The Prediction Method of Large-Scale Land Subsidence Based on Multi-Temporal InSAR and Machine Learning
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摘要: 地面沉降是由自然因素和人为因素综合作用下形成的地面标高损失，为预防这种累进性的缓变地质灾害，高效的大范围地面沉降预测显得尤为重要.现有的预测方法忽略了地面沉降的空间特征，且基于单点循环预测存在高耗时现象.针对上述问题，提出了一种基于时序InSAR与机器学习的大范围地面沉降预测方法.首先，利用SBAS-InSAR技术获取大范围的地面沉降时序信息；其次，采用经验正交函数（empirical orthogonal function，EOF）提取时序信息的空间模态及对应的主成分（principal components，PCs）；最后，采用基于误差反馈的岭多项式神经网络（ridge polynomial neural network with error-output feedbacks，RPNN-EOF）模型训练与预测PCs，将预测结果重构回地面沉降时序.以延安新区2018年8月至2021年5月的84景Sentinel-1A数据为例，获取了新区的地面沉降时序.同时，EOF所提取的空间模态能清晰地表达整个新区的空间变化特征.预测结果显示，相较于传统点循环模式以及主流的时间序列预测方法，本文方法的均方根误差至少降低了22.7%，建模耗时至少降低了27.5%，因此该方法具有良好的实用性.Abstract: Land subsidence is the loss of land elevation formed by a combination of natural and human factors. To prevent the delayed progressive geohazards, it is essential to predict large-scale land subsidence with high efficiency. However, the current prediction methods usually neglect spatial characteristics of land subsidence, which are time-consuming due to the issue of single-point cycle. To address the problem, a new prediction method of large-scale land subsidence based on multi-temporal InSAR and machine learning is proposed. Firstly, the large-scale land subsidence time series information is obtained by the SBAS-InSAR technique. Secondly, the spatial modes and the consistent principal components (PCs) are extracted from the time series information with the empirical orthogonal function (EOF). Finally, the PCs are trained and predicted by predictive model based on the ridge polynomial neural network with error-output feedbacks (RPNN-EOF), and the outcomes are reconstructed back to the land subsidence time series. The 84-view Sentinel-1A data from August 2018 to May 2021 of Yan'an New District were adopted in the land subsidence time seriesacquisition. Simultaneously, the spatial modes extracted by EOF can clearly reveal the spatial variation characteristics of the whole new district. The prediction results show that the root mean square error and modeling time of the proposed method is reduced by at least 22.7% and 27.5% respectively, in comparison with that by the single-point cycle pattern and the prevailing time series methods. Thus it has good practicality and applicability.
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图 4 EOF分解结果
a. 前3个空间模态对应的PCs，且时间系数无量纲；b，c，d.分别为3个空间模态；e.展示了空间模态的总方差占比
Fig. 4. The decomposition results of EOF
图 5 本文方法预测结果与残差
图中左色标条表示监测值与预测值，右色标条表示残差
Fig. 5. The prediction results and residual error diagram of the proposed method
图 6 预测结果残差统计分析
a.预测结果残差的小提琴图；b~f.预测结果残差的分布以及统计直方图
Fig. 6. The statistical analysis chart of predicted result residual
表 1 预测残差的统计情况
Table 1. The statistics of predicted residuals
预测日期 中位数 25%分位数 75%分位数 极值 20210401 ‒0.033 7 0.593 5 ‒0.599 0 ‒9.579 9 20210413 ‒0.133 8 0.484 0 ‒0.800 2 ‒7.208 4 20210425 ‒0.241 0 0.505 2 ‒1.043 3 7.302 9 20210507 ‒0.180 6 0.869 5 ‒1.171 7 ‒9.606 3 20210519 ‒0.815 3 0.210 3 ‒1.794 9 ‒12.270 8 注：单位（mm）. 
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表 2 不同预测模型的试验结果
Table 2. The test results of different prediction models
方法 指标 预测日期 建模耗时(s) 20210401 20210413 20210425 20210507 20210519 EOF-RPNN-EOF MAE 0.757 7 0.814 4 0.940 2 1.299 1 1.471 6 142 RMSE 1.013 3 1.079 8 1.189 5 1.685 7 1.897 2 NMSE 0.000 7 0.000 8 0.001 0 0.002 1 0.002 4 EOF-LSTM MAE 1.019 1 1.243 4 1.618 6 1.922 9 2.118 5 196 RMSE 1.311 8 1.512 2 1.972 0 2.298 1 2.870 3 NMSE 0.001 2 0.001 6 0.002 8 0.003 8 0.005 5 MLR MAE 1.086 7 1.391 1 1.822 9 2.198 0 2.759 7 398 RMSE 1.446 8 1.663 6 2.137 6 2.444 1 3.111 3 NMSE 0.001 5 0.002 2 0.003 3 0.004 7 0.006 8 注：MAE，RMSE单位为：mm；NMSE单位为：mm2.
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