shape clustering. The Residual and Moving Block Bootstrap methods were used to generate pseudo datasets. Polynomial regression was adopted for trend forecasting, whereas the Dense Convolutional Network (DenseNet) and Long Short-Term Memory (LSTM) networks were employed for periodic displacement prediction. An Extreme Learning Machine (ELM) was used to estimate the noise variance, enabling the construction of Prediction Intervals (PIs) and quantification of displacement uncertainty. Failure probabilities (Pf) were derived from PIs using an improved tangential angle criterion and reliability analysis. The model was validated on three step-like landslides in the Three Gorges Reservoir Area, achieving stability assessment accuracies of 99.88% (XD01), 99.93% (ZG93), 99.89% (ZG118), and 100% for ZG110 and ZG111 across the Baishuihe and Bazimen landslides. For the Shuping landslide, the predictions aligned with field observations before and after the 2014–2015 remediation, with Pf remaining near zero post-2015 except for occasional peaks. The model outperformed conventional ML approaches by yielding narrower PIs. At XD01 with 90% PI nominal confidence level (PINC), the coverage width-based criterion (CWC) and PI average width (PIAW) were 3.38 mm. The mean values of the PIs exhibited high accuracy, with a Mean Absolute Error (MAE) of 0.28 mm and Root Mean Square Error (RMSE) of 0.39 mm. These results demonstrate the robustness of the proposed model in improving landslide risk assessment and decision-making under uncertainty.