The measured data of N22 monitoring points.

To study the residual settlement of goaf’s law and prediction model, we investigated the Mentougou mining area in Beijing as an example. Using MATLAB software, the wavelet threshold denoising method was used to optimize measured data, and the grey model (GM) and feed forward back propagation neural network model (FFBPNN) were combined. A grey feed forward back propagation neural network (GM-FFBPNN) model based on wavelet denoising was proposed, the prediction accuracy of different models was calculated, and the prediction results were compared with original data. The results showed that the prediction accuracy of the GM-FFBPNN was higher than that of the individual GM and FFBPNN models. The mean absolute percentage error (MAPE) of the combined model was 7.39%, the root mean square error (RMSE) was 49.01 mm, the scatter index (SI) was 0.06%, and the BIAS was 2.42%. The original monitoring data were applied to the combination model after wavelet denoising, and MAPE and RMSE were only 1.78% and 16.05 mm, respectively. Compared with the combined model before denoising, the prediction error was reduced by 5.61% and 32.96 mm. Thus, the combination model optimized by wavelet analysis had a high prediction accuracy, strong stability, and accorded with the law of change of measured data. The results of this study will contribute to the construction of future surface engineering in goafs and provide a new theoretical basis for similar settlement prediction engineering, which has strong popularization and application value.为研究采空区残余沉降规律及其预测模型，本研究以北京门头沟矿区为研究案例。借助MATLAB软件，采用小波阈值去噪方法对实测数据进行降噪优化，并将灰色模型（GM）与前馈反向传播神经网络模型（FFBPNN）进行耦合。提出了一种基于小波去噪的灰色-前馈反向传播神经网络（GM-FFBPNN）模型，计算了不同模型的预测精度，并将预测结果与原始实测数据进行对比分析。结果表明，GM-FFBPNN模型的预测精度优于单一GM模型与FFBPNN模型。该组合模型的平均绝对百分比误差（MAPE）为7.39%，均方根误差（RMSE）为49.01 mm，散布指数（SI）为0.06%，偏差（BIAS）为2.42%。将经小波去噪处理后的原始监测数据输入该组合模型后，其MAPE与RMSE仅分别为1.78%与16.05 mm。与未经过降噪处理的组合模型相比，该模型的预测误差分别降低了5.61%与32.96 mm。由此可见，经小波分析优化后的组合模型预测精度高、稳定性强，且与实测数据的变化规律相符。本研究成果可为未来采空区地表工程建设提供参考，并为同类沉降预测工程提供全新的理论依据，具备较强的推广应用价值。