Research on high-precision gas concentration inversion based on adaptive infrared multi-band joint spectral analysis
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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。
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关键词:
- 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:ObjectiveFourier 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.
MethodIn 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,
Conclusionthe inversion accuracy and stability are significantly improved.
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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
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
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 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Cn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Hn Ĉ 2.8% C1=2.83%
C2=2.72%2.775% H1=0.67
H2=0.332.794% 3.0% C1=2.93%
C2=3.13%3.030% H1=0.78
H2=0.222.968% 3.2% C1=3.15%
C2=3.35%3.250% H1=0.85
H2=0.153.180% 3.4% C1=3.35%
C2=3.26%3.305% H1=0.88
H2=0.123.339% 3.6% C1=3.63%
C2=3.51%3.570% H1=0.89
H2=0.113.616% 3.8% C1=3.83%
C2=3.89%3.860% H1=0.78
H2=0.223.843% 4.0% C1=4.03%
C2=3.88%3.955% H1=0.91
H2=0.094.016% 4.2% C1=4.17%
C2=4.31%4.240% H1=0.87
H2=0.134.188% 4.4% C1=4.43%
C2=4.37%
C3=4.48%4.427% H1=0.41
H2=0.39
H3=0.204.416% 4.6% C1=4.61%
C2=4.55%
C3=4.52%4.560% H1=0.73
H2=0.18
H3=0.094.591% 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 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 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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