Data-driven models have been extensively employed in landslide displacement prediction. However, predictive uncertainty, which consists of input uncertainty, parameter uncertainty, and model uncertainty, is usually disregarded in deterministic data-driven modeling, and point estimates are separately presented. In this study, a probability-scheme combination ensemble prediction that employs quantile regression neural networks and kernel density estimation (QRNNs-KDE) is proposed for robust and accurate prediction and uncertainty quantification of landslide displacement. In the ensemble model, QRNNs serve as base learning algorithms to generate multiple base learners. Final ensemble prediction is obtained by integration of all base learners through a probability combination scheme based on KDE. The Fanjiaping landslide in the Three Gorges Reservoir area (TGRA) was selected as a case study to explore the performance of the ensemble prediction. Based on long-term (2006–2018) and near real-time monitoring data, a comprehensive analysis of the deformation characteristics was conducted for fully understanding the triggering factors. The experimental results indicate that the QRNNs-KDE approach can perform predictions with perfect performance and outperform the traditional backpropagation (BP), radial basis function (RBF), extreme learning machine (ELM), support vector machine (SVM) methods, bootstrap-extreme learning machine-artificial neural network (bootstrap-ELM-ANN), and Copula-kernel-based support vector machine quantile regression (Copula-KSVMQR). The proposed QRNNs-KDE approach has significant potential in medium-term to long-term horizon forecasting and quantification of uncertainty.

中文翻译：

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使用概率方案组合集合预测技术预测滑坡位移。

数据驱动模型已广泛用于滑坡位移预测中。但是，在确定性数据驱动的建模中通常不考虑由输入不确定性，参数不确定性和模型不确定性组成的预测不确定性，并且分别给出了点估计。在这项研究中，提出了采用分位数回归神经网络和核密度估计（QRNNs-KDE）的概率方案组合集成预测，以对滑坡位移进行稳健而准确的预测和不确定性量化。在集成模型中，QRNN作为基础学习算法来生成多个基础学习器。通过基于KDE的概率组合方案对所有基础学习者进行集成，可以获得最终的整体预测。以三峡库区（TGRA）的范家坪滑坡为例，探讨了整体预测的效果。基于长期（2006-2018年）和近实时监测数据，对变形特征进行了全面分析，以充分了解触发因素。实验结果表明，QRNNs-KDE方法能够以理想的性能执行预测，并且优于传统的反向传播（BP），径向基函数（RBF），极限学习机（ELM），支持向量机（SVM）方法，bootstrap-extreme学习机-人工神经网络（bootstrap-ELM-ANN）和基于Copula核的支持向量机分位数回归（Copula-KSVMQR）。