相对误差最小二乘法的TDLAS气体浓度标定曲线拟合

可调谐半导体激光光谱技术（TDLAS）是光谱检测技术的一个分支，具有高灵敏度、高分辨率、实时监测、便携性好、小型化等优点，在工业环保、医疗检测、气象监测等领域得到了广泛应用。TDLAS气体传感器的测量精度与标定曲线密切相关，标定时，常用最小二乘法对标定曲线进行多项式拟合，但最小二乘法是以绝对误差的最小平方和作为评价标准，无法对相对误差进行约束，在低浓度量程下TDLAS气体传感器的标定曲线相对误差偏大，限制了标定量程。推导了光强透射率对数与气体浓度关系式作为目标函数，提出了基于相对误差意义下的最小二乘法，迭代方法采用高斯-牛顿迭代法（Gauss-Newton iteration method），实验以雅士林DHS-100恒温恒湿箱来产生大量程范围的水汽标定浓度，Vaisala HMT337在线湿度检测仪的测量值作为标定浓度，自主研发的TDLAS湿度传感器选择波数为7 306.752 1 cm-1的水汽吸收峰，气室的光路长为50 mm，对1%~50%VOL的水汽浓度进行了拟合标定，对比了最小二乘法与相对误差最小二乘法的标定拟合结果。实验结果表明：采用最小二乘法拟合时，在低浓度量程下会出现较大的相对误差，高浓度量程下相对误差逐渐减小，无法保证整个大量程下测量精度要求；采用相对误差最小二乘法拟合时，在整个大量程范围下的相对误差波动比较小，相对误差分布曲线比较平稳，最大相对误差和相对误差标准差都远小于最小二乘法的拟合结果；以Ratio-C关系式作为目标函数，采用相对误差最小二乘法进行拟合标定时，最大相对误差为0.049 4，相对误差标准差为0.023 7，远优于最小二乘法的拟合结果，符合TDLAS传感器测量精度要求，验证了相对误差最小二乘法的标定算法可靠性，提高了TDLAS气体传感器的测量精度。

Curve Fitting of TDLAS Gas Concentration Calibration Based on Relative Error Least Square Method

Tunable diode laser absorption spectroscopy(TDLAS)is a branch of spectrum detection technology with high sensitivity,high resolution,real-time monitoring,good portability and miniaturization.It has been widely used in environmental protection,medical treatment,meteorology and other fields.The accuracy of the TDLAS gas sensor is closely related to the calibration curve.The least square method is utilized to perform polynomial fitting on the calibration curve.However the least square method is based on the least square sum of absolute errors as the evaluation criterion.It cannot restrict the relative error.As a result,the relative error of the calibration curve of the TDLAS gas sensor at low concentration ranges is too large.This paper proposes the least square method based on relative error.The relationship between the logarithm of light intensity transmittance and gas concentration is derived as the objective function.The iteration method uses the Gauss-Newton iteration method(Gauss-Newton iteration method).In the experiment Yashilin DHS-100 constant temperature and humidity box were used to generate a large range of water vapor calibration concentrations.Vaisala HMT337 online humidity detector’s value was used as the calibration concentration.Self-developed TDLAS humidity sensor selects the water vapor absorption peak with7306.7521 cm^-1.The optical path of the air chamber is 50 mm.The water vapor concentration of 1%~50%VOL is calibrated.The calibration results of the least square method and least square method based on relative error are compared.The experimental results show that when using the least square method for curve fitting,the calibration curve will have a large relative error in the low concentration range.In the high concentration range the relative error gradually decreases.This cannot guarantee the measurement accuracy requirements for the entire large range.When using the relative error least square method for curve fitting,the relative error curve is relatively stable in the whole range.The maximum relative error and the relative error standard deviation are much lower than the fitting result of the least square method.When the relative error least squares method is used and the Ratio-C formula is used as the objective function for fitting,the maximum relative error is 0.0494 and the relative error standard deviation is 0.0237.The fitting result is far better than the fitting result of the least square method.Thereliability of the calibration algorithm of relative error least squares is verified.The measurement accuracy of the TDLAS gas sensor is improved.