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CLUSTER ANALYSIS FOR JOINT DATA OF THREE-DIMENSIONAL ROCK MASS USING DifFUZZY METHOD
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摘要: 模糊聚类法常常用来分析三维数据组，例如节理产状等，同时，其他方法也被用于分析目标数据的组分，但传统方法在分析复杂数据时通常会遇到困难。本文基于Ornella Cominetti和Anastasios Matzavinos近年提出的一种可用于复杂数据分析的新方法，将其引入并编程实现了DifFUZZY聚类法分析岩体结构面的产状参数。研究成果表明：(1)DifFUZZY聚类法是一种简单且功能强大的新方法，它可以自动分组目标数据形成聚类，且能获得优势产状，为三维真实结构面网络模拟实现提供了新途径；(2)DifFUZZY聚类法不需要高等的结构面产状信息，而是随机选择初始数据进行优势分组后基于自身算法确定分类，并最终给出优势结构面参数，为岩石边坡等区域稳定性快速分析提供可能；(3)基于DifFUZZY聚类法可循环作用寻找聚类编号，并根据数据类型原则自动确定数据点的聚类。Abstract: Fuzzy clustering techniques are often used in the study of three-dimensional data sets,such as orientation data. Other methods are used in finding groups within directional data. But traditional methods usually meet difficulties when dealing with some complicated data sets. In this paper,a new DifFUZZY clustering method proposed by Ornella Cominetti and Anastasios Matzavinos for the complex data sets,is firstly applied to cluster the orientation data. The results show the follows. (1)DifFUZZY is a new simple and powerful method to realize the 3D-simulation of joint sets,which can automatically separate directional data into distinct clusters and get the dominated value of orientation data. (2)DifFUZZY does not require any advanced information about the orientation data,and it just randomly selects the initial values as the dominated orientation and then according to its own algorithm finally decide which points belong to a cluster and the finally dominated orientation values of the clusters. The suggested method makes it possible to analyse the local stability of rock slope quickly. (3)DifFUZZY can self-acting return the cluster number and on the principle of the membership value it can automatically decide the point lies in which cluster or not.
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Key words:
- Engineering Geology /
- Scientific problem /
- Landslide
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图 4 DifFUZZY方法几何示意图
a. 原始数据；b. 构造相似图形划分硬点与软点；c. 基于随机扩散寻找组内距离软点最近的硬点；d. 将软点扩散到距离组内最近的硬点；e. 基于c和d计算软点的扩散距离
Figure 4. Geometry diagram by DifFUZZY
图 5 FCM和DifFUZZY基于实例数据分组结果
a. 实际分组; b. FCM分组; c. DifFUZZY分组
Figure 5. Synthetic data and the cluster results by FCM and DifFUZZY
图 6 结构面数据(San Manual mine，Arizona)示意图
a. 投影图; b. 投影等密度图
Figure 6. Data set diagram of joints(San Manual mine,Arizona)
图 7 3组分组结果的对比
a. San Manual mine 分组结果; b. FCM 分组结果 c. DifFUZZY 分组结果
Figure 7. Comparison of three-group cluster results
表 1 FCM和DifFUZZY计算结果表
Table 1. Calculation results by FCM and DifFUZZY
分组编号 实例数据/(°) FCM法/(°) DifFUZZY法/(°) 1(*) 30/30
(k=40，N=100)32.35/32.66
(N′=102)31.87/31.57
(N′=100)2(+) 140/45
(k=10，N=60)137.73/47.64
(N′=63)138.54/47.28
(N′=61)3(o) 230/60
(k=15，N=30)233.70/63.24
(N′=27)236.29/62.53
(N′=25)4(.) 310/75
(k=30，N=30)308.89/67.90
(N′=28)308.92/69.62
(N′=26)*FCM和DifFUZZY计算结果为结构面倾向和倾角 
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表 2 San Manual mine实例计算结果表
Table 2. Calculation results of San Manual mine
分组编号 原始分组/(°) FCM/(°) DifFUZZY/(°) 1(*) 250/76 250.7374/68 258.59/73.70 2(o) 350/73 245.10/75.87 346.72/76.60 3(+) 128/26 118.9759/53.8795 127.74/26.45 *FCM和DifFUZZY计算结果为结构面倾向和倾角
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