| Citation: | Longqi Li, Yunhuang Yang, Tianzhi Zhou, Mengyun Wang. Data-Driven Combination-Interval Prediction for Landslide Displacement Based on Copula and VMD-WOA-KELM Method. Journal of Earth Science, 2025, 36(1): 291-306. doi: 10.1007/s12583-021-1555-3
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To tackle the difficulties of the point prediction in quantifying the reliability of landslide displacement prediction, a data-driven combination-interval prediction method (CIPM) based on copula and variational-mode-decomposition associated with kernel-based-extreme-learning-machine optimized by the whale optimization algorithm (VMD-WOA-KELM) is proposed in this paper. Firstly, the displacement is decomposed by VMD to three IMF components and a residual component of different fluctuation characteristics. The key impact factors of each IMF component are selected according to Copula model, and the corresponding WOA-KELM is established to conduct point prediction. Subsequently, the parametric method (PM) and non-parametric method (NPM) are used to estimate the prediction error probability density distribution (PDF) of each component, whose prediction interval (PI) under the 95% confidence level is also obtained. By means of the differential evolution algorithm (DE), a weighted combination model based on the PIs is built to construct the combination-interval (CI). Finally, the CIs of each component are added to generate the total PI. A comparative case study shows that the CIPM performs better in constructing landslide displacement PI with high performance.
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