The relationship between subgrade settlement and rail deformation remains unclear, and the impact of subgrade settlement on dynamic responses of the ballasted track, as well as on the running safety and comfort of high-speed trains, has not been adequately quantified. To address such deficiency, a three-dimensional (3D) numerical model of train-ballasted track-subgrade coupled system considering spatial differential subgrade settlements was established. An innovative iterative algorithm was proposed to determine the real-time track-subgrade contact, enabling the analysis of resulting track irregularities and train-induced vibration. The results show that the number of unsupported sleepers increases with greater settlement amplitudes and shorter settlement wavelengths, while spatial differential subgrade settlement significantly affects wheel-rail interaction. Track structures located at the settlement center area on the side with less settlement, as well as those at the settlement boundary area on the side with greater settlement, are more susceptible to damage. These areas also exhibit higher dynamic vertical subgrade stress, thus aggravating differential settlement. The findings could provide theoretical basis and technical guidance for improving high-speed railway operation and maintenance practices.

Predicting Estimated Time of Arrival (ETA) for a Multi-Airport System (MAS) is much more challenging than for a single airport system because of complex air route structure, dense air traffic volume and vagaries of traffic conditions in an MAS. In this work, we propose a novel “Bubble” mechanism to accurately predict medium-term ETA for a Multi-Airport System (MAS), in which the prediction of travel time of an origin–destination (OD) pair is decomposed into two stages, termed as out-MAS and in-MAS stages. For the out-MAS stage, Auto-Regressive Integrated Moving Average (ARIMA) is used to predict the travel time of a flight to reach the MAS boundary. For the in-MAS stage, we construct new spatio-temporal features based on clustering analysis of trajectory patterns facilitated by a novel data-driven hybrid polar sampling method. A sequence-to-sequence prediction model, Multi-variate Stacked Fully connected Bidirectional Long–Short Term Memory, is further developed to achieve multi-step-ahead predictions of in-MAS travel time for each trajectory pattern using the spatio-temporal features as input. Finally, the medium-term ETA prediction for an MAS is achieved by integrating the out-MAS and in-MAS prediction with the help of trajectory pattern prediction via random forest. A case study of predicting medium-term ETA for a typical MAS in China, Guangdong–Hong Kong–Macao Greater Bay Area, is conducted to demonstrate the usage and promising performance of the proposed method in comparison to several commonly used end-to-end learning methods.