基于自适应红外多波段联合光谱分析的高精度气体浓度反演研究

王冠程; 赵百轩; 郑凯丰; 陈宇鹏; 赵莹泽; 秦余欣; 王惟彪; 刘国豪; 盛开洋; 吕金光; 梁静秋

doi:10.37188/CO.2024-0071

基于自适应红外多波段联合光谱分析的高精度气体浓度反演研究

doi: 10.37188/CO.2024-0071

王冠程^{1, 2, 3, 4,},
赵百轩^{1, 3, 4},
郑凯丰^{1, 3, 4},
陈宇鹏^{1, 3, 4},
赵莹泽^{1, 3, 4},
秦余欣^{1, 3, 4},
王惟彪^{1, 3, 4},
刘国豪^{1, 2, 3, 4},
盛开洋^{1, 2, 3, 4},
吕金光^{1, 3, 4,},
梁静秋^{1, 3, 4,}

1.
中国科学院长春光学精密机械与物理研究所, 吉林长春 130033
2.
中国科学院大学, 北京 100049
3.
应用光学国家重点实验室, 吉林长春 130033
4.
光学系统先进制造重点实验室(中国科学院), 吉林长春, 130033

基金项目: 吉林省科技发展计划（No. 20230201049GX，No. 20230508137RC，No. 20230508141RC，No. 20240602066RC）；国家自然科学基金（No. 61627819，No. 62305339，No. 61727818，No. 61805239）；中国科学院青年创新促进会人才基金（No. 2018254）；国家重点研发计划（No. 2022YFB3604702）

详细信息

作者简介:
王冠程（1999—），男，吉林长春人，硕士研究生，2021年于长春理工大学获得学士学位，主要从事红外光谱分析方面的研究。E-mail：wangguancheng21@mails.ucas.ac.cn

吕金光（1984—），男，吉林蛟河人，博士，副研究员，博士生导师，中国科学院青年创新促进会会员，2008 年于吉林大学获得学士学位，2013年于中国科学院长春光学精密机械与物理研究所获得博士学位，主要从事相干光谱成像与光学信息处理方面的研究。E-mail：jinguanglv@163.com

梁静秋（1962—），女，吉林长春人，博士，研究员，博士生导师，2003年于中国科学院长春光学精密机械与物理研究所获得博士学位，主要从事微光机电系统及光通信、红外光谱技术及仪器、Micro LED芯片及应用等方面的研究。E-mail：liangjq@ciomp.ac.cn

中图分类号: TP394.1;TH691.9
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出版历程
- 收稿日期: 2024-04-15
- 录用日期: 2024-05-24
- 网络出版日期: 2024-06-15

Research on high-precision gas concentration inversion based on adaptive infrared multi-band joint spectral analysis

WANG Guan-cheng^{1, 2, 3, 4
,},
ZHAO Bai-xuan^{1, 3, 4},
ZHENG Kai-feng^{1, 3, 4},
CHEN Yu-peng^{1, 3, 4},
ZHAO Ying-ze^{1, 3, 4},
QIN Yu-xin^{1, 3, 4},
WANG Wei-biao^{1, 3, 4},
LIU Guo-hao^{1, 2, 3, 4},
SHENG Kai-yang^{1, 2, 3, 4},
LV Jin-guang^{1, 3, 4
,},
LIANG Jing-qiu^{1, 3, 4
,}

1.
Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun Jilin 130033, China
2.
University of Chinese Academy of Sciences, Beijing 100049, China
3.
State Key Laboratory of Applied Optics, Changchun, Jilin 130033, China
4.
Key Laboratory of Advanced Manufacturing for Optical Systems, Chinese Academy of Sciences, Changchun, Jilin 130033, China

Funds: Supported by Jilin Provincial Scientific and Technological Development Program (No. 20230201049GX, No. 20230508137RC, No. 20230508141RC, No. 20240602066RC); National Natural Science Foundation of China (No. 61627819, No. 62305339, No. 61727818, No. 61805239); Youth Innovation Promotion Association Foundation of the Chinese Academy of Sciences (No. 2018254); National Key R&D Program of China (No. 2022YFB3604702)

摘要

摘要:
目的
傅里叶变换光谱技术（FTS）是气体成分分析及浓度的精准测量的有效手段，但在分析过程中待测气体的饱和吸收与弱吸收使某些波段的透过率偏离稳定区间，导致光谱信噪比降低以及仪器的非线性响应，降低浓度反演精度。
方法
本文提出一种自适应多波段联合浓度反演算法，结合透过率稳定区间与谱宽阈值自适应选择待测气体的有效波段；采用非线性最小二乘拟合方法对各有效波段进行浓度反演并进行残差分析，获得各有效波段的浓度反演结果及其权重，通过加权平均实现待测气体浓度的精确定量分析。
结果
设计并进行了算法验证实验，结果表明，自适应多波段联合浓度反演算法的稳定系数达到了0.9976，相较于传统的单波段及多波段浓度反演算法，反演结果的均方根误差分别降低了64.44%、41.52%，平均相对误差分别降低了65.97%、46.72%，平均绝对误差分别降低了66.32%、47.74%，
结论
反演精度与稳定性得到了明显提升。
- 有效波段选择 /
- 残差分析 /
- 加权平均 /
- 自适应多波段联合浓度反演
Abstract:
Objective
Fourier transform spectroscopy (FTS) is an effective method for gas composition analysis and accurate measurement of concentration. However, in the process of analysis, the saturated absorption and weak absorption of the measured gas make the transmittance of some bands deviate from the stable range, which leads to the decrease of spectral signal-to-noise ratio and the nonlinear response of the instrument, and reduces the accuracy of concentration inversion.
Method
In this paper, an adaptive multi-band joint concentration inversion algorithm is proposed, which combines the transmittance stable range and the spectral width threshold to adaptively select the effective band of the measured gas. The nonlinear least squares fitting method is used to invert the concentration of each effective band and the residual analysis is carried out to obtain the concentration inversion results and their weights of each effective band. The accurate quantitative analysis of the measured gas is realized by weighted average.
Result
: The algorithm verification experiment is designed and carried out; the results show that the stability coefficient of the adaptive multi-band joint concentration inversion algorithm is 0.9976. Compared with the traditional single-band and multi-band concentration inversion algorithms, the root mean square error of the inversion results is reduced by 64.44% and 41.52%, the mean relative error is reduced by 65.97% and 46.72%, and the mean absolute error is reduced by 66.32% and 47.74% respectively,
Conclusion
the inversion accuracy and stability are significantly improved.
- effective band selection /
- residual analysis /
- weight average /
- adaptive multi-band joint concentration inversion

HTML全文

图 1 自适应多波段联合浓度反演算法流程图

Figure 1. Flow chart of adaptive multi-band joint concentration inversion algorithm

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图 2 实验原理图

Figure 2. Experimental schematic diagram

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图 3 实验装置图

Figure 3. Experimental device diagram

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图 4 (1)~(10)分别为10种浓度N₂O气体的实测透过率光谱与理论透过率光谱，其中a~b、c~d以及e~f为实测有效波段范围

Figure 4. (1) to (10) are the measured and theoretical transmittance spectra of 10 concentrations of N₂O gas, where a to b, c to d and e to f are the measured effective band ranges

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图 5 (1)2.8%浓度N₂O气体在有效波段2144~2176 cm⁻¹的光谱拟合结果及其残差分布(2)2.8%浓度N₂O气体在有效波段2519~2600 cm⁻¹的光谱拟合结果及其残差分布

Figure 5. (1) The spectral fitting results and residual distribution of N₂O gas with concentration of 2.8% in the effective band of 2144 to 2176 cm⁻¹. (2) The spectral fitting results and residual distribution of N₂O gas with concentration of 2.8% in the effective band of 2519 to 2600 cm⁻¹

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图 6 (1)4.4%浓度N₂O气体在有效波段2144~2176 cm⁻¹的光谱拟合结果及其残差分布(2)4.4%浓度N₂O气体在有效波段2430~2491 cm⁻¹的光谱拟合结果及其残差分布(3)4.4%浓度N₂O气体在有效波段2519~2600 cm⁻¹的光谱拟合结果及其残差分布

Figure 6. (1) The spectral fitting results and residual distribution of N₂O gas with concentration of 4.4% in the effective band of 2144 to 2176 cm⁻¹. (2) The spectral fitting results and residual distribution of N₂O gas with concentration of 4.4% in the effective band of 2430 to 2491 cm⁻¹. (3) The spectral fitting results and residual distribution of N₂O gas with concentration of 4.4% in the effective band of 2519 to 2600 cm⁻¹

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图 7 传统单波段与多波段以及自适应多波段联合的浓度反演结果相较于真实值的误差分布

Figure 7. The error distribution of the traditional single-band, multi-band, and adaptive multi-band joint concentration inversion results compared with the real values

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图 8 自适应多波段联合浓度反演结果的分布曲线

Figure 8. Distribution curve of adaptive multi-band joint concentration inversion results

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表 1 10种浓度N₂O气体的实测有效波段与理论有效波段及其误差分析

Table 1. The measured effective band and theoretical effective band of 10 concentrations of N₂O gas and their error analysis

浓度	实测有效波段( cm⁻¹)	理论有效波段( cm⁻¹)	误差
2.8%	2144~2176, 2519~2600	2141~2173, 2520~2600	≤4 cm⁻¹
3.0%	2144~2176, 2518~2600	2141~2173, 2520~2600	≤4 cm⁻¹
3.2%	2143~2176, 2518~2600	2141~2173, 2520~2600	≤4 cm⁻¹
3.4%	2144~2176, 2518~2600	2142~2174, 2520~2600	≤4 cm⁻¹
3.6%	2143~2176, 2519~2600	2142~2175, 2519~2600	≤4 cm⁻¹
3.8%	2144~2176, 2519~2600	2142~2174, 2519~2600	≤4 cm⁻¹
4.0%	2144~2176, 2519~2600	2144~2176, 2519~2600	≤4 cm⁻¹
4.2%	2144~2176, 2519~2600	2144~2176, 2519~2600	≤4 cm⁻¹
4.4%	2144~2176, 2430~2491, 2519~2600	2144~2176, 2430~2492, 2519~2600	≤4 cm⁻¹
4.6%	2144~2176, 2430~2491, 2519~2600	2144~2176, 2430~2492, 2519~2600	≤4 cm⁻¹

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表 2 传统单波段与多波段以及自适应多波段联合浓度反演结果

Table 2. Traditional single-band, multi-band, and adaptive multi-band joint concentration inversion results

真实值	传统单波段浓度反演结果C_n	传统多波段浓度反演结果`C	自适应多波段联合浓度反演结果
真实值	传统单波段浓度反演结果C_n	传统多波段浓度反演结果`C	H_n	Ĉ
2.8%	C₁=2.83% C₂=2.72%	2.775%	H₁=0.67 H₂=0.33	2.794%
3.0%	C₁=2.93% C₂=3.13%	3.030%	H₁=0.78 H₂=0.22	2.968%
3.2%	C₁=3.15% C₂=3.35%	3.250%	H₁=0.85 H₂=0.15	3.180%
3.4%	C₁=3.35% C₂=3.26%	3.305%	H₁=0.88 H₂=0.12	3.339%
3.6%	C₁=3.63% C₂=3.51%	3.570%	H₁=0.89 H₂=0.11	3.616%
3.8%	C₁=3.83% C₂=3.89%	3.860%	H₁=0.78 H₂=0.22	3.843%
4.0%	C₁=4.03% C₂=3.88%	3.955%	H₁=0.91 H₂=0.09	4.016%
4.2%	C₁=4.17% C₂=4.31%	4.240%	H₁=0.87 H₂=0.13	4.188%
4.4%	C₁=4.43% C₂=4.37% C₃=4.48%	4.427%	H₁=0.41 H₂=0.39 H₃=0.20	4.416%
4.6%	C₁=4.61% C₂=4.55% C₃=4.52%	4.560%	H₁=0.73 H₂=0.18 H₃=0.09	4.591%

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表 3 传统单波段与多波段浓度反演以及自适应多波段联合浓度反演算法评价结果

Table 3. The evaluation results of traditional single-band, multi-band, and adaptive multi-band joint concentration inversion algorithm

算法	S	R²	RMSE	MAE	MRE
传统单波段浓度反演	22	0.9820	0.0796	0.0686	0.0191
传统多波段联合浓度反演	10	0.9928	0.0484	0.0442	0.0122
自适应多波段联合浓度反演	10	0.9976	0.0283	0.0231	0.0065

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表 4 不同浓度N₂O的相关系数

Table 4. The correlation coefficients of different concentrations of N₂O

浓度	相关系数
2.0%	0.999177
2.2%	0.999622
2.4%	0.999286
2.6%	0.999139
4.8%	0.999201
5.0%	0.999148
5.2%	0.999172
5.4%	0.999379
5.6%	0.999485
5.8%	0.999521

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表 5 SO₂与CO的自适应多波段联合浓度反演算法评价结果

Table 5. The evaluation results of adaptive multi-band joint concentration inversion algorithm of CO and SO₂

气体	浓度\间隔	R²	RMSE	MAE	MRE
SO₂	1%~10%\1%	0.9652	0.0393	0.0237	0.0172
CO	0.1%~1%\0.1%	0.9943	0.0205	0.0147	0.0065

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