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摘要:
水库大坝是重大生命线工程，地震发生后如何快速有效地进行水库大坝的震害评估，对制定抢险方案和灾后修复意义重大。为了快速准确地对遭受地震侵袭的水库大坝的破坏程度进行评估，选取汶川8.0级大地震各水库大坝的震损详情，结合大坝的结构特点和地震强度构建评估指标体系和数据集，使用k近邻插补法对样本的缺失值进行处理，并判断样本特征相关性，提出了一种基于梯度提升树算法的水库大坝震害快速评估模型。使用网格搜索（grid search，GS）、粒子群搜索（particle swarm optimization，PSO）、贝叶斯搜索（Bayesian optimization，BO）和超带搜索（hyperband search，HS）4种超参数优化方法对梯度提升树（GBDT）回归算法进行参数优化，根据各模型的性能指标（决定系数
R 2、均方根误差RMSE 、平均绝对误差MAE ）进行对比，并对最优模型的特征重要性进行排序。结果表明：BO-GBDT模型能以最短的耗时以及较高精度对水库大坝震害程度进行评估，其决定系数R 2高达0.99，特征重要性分数表明最大缝宽是影响最大的因素。使用该模型与基于改进经验统计模型的土坝震害评估模型评估结果对比，准确度有进一步提高，验证了该模型在水库大坝震后震害快速调查评估应用上的可靠性。Abstract:Reservoir dams are major lifeline projects, and how to quickly and effectively assess the damage of reservoir dams after an earthquake is of great significance to the development of rescue programs and post-disaster restoration.
Objective In order to quickly and accurately assess the damage degree of reservoir dams hit by earthquakes,
Methods This paper selects the earthquake damage details of each reservoir dam of the Wenchuan 8.0 magnitude earthquake, combines the structural characteristics of the dams and the intensity of earthquakes to construct the assessment index system and data set, uses the k-nearest-neighbor interpolation method to deal with the missing value of the samples and judges the sample feature correlation, and proposed a rapid assessment model of reservoir dam earthquake damage based on gradient boosting algorithm. Four hyper-parameter optimization methods, namely Grid Search (GS), Particle swarm optimization (PSO), Bayesian optimization (BO) and HyperBand Search (HS), are used to optimize the parameters of the Gradient Boosted Tree (GBDT) regression algorithm,compare the models based on their performance metrics (coefficient of determination R2, root mean square error RMSE, mean absolute error MAE), and rank the feature importance of the optimal models.
Conclusion The results show that the BO-GBDT model can assess the degree of earthquake damage of reservoir dams with the shortest time consumption as well as high accuracy, with a high coefficient of determination R2 of 0.99, and a feature importance score indicating that the maximum crack width is the most influential factor. Comparing the results of using this model with those of the earth dam damage assessment model based on the improved empirical statistical model, the accuracy is further improved, which verifies the reliability of the model in the application of rapid investigation and assessment of post-earthquake damage of reservoir dams.
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图 1 水库大坝震害快速评估流程图
Figure 1. Flowchart for rapid assessment of earthquake damage of reservoir dams
图 2 四川省水库大坝震害基本特征与震害分布
Figure 2. Basic characteristics and distribution of earthquake damage of reservoir dams in Sichuan Province
图 3 水库大坝震害评估指标体系
Figure 3. Indicator system for seismic damage assessment of reservoir dams
图 5 4种插值法的性能指标对比图
Figure 5. Comparison of performance metrics of multiple interpolation filling methods
图 6 k邻近插补法不同k值下的样本训练性能指标
Figure 6. Sample training performance metrics of k-neighborhood interpolation method with different values of k
图 7 主要变量相关性、统计特征及大坝震害等级占比
Figure 7. Correlations, Statistical Characteristics, and Dam Damage Levels as a Percentage of Major Variables
图 8 3种机器学习算法在训练集上的表现
Figure 8. Performance of the three machine learning in the training set
图 9 4种超参数优化算法下模型的拟合曲线
Figure 9. Fitting curves of the model under four hyperparameter optimizations
图 10 4种超参数优化下模型的R2指标(a)、RMSE指标(b)和MAE指标(c)
Figure 10. R2 metrics under four hyperparameter optimizations RMSE metrics under four hyperparameter optimizations model MAE metrics under four hyperparameter optimizations model
图 11 4种超参数优化算法下GBDT的预测结果分布散点图
Figure 11. Prediction results of GBDT under four hyperparameter optimization algorithms
图 13 GBDT分类模型(a)和BO-GBDT模型(b)预测结果混淆矩阵
Figure 13. Confusion matrix of GBDT classification model (a) and BO-GBDT model (b) prediction results
表 1 4种超参数优化算法参数设定、训练完成时间及最佳模型参数组合和交叉验证误差
Table 1. Parameter settings, training time, and optimal parameter combinations and cross-validation errors for each optimization algorithm and model
优化算法 优化算法参数 最佳模型参数组合 训练完成
时间/s交叉验
证误差网格搜索 迭代次数：256 迭代次数：80
最大树深度：40
最小分割节点：5
特征分割数：386.52 0.4 粒子群
搜索迭代次数：30
粒子群数量：30
随机种子数：42迭代次数：76
最大树深度：63
最小分割节点：7
特征分割数：126.52 0.39 贝叶斯
搜索迭代次数：30
初始化参数：30
随机参数集：1000
随机种子数：42迭代次数：74
最大树深度：62
最小分割节点：7
特征分割数：369.23 0.38 超带搜索 最大预算：81
保留参数组合：3
随机种子数：42迭代次数：86
最大树深度：95
最小分割节点：8
特征分割数：246.35 0.36 
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表 2 部分水库大坝震害因子取值与震害等级预测结果
Table 2. Values of seismic damage factors and predicted seismic damage levels of some reservoir dams
序号 坝名 建成时间 地震烈度 坝型 坝长/m 坝高/m 坝顶宽/m 震害等级 Y1 Y2 1 上坝水库 1978 8 1 120 28 8 3 3.06 3.27 2 龙泉水库 1957 8 1 174 18.9 3.5 2 2.08 2.45 3 团结水库（玉皇） 1977 7 1 168 30.05 4 3 2.99 3.33 4 红刺藤水库 1962 9 1 156 12 6 4 4.07 2.33 5 民乐水库 1957 9 1 167 10 2 4 3.94 4.04 6 众力水库 1969 9 1 1095 9.3 2 2 2.09 2.67 7 新坪水库 1959 7 1 106 17.4 2 3 3.03 3.33 8 太平水库 1959 6 1 294 10.2 3.6 3 2.99 3.58 9 庆丰水库 1958 7 2 247 15.1 3 3 2.95 2.72 10 跃进水库 1958 7 1 284 11.3 3 3 2.99 2.45 11 拦沟堰水库 1960 6 1 234 5 3 1 1.45 1.29 12 八一水库 1975 7 1 130 10.5 2.5 4 3.83 3.82 13 罗家湾水库 1957 7 1 246 12.8 3.7 3 2.96 2.99 14 团结水库（百善） 1971 7 1 118 11.2 1 3 3.14 3.28 15 一根松水库 1973 7 1 167 9.8 3.3 3 3.00 3.82 16 尖梁子水库 1972 7 1 167 10 1.5 3 2.99 2.45 17 长岭水库 1957 7 1 256 10.6 3.3 3 3.00 2.99 18 新桥水库 1956 7 1 107 17 3.2 3 2.91 2.23 19 五七水库 1979 8 1 110 21.6 2.8 3 2.98 2.43 20 观音堂水库 1958 8 1 148 9 4 4 4.03 4.07 21 吴家大堰水库 1978 8 1 124 8 4 4 3.94 4.07 22 狮儿河水库 1958 8 1 131 17.4 4 4 3.89 4.07 23 合作水库 1975 8 1 120 20 2.5 4 3.93 4.07 24 岐山水库 1959 8 1 314 21 4 4 3.95 4.07 25 大田水库 1956 8 1 100.3 7.55 3 4 3.81 4.07 26 幸福水库 1971 8 1 101 14 4.5 3 3.03 2.23 27 牛角埝水库 1974 8 1 37 6 7 3 2.87 2.43 28 上游水库 1973 7 1 470 22 54 3 2.96 2.45 29 洞子沟水库 1985 8 1 182 18 2.2 3 3.00 2.97 30 火烧坡水库 1976 8 1 45 9 4 3 3.14 2.97 31 漆树坝水库 1974 8 1 38 10 3 3 3.09 2.97 32 三要水库 1975 7 1 400 7.4 13.52 3 2.92 3.33 33 和平水库 1977 8 1 175 24.4 3 3 2.91 2.67 34 金花水库 1957 8 1 240 18.6 3.14 3 3.13 2.67 35 崇林水库 1977 8 1 150 10 4.5 4 3.89 2.67 36 向阳水库 1964 7 1 405 20 4 3 3.01 2.99 37 朝阳水库 1985 7 1 130 18 10 3 2.90 3.33 38 红旗水库 1959 7 1 420 11.4 3 2 2.03 2.45 坝型1表示均质坝，2表示黏土心墙坝，Y1为BO-GBDT模型预测震害结果，Y2为改进的大坝震害经验统计模型预测的震害结果（文献[10]）
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表 3 模型对比分析
Table 3. Comparative analysis of models
模型 震害等级相符的土坝 震害等级错分的土坝 平均误差 相关系数 数量/座 比例 数量/座 比例 改进的土坝震害经验统计型判断模型 26 68.4% 12 31.6% 0.363 0.908 BO-GBDT模型 38 100% 0 0% 0.07 0.972
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