Roughness coefficient of rock discontinuities based on random forest regression analyses
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摘要:
岩体结构面粗糙度系数是快速估算结构面峰值抗剪强度的重要参数。但是结构面轮廓曲线复杂，单一统计参数无法量化表征粗糙度。为解决这一问题，收集了112条结构面轮廓曲线起伏角、起伏度、迹线长度3方面的8项统计参数，利用随机森林回归模型交叉验证的方法评估统计参数的重要性。结果表明：最大起伏度、起伏高度标准偏差、平均起伏角、起伏角标准差、平均相对起伏度及粗糙度剖面指数等6项统计参数重要性占比达到93.2%，且回归拟合系数趋于平稳，基于重要性评估结果建立最优超参数决策树数目（ntree）为400、参与节点分割的数目（mtry）为2的随机森林回归模型，模型预测结果拟合优度高达98.1%。与基于坡度均方根、结构函数及粗糙度剖面指数等传统线性回归结果对比，随机森林回归模型结果精度更高，误差更小，拟合优度提高6%以上，表明随机森林回归模型更适用于结构面粗糙度反演。
Abstract:The peak shear strength of the discontinuities can be estimated quickly by the roughness of the discontinuities. However, it is difficult to quantify the roughness of the structural surface using the single statistical parameter. In order to improve the prediction accuracy of the standard discontinuities roughness, eight statistical parameters in the aspects of undulating degree and trace length of 112 structural profile curves are collected, and the method of cross-validation of random forest regression model is used to evaluate the importance of statistical parameters. The evaluation results show that the importance of six statistical parameters, including the maximum undulation, undulation height standard deviation, mean undulating angle, undulating angle standard deviation, mean relative undulation rave and roughness profile index, accounts for 93.2%, and the regression fitting coefficient tends to be stable. Based on the importance assessment results, a random forest regression model is established. The model prediction results fitting excellence is up to 98.1%, showing the excellent prediction results. Compared with the traditional linear regression results, such as the results of the slope-based mean square root, structural function and roughness profile index, the random forest regression model has higher accuracy, smaller error and better fit. The random forest regression model is more suitable for structural roughness inversion.
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Key words:
- random forest /
- roughness /
- rock structure surface /
- statistical parameters /
- importance assessment
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表 1 结构面粗糙度统计参数重要性评分
Table 1. The importance score of the discontinuity roughness statistical parameters
变量 Rmax SDh iave SDi Rave Rp SF Z2 重要性评分 0.323 0.270 0.159 0.069 0.066 0.044 0.041 0.027 
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表 2 各模型预测精度
Table 2. Predictive accuracy for each mode
模型精度 RF SF RP Z2 R2/% 98.1 92.1 91.7 91.3 MSE 0.219 3.363 6.366 13.974 RMSE 0.502 1.227 1.623 1.781
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