引入因子分析的结构面粗糙度RBF复合参数模型

尹宏; 王述红; 董卓然; 侯钦宽

doi:10.11779/CJGE202204015

引入因子分析的结构面粗糙度RBF复合参数模型 English Version

东北大学资源与土木工程学院, 辽宁沈阳 110819

基金项目:

国家自然科学基金项目 U1602232

中央高校基本科研业务费专项资金项目 N170108029

辽宁省重点研发计划项目 2019JH2/10100035

详细信息

作者简介:
尹宏(1997—)，男，博士研究生，主要从事岩石剪切力学方面的研究。E-mail: neuyinhong@126.com

通讯作者:
王述红, E-mail: shwang@mail.neu.edu.cn

中图分类号: TU452
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- 文章访问数: 207
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出版历程
- 收稿日期: 2021-04-11
- 网络出版日期: 2022-09-22
- 刊出日期: 2022-03-31

RBF composite parameter model for structural surface roughness with factor analysis

School of Resources and Civil Engineering, Northeastern University, Shenyang 110819, China

摘要

摘要: 结构面粗糙度的表征是预测峰值剪切强度的基础性工作，单一参数无法全面反映结构面的形貌特征，而由各表征参数并列构成的指标系统是一个存在信息重叠的非线性系统，为此引入因子分析通过正向标准化实现参数降维可有效剥离交叉信息，同时将正向标准化的指标系统通过RBF神经网络结构实现非线性参数的线性映射，实际运行过程中选取6个反映结构面粗糙度的统计参数并建立JRC反算关系，构建76组训练样本和37组测试样本，建立了一个反映结构面形貌起伏高、起伏角、接触度的多指标复合参数模型，同时固定隐含层神经元的数目从而提高运算速度，通过实测数据计算相对误差和决定系数进行性能评价。利用样本数据和岩石结构面直剪实验验证了模型的预测精度。最后讨论了因子分析的适用性和可能的误差分析。
- 岩石 /
- 结构面 /
- 粗糙度 /
- RBF神经网络 /
- 因子分析
Abstract: The characterization of the structural surface roughness is the groundwork for predicting the peak shear strength. The single parameter cannot fully reflect the characteristics of structural surface morphology. The index system composed of some single characterization parameters is a nonlinear system with much overlapping information. The factor analysis is conducted to reduce the dimension and strip the overlapping information by canonical normalization. At the same time, the standardized index system is transformed from nonlinear into linear by the RBF neural network structure. In practice, 6 statistical parameters reflecting the structural surface roughness are selected, the inverse calculation of JRC is established, 76 training samples and 37 group test samples are built. The multi-index composite parameters are established considering the characteristics of embossment of joints, such as height, angle and contact degree. In the mean time, the number of neurons in the hidden layer is fixed to improve the calculation speed. The prediction accuracy of the model is verified by the sample data and the direct shear tests of rock joints. The relative error and determination coefficient are calculated through the measured data to evaluate the performance. Finally, the applicability of the factor analysis and possible error analysis are discussed.
- rock /
- structural surface /
- roughness /
- RBF neural network /
- factor analysis

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图 1 RBF神经网络结构

Figure 1. Structure of RBF neural network

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图 2 RBF复合参数模型预测JRC的流程图

Figure 2. Flow chart of JRC predicted by RBF composite parameter model

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图 3 公共因子的（累计）方差贡献率分布图

Figure 3. Distribution of (cumulative) variance contribution rate of common factors

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图 4 R²-Spread关系图

Figure 4. Relationship between R² and spread

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图 5 基于学习样本JRC预测值与实测值的对比

Figure 5. Comparison between predicted and measured values of JRC based on learning samples

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图 6 基于测试样本RBF模型和单参数模型JRC预测值的对比

Figure 6. Comparison of predicted values of JRC between RBF model and single-parameter model based on test samples

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图 7 经巴西劈裂产生的12组结构面样本

Figure 7. 12 groups of joint samples generated by Brazil splitting

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图 8 实验室获取结构面三维形貌的采集设备

Figure 8. Equipments of obtaining three-dimensional morphology of joints in laboratory

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图 9 用于计算JRC值的剖面轮廓线提取

Figure 9. Profile line extraction used to calculate JRC value

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图 10 公共因子与JRC值趋势对比

Figure 10. Comparison between common factor and JRC value trend

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表 1 RBF指标系统及JRC计算式

Table 1 RBF index system and formulas for JRC

指标	定义式	JRC计算式
${\text{CLA}}$	$\frac{1}{N}\sum\nolimits_{i = 1}^{i = N} {\left\| {{y_i}} \right\|}$	$2.76 + 78.87{\text{CLA}}$
${\text{S}}{{\text{D}}_{\text{i}}}$	$\left\{\begin{array}{l} \arctan \left[\frac{1}{N-1} \sum_{i=1}^{i=N-1}(\lambda)^{2}\right]^{1 / 2} \\ \lambda=\frac{y_{i+1}-y_{i}}{x_{i+1}-x_{i}}-\tan i_{\text {ave }} \end{array}\right.$	$1.042{\text{S}}{{\text{D}}_{\text{i}}} - 4.733$
${\text{SF}}$	$\frac{1}{{N - 1}}{\sum\nolimits_{i = 1}^{i = N} {{\text{(}}y_{i + 1}^{} - y_i^{}{\text{)}}} ^2}$	$37.63 + 16.5\lg {\text{SF}}$
${R_{\text{p}}}$	$\frac{{\sum\nolimits_{i = 1}^{i = N - 1} {{{[{{({x_{i + 1}} - {x_i})}^2} + {{({y_{i + 1}} - {y_i})}^2}]}^{1/2}}} }}{{\sum\nolimits_{i = 1}^{i = N - 1} {({x_{i + 1}} - {x_i})} }}$	$229.44{R_{\text{p}}} - 226.94$
${Z_2}$	$\sqrt {\frac{1}{{N - 1}}\sum\nolimits_{i = 1}^{i = N - 1} {{{\left( {\frac{{{y_{i + 1}} - {y_i}}}{{{x_{i + 1}} - {x_i}}}} \right)}^2}} }$	$32.69 + 32.98\lg {Z_2}$
$C_{{\text{2D}}}^*$	$90{°}^{（\text{2D}）}/\text{(}{C}^{*}+1\text{)}$	$3.95{(C_{{\text{2D}}}^*)^{0.7}} - 7.98$

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表 2 相关系数矩阵

Table 2 Matrices of correlation coefficient

指标	^*SD_i	^*R_p	^*Z₂	^*SF	^*CLA	^*C_2D
^*SD_i	1
^*R_p	0.953	1
^*Z₂	0.986	0.947	1
^*SF	0.875	0.997	0.967	1
^*CLA	0.742	0.756	0.856	0.84	1
^*C_2D	0.642	0.912	0.653	0.756	0.954	1

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表 3 旋转后的载荷系数

Table 3 Load coefficients after rotation

指标	^*Z₂	^*SD_i	^*R_p	^*C_2D	^*SF	^*CLA
F₁	0.873	0.802	0.786	0.694	0.432	0.537
F₂	0.462	0.411	0.364	0.679	0.927	0.934

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表 4 基于不同方法测算的S~A₁号试样结构面JRC值

Table 4 JRC values of S-A₁ joints measured by different methods

指标	最小值	最大值	平均值	实测值	相对误差/%
RBF	4.01	8.69	6.34	6.53	2.9~7.86
Z₂	2.13	9.02	4.78	6.53	26.7~38.1
R_p	3.87	9.34	5.20	6.53	0.3~43.02
SD_i	3.45	10.78	7.94	6.53	21.6~37

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