A Combined Wavelet–SVD Denoising and Wavelet Packet Decomposition Method for Quantitative GPR-Based Assessment of Compaction

Ballast compaction is a critical factor influencing ballast bed condition and the operational safety of heavy-haul railways. However, existing quantitative evaluation methods often suffer from overly idealized simulation models and limitations in signal processing and assessment frameworks. To address these issues, this study proposes a quantitative analysis approach for ballast compaction by integrating non-uniform medium simulation modeling, wavelet–Singular Value Decomposition (SVD) joint denoising, frequency–wavenumber (F-K) migration imaging, and wavelet packet decomposition (WPD)-based feature extraction. Forward simulations were conducted based on the constructed model, and the proposed methodology was validated using 1.5 GHz (gigahertz, 1 GHz = 109 Hz) ground penetrating radar (GPR) data acquired from compaction experiments. The results demonstrate that wavelet–SVD joint denoising effectively suppresses deep coherent noise caused by strong reflections from sleepers, significantly enhancing the identification of deep effective signals and ensuring accurate localization and feature extraction of compaction zones. The Geometric Mean of WPD High/Low-Frequency Energy Ratio (GMHLFER) exhibits a strong positive correlation with the degree of compaction. In simulations, as the proportion of compacted material increased from 9% to 21%, the GMHLFER rose from 21.555 to 26.581. In field tests, the value increased from 22.012 to 26.012 as compaction severity progressed from slight to severe, demonstrating stable responses across full-gradient compaction conditions and indicating high robustness and sensitivity. The proposed method provides an effective approach for quantitative characterization of ballast compaction in heavy-haul railways, and offers a promising technical pathway for intelligent inspection and condition assessment of railway ballast beds.