To address the uncertainty of optimal vibratory frequency f_ov of high-speed railway graded gravel (HRGG) and achieve high-precision prediction of the f_ov, the following research was conducted. Firstly, commencing with vibratory compaction experiments and the hammering modal analysis method, the resonance frequency f₀ of HRGG fillers, varying in compactness K, was initially determined. The correlation between f₀ and f_ov was revealed through vibratory compaction experiments conducted at different vibratory frequencies. This correlation was established based on the compaction physical–mechanical properties of HRGG fillers, encompassing maximum dry density ρd_max, stiffness K_rd, and bearing capacity coefficient K₂₀. Secondly, the gray relational analysis algorithm was used to determine the key feature influencing the f_ov based on the quantified relationship between the filler feature and f_ov. Finally, the key features influencing the f_ov were used as input parameters to establish the artificial neural network prediction model (ANN-PM) for f_ov. The predictive performance of ANN-PM was evaluated from the ablation study, prediction accuracy, and prediction error. The results showed that the ρ_dmax, K_rd, and K₂₀ all obtained optimal states when f_ov was set as f₀ for different gradation HRGG fillers. Furthermore, it was found that the key features influencing the f_ov were determined to be the maximum particle diameter d_max, gradation parameters b and m, flat and elongated particles in coarse aggregate Q_e, and the Los Angeles abrasion of coarse aggregate LAA. Among them, the influence of d_max on the ANN-PM predictive performance was the most significant. On the training and testing sets, the goodness-of-fit R² of ANN-PM all exceeded 0.95, and the prediction errors were small, which indicated that the accuracy of ANN-PM predictions was relatively high. In addition, it was clear that the ANN-PM exhibited excellent robust performance. The research results provide a novel method for determining the f_ov of subgrade fillers and provide theoretical guidance for the intelligent construction of high-speed railway subgrades.

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 ($R^2>0.92$). 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.

In the small-deformation scenario of high-speed railway (HSR) rigid pile–raft composite foundations, the coupled effects of non-equidistant and non-stationary (NENS) characteristics in observational data significantly affect the system response of prediction models. Existing research has predominantly focused on single evaluation metrics or large-deformation scenarios, lacking a comprehensive evaluation system for the multidimensional performance of these models under small-deformation conditions. NENS time-series data were generated via Monte Carlo simulation. The coupled effect was quantified through a process involving “theoretical curve extraction–non-equidistant sampling–random disturbance injection”. Parameters such as pile length, displacement ratio, and pile–soil modulus ratio were normalized using the composite modulus (CMA) method to uniformly characterize the influence of foundation stiffness on time-varying settlement characteristics. A robust entropy-weighted method was then used to construct a comprehensive evaluation index (CEI), which integrates goodness-of-fit (36%), prediction accuracy (26%), and stability (38%) to systematically assess four empirical models: the hyperbolic method, exponential curve method, Asaoka method, and Hoshino method. The results indicate that when CMA ≤ 100 MPa, settlement curves exhibit nonlinearity, and the Hoshino and hyperbolic methods perform optimally. Between 100 and 1000 MPa, pile–soil interaction intensifies, highlighting the Hoshino method’s superior stability. When CMA ≥ 1000 MPa, pile–soil interaction becomes load-dominated, with the Hoshino method remaining optimal while the hyperbolic and exponential curve methods exhibit significantly increased errors. The proposed NENS time-series simulation–multi-criteria coupling evaluation framework resolves model selection challenges in small-deformation scenarios and provides robust decision support for HSR settlement prediction.