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

cstr: 32171.14.CO.2024-0071

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

1.
中国科学院长春光学精密机械与物理研究所应用光学国家重点实验室, 吉林长春 130033
2.
中国科学院大学, 北京 100049

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:
吕金光（1984—），男，吉林蛟河人，博士，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
- 修回日期: 2024-05-06
- 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

1.
State Key Laboratory of Applied Optics, Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China
2.
University of Chinese Academy of Sciences, Beijing 100049, 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)

More Information

Corresponding author: jinguanglv@163.com

摘要

摘要:
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及残差分析，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。设计并进行实验验证，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，与传统的单波段及多波段浓度反演算法相比，该反演结果的均方根误差分别降低了64.44%和41.52%，平均相对误差分别降低了65.97%和46.72%，平均绝对误差分别降低了66.32%和47.74%，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:
In this paper, we proposed an adaptive multi-band joint concentration inversion algorithm, 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 analyze the residual to obtain the concentration inversion results and their weights of each effective band. The accurate quantitative analysis of the concentration of the measured gas is realized by weighted averaging. The algorithm verification experiment is 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. It can be concluded that the inversion accuracy and stability are significantly improved.
- effective band selection /
- residual analysis /
- weight average /
- adaptive multi-band joint concentration inversion

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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 principal diagram

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图 3 实验装置图

Figure 3. Experimental device

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图 4 (a)~(j)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1~2、3~4以及5~6为实测有效波段范围

Figure 4. (a) to (j) are the measured and theoretical transmittance spectra of N₂O gas with different concentrations, where 1 to 2, 3 to 4 and 5 to 6 are the measured effective band ranges

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

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

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

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

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图 7 传统单波段与传统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, traditional 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 and theoretical effective bands of N₂O gas with 10 concentrations and their error analysis

浓度	实测有效波段( cm⁻¹)	理论有效波段( cm⁻¹)	区间误差
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 传统单波段与传统多波段以及自适应多波段联合浓度反演结果

Table 2. Inversion results of traditional single-band, traditional multi-band, and adaptive multi-band joint concentration methods

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$\bar{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$\bar{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 传统单波段与传统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, traditional multi-band, and adaptive multi-band joint concentration inversion algorithms

	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 N₂O with different concentrations

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 CO and SO₂ by adaptive multi-band joint concentration inversion algorithm

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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