基于高斯过程回归的岩体结构面粗糙度系数预测模型

郑可馨; 吴益平; 李江; 苗发盛; 柯超

doi:10.19509/j.cnki.dzkq.tb20230113

基于高斯过程回归的岩体结构面粗糙度系数预测模型

doi: 10.19509/j.cnki.dzkq.tb20230113

郑可馨^1,,
吴益平^1, ,,
李江²,
苗发盛¹,
柯超¹

1.
中国地质大学(武汉)工程学院, 武汉 430074
2.
湖北省自然资源厅信息中心, 武汉 430071

基金项目:

湖北省自然科学基金项目 2023AFB580

贵州省省级科技计划项目黔科合支撑[2023]一般127

国家自然科学基金项目 42377161

国家自然科学基金项目 41977244

详细信息

作者简介:
郑可馨, E-mail: zkx1998@cug.edu.cn

通讯作者:
吴益平, E-mail: ypwu@cug.edu.cn

中图分类号: P642
计量
- 文章访问数: 1140
- PDF下载量: 81
- 被引次数: 0
出版历程
- 收稿日期: 2023-03-06
- 录用日期: 2023-04-19
- 修回日期: 2023-04-18

A prediction model of the joint roughness coefficient based on Gaussian process regression

1.
Faculty of Engineering, China Universityof Geosciences (Wuhan), Wuhan 430074, China
2.
Information Center, Department of Natural Resources of Hubei Province, Wuhan 430071, China

More Information

Author Bio:
ZHENG Kexin, E-mail: zkx1998@cug.edu.cn

Corresponding author: WU Yiping, E-mail: ypwu@cug.edu.cn

摘要

摘要:
岩体结构面粗糙度系数(JRC)的估算是岩体力学性质评价的重要环节, 由于单一统计参数法难以全面表征岩体结构面的复杂粗糙形貌, 单一统计参数法建立的JRC计算模型精度较低。选取表征结构面粗糙形态的8种统计参数, 结合主成分分析法(PCA)和高斯过程回归(GPR)算法, 构建基于多参数融合的JRC预测模型。以公开的112条岩体结构面剖面线数据集(其中95条作为训练样本, 17条为验证样本)为例进行分析研究, 最后将预测所得JRC与实测值对比并分析预测效果。结果表明: 由高斯过程回归构建的JRC预测模型决定系数(R²)高达0.972, 均方根误差(MSE)为0.517, 反映出高斯过程回归方法在小样本条件下构建多统计参数与JRC值隐式关系的适用性, 为今后人工智能在JRC指标预测方面实现合理预测提供了思路。
- 岩体结构面 /
- 粗糙度 /
- 高斯过程回归 /
- 统计参数 /
- 预测
Abstract: Objective
Estimating the joint roughness coefficient (JRC) is essential for evaluating the mechanical properties of a rock mass. Due to the limitation of a single statistical parameter for characterizing morphology, JRC values estimation by a single statistical parameter may produce a sufficiently unreliable result.
Methods
To address the existing challenges in determining JRC values, a model based on Gaussian process regression (GPR) combined with principal component analysis (PCA) was proposed for the quantitative evaluation of JRC. Notably, eight parameters were selected as indicators for the comprehensive expression of the rock joint roughness. To analyse the model's performance, a publicly available dataset of 112 rock joint profiles was used as an example, of which 95 were chosen as training samples and 17 were chosen as validation samples. The reliability of the model was verified by comparing the predicted results with the measured JRC values.
Results
The results show that the derived GPR model demonstrates promising performance (R²=0.972, MSE =0.517) for estimation of JRC values, indicating the high applicability of the model in constructing implicit relationships between multiple statistical parameters and JRC values even under small sample conditions.
Conclusion
In general, the GPR model may provide a new way of estimating JRC values with artificial intelligence.
- rock joints /
- roughness /
- Gaussian process regression /
- statistical parameter /
- prediction
注释:

所有作者声明不存在利益冲突。

HTML全文

图 1 高斯过程回归模型预测JRC流程

JRC.岩体结构面粗糙度系数

Figure 1. Flowchart of the JRC prediction based on GPR

下载: 全尺寸图片幻灯片

图 2 数据集中样本的JRC分布

Figure 2. Distribution of the JRC values in the dataset

下载: 全尺寸图片幻灯片

图 3 岩体结构面粗糙度系数与各统计参数的直方图与散点图矩阵

Figure 3. Scatterplot matrix of the JRC values and statistical parameters with the histogram on the diagonal

下载: 全尺寸图片幻灯片

图 4 训练集中典型岩体结构面样本的剖面线

Figure 4. Profiles of typical rock joint samples in the training set

下载: 全尺寸图片幻灯片

图 5 主成分方差贡献率分布图

Figure 5. Distribution of the variance contribution of the principal components

下载: 全尺寸图片幻灯片

图 6 验证样本集预测JRC与实际JRC值对比

Figure 6. Comparison between the predicted and measured JRC values based on the validation database

下载: 全尺寸图片幻灯片

图 7 基于GPR模型的JRC预测与单参数预测对比

Figure 7. Comparison of JRC values prediction based on the GPR method with various single-parameter models

下载: 全尺寸图片幻灯片

表 1 形貌指标的统计学特征

Table 1. Statistical features of these morphological indicators

参数	均值	最大值	最小值	标准差
R_ave	0.006 9	0.036 0	0.001 1	0.005 8
SD_h/mm	0.453 0	2.585 5	0.076 4	0.405 5
i_ave/(°)	10.306 4	27.861 0	3.104 2	4.223 0
SD_i/(°)	16.867 3	40.323 1	5.159 1	6.166 0
R_max	0.033 9	0.165 3	0.006 6	0.027 0
R_p	1.032 6	1.181 3	1.002 8	0.029 6
SF/mm²	0.011 4	0.072 6	0.000 9	0.011 7
Z₂	0.248 0	0.675 0	0.074 6	0.101 0
R_ave, R_max.分别为平均和最大相对起伏高度；SD_h.起伏高度标准差；i_ave.平均起伏角；SD_i.起伏角标准差；R_p.剖面线粗糙系数；SF.结构函数；Z₂.坡度均方根参数；下同

下载: 导出CSV

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