Landslide susceptibility assessment and zonation using negative sampling strategy: A case study of Bazhong area, Sichuan Province
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摘要:
滑坡易发性评价是滑坡风险管理的重要环节，能够有效指导防灾减灾工作，但滑坡易发性评价精度受到多种因素制约。当前针对斜坡单元的负样本采样优化策略研究相对较少。文章以四川省巴中地区为研究对象，选取高程、相对高差、历年平均降雨等11个影响因子，以优化斜坡单元负样本采样策略建立地理加权回归-随机森林（GWR-RF）耦合模型，并将评估结果与多次全域随机采样策略进行对比。结果表明：（1）全域随机采样会导致易发性评价结果存在较大差异，且评估结果准确率较差，全域随机采样不适用于以斜坡单元为基础的滑坡易发性评价；（2）GWR-RF耦合模型的滑坡易发性评价结果存在空间差异，主要分布于研究区的恩阳区、巴州区、平昌县，以及南江县中—南部，文章提出的GWR-RF耦合模型通过优化负样本取样策略，提升了滑坡易发性评价的精度，可为巴中地区滑坡灾害防治提供科学依据。
Abstract:Landslide susceptibility assessment is a crucial component of landslide risk management, effectively guiding disaster prevention and mitigation efforts. However, the accuracy of landslide susceptibility assessments is constrained by various factors, and current research on optimizing negative sample sampling strategies based on slope units remains relatively limited. This study, focuses on Bazhong City as the research area, incorporates eleven conditioning factors including elevation, relief, and annual average rainfall to develop a geographically weighted regression - random forest (GWR-RF) coupling model. This model optimize the negative sampling strategy by comparing it against traditional random sampling across the entire area. The results indicate the following: (1) Random sampling from the entire area leads to significant disparities in susceptibility assessments, accompanied by a relatively diminished accuracy, rendering it unsuitable for slope unit-based assessments. (2) The coupled GWR-RF model demonstrates spatial variations in landslide susceptibility, predominantly distributing in the Enyang, Bazhou, Pingchang Counties, and the central - southern region of Nanjiang County. The proposed GWR-RF coupled model improves the accuracy of landslide susceptibility assessments by optimizing the negative sample sampling strategy, providing a scientific basis for landslide disaster prevention and mitigation in the Bazhong region.
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0. 引言
滑坡易发性评价通常使用数据驱动模型对一组影响滑坡的环境因子进行概率建模，从而预测潜在滑坡的空间位置，其是滑坡风险管理环节之一，对灾害防治和风险管理有重要意义[1]。滑坡易发性评价结果的可靠性极大依赖于数据质量及建模方法。以信息量、证据权等为代表的统计模型是最常用的滑坡易发性评价方法，这类方法主要是分析各影响因子与灾害之间的影响权重，根据加权所有影响因子权重表征灾害的地理空间约束特征，从而确定滑坡的易发区[2]。随着人工智能的发展，建模方法逐渐从传统的启发式和统计学方法向机器学习方法转变，如随机森林、支持向量机、梯度上升树等机器学习模型已在灾害评估领域得到了广泛应用[3 − 5]。然而，基于机器学习方法的滑坡易发性评价通常表现为二分类问题，以往研究表明负样本的不确定性会对模型精度造成影响[3, 6]。因此，学者通常将统计模型与机器学习模型相耦合以优化滑坡负样本采样策略，从而提高机器学习模型的建模质量[7 − 8]。尽管大量学者意识到优化负样本采样策略可以有效提高易发性评价模型的性能，但以往的研究主要聚焦于以栅格单元为基础的滑坡易发性评价[9 − 11]。相较于斜坡单元，栅格单元与地形地貌特征关联性较弱，且受栅格分辨率影响较大。此外，相关研究也表明在滑坡易发性评价时采用斜坡单元更加合理[12]。然而，针对斜坡单元的负样本采样优化策略的研究目前相对较少。
四川省巴中地区地层岩性以侏罗系和白垩系的红层岩体为主,在地质构造作用下，红层岩体为软硬相间的砂泥岩互层，在降雨作用下该区域易发生滑坡灾害[13]。故本文以四川省巴中市行政区域作为研究区并划分斜坡单元，选取高程、相对高差、历年平均降雨等11个影响因子，将地理加权回归模型能分析空间异质性的优势[14]运用于优化负样本取样策略，并与分类预测性能优越的随机森林模型[3]相耦合，并将建立的地理加权-随机森林耦合（GWR-RF）模型与多次全域随机采样结果进行对比，分析负样本对模型性能的影响。本文所提出的GWR-RF模型为斜坡单元负样本采样提供了一种有效的方法，同时可为研究区滑坡预警预报工作提供参考。
1. 耦合模型概述
1.1 地理加权回归模型
地理学第一定律指出具有相似空间分布特征的空间对象往往表现出相似属性特征关系，并且随着空间距离的增加，这种关联程度逐渐衰减[14]。地理加权回归（geographically weighted regression，GWR）模型则将地理学第一定律引入回归模型，通过分析空间对象与相关属性对应的回归系数和统计参数值，度量了两者的空间依赖关系。该方法对每个独立样本点建立回归模型，求解了与空间位置对应的回归系数，回归系数随空间位置变化的参数值就表征了空间差异性特征[15 − 16]。具体地，GWR模型函数形式如下：
$$ {y_i} = {\lambda _0}({u_i},{\nu _i}) + \sum\limits_{k = 1}^m {{\lambda _p}({u_i},{\nu _i}){x_{ip}}} + {\varepsilon _i} $$ (1) 式中，$ i = 1,2, \cdots ,n $；$ {y_i} $为i处函数响应变量，$ {x_{ip}} $为i处的第k个解释变量，n和m分别为样本和解释变量数量，$ {\lambda _p}({u_i},{\nu _i}) $为i处第p个解释变量的局部回归参数，$ {\lambda _0}({u_i},{\nu _i}) $为i处的截距。
1.2 随机森林模型
随机森林模型（random forest，RF）是由多棵决策树组合形成的一种集成学习算法。该方法通过对多棵决策树的结果进行分类预测，来构建预测模型，能有效避免出现过拟合现象[17 − 18]。主要建模过程步骤如下：①使用bootstrap重采样方法从训练样本中抽取t个随机样本，每个随机样本具有z个特征数；②对t个随机样本分别随机抽取q （q<z） 个特征数建立t个决策树；③对t个决策树的分类结果进行投票，得票最多的结果确定为最终分类结果[19]，表达式如下[17]：
$$ F(x) = \arg \mathop {\max }\limits_Y \sum_{i = 1}^t {I({f_i}(x) = Y)} $$ (2) 式中：F(x)——随机森林分类结果；
fi(x)——决策树分类结果；
Y——模型输出变量；
I——示性函数。
1.3 地理加权-随机森林耦合模型
为优化负样本采样，本文提出了GWR-RF耦合模型，流程如下：①将斜坡单元滑坡数量与11个影响因子导入地理加权回归模型；②建立11个因子地理空间加权函数，然后使用加权回归系数表征11个因子的地理加权回归结果；③在GIS平台上对11个因子的归一化后加权回归系数进行空间叠加，并采用分位数法分区得到加权回归系数空间分类图；④统计空间分类图各区域滑坡斜坡单元面积，在滑坡斜坡单元面积占比最少的区域进行随机采样。⑤将地理加权模型优化后的滑坡正负样本集分为70%训练集和30%测试集，使用随机森林模型对样本集进行分类预测。
2. 研究区基本概况
2.1 研究区地质条件
研究区位于四川省巴中市，地处四川盆地盆周山区，大巴山系米仓山南麓，平均高度766 m，地势总体北高南低，北部为中—深切中山峡谷地貌，中部和南部为低山丘陵地貌（图1a）。受地质构造控制，区内褶皱带发育，地层岩性复杂，出露吕梁期岩浆岩，除志留、泥盆系地层未出露外，其余地层均有分布，主要地层为白垩系和侏罗系，占比84.28%。研究区气候夏季湿热，冬季温润，年降雨量1 090 mm，降雨多集中在5—9月。
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图 1 研究区位置及斜坡单元划分图注：a为研究区位置；b为斜坡单元划分；c为斜坡单元形态示意图。Figure 1. Location and slope unit division of the research area3. 斜坡单元划分及影响因子选取
3.1 斜坡单元划分
斜坡单元能有效反映不同尺度斜坡地形地貌特征，在大尺度精细化滑坡易发性评价中应用较多[19 − 20]。本文采用水文分析法划分斜坡单元，为减小斜坡单元选取误差，结合研究区卫星影像使得斜坡单元与实际山体斜坡吻合[21]，并进行人工处理修正斜坡单元几何拓扑错误，最终将研究区划分为8 643个斜坡单元（图1b、c）。
3.2 影响因子选取
滑坡是受内在因素控制，多种外在因素耦合诱发的一种自然灾害，选择合适的影响因子进行易发性评价，能够提高滑坡灾害监测预警的准确性[22]。然而当前影响因子没有统一的选取标准，本文根据前人研究，从地形地貌、地质构造、气象水文和人类工程活动4个一级指标中，选取高程、坡度、坡向、相对高差、平面曲率、剖面曲率、距道路距离、距河流距离、距断层距离、岩土类型、历年平均降雨共11项影响因子[23 − 27]。基于GIS平台，使用DEM数据以及地质基础资料获取11个影响因子图（图2）。
4. 滑坡易发性评价
4.1 地理加权回归（GWR）结果
本文从研究区共创建8 463个斜坡单元，其中有853个斜坡单元包含滑坡。考虑到正负样本数量不等可能造成抽样偏差，故制备了相同数量的非滑坡斜坡单元，以避免因样品不一致造成的误差[28]。本文以斜坡单元滑坡数量为因变量，将11个影响因子作为解释变量进行地理加权。如图3所示，根据地理加权结果得到11幅因子加权回归系数图。回归系数为正表示影响因素与滑坡分布正相关，反之则为负相关，且回归系数绝对值越大对滑坡分布影响越大[29 − 30]。随后将11幅因子加权系数图归一化后进行空间叠加，并采用分位数法将叠加结果分割为4个区域（根据叠加结果由大到小编为4个区域）。
如图4结果所示，区域1和区域4回归系数绝对值大，影响因素与滑坡分布的相关性大，同理可知，区域2内影响因素与滑坡分布相关性较小[30]。而本文为提高滑坡负样本的可靠度，统计了4个区域的滑坡斜坡单元面积，选取滑坡斜坡单元面积占比最少的区域进行随机采样。如图4，区域2内滑坡斜坡单元面积占比最少，为19.0%。故本文从区域2中随机采取853个非滑坡斜坡单元。同时在滑坡斜坡单元区域外进行了随机采样，共获得9组滑坡负样本（$ \text{RS}i,\;i\in 1,2,\cdots ,9 $）。滑坡样本记为“1”，非滑坡样本记为“0”。
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图 4 地理加权空间分类图Figure 4. Spatial classification map from geographically weighted results依据对模型训练测试集比例合理性的研究，将滑坡清单划分为70%训练样本和30%测试样本，随后采用随机森林模型进行滑坡易发性预测[31]。
4.2 GWR-RF模型与随机采样结果比较
将随机森林得到的易发性指数导入GIS平台进行处理，为便于GWR-RF模型与随机采样结果比较，以0.2为间隔划分易发性指数为极低、低、中、高、极高易发区5个等级，滑坡易发性分区结果如表1、图5所示，选取9次随机采样中具有代表性的RS2、RS3和RS7与GWR-RF耦合模型进行比较。GWR-RF耦合模型滑坡的高和极高易发区占区域总面积57.13%，且滑坡数量占比91.71%。其中，极高易发区面积占比为27.07%，滑坡数量占比为50.33%。区域滑坡空间部分呈现区域南部大面积集中，北部局部集中的特点，滑坡主要分布在恩阳区、巴州区和平昌县，以及南江县中～南部。
表 1 滑坡易发性分区结果Table 1. Results of landslide susceptibility zoning模型 易发性等级 分区面积/km2 面积占比/% 分区滑坡数量/个 滑坡数量占比/% 滑坡密度/（个每100 km2） GWR-RF 极低易发 1704.02 13.85 7 0.65 0.41 低易发 1339.37 10.89 16 1.49 1.19 中易发 2231.27 18.13 66 6.15 2.96 高易发 3698.50 30.06 444 41.38 12.00 极高易发 3331.41 27.07 540 50.33 16.21 RS2 极低易发 1380.00 11.22 4 0.37 0.29 低易发 1344.82 10.93 17 1.58 1.26 中易发 2560.44 20.81 88 8.20 3.44 高易发 6959.27 56.56 935 87.14 13.44 极高易发 60.04 0.49 29 2.70 48.30 RS3 极低易发 1101.49 8.95 1 0.09 0.09 低易发 1219.89 9.91 13 1.21 1.07 中易发 1118.98 9.09 23 2.14 2.06 高易发 5489.84 44.62 522 48.65 9.51 极高易发 3374.37 27.42 514 47.90 15.23 RS7 极低易发 1987.32 16.15 8 0.75 0.40 低易发 1800.17 14.63 17 1.58 0.94 中易发 4941.03 40.16 234 21.81 4.74 高易发 3430.03 27.88 733 68.31 21.37 极高易发 146.07 1.19 81 7.55 55.45 RS2中高和极高易发区面积总占比为57.05%，滑坡数量总占比为90.58%，该模型结果和GWR-RF接近，但高易发区面积占比达到56.56%，极高易发区面积仅占0.49%，模型评估结果较差；RS3分区结果从中部大致沿NE向分割，上部分主要为极高易发区，下部主要为高易发区,滑坡数量总占比为96.55%，模型评价结果比GWR-RF略好，但高和极高易发区面积总占比为72.04%，高处GWR-RF模型14.91%，该模型产生了过拟合现象；RS7中高和极高易发区滑坡数量占比为75.86%，而区内中易发区达到40.16%，高和极高易发区总占比仅29.07%，故该模型评价结果较差。总体上，三次随机采样的极低易发区和低易发区分区结果较一致，都集中在区域北部边界一带，而高和极高易发区分区结果存在极大的波动性，分区结果较差。GWR-RF模型得到了比随机采样更合理的分区结果。
4.3 模型精度对比
滑坡易发性的模型精度常用混淆矩阵进行评估，包括精准率（PR）、召回率（RE）、准确率（ACC）、F1分数（F1）和AUC等。模型评价结果见表2。
表 2 模型效果对比Table 2. Comparative analysis of model performance模型 评价指标 精确率 召回率 F1分数 准确率 AUC RS1 0.763 0.798 0.744 0.846 0.873 RS2 0.649 0.693 0.825 0.801 0.730 RS3 0.749 0.785 0.669 0.839 0.847 RS4 0.619 0.643 0.661 0.779 0.698 RS5 0.595 0.626 0.670 0.778 0.663 RS6 0.608 0.637 0.671 0.780 0.684 RS7 0.581 0.623 0.679 0.781 0.624 RS8 0.613 0.644 0.682 0.782 0.679 RS9 0.619 0.649 0.785 0.783 0.695 $\overline {{\text{RS}}} $ 0.644±0.066 0.678±0.068 0.715±0.070 0.796±0.027 0.721±0.084 GWR-RF 0.700 0.735 0.773 0.814 0.845 随机采样的精确率、召回率、F1分数、准确率和AUC分别为0.644±0.066、0.678±0.068、0.715±0.070、0.796±0.027和0.721±0.084。其中，仅有RS1和RS3评估指标接近GWR-RF模型评估指标，其余7次随机采样评估指标均远低于GWR-RF模型评估指标，且随机采样各指标标准差较大，该结果表明多次随机采样评估结果存在较大的不确定性，而GWR-RF模型通过优化负样本取样，AUC达到了0.845，显著提高了模型评估性能（图6）。
5. 结论
（1）多次全域随机采样AUC均值为0.721±0.084，负样本质量波动性对模型精度影响较大，且全域随机采样的评估结果准确率较差，全域随机采样策略不适用于本研究区的易发性评价。
（2）在GWR-RF模型中，影响因子回归系数绝对值小的区域，影响因子与滑坡分布相关性小，相应地滑坡斜坡单元面积占比也越小。GWR-RF耦合模型AUC为0.845，故该模型有效优化了负样本取样策略，表现出较好的滑坡易发性评价性能。
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图 1 研究区位置及斜坡单元划分图
注：a为研究区位置；b为斜坡单元划分；c为斜坡单元形态示意图。
Figure 1. Location and slope unit division of the research area
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图 4 地理加权空间分类图
Figure 4. Spatial classification map from geographically weighted results
表 1 滑坡易发性分区结果
Table 1 Results of landslide susceptibility zoning
模型 易发性等级 分区面积/km2 面积占比/% 分区滑坡数量/个 滑坡数量占比/% 滑坡密度/（个每100 km2） GWR-RF 极低易发 1704.02 13.85 7 0.65 0.41 低易发 1339.37 10.89 16 1.49 1.19 中易发 2231.27 18.13 66 6.15 2.96 高易发 3698.50 30.06 444 41.38 12.00 极高易发 3331.41 27.07 540 50.33 16.21 RS2 极低易发 1380.00 11.22 4 0.37 0.29 低易发 1344.82 10.93 17 1.58 1.26 中易发 2560.44 20.81 88 8.20 3.44 高易发 6959.27 56.56 935 87.14 13.44 极高易发 60.04 0.49 29 2.70 48.30 RS3 极低易发 1101.49 8.95 1 0.09 0.09 低易发 1219.89 9.91 13 1.21 1.07 中易发 1118.98 9.09 23 2.14 2.06 高易发 5489.84 44.62 522 48.65 9.51 极高易发 3374.37 27.42 514 47.90 15.23 RS7 极低易发 1987.32 16.15 8 0.75 0.40 低易发 1800.17 14.63 17 1.58 0.94 中易发 4941.03 40.16 234 21.81 4.74 高易发 3430.03 27.88 733 68.31 21.37 极高易发 146.07 1.19 81 7.55 55.45 
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表 2 模型效果对比
Table 2 Comparative analysis of model performance
模型 评价指标 精确率 召回率 F1分数 准确率 AUC RS1 0.763 0.798 0.744 0.846 0.873 RS2 0.649 0.693 0.825 0.801 0.730 RS3 0.749 0.785 0.669 0.839 0.847 RS4 0.619 0.643 0.661 0.779 0.698 RS5 0.595 0.626 0.670 0.778 0.663 RS6 0.608 0.637 0.671 0.780 0.684 RS7 0.581 0.623 0.679 0.781 0.624 RS8 0.613 0.644 0.682 0.782 0.679 RS9 0.619 0.649 0.785 0.783 0.695 $\overline {{\text{RS}}} $ 0.644±0.066 0.678±0.068 0.715±0.070 0.796±0.027 0.721±0.084 GWR-RF 0.700 0.735 0.773 0.814 0.845
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