岩体分级的多分类有序因变量Logistic回归模型

Multi-Category Ordered-Dependent-Variable Logistic Regression Model for Rock Mass Classification

将多分类有序因变量的Logistic回归分析引入到岩体质量分级问题中.从工程岩体实测数据出发,以影响岩体质量的单轴抗压强度、岩体声波纵波速度、体积节理数等6个因素为自变量,有序多分类的岩体级别为响应变量,建立岩体分级判别公式.检验模型拟合优度及预测能力.结果表明,Logistic回归模型性能良好,回判估计的误判率为零,预测准确率高.相比距离判别分析和线性回归分析,Logistic回归分析对变量分布无要求,理论上更适于响应变量为有序多类别的岩体分级问题;模型可以输出岩体属于各级别的概率,为工程设计人员提供更多的岩体质量信息.因而Logistic回归模型是一种更优的工程岩体分级方法.

Multi-category ordered-dependent-variable logistic regression model was introduced into the rock mass classification.Based on rock mass samples data,rock uniaxial compressive strength,rock acoustic wave velocity,intensity of jointing,joint roughness coefficient,weathering variation coefficient of joint surface and permeability coefficient were chosen as independent variables,rock mass level was considered as dependent variable,then rock mass classification judgment formula was established.Goodness of fit and model predictive ability test were carried out to evaluate the model correctness.The results show that Logistic regression analysis model has excellent performance,misjudging rate of training samples is zero,and predictive ability is strong.Compared to the distance discriminant analysis,and linear regression analysis,Logistic regression analysis has no normal distribution restriction to independent variables,and it is theologically appropriate to analyze rock mass classification problems whose dependent variable is discrete ordered variable,the output of this method is probability value of all levels that rock mass belong to,which provides additional rock mass information to engineering designer.Thus multi-category ordered-dependent-variable regression is a superior method for rock mass classification.