1、第 42 卷 第 3 期 岩石力学与工程学报 Vol.42 No.3 2023 年 3 月 Chinese Journal of Rock Mechanics and Engineering March，2023 收稿日期：收稿日期：20220417；修回日期：修回日期：20220616 基金项目：基金项目：中央高校基本科研业务费专项资金(300102261720，300102341308)；陕西省自然科学基础研究计划项目(2019JQ685)Supported by the Fundamental Research Funds for the Central Universities Nat
2、ional(Grant Nos.300102261720 and 300102341308)and Natural Science Basic Research Project of Shaanxi Province(Grant No.2019JQ685)作者简介：作者简介：宋宇飞(1992)，男，2015 年毕业于西北大学勘查技术与工程专业，现为博士研究生，主要从事地质灾害风险和区域滑坡预报预警方面的研究工作。E-mail：。通讯作者：范 文(1967)，男，博士，现任教授、博士生导师。E-mail： DOI：10.13722/ki.jrme.2022.0382 基于贝叶斯方法的降雨诱发滑坡
3、概率型 预警模型研究 基于贝叶斯方法的降雨诱发滑坡概率型 预警模型研究 宋宇飞1，曹琰波1，2，范 文1，2，于宁宇1，左 琛3，陶 虹4(1.长安大学 地质工程与测绘学院，陕西 西安 710069；2.信息产业部电子综合勘察研究院，陕西 西安 710054；3.长安大学 运输工程学院，陕西 西安 710069；4.陕西省地质环境监测总站，陕西 西安 710054)摘要：摘要：为提高区域降雨型滑坡的预警精度，以陕南秦巴山区为例，首先通过人工神经网络(ANN)和逻辑回归模型(LR)进行滑坡易发性建模，使用滑坡发生频率比(FR)对易发性模型进行检验和校准，用来表达滑坡发生的空间概率；其次在敏感性分
4、析的基础上选取最优的降雨变量组合和衰减系数，在二维贝叶斯公式的基础上构建概率型降雨阈值模型，用以计算滑坡发生的时间概率，并使用20162020年的降雨数据进行验证；之后在贝叶斯公式的基础上对滑坡发生的时空概率进行耦合，构建研究区降雨型滑坡的概率型预警模型(PLEWM)，并对20162020年的雨季(79月份)逐日进行模拟预警；最后分别从预警效果和成本效益角度出发，使用预警成本投入、滑坡造成的损失、预警成功率、漏报率、误报率等指标对预警模型的性能进行评估。结果表明：(1)研究区构建降雨阈值模型最优的变量组合为有效降雨量持时(EE-D)，最优的衰减系数为0.816；(2)概率型阈值模型预测2016
5、2020年发生致灾降雨213.71起，实际发生201起，累积误差为10.07%，各概率区间内的预测值与实际发生数量沿着斜率为1的对角线分布；(3)模拟预警结果显示，PLEWM模型的成本投入和滑坡造成的损失分别为传统启发式预警模型的62.86%和63.48%；预警成功率、漏报率和误报率分别为63.99%，34.71%和1.3%，均优于启发式预警模型；而在长持时高强度降雨条件下，PLEWM的预警成功率显著高于传统预警模型。关键词：关键词：边坡工程；降雨型滑坡；滑坡易发性；概率型降雨阈值；贝叶斯公式；概率型预警模型 中图分类号：中图分类号：P 642 文献标识码：文献标识码：A 文章编号：文章编号：
6、10006915(2023)03055817 Probabilistic early warning model for rainfall-induced landslides based on Bayesian approach SONG Yufei1，CAO Yanbo1，2，FAN Wen1，2，YU Ningyu1，ZUO Chen3，TAO Hong4(1.School of Geological Engineering，Changan University，Xian，Shaanxi 710069，China；2.China Electronic Research Institute
7、 of Engineering Investigations and Design，Xian，Shaanxi 710054，China；3.College of Transportation Engineering，Changan University，Xian，Shaanxi 710069，China；4.Shaanxi Institute of Geo-environment Monitoring，Xian，Shaanxi 710054，China)Abstract：To improve the early warning accuracy of rainfall-induced land
8、slides，the Qinba Mountains region in southern Shaanxi province is taken as an example.At first，artificial neural network(ANN)and logistic regression model(LR)were used to establish the landslide susceptibility model，and the established susceptibility model was tested and corrected by frequency ratio
9、 model(FR)to express the spatial probability of landslide occurrence；第 42 卷 第 3 期 宋宇飞等：基于贝叶斯方法的降雨诱发滑坡概率型预警模型研究 559 Secondly，sensitivity analysis method was employed to select the optimal rainfall variables and the attenuation coefficient K，and then，two-dimensional Bayesian approach was be used to es
10、tablish probabilistic threshold model，which can be used to calculate the temporal probability of landslide.The model was tested by the rainfall data from 2016 to 2020；Then，the spatial probability and temporal probability of rainfall-induced landslides were coupled base on Bayesian formula，and a prob
11、abilistic early warning model for rainfall-induced landslide(PLEWM)was proposed.To test the performance advantages of PLEWM，PLEWM and traditional early warning model were separately used to issue warning information day-by-day for the rainy season(July to September)from 2016 to 2020.It is proposed t
12、o use the investment of operating LEWM(Invest)，losses caused by landslides(Loss)，correct alert rate，missed alert rate and false alert rate as warning model performance indicators，to compare the performance differences between the PLEWM and traditional early warning model.The results show that：(1)EE-
13、D is the optimal combination for rainfall threshold model in the study area，and the optimal attenuation coefficient K is 0.816.(2)Probabilistic threshold model predicts that 213.71 triggering rainfalls will occur from 2016 to 2020，and 201 actually recorded，with a cumulative error of 10.07%，the predi
14、cted triggering rainfall and the actual recorded in each probability intervals are distributed along a diagonal line with a slope of 1.(3)According to the statistics of the warning information issued in the rainy season from 2016 to 2020，The Invest and Loss of the PLEWM are 62.86%and 63.48%of tradit
15、ional early warning model，respectively.The correct alert rate，missed alert rate and false alert rate are 63.99%，34.71%and 1.3%respectively，which are better than the traditional warning model；During the condition of long-lasting and high-intensity rainfall，the performance of PLEWM is significantly hi
16、gher than traditional warning model.Key words：slope engineering；rainfall-induced landslide；landslide susceptibility；probabilistic rainfall threshold；Bayesian approach；probabilistic landslide early warning model 1 引引 言言 降雨是诱发滑坡的主要因素，据统计研究区内近 20 年 85%以上的致灾滑坡均由降雨诱发，降雨型滑坡造成了严重的人员伤亡和财产损失，如何对区域降雨型滑坡实现精确预警成为了防灾减灾工作中的热点问题1-3。降雨数据的监测和预报方式成熟，准确率高4-5，通过分析历史降雨数据与滑坡发生之间的统计关系，建立降雨阈值模型，可以实现降雨致灾危险性的判别，同时也是区域降雨型滑坡早期预警模型(rainfall-induced landslide early warning model，LEWM)的重要组成部分3，6-8。LEWM 可以提供及时有效的预警信息，从而减少由降雨诱发
