Data assimilation of PS-InSAR vertical deformation into a frost heave model to analyze subgrade deformation of high-speed railway in northwest China

Temperature changes may cause irregular soil uplift or thawing settlements in frozen soil areas, potentially affecting the safe operation of High-Speed Railways (HSR). Analyzing and predicting these deformation characteristics is thus critical. However, the conventional forecasting and analysis techniques rarely considered factors such as dynamic parameter variations, uncertainties, and measurement errors, which hinder accurate regional scale forecasting. To bridge this gap, this paper introduces a novel time-series coupling method, which integrates post-processing deformation from Interferometric Synthetic Aperture Radar (InSAR) with a frost heave model (FHM), facilitated by the ensemble Kalman filter (EnKF) assimilation algorithm. We obtained deformation observations along the HSR using Persistent Scatterer InSAR (PS-InSAR) technology in combination with time series post-processing techniques. Considering the causative factors for deformation, we structured the FHM. By integrating FHM with observational data using the EnKF algorithm achieved an efficient upgrade of the posterior distribution of model parameters. This integration significantly improves the predictive accuracy, it facilitates an efficient update to the posterior distribution of model parameters, leading to enhanced prediction accuracy of our model. Our experimental results indicate that the effectiveness of this approach, with observational data assimilation into FHM reducing the average Root Mean Square Error (RMSE) to a mere 0.247 mm. Concurrently, both the Normalized Reduction Error Index (NER) and the Assimilation Efficiency Factor (EFF) values surpassed 0.60 and 0.84 respectively. These underlines signify a successful update of our model parameters, which in turn elevates the accuracy of future deformation predictions, thereby promising safer railway operations.