Quantitative Analysis of CO<sub>2</sub> Infrared Absorption Spectrum Based on Improved Particle Swarm Optimization-Back Propagation Neural Network

Xuyang Wu; Gangyun Guan; Zhiwei Liu; Bingjie Zhu; Zixun Geng; Chuantao Zheng; Guofeng Yan; Yu Zhang; Yiding Wang

doi:10.3788/AOS232020

Acta Optica Sinica, Volume. 44, Issue 11, 1130003(2024)

Quantitative Analysis of CO₂ Infrared Absorption Spectrum Based on Improved Particle Swarm Optimization-Back Propagation Neural Network

Xuyang Wu¹, Gangyun Guan¹, Zhiwei Liu², Bingjie Zhu¹, Zixun Geng¹, Chuantao Zheng^1、*, Guofeng Yan^2、**, Yu Zhang¹, and Yiding Wang¹

Author Affiliations

¹State Key Laboratory of Integrated Optoelectronics, College of Electronic Science and Engineering, Jilin University, Changchun 130012, Jilin, China

²Research Center for Optical Fiber Sensing, Zhejiang Laboratory, Hangzhou 311100, Zhejiang, China

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Figures & Tables(11)

Fig. 1. Structure diagram of IPSO-BPNN algorithm

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Fig. 2. Flow chart of IPSO-BPNN algorithm

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Fig. 3. Structure diagram of CO₂ sensing system based on optical frequency comb direct absorption spectrometry

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Fig. 4. Pretreatment process of spectra. (a) Absorption spectrum and background spectrum; (b) original absorbance spectrum and denoised absorbance spectrum; (c) denoised absorbance spectrum and fitting baseline; (d) baseline-corrected absorbance spectrum

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Fig. 5. Partial absorbance spectra before and after pretreatment. (a) Partial original absorbance spectra; (b) partial preprocessed absorbance spectra

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Fig. 6. Optimization processes of IPSO-BPNN and PSO-BPNN

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Fig. 7. Iteration diagram of MSEs of validation set for IPSO-BPNN, PSO-BPNN, and BPNN

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Fig. 8. Inversion results of each gas concentration inversion model. (a) Inversion results of IPSO-BPNN; (b) inversion results of PSO-BPNN; (c) inversion results of BPNN; (d) inversion results of SVM; (e) inversion results of ELM; (f) inversion results of MAE

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Table 1. Parameters of PSO algorithm and IPSO algorithm
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Table 1. Parameters of PSO algorithm and IPSO algorithm
Algorithm Parameter
PSO
$M = 10, t_{m a x} = 100, ω = 0.6,$
$c_{1} = 1.5, c_{2} = 1.5,$ $x_{m a x} = 1.5, v_{m a x} = 0.2$
IPSO
$M = 10, t_{m a x} = 100,$ $ω_{m a x} = 0.9, ω_{m i n} = 0.4,$
$c_{1 m a x} = 1.5, c_{1 m i n} = 0.8,$ $c_{2 m a x} = 2.5, c_{2 m i n} = 1.5,$
$x_{m a x} = 1.5, v_{1} = 0.2, v_{2} = 0.05$

Table 2. Experimental data set

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Table 2. Experimental data set

Data set	Training set	Validation set	Testing set
Concentration	2%, 4%, 6%, 8%, 10%, 14%, 16%, 20%, 22%, 26%, 28%	12%, 18%, 24%	3%, 5%, 7%, 9%, 11%, 13%, 15%, 17%, 19%, 21%, 23%, 25%, 27%, 29%
Sample number	55	15	14

Table 3. Inversion performance of each gas concentration inversion model

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Table 3. Inversion performance of each gas concentration inversion model

Evaluation indicator	Model
Evaluation indicator	IPSO-BPNN	PSO-BPNN	BPNN	SVM	ELM	MAE
MSE	0.00000195	0.00000525	0.0000841	0.00000516	0.0001426	0.0001862
MAPE	0.0112	0.0184	0.0219	0.0201	0.0304	0.0483
$R^{2}$	0.9997	0.9989	0.9987	0.9992	0.9921	0.9973
Running time /s	0.004634	0.004739	0.004572	0.001515	0.002242	0.000020

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Xuyang Wu, Gangyun Guan, Zhiwei Liu, Bingjie Zhu, Zixun Geng, Chuantao Zheng, Guofeng Yan, Yu Zhang, Yiding Wang. Quantitative Analysis of CO₂ Infrared Absorption Spectrum Based on Improved Particle Swarm Optimization-Back Propagation Neural Network[J]. Acta Optica Sinica, 2024, 44(11): 1130003

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