Monte Carlo Simulation-Based Robustness Analysis of High-Speed Railway Settlement Prediction Models for Non-Stationary Time Series

Accurate prediction of post-construction settlement in high-speed railway (HSR) soft foundations is critical for operational safety yet challenging due to the non-equidistant and non-stationary nature of observation data. This study systematically evaluated the robustness and accuracy of settlement prediction models using a Monte Carlo simulation approach. A numerical model incorporating the permeability characteristics of soft foundations was established to simulate stochastic system responses. Furthermore, an innovative multi-metric evaluation framework was constructed using the entropy weight method, integrating goodness-of-fit, prediction accuracy (systematic error), and stability (random error). Four classical empirical models—Hyperbolic, Exponential Curve, Asaoka, and Hoshino—were assessed. The results indicate that: (1) The Hyperbolic Method significantly outperformed other models (p<0.01) in goodness-of-fit (mean correlation coefficient: 0.983 ± 0.006) and accuracy (systematic error: 3.2% ± 1.1%); (2) The Hoshino Method exhibited optimal stability, characterized by the lowest random error (3.8 ± 2.0 mm); and (3) Model performance showed a significant positive correlation with the permeability coefficient (R2>0.92). Validated by five distinct engineering cases, the comprehensive performance ranking was determined as: Hyperbolic > Hoshino > Exponential Curve > Asaoka. These findings provide a scientific strategy for model selection under non-stationary conditions and offer theoretical support for refining railway deformation monitoring standards.