Interval prediction is an efficient approach to quantifying the uncertainties associated with landslide evolution. In this paper, a novel method, termed lower upper bound estimation (LUBE), of constructing prediction intervals (PIs) based on neural networks (NNs) is applied and extended to landslide displacement prediction. A random vector functional link network (RVFLN) is adopted as the NN used in the improved LUBE. A hybrid evolutionary algorithm, termed PSOGSA, that combines particle swarm optimization (PSO) and gravitational search algorithm (GSA) is utilized to train LUBE. The loss function of LUBE is redesigned by considering the quality of PI centre, which allows for a more comprehensive evaluation of PIs. The population initialization in the training process of LUBE is implemented by transferring the weights of a series of pre-trained RVFLNs. The performance of the improved LUBE method is validated by considering a comprehensive set of cases using seven benchmark datasets. In addition, a hybrid method that integrates ensemble empirical mode decomposition (EEMD) with the improved LUBE is proposed for the special case of landslide displacement prediction. Six real-world reservoir-induced landslides are considered to validate the capability and merit of the proposed hybrid method.

间隔预测是一种量化与滑坡演化相关的不确定性的有效方法。本文提出了一种基于神经网络（NNs）构造预测区间（PI）的新方法，称为下上限估计法（LUBE），并将其推广到滑坡位移预测中。改进的LUBE中使用了随机矢量功能链接网络（RVFLN）作为NN。结合粒子群优化（PSO）和引力搜索算法（GSA）的混合进化算法称为PSOGSA，用于训练LUBE。考虑到PI中心的质量，对LUBE的损失函数进行了重新设计，从而可以对PI进行更全面的评估。LUBE训练过程中的总体初始化是通过传递一系列预训练的RVFLN的权重来实现的。通过考虑使用七个基准数据集的一整套案例，验证了改进的LUBE方法的性能。此外，针对滑坡位移预测的特殊情况，提出了一种将整体经验模式分解（EEMD）与改进的LUBE相结合的混合方法。考虑了六个现实世界中水库诱发的滑坡，以验证所提出的混合方法的能力和优点。针对滑坡位移的特殊情况，提出了一种将经验模态分解（EEMD）与改进的LUBE相结合的混合方法。考虑了六个现实世界中水库诱发的滑坡，以验证所提出的混合方法的能力和优点。针对滑坡位移的特殊情况，提出了一种将经验模态分解（EEMD）与改进的LUBE相结合的混合方法。考虑了六个真实世界的水库诱发滑坡，以验证所提出的混合方法的能力和优点。