Application of the Discrete Fréchet Distance in Site Classifications at Strong Motion Stations
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摘要: 当强震台站场地资料不完整时，所收集到的强震数据因缺乏准确的场地类别信息而难以有效利用。为解决这一问题，本文提出一种基于离散Fréchet距离的强震台站场地分类方法。将获取到的664个KiK-net台站场地按照《建筑抗震设计规范（GB 50011—2010）》进行分类，并构建2个数据集。利用数据集1得到Ⅰ、Ⅱ、Ⅲ类场地标准谱比曲线，并结合离散Fréchet距离对数据集2中的台站进行场地分类，统计分类成功率与误判率。统计结果表明，本文方法能较准确地对场地进行分类，且误判率在可接受范围内。将本文方法分类统计结果与斯皮尔曼秩相关系数法分类的成功率与误判率进行对比，结合本文方法分类后得到的平均谱比曲线，均可表明应用本文方法进行强震台站场地分类具有合理性。
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关键词:
- 强震台站 /
- 场地分类 /
- 离散Fréchet距离 /
- 标准谱比曲线 /
- 数据集
Abstract: Without complete site information of strong motion stations, the collected data cannot be effectively used due to lack of accurate site category information. In order to overcome this problem, this study proposed a site classification method for strong motion stations based on discrete Fréchet distance, which is a measurement of the similarity between curves. The site conditions at 664 strong motion stations from KiK-net were firstly classified according to the Chinese Code for Seismic Design of Buildings (GB 50011-2010), and then divided into two sets. Standard spectra-ratio curves for site class Ⅰ, Ⅱ and Ⅲ were derived for the sites in dataset1 and there were obvious differences between those three curves. At the same time, the distribution of the natural logarithmic deviation on response spectra periods of those standard curves was also calculated in order to examine the divergence of the dataset. The sites in dataset2 were reclassified based on the method proposed in this paper, and the corresponding success rates and error rates of classifications were calculated. The result shows that not only could the proposed method classify sites with accuracy but also the error rates would be acceptable. The proposed method shows reasonability, by the comparison of the results derived from the proposed method with those from the method of Spearman's rank correlation coefficient, combined with the average spectra ratio curves derived from the proposed method. -
图 1 离散Fréchet距离与多边形链相似性
Figure 1. Discrete Fréchet distance and similarity between polygonal chains
图 3 3类场地标准谱比曲线及其自然对数标准差曲线
Figure 3. Standard spectra ratio curves and natural logarithmic standard deviation for three site classses
图 5 2种方法划分成功率及误判率
Figure 5. Success rates and failure rates of two classification methods
图 6 分类前后3类场地平均谱比曲线及其自然对数标准差曲线
Figure 6. Standard spectra ratio curves and natural logarithmic standard deviation before and after classification for three site classes
表 1 KiK-net台站场地分类结果
Table 1. Classification result of KiK-net stations
场地类别 数量 比例/% 描述 I 94 14.16 包括I0跟I1 Ⅱ 481 72.44 - Ⅲ 36 5.42 - Ⅳ 4 0.60 - 5（剔除） 43 6.48 含有推测剪切波速 6（剔除） 6 0.90 含有软夹层 
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表 2 地震动记录选取信息
Table 2. Details on ground motion record selection
场地类别 数据集1 数据集2 场地数量 记录数量/组 记录占比/% 场地数量 记录数量/组 记录占比/% I 61 4153 26.06 25 1418 31.99 Ⅱ 367 8624 54.11 33 2294 51.76 Ⅲ 24 3160 19.83 4 720 16.25
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表 3 KGWH03场地钻孔及场地分类
Table 3. Boring Information and Site Classification of KGWH03
层序 厚度/m 剪切波速/（m·s-1） 1 5.00 600.00 2 19.00 1820.00 3 26.00 2400.00 4 — 2950.00 等效剪切波速/（m·s-1） 600.00 覆盖层厚度/m 5.00 场地类别 I
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