基于K-MLE的宽浓度范围气体吸收光谱反演方法研究

doi:10.3964/j.issn.1000-0593(2025)09-2475-09

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摘要：基于朗伯-比尔定律的气体吸收光谱技术被广泛运用于各类污染气体的排放检测研究中，然而在进行高浓度气体测量时，由于设备局限性、气体饱和吸收等因素影响，光谱吸光度与浓度间出现的非线性偏移将使待测气体浓度的测量结果出现严重偏差。利用待测光谱与标准光谱间的线性信号相关性反映两者浓度间的关系，提出对差分光密度谱间线性相关系数K值进行极大似然估计(K-MLE)来实现宽浓度范围内的气体浓度反演。基于移动区间法计算了气体吸收波段内不同波长处、不同区间大小内的线性相关系数，对相关系数集合进行区间估计后分段构建似然函数并求解最佳系数估计值，能够有效避免因信号扰动等问题引起的测量结果波动，最终结合浓度阈值与补偿方程实现宽范围内浓度反演。以对二氧化硫(SO₂)气体的浓度检测为例，对不同浓度气体样品获得的30组光谱信号数据进行处理，用30组浓度均值的相对误差表征反演方法的准确性，用浓度测量值的标准差衡量反演方法的稳定性。在相同的低浓度条件下，宽带法、窄带法和K-MLE法计算得出的反演浓度均值误差分别为6.14%、22.13%和0.11%，在保证结果较好稳定性的前提下，K-MLE法实现了最佳测量精度；在0~508 μL·L^-1的宽浓度范围内，K-MLE法浓度反演结果最大均值误差为0.98%，最大标准差为1.25，反演效果明显优于其他两种经典方法。结果表明，K-MLE法提供了一种有效的非线性偏移补偿方法，能够准确且稳定地实现宽浓度范围内的气体浓度反演。

关键词：信号相关分析；极大似然估计；宽浓度范围；浓度反演方法

Abstract：The gas absorption spectroscopy technique, based on the Lambert-Beer Law, is extensively employed for the detection of various pollutant gases. However, challenges arise due to the limitations of devices, the saturation absorption of gases, and other interfering factors. When measuring gases at high concentrations, these issues create a nonlinear relationship between absorbance and concentration, resulting in significant deviations in gas detection across a wide concentration range.In this paper, we leverage the linear signal correlation between the measured spectra and reference spectra to reflect the relationship between the concentrations of the two. We propose employing Maximum Likelihood Estimation (MLE) to determine the linear correlation coefficient K between spectra signals, facilitating the inversion of gas concentrationsover a wide concentration range.To determine the linear correlation coefficients across variable spectral intervals in the gas absorption band, we implement a moving internal algorithm with adjustable parameters. The interval-wise statistical inference is carried out on the set of correlation coefficients, and optimal parameter estimators, K-values, are derived by constructing a piecewise likelihood function. This approach effectively mitigates fluctuations in measurement results caused by signal perturbation.Ultimately, gas concentration inversion across a wide concentration range is achieved through a combination of concentration threshold and compensation equation. Using sulfur dioxide (SO₂) gas concentration detection as a case study, we process thirty sets of spectral datasets acquired under each predetermined concentration condition. The accuracy of the concentration inversion methodologywas quantified through the relative error of the mean concentrations calculated from thirty replicate measurements. At the same time,its stability wasevaluatedusing the standard deviation of the concentration values. Under identical low-concentration conditions, the broadband method, narrowband method, and K-MLE algorithm demonstrated mean retrieved concentration errors of 6.14%, 22.13%, and 0.11% respectively. Under the premise of ensuring the stability of the results, the K-MLE algorithm achieved superior measurement accuracy. Furthermore, across a wide concentration range of 0~508 μL·L^-1, the maximum mean error for concentration inversion of the K-MLE method is only 0.98%, with a maximum standard deviation of 1.25, outperforming the other two conventional methods. The results demonstrate that the K-MLE method offers an effective approach for nonlinear offset compensation, enabling accurate and stable gas concentration inversion across a wide range of concentrations.

Key words：Signal correlation analysis; Maximum likelihood estimation; Wide concentration range; Concentration inversion methodology

收稿日期: 2024-10-21 修订日期: 2025-04-22

中图分类号:

O433.51

基金资助: 国家重点研发计划项目（2023YFC3705402），国家自然科学基金项目（62033012），中国科学院合肥研究院院长基金项目（YZJJ2024QN11）资助

通讯作者: 张玉钧 E-mail: yjzhang@aiofm.ac.cn

作者简介: 俞沁怡，2000年生，中国科学技术大学与中国科学院合肥物质科学研究院联合培养博士研究生 e-mail: qyyu@aiofm.ac.cn

引用本文:

俞沁怡，范博强，尤坤，何莹，张世奇，蔡傲雪，韩泠然，张玉钧. 基于K-MLE的宽浓度范围气体吸收光谱反演方法研究[J]. 光谱学与光谱分析, 2025, 45(09): 2475-2483.
YU Qin-yi, FAN Bo-qiang, YOU Kun, HE Ying, ZHANG Shi-qi, CAI Ao-xue, HAN Ling-ran, ZHANG Yu-jun. A Study of Gas Absorption Spectral Inversion Method Based on K-MLE With Wide Concentration Range. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2025, 45(09): 2475-2483.

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