非平稳滑坡位移的奇异值分解归一化预测方法

doi:10.11947/j.AGCS.2025.20240463

测绘学报 ›› 2025, Vol. 54 ›› Issue (9): 1647-1663.doi: 10.11947/j.AGCS.2025.20240463

非平稳滑坡位移的奇异值分解归一化预测方法

瞿伟(), 徐荣堂, 李久元, 唐兴友, 陈沛男

长安大学地质工程与测绘学院，陕西　西安　710054

收稿日期:2024-11-14 修回日期:2025-07-30 出版日期:2025-10-10 发布日期:2025-10-10
作者简介:瞿伟（1982—），男，博士，教授，博士生导师，主要从事地质灾害大地测量高精度监测与灾害成因机理研究。E-mail：quwei@chd.edu.cn
基金资助:
国家自然科学基金(42174006);陕西省杰出青年科学基金(2022JC-18);长安大学中央高校基本科研业务费专项资金(300102263201)

Singular value decomposition normalization prediction method for non-steady landslide displacement

Wei QU(), Rongtang XU, Jiuyuan LI, Xingyou TANG, Peinan CHEN

College of Geology Engineering and Geomatics, Chang'an University, Xi'an 710054, China

Received:2024-11-14 Revised:2025-07-30 Online:2025-10-10 Published:2025-10-10
About author:QU Wei (1982—), male, PhD, professor, PhD supervisor, majors in geological disaster high-precision geodetic monitoring and disaster mechanism. E-mail: quwei@chd.edu.cn
Supported by:
The National Natural Science Foundation of China(42174006);Science Fund for Distinguished Young Scholars of Shaanxi Province(2022JC-18);The Fundamental Research Funds for the Central Universities, CHD(300102263201)

摘要/Abstract

摘要：

滑坡位移高精度预测模型的合理建立对滑坡灾害防灾预警具有重要的参考价值。本文针对当前数据驱动型滑坡位移预测模型对数据量有较强依赖性，以及在处理非平稳性滑坡位移监测数据具有的分布漂移特性上的局限性，发展了一种基于奇异值分解且结构简单的归一化方法。该方法通过分段归一化滑坡位移监测数据，结合统计特性的外推模型进行反归一化处理，可有效解决非平稳滑坡位移数据的分布漂移问题，且无须依赖大规模数据训练，可显著提升预测模型对非平稳滑坡位移的预测能力。以我国典型滑坡域甘肃黑方台滑坡实测数据进行测试，结果表明，与传统z-score归一化方法及无归一化相比，本文方法可显著提升多类模型（如多层感知器（multi-layer perceptron，MLP）、长短期记忆神经网络（long short-term memory，LSTM）、门控循环单元（gated recurrent unit，GRU）、时序卷积网络（temporal convolutional network，TCN））的预测精度，均方根误差（root mean square error，RMSE）和平均绝对误差（mean absolute error，MAE）平均提升率均超过50%。本文方法能够显著提升模型训练过程中的稳定性，有效预测出滑坡位移的突变情况，具有较高的实际推广应用价值。

关键词: 滑坡位移预测, 非平稳性, 分布漂移, 归一化, 奇异值分解, 统计特性外推

Abstract:

The reasonable establishment of high-precision landslide displacement prediction model has important reference value for landslide disaster prevention and early warning. In this study, a simple normalization method based on singular value decomposition is developed for the current data-driven landslide displacement prediction model, which has a strong dependence on the amount of data and limitations in dealing with the distributional drift characteristics of non-stationary landslide displacement monitoring data. This method can effectively solve the distribution drift problem of non-stationary landslide displacement data by segmentally normalizing the landslide displacement monitoring data and then combining the statistical characteristics of the extrapolation model for the inverse normalization process, and does not need to rely on large-scale data training, which can significantly improve the prediction ability of the prediction model for non-stationary landslide displacement. Tests with measured data of Heifangtai landslide in Gansu, a typical landslide domain in China, show that compared with the traditional z-score normalization method and no normalization, the method developed in this study can significantly improve the prediction accuracy of multi-class models, such as (multi-layer perceptron MLP), (long short-term memory LSTM), (gated recurrent unit GRU), and (temporal convolutional network TCN), and the average enhancement rate of (root mean square error RMSE) and (mean absolute error MAE) is more than 50%. The method in this study can significantly improve the stability of the model training process, effectively predict the sudden change of landslide displacement, and has a high value of practical popularization and application.

Key words: landslide displacement prediction, non-stationarity, distributional drift, normalization, singular value decomposition, extrapolation of statistical properties

中图分类号:

P228

瞿伟, 徐荣堂, 李久元, 唐兴友, 陈沛男. 非平稳滑坡位移的奇异值分解归一化预测方法[J]. 测绘学报, 2025, 54(9): 1647-1663.

Wei QU, Rongtang XU, Jiuyuan LI, Xingyou TANG, Peinan CHEN. Singular value decomposition normalization prediction method for non-steady landslide displacement[J]. Acta Geodaetica et Cartographica Sinica, 2025, 54(9): 1647-1663.

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基础模型	归一化策略	基础配置（模型结构）	额外配置参数	模型编号
MLP	-	（12-64-Re LU-4），MSE	-	M-1
	z-score	（z-score）-（12-64-ReLU-4），MSE	-	M-2
	svd_norm	（svd_norm）-（12-64-Re LU-4），MSE	svd_norm（4）	M-3
LSTM	-	（12-128*2-4），MSE	-	L-1
	z-score	（z-score）-（12-128*2-4），MSE	-	L-2
	svd_norm	（svd_norm）-（12-128*2-4），MSE	svd_norm（4）	L-3
GRU	-	（12-128*2-4），MSE	-	G-1
	z-score	（z-score）-（12-128*2-4），MSE	-	G-2
	svd_norm	（svd_norm）-（12-128*2-4），MSE	svd_norm（4）	G-3
TCN	-	（1，4，[16，32，16]），MSE	-	T-1
	z-score	（z-score）-（1，4，[16，32，16]），MSE	-	T-2
	svd_norm	（svd_norm）-（1，4，[16，32，16]），MSE	svd_norm（4）	T-3

模型	HF05			HF09
模型	RMSE/m	MAE/m	R²	RMSE/m	MAE/m	R²
M-1	0.030	0.025	0.989	0.085	0.077	0.975
M-2	0.021	0.016	0.987	0.046	0.038	0.973
M-3	0.007	0.004	0.996	0.025	0.018	0.978
L-1	0.047	0.040	0.986	0.066	0.059	0.968
L-2	0.132	0.116	0.976	0.158	0.149	0.962
L-3	0.008	0.004	0.997	0.019	0.011	0.975
G-1	0.035	0.029	0.987	0.096	0.090	0.965
G-2	0.085	0.074	0.983	0.159	0.149	0.961
G-3	0.007	0.004	0.997	0.019	0.011	0.975
T-1	0.500	0.494	0.994	0.312	0.306	0.972
T-2	0.150	0.142	0.993	0.161	0.150	0.971
T-3	0.008	0.005	0.996	0.042	0.033	0.974

模型	数据分割方案
模型	（12，3，4）	（9，3，3）	（6，3，2）	（8，4，2）	（6，2，3）	（8，2，4）	（10，2，5）	（12，2，6）
HF05_M-1	0.024 7	0.031 6	0.015 7	0.025 8	0.041 7	0.026 3	0.030 5	0.023 0
HF05_L-1	0.046 9	0.034 8	0.017 3	0.018 4	0.010 7	0.012 8	0.029 8	0.029 9
HF05_G-1	0.026 6	0.020 7	0.019 8	0.025 6	0.011 1	0.018 0	0.022 9	0.032 6
HF05_T-1	0.459 5	0.538 8	0.517 8	0.545 9	0.521 8	0.520 8	0.462 8	0.493 5
HF05_M-2	0.019 1	0.023 3	0.034 1	0.018 7	0.014 4	0.012 9	0.028 8	0.024 3
HF05_L-2	0.124 4	0.116 5	0.081 3	0.112 1	0.082 9	0.105 5	0.115 4	0.129 9
HF05_G-2	0.087 3	0.070 2	0.060 4	0.071 7	0.062 8	0.069 4	0.078 1	0.093 6
HF05_T-2	0.089 2	0.234 2	0.206 5	0.357 6	0.171 2	0.189 3	0.209 4	0.331 1
HF05_M-3	0.006 5	0.006 3	0.006 3	0.008 2	0.004 7	0.004 9	0.004 8	0.005 0
HF05_L-3	0.006 5	0.006 3	0.006 2	0.008 0	0.004 7	0.004 8	0.004 8	0.005 0
HF05_G-3	0.006 5	0.006 3	0.006 3	0.008 0	0.004 8	0.004 9	0.004 7	0.004 9
HF05_T-3	0.006 6	0.006 2	0.006 4	0.008 4	0.004 6	0.004 8	0.004 7	0.004 9
HF09_M-1	0.084 9	0.060 6	0.124 5	0.105 0	0.058 2	0.115 0	0.097 3	0.063 6
HF09_L-1	0.049 1	0.055 7	0.081 1	0.072 6	0.069 9	0.046 9	0.040 5	0.049 3
HF09_G-1	0.086 6	0.069 4	0.071 0	0.084 6	0.097 7	0.080 4	0.073 9	0.093 9
HF09_T-1	0.295 6	0.311 5	0.315 1	0.288 9	0.323 7	0.329 4	0.323 0	0.302 0
HF09_M-2	0.024 9	0.049 8	0.062 3	0.043 4	0.027 0	0.042 8	0.059 1	0.037 6
HF09_L-2	0.150 0	0.150 7	0.166 7	0.163 2	0.151 6	0.156 1	0.157 6	0.153 2
HF09_G-2	0.152 6	0.144 7	0.141 0	0.148 4	0.142 3	0.138 6	0.156 9	0.159 8
HF09_T-2	0.149 3	0.173 4	0.114 0	0.128 3	0.125 9	0.346 0	0.191 6	0.338 8
HF09_M-3	0.046 4	0.039 3	0.031 4	0.052 3	0.105 1	0.101 0	0.028 2	0.041 5
HF09_L-3	0.018 0	0.018 3	0.022 1	0.023 0	0.019 6	0.017 3	0.017 1	0.016 7
HF09_G-3	0.017 8	0.018 2	0.022 1	0.022 9	0.019 6	0.017 2	0.017 1	0.015 8
HF09_T-3	0.021 3	0.016 9	0.019 2	0.034 0	0.019 4	0.016 3	0.020 8	0.019 7

模型	数据分割方案
模型	（12，4，3）	（12，3，4）	（9，3，3）	（6，3，2）	（8，4，2）	（6，2，3）	（8，2，4）	（10，2，5）	（12，2，6）
Bazimen_M-1	0.334 3	0.366 6	0.337 5	0.447 9	0.629 5	0.330 1	0.245 3	0.211 6	0.162 4
Bazimen_L-1	0.136 1	0.103 6	0.132 3	0.224 8	0.187 2	0.196 6	0.135 1	0.1193	0.090 9
Bazimen_G-1	0.136 4	0.154 0	0.152 5	0.202 3	0.142 8	0.202 3	0.169 9	0.171 7	0.096 9
Bazimen_T-1	0.582 4	0.718 5	0.582 9	0.583 4	0.602 5	0.583 1	0.567 8	0.578 6	0.538 8
Bazimen_M-2	0.485 3	0.329 4	0.416 5	0.372 7	0.392	0.315 3	0.226 2	0.301 2	0.369 7
Bazimen_L-2	0.228 8	0.215 9	0.234 3	0.237 1	0.230 3	0.19 9	0.169 9	0.176 2	0.140 7
Bazimen_G-2	0.136 2	0.111 3	0.140 1	0.129 2	0.168 4	0.116 7	0.118 8	0.099 9	0.116 4
Bazimen_T-2	0.609 5	0.596 7	0.611 7	0.619 2	0.605 9	0.625 7	0.608 2	0.605 8	0.578 3
Bazimen_M-3	0.055 9	0.045 3	0.029 2	0.047 7	0.052 2	0.034 3	0.024 8	0.029 8	0.027 5
Bazimen_L-3	0.074 4	0.044 6	0.040 5	0.047 7	0.074 2	0.034 2	0.025 7	0.029 9	0.032 7
Bazimen_G-3	0.044 8	0.032 7	0.039 7	0.046 8	0.075 6	0.034 8	0.021 4	0.029 8	0.027 2
Bazimen_T-3	0.058 2	0.046 2	0.0650	0.047 8	0.069 1	0.034 2	0.026 4	0.030 1	0.027 0

数据集站点	模型	RMSE/m	MAE/m	R²
HF05	M-3	0.007	0.004	0.996
	L-3	0.008	0.004	0.997
	G-3	0.007	0.004	0.997
	T-3	0.008	0.005	0.996
	Non-Stationary Transformer	0.007 73	0.005 33	0.996 92
HF09	M-3	0.025	0.018	0.978
	L-3	0.019	0.011	0.975
	G-3	0.019	0.011	0.975
	T-3	0.042	0.033	0.974
	Non-Stationary Transformer	0.022 42	0.014 9	0.970 93

非平稳滑坡位移的奇异值分解归一化预测方法

Singular value decomposition normalization prediction method for non-steady landslide displacement

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