摘要： 煤矿开采安全问题尤其是采空区地表沉降现象会对人员安全及工程安全造成威胁，研究合适的矿区地表沉降预测具有很大意义。矿区地表沉降影响因素复杂，单一的深度学习模型对矿区地表沉降数据拟合效果差且现有的地表沉降预测研究多是单独进行概率预测或考虑时序特性进行点预测，难以在考虑数据的时序特征的同时对其随机性进行定量描述。针对此问题，在对数据本身性质进行观察分析后选择了差分整合移动平均自回归（ARIMA）模型进行时序特征的概率预测，结合长短时记忆网络（LSTM）模型来学习复杂的且具有长期依赖性的非线性时序序列特征。提出了基于ARIMA-LSTM的地表沉降预测模型，通过利用ARIMA模型对数据的时序线性部分进行预测，并将ARIMA模型预测的残差数据辅助LSTM模型训练，以在考虑时序特征的同时对数据的随机性进行描述。研究结果表明，相较于单独采用ARIMA或LSTM模型，该方法具有更高的预测精度（MSE为0.26287、MAE为0.40815、RMSE为0.51271）。进一步的对比验证显示，预测结果与雷达卫星影像数据（经SBAS-INSAR处理后）趋势一致，证实了该方法的有效性。

Abstract: Safety concerns in coal mining, particularly the phenomenon of surface subsidence in goaf areas, pose threats to personnel and engineering safety. Investigating appropriate prediction methods for surface subsidence in mining areas is of great significance. The influencing factors of surface subsidence in mining areas are complex. Single deep learning models exhibit poor fitting performance for subsidence data, and existing subsidence prediction studies often focus on either probabilistic predictions or point predictions considering temporal characteristics. It is challenging to quantitatively describe randomness while considering the temporal features of the data simultaneously. Addressing this issue, this study, after observing and analyzing the nature of the data, selected the Autoregressive Integrated Moving Average (ARIMA) model for probabilistic prediction of temporal features. This was combined with the Long Short-Term Memory (LSTM) model to learn complex and long-term dependent nonlinear temporal sequences. We propose an ARIMA-LSTM-based surface subsidence prediction model. The ARIMA model predicts the temporal linear part of the data, and the residual data predicted by the ARIMA model assists in training the LSTM model. This approach allows for the consideration of both temporal features and the randomness of the data. The research results indicate that compared to using ARIMA or LSTM models alone, this method demonstrates higher prediction accuracy (MSE of 0.26287, MAE of 0.40815, RMSE of 0.51271). Further comparative validation shows that the predicted results align with trends observed in radar satellite imagery data (processed through SBAS-INSAR), confirming the effectiveness of the proposed method.