Surface Settlement Prediction in Goaf Areas Based on the Improved Radial Movement Optimization–Variational Mode Decomposition–Gated Recurrent Unit Model

To solve the low-precision prediction problem of noisy non-stationary goaf subsidence sequences, this study aims to establish a high-accuracy hybrid prediction model for mining surface deformation monitoring. The Global Navigation Satellite System (GNSS) monitoring data of surface subsidence in goaf areas exhibits non-stationary and noisy characteristics, which limits the accuracy of traditional prediction models. In this paper, a hybrid prediction model, namely the Improved Radial Movement Optimization–Variational Mode Decomposition–Gated Recurrent Unit (IRMO-VMD-GRU) model, is proposed. The IRMO algorithm is employed to globally optimize the key parameters of VMD, achieving adaptive and stable decomposition of the settlement sequences. The obtained Intrinsic Mode Function (IMF) sub-sequences are input into the GRU network for independent training and prediction, followed by superposition and reconstruction. The model is validated using the GNSS monitoring data from three monitoring points at a coal mine in Shaanxi Province, China. The results show that the proposed model outperforms the comparison models in all four evaluation indicators, namely Mean Absolute Error (MAE), Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), and Coefficient of Determination (R²), with all R² values exceeding 0.8. The model demonstrates superior fitting performance, correlation, and generalization ability, which provides important practical technical support for goaf subsidence early warning, geological disaster prevention and engineering safety management in mining areas.