
科学技术与工程

中国技术经济学会
不同拟合指标下模拟节理岩体结构面产状的Copula函数方法
任青阳 , 施俭 , 王彦丁 , 肖宋强
科学技术与工程 ›› 2025, Vol. 25 ›› Issue (10) :4274-4283
不同拟合指标下模拟节理岩体结构面产状的Copula函数方法
Copula Function Method for Simulating the Occurrence of Jointed Rock Mass Structural Plane under Different Fitting Indexes
为准确选取模拟节理岩体结构面产状互相关性的Copula函数,提出了不同拟合指标下模拟节理岩体结构面产状的Copula函数方法,通过采用最小平方欧式、AIC(Akaike information criterion)信息准则、BIC(Bayesian information criterion)信息准则这3种拟合指标确定各自的最优Copula函数并通过MATLAB确定实测产状数据的最优边缘分布,建立倾角和倾向的二维联合分布函数。同时结合蒙特卡洛抽样法自动生成模拟数据,将数据导入Dips软件中进行可视化处理,得到产状的赤平投影图,对比实测的倾角和倾向数据和不同拟合指标下确定的Copula函数模拟数据间的差异。最后,基于工程案例检验方法的有效性。结果表明:不同的拟合指标会产生不同的Copula函数,对模拟产状的有效性也会有较大差异,若是选择不当的拟合指标可能导致选择不准确的Copula函数,从而使模型无法准确地捕捉数据的相关结构和特征;不适当的拟合指标可能导致拟合模型与真实数据之间存在较大的误差,使得模型的预测能力和解释能力下降,就本文案例表明在最小平方欧式值拟合指标下选择的Gaussian Copula函数拟合实测数据效果最好。此研究将有助在应用Coupla函数时选用恰当的拟合指标。
In order to accurately select the Copula function to simulate the mutual correlation between inclination and dip of jointed rock mass structural plane, the Copula function method to simulate the occurrence of jointed rock mass structural plane under different fitting indexes was proposed. The optimal Copula function was determined by using the least square Euclidian, AIC information criterion and BIC information criterion, and the optimal edge distribution type of the observed occurrence data of the structural plane was determined by Matlab software. At the same time, Monte Carlo sampling method was used to automatically generate simulation data, and the data was imported into Dips software for visualization processing, and the erP projection map of occurrence was obtained. The difference between the measured dip and inclination data and the simulated data determined by Copula function under different fitting indexes was compared. Finally, the validity of the method is tested based on engineering cases. The results show that different fitting indicators will produce different Copula functions, and there will be great differences in the effectiveness of simulation occurrence. Improper fitting indicators may lead to the selection of inaccurate Copula functions, so that the model can not accurately capture the relevant structure and features of the data. Inappropriate fitting indexes may lead to large errors between the fitting model and the real data, which will decrease the predictive ability and interpretation ability of the model. In this case, it is shown that the Gaussian Copula function selected under the fitting index of least square Euclidene values has the best fitting effect on the measured data. This research will help to select the appropriate fitting index when using Coupla function.
结构面 / Copula函数 / 产状 / 拟合指标 / 互相关性 / 赤平投影
structural plane / copula function / attitude / fitting index / cross-correlation / equatorial projection
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