Curve Fitting of TDLAS Gas Concentration Calibration Based on Relative Error Least Square Method
CHEN Hao1, 2, JU Yu3, HAN Li1, CHANG Yang3
1. Institute of Electrical Engineering, Chinese Academy of Sciences, Beijing 100190, China
2. University of Chinese Academy of Sciences, Beijing 100049, China
3. Beijing Aerospace Yilian Science and Technology Development Company, Beijing 100176, China
Abstract：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 with 7 306.752 1 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 0.049 4 and the relative error standard deviation is 0.023 7. The fitting result is far better than the fitting result of the least square method. The reliability of the calibration algorithm of relative error least squares is verified. The measurement accuracy of the TDLAS gas sensor is improved.
Key words：TDLAS; Least squares method; Relative error; Calibration
陈 昊，鞠 昱，韩 立，常 洋. 相对误差最小二乘法的TDLAS气体浓度标定曲线拟合[J]. 光谱学与光谱分析, 2021, 41(05): 1580-1585.
CHEN Hao, JU Yu, HAN Li, CHANG Yang. Curve Fitting of TDLAS Gas Concentration Calibration Based on Relative Error Least Square Method. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2021, 41(05): 1580-1585.
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