Modelling rules of landslide susceptibility prediction considering the suitability of linear environmental factors and different machine learning models
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摘要: 对于滑坡易发性预测中的水系、公路和断层等线状环境因子, 现有研究大多采用缓冲分析提取距离线状因子的距离。但缓冲分析得到的线距离属于离散型变量, 带有大小不等的随机波动性且对点或线要素的误差较为敏感, 导致滑坡易发性建模精度下降。提出了使用水系和公路的空间密度等连续型变量改进线状环境因子的适宜性。以江西省安远县为例, 选取高程、地形起伏度、距水系和公路距离等14个环境因子(原始因子), 再将距水系和公路距离2个线状因子改进为水系密度和公路密度(改进因子); 之后采用逻辑回归、多层感知器、支持向量机和C5.0决策树等机器学习模型, 分别构建了基于原始因子和改进因子的机器学习模型以预测滑坡易发性; 最后利用ROC曲线和易发性指数分布特征等来研究建模规律。结果表明: ①改进因子机器学习预测精度均高于原始因子机器学习模型, 表明空间密度对于易发性预测的适宜性更好; ②在4类机器学习模型中C5.0模型对于滑坡易发性预测性能最好, 其次是SVM、MLP和LR; ③水系和公路两类环境因子的重要性较高且使用改进因子机器学习后这两类环境因子重要性排名依然非常靠前。Abstract: For linear environmental factors such as river, road and geological fault networks, buffer analysis in GIS is commonly used to extract the buffer distances to the river and/or road networks. However, the line distances are discrete variables with random fluctuations of different grid sizes and are more sensitive to the errors of point and/or line elements, leading to a reduction in the accuracy of landslide susceptibility prediction (LSP). This study aims to use continuous environmental factors, such as the spatial density of river and road networks, to improve the suitability of linear environmental factors. Taking An'yuan County of Jiangxi Province as an example, 14 environmental factors, such as elevation, topographic relief, distances to river and road networks (original factors), are selected. Then, the two linear environmental factors of distances to river and road networks are improved to river and road density (improved factors). Based on machine learning models such as logistic regression (LR), multilayer perceptron (MLP), support vector machine (SVM) and C5.0 decision tree, original factor-based and improved factor-based machine learning models are built to carry out the LSP. The receiver operating characteristic (ROC) curves and the distribution characteristics of landslide susceptibility indexes are used to evaluate the LSP modelling rules. The results show that ① the LSP accuracy of the improved factor-based models are higher than those of the original factor-based models, indicating that the spatial density is more suitable for LSP; ② the C5.0 model has the best LSP performance among the four machine learning models, followed by the SVM, MLP and LR models; and ③ river and road factors are of great significance for landslide evolution, and their importance does not decrease underimproved factor-based machine learning models.
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图 1 研究区地理位置及概况
Figure 1. Geographical location and general situation of the study area
图 2 滑坡易发性评价MLP结构图
Figure 2. Multilayer perceptron structure diagram of landslide susceptibility evaluation
图 4 各模型不同线密度参数改进因子组合及原始因子组合的ROC曲线
Figure 4. ROC curves of improved factors under different linear density parameters and original factors on each model
图 6 各模型下改进因子组合与原始因子组合机器学习模型的ROC曲线
Figure 6. ROC of improved factors and original factors of machine learning of each model
图 7 原始因子组合(a)与改进因子组合(b)在不同模型下的ROC曲线
Figure 7. ROC curve original of factors (a) and improved factors (b) under different models
图 8 改进因子和原始因子模型的滑坡易发性指数分布规律
Figure 8. Distribution rule of landslide susceptibility indexes of improved factor-based and original factor-based models
图 9 改进因子组合(a)及原始因子组合(b)环境因子重要性图
Figure 9. Importance diagram of environmental factors of improved factors (a) and original factors (b)
表 1 各基础环境因子FR值
Table 1. Frequency ratio of every basic environmental factor
基础环境因子 变量值 全区栅格/个 栅格比例/% 滑坡栅格/个 滑坡栅格比例/% FR值 高程/m
(连续型)[181.9, 288.3) 496 187 18.68 3 200 38.57 2.064 [288.3, 368.1) 685 240 25.80 2 366 28.52 1.105 [368.1, 451.7) 462 583 17.42 1 058 12.75 0.732 [451.7, 539.1) 382 432 14.40 667 8.04 0.558 [539.1, 630.3) 279 769 10.53 801 9.65 0.917 [630.3, 736.7) 190 734 7.18 149 1.80 0.250 [736.7, 873.5) 113 403 4.27 56 0.67 0.158 [873.5, 1 194.4] 45 624 1.72 0 0.00 0.000 坡向/(°)
(连续型)[-1, 44.3) 280 739 10.57 662 7.98 0.755 [44.3, 89.6) 304 482 11.46 1 048 12.63 1.102 [89.6, 133.5) 353 235 13.30 1 297 15.63 1.175 [133.5, 178.8) 353 072 13.29 1 269 15.29 1.151 [178.8, 225.5) 325 285 12.25 967 11.65 0.952 [225.5, 270.8) 324 212 12.21 1 145 13.80 1.131 [270.8, 314.7) 358 227 13.49 1 178 14.20 1.053 [314.7, 360.0] 356 720 13.43 731 8.81 0.656 坡度/(°)
(连续型)[0, 4.3) 415 986 15.66 337 4.06 0.259 [4.3, 8.2) 574 723 21.64 1 729 20.84 0.963 [8.2, 11.9) 533 748 20.10 2 352 28.35 1.411 [11.9, 15.5) 437 498 16.47 1 868 22.51 1.367 [15.5, 19.6) 338 458 12.74 1 167 14.07 1.104 [19.6, 24.2) 208 331 7.84 626 7.54 0.962 [24.2, 30.1) 110 358 4.16 197 2.37 0.571 [30.1, 58.2] 36 870 1.39 21 0.25 0.182 平面曲率
(连续型)[0, 10.2) 452 767 17.05 2 161 26.05 1.528 [10.2, 18.9) 525 698 19.79 2 208 26.61 1.345 [18.9, 27.8) 420 490 15.83 1 566 18.87 1.192 [27.8, 37.7) 332 054 12.50 958 11.55 0.924 [37.7, 48.3) 253 510 9.54 480 5.79 0.606 [48.3, 59.1) 205 977 7.76 254 3.06 0.395 [59.1, 70.6) 185 689 6.99 234 2.82 0.403 [70.6, 81.5] 279 787 10.53 436 5.25 0.499 剖面曲率
(连续型)[0, 1.8) 543 228 20.45 1 655 19.95 0.975 [1.8, 3.6) 715 475 26.94 2 495 30.07 1.116 [3.6, 5.4) 565 403 21.29 1 840 22.18 1.042 [5.4, 7.3) 392 134 14.76 1 112 13.40 0.908 [7.3, 9.5) 242 871 9.14 690 8.32 0.909 [9.5, 12.2) 127 410 4.80 380 4.58 0.955 [12.2, 15.9) 54 936 2.07 102 1.23 0.594 [15.9, 38.0] 14 515 0.55 23 0.28 0.507 地形起伏度/m
(连续型)[0, 29.1) 402 714 15.16 1 036 12.49 0.824 [29.1, 49.3) 669 778 25.22 3 105 37.42 1.484 [49.3, 68.4) 572 886 21.57 2 020 24.35 1.129 [68.4, 87.4) 424 833 16.00 1 026 12.37 0.773 [87.4, 108.7) 294 698 11.10 723 8.71 0.785 [108.7, 134.5) 177 688 6.69 354 4.27 0.638 [134.5, 169.2) 85 789 3.23 33 0.40 0.123 [169.2, 285.8] 27 586 1.04 0 0.00 0.000 地形湿度
(连续型)[4.0, 6.3) 739 489 27.84 2 430 29.29 1.052 [6.3, 7.8) 949 906 35.76 3 395 40.92 1.144 [7.8, 9.4) 554 597 20.88 1 759 21.20 1.015 [9.4, 11.2) 226 192 8.52 424 5.11 0.600 [11.3, 13.6) 113 458 4.27 127 1.53 0.358 [13.6, 16.4) 53 428 2.01 131 1.58 0.785 [16.4, 24.0] 18 829 0.71 31 0.37 0.527 [24.0, 40.845] 73 0.00 0 0.00 0.000 NDVI
(连续型)[-0.132, 0.085 3) 11 703 0.44 18 0.22 0.492 [0.085, 0.169) 59 295 2.23 143 1.72 0.772 [0.169, 0.229) 132 723 5.00 580 6.99 1.399 [0.229, 0.274) 312 822 11.78 1 265 15.25 1.294 [0.274, 0.311) 527 207 19.85 1 986 23.94 1.206 [0.311, 0.347) 659 184 24.82 2 135 25.73 1.037 [0.347, 0.389) 621 304 23.39 1 768 21.31 0.911 [0.389, 0.536] 331 734 12.49 402 4.85 0.388 NDBI
(连续型)[-0.530, -0.408) 414 877 15.62 377 4.54 0.291 [-0.408, -0.367) 733 961 27.63 1 541 18.57 0.672 [-0.367, -0.326) 672 071 25.30 2 335 28.14 1.112 [-0.326, -0.282) 383 889 14.45 1 851 22.31 1.543 [-0.282, -0.232) 211 736 7.97 1 120 13.50 1.693 [-0.232, -0.175) 130 136 4.90 661 7.97 1.626 [-0.175, -0.103) 77 499 2.92 320 3.86 1.322 [-0.103, 0.272] 31 803 1.20 92 1.11 0.926 MNDWI
(连续型)[0, 35) 156 772 5.90 554 6.68 1.131 [35, 71) 279 294 10.52 1 294 15.60 1.483 [71, 100) 393 799 14.83 1 663 20.04 1.352 [100, 127) 462 074 17.40 1 604 19.33 1.111 [127, 154) 456 527 17.19 1 336 16.10 0.937 [154, 183) 417 431 15.72 1 015 12.23 0.778 [183, 216) 315 966 11.90 592 7.14 0.600 [216, 255] 174 109 6.56 239 2.88 0.439 岩性
(离散型)变质岩 854 749 32.18 2 690 32.36 1.005 岩浆岩 1 110 912 41.83 2 235 26.89 0.643 碎屑岩 687 217 25.87 3 388 40.76 1.575 碳酸岩 3 094 0.12 0 0.00 0.000 断层密度/(km·km-2)
(连续型)[0, 0.96) 2 246 640 84.59 6 168 74.20 0.877 [0.96, 1.93) 181 229 6.82 811 9.76 1.430 [1.93, 2.89) 104 227 3.92 410 4.93 1.257 [2.89, 3.86) 67 033 2.52 501 6.03 2.388 [3.86, 4.82) 23 831 0.90 138 1.66 1.850 [4.82, 5.79) 21 856 0.82 222 2.67 3.245 [5.79, 6.75) 10 746 0.40 61 0.73 1.814 [6.75, 7.71] 410 0.02 2 0.02 1.559 距断层距离/m
(离散型)< 150 355 996 13.40 1 856 22.33 1.667 [150, 300) 332 812 12.53 1 336 16.07 1.283 [300, 450) 296 570 11.17 854 10.27 0.920 [450, 600) 258 642 9.74 793 9.54 0.980 [600, 800] 289 242 10.89 730 8.78 0.806 > 800 1 122 710 42.27 2 744 33.01 0.781 距公路距离/m
(离散型)< 150 743 873 28.01 4 740 57.02 2.036 [150, 300) 433 925 16.34 2 220 26.71 1.635 [300, 450) 305 927 11.52 802 9.65 0.838 [450, 600) 234 977 8.85 177 2.13 0.241 [600, 800] 240 829 9.07 40 0.48 0.053 > 800 696 441 26.22 334 4.02 0.153 距水系距离/m
(离散型)< 150 934 647 35.19 4 981 59.92 1.703 [150, 300) 763 304 28.74 2 431 29.24 1.018 [300, 450) 536 148 20.19 481 5.79 0.287 [450, 600) 258 803 9.74 171 2.06 0.211 [600, 800] 85 055 3.20 41 0.49 0.154 > 800 78 015 2.94 208 2.50 0.852 公路密度/(km·km-2)
(连续型)[0, 1.78) 1 658 283 62.44 3 215 38.67 0.619 [1.78, 3.56) 596 349 22.45 3 480 41.86 1.864 [3.56, 5.34) 218 100 8.21 765 9.20 1.121 [5.34, 7.12) 88 913 3.35 309 3.72 1.110 [7.12, 8.90) 50 822 1.91 251 3.02 1.578 [8.90, 10.68) 24 483 0.92 146 1.76 1.905 [10.68, 12.46) 16 911 0.64 147 1.77 2.777 [12.46, 14.23] 2 112 0.08 0 0.00 0.000 水系密度/(km·km-2)
(连续型)[0, 0.28) 907 613 34.17 818 9.84 0.288 [0.28, 0.81) 332 419 12.52 364 4.38 0.350 [0.81, 1.32) 330 831 12.46 701 8.43 0.677 [1.32, 1.82) 431 403 16.24 1 960 23.58 1.452 [1.82, 2.31) 254 193 9.57 1 655 19.91 2.080 [2.31, 2.82) 219 790 8.28 1 371 16.49 1.993 [2.82, 3.42) 125 981 4.74 922 11.09 2.338 [3.42, 5.45] 53 745 2.02 522 6.28 3.103 
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表 2 原始因子相关性系数矩阵
Table 2. Correlation coefficient matrix diagram of the original factors
地形起伏度 剖面曲率 坡度 NDVI NDBI 平面曲率 高程 坡向 MNDWI 地形湿度 岩性 断层密度 距水系距离 距公路距离 地形起伏度 1 剖面曲率 0.123 1 坡度 0.172 -0.074 1 NDV 0.109 0.037 -0.100 1 NDBI 0.124 0.042 -0.206 0.313 1 平面曲率 -0.222 0.07 0.208 -0.091 -0.102 1 高程 0.265 0.093 -0.237 0.208 0.317 -0.107 1 坡向 0.042 0.013 -0.003 -0.211 -0.142 0.136 0.035 1 MNDWI 0.086 0.041 -0.131 -0.286 0.094 -0.014 0.181 0.221 1 地形湿度 -0.056 -0.027 0.280 -0.02 -0.122 0.270 -0.202 0.069 -0.169 1 岩性 0.098 0.028 0.004 -0.009 0.026 -0.038 0.013 0.026 0.052 -0.011 1 断层密度 0.037 0.004 -0.021 0.032 0.062 -0.004 0.139 0.012 0.046 -0.025 0.002 1 距水系距离 0.152 -0.001 -0.097 0.064 0.164 -0.054 0.274 0.011 0.148 -0.215 0.012 0.085 1 距公路距离 0.193 0.074 -0.195 0.270 0.400 -0.075 0.474 -0.021 0.183 -0.143 0.075 0.094 0.258 1
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表 3 改进因子相关性系数矩阵
Table 3. Correlation coefficient matrix diagram of the improved factors
地形起伏度 剖面曲率 坡度 NDVI NDBI 平面曲率 高程 坡向 MNDWI 地形湿度 岩性 断层密度 水系密度 公路密度 地形起伏度 1 剖面曲率 0.123 1 坡度 0.172 -0.074 1 NDVI 0.109 0.037 -0.100 1 NDBI 0.124 0.042 -0.206 0.313 1 平面曲率 -0.222 0.070 0.208 -0.091 -0.102 1 高程 0.265 0.093 -0.237 0.208 0.317 -0.107 1 坡向 0.042 0.013 -0.003 -0.211 -0.142 0.136 0.035 1 MNDWI 0.086 0.041 -0.131 -0.286 0.094 -0.014 0.181 0.221 1 地形湿度 -0.056 -0.027 0.280 -0.020 -0.122 0.270 -0.202 0.069 -0.169 1 岩性 0.098 0.028 0.004 -0.009 0.026 -0.038 0.013 0.026 0.052 -0.011 1 断层密度 0.037 0.004 -0.021 0.032 0.062 -0.004 0.139 0.012 0.046 -0.025 0.002 1 水系密度 0.130 0.052 -0.148 0.183 0.283 -0.047 0.341 -0.000 0.145 -0.106 -0.053 0.076 1 公路密度 0.128 -0.002 -0.139 0.115 0.211 -0.054 0.322 -0.011 0.123 -0.159 0.019 0.110 0.262 1
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表 4 原始因子与改进因子回归系数
Table 4. Regression coefficient table of the original factor and improved factor
环境因子 原始因子 改进因子 环境因子 原始因子 改进因子 高程 -0.002 0.143 地形湿度 1.105 0.984 坡度 1.474 1.509 地形起伏度 -0.167 -0.066 坡向 0.756 0.655 岩性 4.034 4.253 平面曲率 1.153 1.233 断层密度 0.126 0.080 剖面曲率 0.311 0.370 距水系距离 0.849 - NDVI 0.148 0.359 距公路距离 0.967 - NDBI 0.515 0.613 水系密度 - 0.715 MNDWI 0.346 0.427 公路密度 - 0.790
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表 5 各模型不同线密度参数下改进因子组合及原始因子组合的AUC值
Table 5. AUC values of the improved factors under different linear density parameters and original factors on each model
工况 水系密度 公路密度 MLP LR SVM C5.0 汇流累积阈值 搜索半径/m 搜索半径/m AUC值 1 300 300 200 0.913 0.881 0.942 0.965 2 300 300 250 0.912 0.884 0.943 0.962 3 300 300 300 0.922 0.888 0.949 0.975 4 300 300 400 0.920 0.886 0.946 0.975 5 400 300 400 0.924 0.892 0.951 0.976 6 400 400 400 0.922 0.898 0.951 0.983 7 原始因子组合 0.896 0.888 0.919 0.939
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