采空区煤自燃是影响矿井安全生产的主要灾害之一，标志气体与煤温是煤自燃预警的关键参数，2者之间的数学模型及其统计学特征是构建煤自燃预警指标体系的基础。通过程序升温控制实验，获得了88组煤样气体体积分数随煤温的变化曲线，选择指数函数、多项式函数和Logistic回归函数对气体体积分数进行拟合，以R₂，方差SSE和均方差MSE等参数为评价指标，确定了Logistic回归函数为最佳拟合函数;利用Logistic函数拟合标志气体的变化曲线，得到CO与C₂H₄体积分数的4个参数A₁，A₂，p和x₀，基于统计学特征确定上述4个参数的值并检验其有效性，得到“气体-温度”的本构方程;最后，归纳了不同标志气体的初现温度、拐点温度的统计学特征，构建了基于气体统计学特征的煤自燃预警体系并进行了煤自燃危险阶段划分。结果表明：① 30~350 ℃实验温度内，标志气体体积分数变化分为波动段、稳定段和衰减段，气体体积分数与煤温符合Logistic回归模型：CO与C₂H₄的拟合参数分别为A₁(CO)=23,A₂(CO)=14 990,p(CO)=11,x0(CO)=294;A₁(C₂H₄)=0.3,A₂(C₂H₄)=27,p(C₂H₄)=17,x0(C₂H₄)=283；② CO初现温度、第1拐点温度、C₂H₄初现温度、第1拐点温度和C₂H₂初现温度可作为煤自燃预警指标，预警值分别为30，156，120，204和285 ℃；③ 基于初现温度和拐点温度将煤自燃分为6个危险等级：安全、低风险、一般风险、较大风险、重大风险和特大风险，可根据等级不同采取相应的响应措施。

Coal spontaneous combustion in goaf is one of the main disasters affecting mine safety.Index gases and coal temperature are the key parameters for the early warning of coal spontaneous combustion.The mathematical model between them and their statistical characteristics are the bases of constructing coal spontaneous combustion early warning system.Through temperature programmed control experiment,the gases concentrations curve of 88 groups of coal samples with coal temperature are obtained.The gas concentration is fitted by exponential function,polynomial function and Logistic regression function.R₂ and SSE and MES are used as evaluation indexes to select Logistic regression function as the best fitting function.Logistic model is used to fit the curve of index gases to obtain the four parameters A₁,A₂,p and x0 of the CO and C₂H₄.Based on the statistical characteristics,the values of the above four parameters are determined and their validity is tested,and the constitutive equation of “gas-temperature” is obtained.Finally,based on the statistical characteristics,the first occurrence and inflection temperatures of gases with different indexes are summarized and the early warning indexes of coal spontaneous combustion are constructed.from the experimental results,it can be concluded that ① within the range of 30-350 ℃ experimental temperature,the variation of index gas concentration is divided into fluctuation section,stable section and attenuation section,and the gas concentration and coal temperature conform to Logistic regression model:the fitted parameters for CO and C₂H₄ were A₁(CO)=23,A₂(CO)=14 990,p(CO)=11,x0(CO)=294; A₁(C₂H₄)=0.3,A₂(C₂H₄)=27,p(C₂H₄)=17,x0(C₂H₄)=283.② CO initial temperature,first inflection point temperature,C₂H₄ initial temperature,first inflection point temperature,and C₂H₂ initial temperature can be used as the early warning indexes of coal spontaneous combustion with values are 30,158,120,204 and 285 ℃,respectively.③ Based on the initial temperature and inflection point temperature,coal spontaneous combustion is divided into 6 hazard levels:safety,low risk,average risk,greater risk,significant risk and mega risk.The corresponding response measures can be taken according to the different levels.

1 煤样程序升温实验

2 模型的建立与求解

   2.1 变质程度对标志气体的影响

   2.2 拟合模型优选

   2.3 模型参数确定

   2.4 模型有效性验证

3 煤自燃预警指标构建

   3.1 初现温度

   3.2 拐点温度

   3.3 预警指标构建

4 结论