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

doi:10.11947/j.AGCS.2025.20240463

Abstract

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

CLC Number:

P228

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