气体测量中的线性拟合

    Linear Fitting in Gas Measurement

    • 摘要: 气体成分测量中可使用单点、双点、线性等多种校准方法,线性校准可分为普通线性最小二乘法、加权双变量最小二乘法线性拟合等多种细分方法。对不同文献介绍的上述两种方法进行了比较分析,并对加权双变量最小二乘法线性拟合中应注意的事项进行了介绍。当测量信号的不确定度已经与气体标准物质的不确定度水平接近,甚至低于标准物质的不确定度时,采用加权双变量最小二乘法线性拟合的方法处理测量结果更加合理。使用加权双变量最小二乘法线性拟合时,权重为标准不确定度平方的倒数,可采用二步迭代法计算截矩和斜率的数值;采用数值微分法计算截矩和斜率的标准不确定度。分析函数和校准函数都可以用于加权双变量最小二乘法线性拟合,对于被测样品浓度及其不确定度的计算,采用这两种函数所获得的结果是相同的,但是在计算不确定度时,采用分析函数更为简便。

       

      Abstract: Various calibration methods such as single-point, double-point, and linear can be used in gas composition measurements, and linear calibration can be divided into various subdivision methods such as ordinary linear least squares and weighted bivariate least squares linear fitting. In this paper, the above two methods introduced in different literatures are compared and analyzed, and the matters that should be noted in the weighted bivariate least squares linear fitting are introduced. When the uncertainty of the measured signal is already close to or even lower than the uncertainty level of the gas standard, it is more reasonable to use the weighted bivariate least squares linear fitting method to process the measurement results. When using the weighted bivariate least squares linear fit, the weights are the reciprocal of the squared standard uncertainty, and the values of the intercept and slope can be calculated using the two-step iterative method; the standard uncertainty of the intercept and slope is calculated using the numerical differentiation method. Both analytical and calibration functions can be used for weighted bivariate least squares linear fitting. For the calculation of the measured sample concentration and its uncertainty, the results obtained by using these two functions are the same, but it is easier to use the analytical function when calculating the uncertainty.

       

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