Multiband infrared inversion for low-concentration methane monitoring in a confined dust-polluted atmosphere

Wenzheng Wang; Yanming Wang; Wujun Song; Xueqin Li

doi:10.1364/AO.56.002548

1. INTRODUCTION

Methane gas explosions usually accompanied with coal dust blast are the major hazards in the face area of most coal mines as well as other mines considering that in many cases miners did not have sufficient time to escape from high-temperature, toxic gas sites [1,2]. Previous studies have shown that, during the 2001–2010 period, there were 675 accidents caused by methane gas explosions. This accounted for 35.53% of all the 1900 major coal mine accidents. 6057 people died from methane gas explosions, accounting for 45% of all workplace related fatalities [3]. Thus, large numbers of research studies have been conducted to study the mechanism and strengthen the prevention of gas explosion in order to reduce the losses by accidents in underground mines [4]. The prerequisite for most gas explosions in underground mines is to develop explosive methane-air/methane-coal dust-air mixtures in the mine tunnel; and the explosion may happen when methane gas reaches its explosion limit under appropriate temperature and oxygen condition [5]. So, it is quite vital to conduct real-time and accurate monitoring of the methane concentration in the underground mine atmosphere, and actions should be taken when an increasing trend of methane concentration is detected.

Currently, the catalytic combustion methane sensor is widely used to monitor methane concentrations and can also be connected with the monitoring system. However, the catalytic element is greatly influenced by the highly dust-polluted and high-humidity underground environment and always needs to conduct zero point and sensitivity correction [6]. Meanwhile, the lower sensitivity of the reported catalytic combustion methane sensor limits its utility to monitor the lower concentration methane gas [7]. The optical-interference methane sensor is also adopted in underground mines to detect methane concentration because it is easy to operate, safe, and reliably used with adequate accuracy. However, the optical signal in this sensor is difficult to accurately convert to an electrical signal and cannot be connected with monitoring and control systems [8]. The variation of other gases besides methane in the underground mine atmosphere can also cause measurement error. Meanwhile, the underground atmosphere is heavily polluted by coal dust particles and filled with water-vapor [9,10] which has a strong disturbance on methane gas monitoring. The disturbance should be removed and eliminated when detecting methane concentrations in underground coal mines. A filtering device was adopted to remove coal dust particles and water-vapor when air was suctioned into the gas sensor, but the original atmosphere would be disturbed which may cause a certain error in the measured results. Thus, currently used devices and methods cannot achieve the real-time and accurate monitoring of methane gas in underground dust-polluted atmospheres.

On the other side, the explosion range for methane-air mixtures in underground atmospheres is 5.00%–16.00% based on the current literature. The maximum allowable methane concentration in the underground coal mine working face is 1% as required by coal mine safety regulation of China [11]. The detection of low-concentration methane gas and its increasing trend is of great significance. However, the currently used methane sensors cannot detect low concentrations accurately in underground dust-polluted atmospheres and may become invalid when the gas concentration is as low as 0.1%.

In this paper, an inverse method was proposed and studied to retrieve methane from optical transmittance signals in underground dust-polluted atmospheres. First, the spatial distribution and optical properties of mine dust particles and gases were measured and tested, respectively. The infrared spectral transmittance of the mixed atmosphere was obtained by the discrete ordinate method (DOM) combined with Mie scattering and the line by line model. Then, inverse calculation was conducted by the stochastic particle swarm optimization (SPSO) algorithm to retrieve methane from transmission spectra.

2. EXPERIMENTAL SETUP AND NUMERICAL SIMULATION CODE

A. Experimental Setup and Measurement

This study was conducted in the Huangbaici coal mine in the Wuda Coal District of the Inner Mongolia Autonomous Region, northwest China. According to previous research, toxic gases, especially methane which is released from coal seams (not shown in Fig. 1 for clarity), and mine goaf always accumulate on the upper corner of the air-return tunnel [12,13]. Meanwhile, coal dust particles are continuously generated from the mining face and dispersed downwards with the flow of ventilation air. Six sampling points were set up in the air-return tunnel from mine goaf with an interval of 2 m to measure the spatial distribution of coal dust particles, as depicted in Fig. 1.

Fig. 1. Schematic of the underground mining area and sampling points.

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According to the GB5748-85 (determination method of dust in the air of the workplace) jointly issued by the Ministry of Health and Ministry of Labor and Personnel of China [14], the dust filter measurement method is adopted in our study to sample and measure the concentration of coal dust. The particle size distribution of coal dust was determined by a particle size analyzer (Bettersize 2000), as shown in Table 1.

Table 1. Spatial Distribution of Coal Dust

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In order to validate the obtained particle size scale and study the microstructure of coal particles, the SEM experiment was conducted on the sampled coal dust under high vacuum and a nonconductive mode as presented in Fig. 2.

Fig. 2. SEM image of coal dust particles: (a) $scale = 20 μm$ and (b) $scale = 50 μm$ .

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The complex refractive index of coal dust is a prerequisite in this study for calculating the radiative heat transfer properties of underground dust-polluted atmospheres. The FT-IR test and the Kramers–Kronig (K–K) relation were both performed to obtain the complex refractive index of coal dust [15,16]. The FT-IR test was conducted by the Bruker Vertex 80v in the Advanced Analysis & Computation Center of China, University of Mining and Technology. Bruker Vertex 80v is an evacuated optics bench that can eliminate atmospheric moisture absorption and prevent external signal disturbance by Bruker Optics DigiTect technology. KBr powder is also dried before making the KBr matrix to remove moisture [17]. According to the requirement of sample preparation for the FT-IR test [18], the sampled coal dust particles were first pulverized to less than 200 mesh (74 μm) and dried at 105°C for 4 h. Then, coal dust particles were suspended and pressed in a dried KBr matrix with the thickness of 1 mm and the proportion of 1:100 under the pressure of 10 $t / {cm}^{2}$ for 3 min. The well prepared KBr matrix was subsequently measured according to its spectral transmittance within $400 - 4000 {cm}^{- 1}$ , as shown in Fig. 3.

Fig. 3. Spectral transmittance of coal dust particles from FT-IR test.

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Based on the spectral transmittance of coal particles, the K–K relation was adopted to retrieve the complex refractive index of coal particles, as shown in Fig. 4.

Fig. 4. Complex refractive index of coal particles.

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Normally, the gas component in underground atmosphere is stable when there are no disasters in coal seams including coal-mine fires and gas outbursts. The conventional gases and their proportion of fresh air are listed in Table 2. Then, 1% methane is added by us to set the comparison group, namely, contaminated air. The proportion of contaminated air would decrease correspondingly in Table 2.

Table 2. Conventional Gas Composition in Underground Atmosphere

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When there is methane gas released from coal seams, the gas component and its proportion change correspondingly. In our study, different methane gas concentrations were set up for further analysis.

B. Simulation Code

Based on the spatial distribution of dust particles and gases in underground mine atmospheres, the Mie scattering method was used to calculate the attenuation coefficient of dust particles at each sampling point, and the line-by-line method was adopted to calculate the absorption coefficient of mine gases [19–22]. Among the various numerical solution methods [23–25], the radiative transfer equation was solved in one dimension by the discrete ordinate method (DOM) to obtain the transmission properties of the confined dust-polluted atmosphere [26]. The calculation code and procedure have been reported in our previous research.

For the present work, the inverse simulation could be regarded as solving a problem of fitness minimization where the fitness or objective function could be written as

f (c, ρ, α, β) = \frac{1}{N} \sqrt{\sum_{i = 1}^{N} {(\frac{τ - \bar{τ}}{τ})}^{2}},

where

c

and

ρ

are the equivalent concentrations of methane and dust, respectively,

α

and

β

are the equivalent dispersed parameters of particles,

τ

and

\bar{τ}

are the measured and simulated spectral transmittance, and

N

is the total number of detecting wavebands.

Among the various inverse methods, the particle swarm optimization (PSO) algorithm is able to find a global optimum solution or a good approximation of the solution, usually without a theoretical proof which has been widely used in inverse calculation problems [27]. Application of the PSO algorithm in underground coal mines to solve the inverse problem was also reported in the past few years [28]. So, we also adopted the PSO algorithm to retrieve the concentration of methane and coal dust according to the obtained transmittance signal. To avoid premature convergence, an extra particle is generated randomly in the search domain at any iteration step, thus improving the global searching ability [29]. The improved PSO algorithm is called a stochastic particle swarm optimization (SPSO) algorithm which has been used and reported in our previous study [30]. The implementation of the inversion approach for gas/solid distribution can be carried out according to the following procedures.

Step 1. Input system configuration, control parameters, and initialize the particle swarm with stochastic gas/solid parameters of every particle.

Step 2. For each particle, carry out the forward simulation of transmittance with the given variables. Then, calculate the objective function or fitness for each particle, considering all the selected wavebands.

Step 3. Compare all the fitness in the same generation with a priori best values and choose the minimized one as the current global best particle and record the corresponding position and particle variables.

Step 4. Introduce a randomly selected particle into the particle population, and update the position for each particle.

Step 5. Check the stop criterion of maximum iterations or simulation convergence, then terminate the process or loop to Step 2.

3. RESULTS

A. Forward Calculation

In this study, coal dust particles and conventional gas were considered as optical background, methane gas is target gas which needs to be monitored. Following the procedure described in Section 2.B, the spectral transmittances of the atmosphere with methane (1% concentration) and without methane were calculated separately as depicted in Fig. 5.

Fig. 5. Spectral transmittance of confined atmosphere with/without methane gas.

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Methane gas only has an absorption effect at certain bands which causes the spectral transmittances of dust-polluted atmospheres with/without methane gas to be the same at most bands. In order to clearly illustrate the absorption band of methane gas in dust-polluted atmospheres, the spectral transmittance of atmosphere with 1% methane is shifted downwards by 0.05, as seen in the right Y axis of Fig. 5. Obviously, there are two methane absorption bands within $400 - 4000 {cm}^{- 1}$ compared with the optical background (coal dust and conventional gas). The two bands including ( $1225 - 1335 {cm}^{- 1}$ ) and ( $2850 - 3150 {cm}^{- 1}$ ) were selected and enlarged for further analysis as follows.

Figure 6 shows that methane gas has a strong absorption effect at 1255, 1275, 1305, 3015, and $3095 {cm}^{- 1}$ . Meanwhile, conventional gases (including $N_{2}$ , $O_{2}$ , ${CO}_{2}$ , and $H_{2} O$ ) have no absorption effect within the two selected wavebands [( $1225 - 1335 {cm}^{- 1}$ ) and ( $2850 - 3150 {cm}^{- 1}$ )]. These spectral transmittances are the combined attenuation of dust particles and absorption of methane. There are four parameters influencing the spectral transmittance including gas concentration, dust concentration, and particle-size distribution (two control parameters). So, four independent spectral bands at $1275 \pm 10$ , $1305 \pm 10$ , $3015 \pm 10$ , and $3095 \pm 10 {cm}^{- 1}$ were selected to conduct inverse calculation to retrieve the methane concentration.

Fig. 6. Selection of spectral bands for inverse calculation.

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B. Inverse Calculation

Based on the four independent spectral transmittances, the SPSO algorithm was used in this study to retrieve the gas concentration in underground atmosphere. In the SPSO algorithm, the number of random search particles is set to be 20; the number of optimal variables is four; the maximum number of iteration and convergence residuals are set to be 1000 and $1.0 E - 3$ , respectively. Inversed process and results are listed in Fig. 7 and Table 3 as follows.

Table 3. Inversed Result of Methane Concentration and Coal Dust Parameters

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Fig. 7. Convergence process of the inversed calculation.

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As presented in Fig. 7, the residuals of the three calculations drop sharply and stabilize when the interaction is beyond 50. Meanwhile, the stabilized residual of the three calculations are almost the same. Thus, this inverse calculation method is robust which can be used in this study to retrieve methane concentrations. The relative error of inversed results can be obtained as follows:

δ = \frac{| c - \bar{c} |}{c} \times 100,

where

c

is the true gas concentration in our forward calculation, and

\bar{c}

is the inversed methane concentration.

The molecular diffusion coefficient of methane gas is $2.0 E - 5 m^{2} / s$ whose diffusion velocity is about 1.5 times that of air [31]. Meanwhile, the wind speed in a mining face is approximately 2.5 m/s which would also accelerate the diffusion of methane gas. So, the methane gas in underground coal mine atmospheres is well mixed with the air. Thus, our inversion calculation is meaningful, and the retrieved results can be found in Table 3.

Considering that the lower explosion limit for an methane-air mixture is 5%, different gas concentrations from 0.01% to 5.0% were used to calculate and validate our inverse calculation method. The inversed methane concentration is in good agreement with the true value in our forward calculation. Almost all the relative errors are within 10% except when gas concentration is as low as 0.01%. Also, an obvious downward variation trend of relative error can be observed with the increase in gas concentration, this is to say, this inverse calculation performs much better for retrieving higher gas concentrations. The integral area of coal dust concentration in forward calculation is 2206.346, and the corresponding average integral dust concentration is $220.6 mg / m^{3}$ as shown in Fig. 8. The inversed dust concentration in Table 3 remains stable at approximately $210 mg / m^{3}$ which is consistent with the coal dust in our forward calculation.

Fig. 8. Coal dust concentration distribution in forward calculation and its area integral.

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Fig. 9. Variation range of inversed gas concentration.

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During the diffusion process of coal particles with the flow of mine air, the coal particles would gradually fall under the effect of gravity. When the dropping particles reach the ground, some particles would rebound to the mine atmosphere again. Thus, the dust concentration increases slightly between 8 and 10 m, as seen in Fig. 8.

This inverse calculation has a different performance when retrieving different methane concentrations. Therefore, further analysis was conducted to investigate the exact variation range. Ten optimized calculations (each with 1000 calculation interactions and convergence residual of $1.0 E - 3$ ) were conducted to obtain the variation range for each gas concentration.

As can be seen in Fig. 9, the maximum variation of methane concentration at 0.01% can reach 20% and $- 28 %$ , respectively, which indicates the inversed value is very unstable and of high uncertainty. With the increase of gas concentration, the variation range gradually stabilizes within $\pm 5 %$ and even $\pm 1 %$ when the gas concentration is up to 0.6%. The inversed value is stable and of high credibility when the gas concentration is up to 0.1%.

Meanwhile, the accuracy of our multiband infrared diagnostic (MBID) method for methane monitoring was compared with that of the catalytic combustion method which is widely used in underground coal mine evaluations for methane monitoring as in Table 4. The absolute error of our inverse method is almost two orders of magnitude lower than the absolute error of the catalytic combustion method (take KG9001B as a representative) which is provided by its qualification [6]. Our MBID method can yield a better monitoring result compared with the current device.

Table 4. Comparison of Accuracy between MBID Method and Catalytic Combustion Method

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In summary, our MBID method can retrieve target methane concentrations from transmission signals with all the relative errors within 10% when the gas concentration is beyond 0.05%. Meanwhile, the inversed result is very stable. The relative error is decreased to 5% when the methane concentration rises to 0.5%. The methane hazards can be ignored when its concentration is as low as 0.05% or lower because its explosion risk would be greatly reduced. So, this MBID method is robust and effective for methane gas monitoring in underground dust-polluted atmospheres.

4. DISCUSSION

The presented MBID method in Section 3 has been proved to be robust and effective for retrieving gas concentrations based on the four selected spectral signals. The number of spectral signals is a vital factor which influences the performance of the inverse calculation. Meanwhile, there would be a variation of the optical background and random disturbance when receiving these optical signals. Thus, the influence of these factors was further studied and discussed in this section.

A. Determination of the Optimized Number of Spectral Bands

Four spectral bands selected in this study [Type (a) in Table 5] have been validated to be effective for retrieving methane concentrations. Considering the demand of real-time monitoring, if we can reduce the number of uploaded signals, the reaction time of our method would also be greatly reduced. Reaction time is defined as the interval of time between the reception of the transmittance signal and the initiation of giving methane concentrations. We tried to change some spectral bands and reduced the number of uploaded signals to study their inverse calculation performance.

Table 5. Four Types of Combination of Spectral Bands

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Thus, another two spectral bands at $1115 \pm 10$ and $2505 \pm 10 {cm}^{- 1}$ which are only influenced by dust particles in underground atmospheres were added and mixed in the next three types to investigate their corresponding inverse calculation performance. The detailed combinations of these spectral bands are listed in Table 5.

The optical transmittances under these four combined types were uploaded into our inverse calculation, respectively, to retrieve methane concentrations. The relative error of the inversed results of the four types in Table 4 is depicted in Fig. 10.

Fig. 10. Relative error of inversed result with different spectral band combination.

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The relative error of the three added types [Types (b)–(d)] is very high which is far beyond 10% at low methane concentrations. Only when the gas concentration is up to 2%, can the relative error of the three added types be reduced to an acceptable value (lower than 5%). In contrast, Type (a) used in this study performed very well considering its low relative error of inversed results. So, by reducing the number of uploaded spectral bands or changing spectral bands to reduce reaction time is impractical. Also, by adding uploaded spectral signals can also yield a good inversed result but would significantly increase the reaction time which is contrary to our real-time monitoring demand. All in all, the four selected spectral bands including $1275 \pm 10$ , $1305 \pm 10$ , $3015 \pm 10$ , and $3095 \pm 10 {cm}^{- 1}$ in Type (a) comprise the best spectral combination for the inverse calculation in this study.

B. Influence of Optical Background

The strong optical background in underground dust-polluted atmospheres which is mainly caused by the attenuation of dust particles has an obvious influence on the accuracy of inversed results. Thus, validations with a methane concentration of 1%, at different dust concentrations and detection distances in forward calculation were conducted to investigate their influence on inversed results. The inversed results were compared with our given methane concentration to obtain the inversed relative error as depicted in Fig. 11.

Fig. 11. Influence of (a) dust concentration and (b) detection distance on inversed result.

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Figure 11(a) shows that the relative error of inversed results rises approximately linearly with the increase of dust concentration. We can also observe even when the dust concentration is up to $500 mg / m^{3}$ which can be considered as the upper limit for dust pollution in air-return tunnels, the inversed relative error is still within 2.5%. That is to say, considering the level of coal dust pollution in air-return tunnels, our MBID method is still effective in identifying methane gas and limitedly influenced by the variation of dust concentrations.

The impact of detection distance was proved to be more sensitive as shown in Fig. 11(b). A nearly exponential growth of relative error can be observed with the increase of detection distance. Especially when the detection distance is up to 60 m and 100 m, the relative error goes dramatically up to 4% and 11%, respectively. In this case, our MBID method is invalid. Thus, the detection distance should be less than 50 m to keep the inversed relative error within 5% at 1% methane concentration when applied in similar circumstances.

C. Robustness of MBID Method under Transmission Signal Errors

The underground coal mine is an extreme environment where dust particles are continuously generated, and various toxic gases (including ${CH}_{4}$ and CO) are released from coal seam/mine goaf [32]. Considering the transmission signal error generated due to the complicated conditions, such as ventilation disturbance and turbulence, different random error $γ$ of 1%, 2%, and 5% with normal distribution were added on the original spectral transmittance. The disturbed spectral transmittance was further uploaded into our inverse calculation for further analysis to investigate the robustness of our MBID method. Three optimized calculations were carried out for each gas concentration and disturbance. The average value of inversed gas concentration and its deviation are given in Table 6.

Table 6. Inverse Calculation Performance When Different Transmission Signal Errors Added

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Table 6 indicates that the average inversed results under different signal errors are consistent with the gas concentrations set up in our forward calculation. The absolute deviation of inversed values almost remains constant under a different intensity of signal errors. However, as seen in the variation of the maximum relative error, the influence of signal error was significantly weakened with the increase of methane concentrations. This is because the absorption effect of methane gas would be greatly strengthened with the increase of its concentration; in this case, the effect of signal error would be weakened correspondingly. Thus, the disturbance on the transmission signal does have some influence on our inverse calculation, but such influence is greatly weakened with the increase of gas concentration. The presented MBID method is still robust under transmission signal errors.

5. CONCLUSION

In this study, a MBID method was presented and validated for retrieving methane concentrations in underground dust-polluted atmospheres. Coal dust particles generated during mechanized mining were sampled, and their attenuation properties on spectral signals were calculated based on the Mie scattering method. The absorption of methane and conventional gases in coal mine environments was obtained by line-by-line calculation. The radiative transfer equation was solved by the DOM method to simulate the spectral transmittance through the confined dust-polluted atmosphere. According to the transmission spectrum, four independent infrared wavebands were selected to conduct the inverse calculation by the SPSO algorithm for retrieving methane concentrations.

Several interesting results were obtained through further analysis as follows: (a) the inverse calculation method is robust and effective in this study, and the inversed methane concentration by the SPSO algorithm is in good agreement with the true concentration in the forward calculation. (b) The four spectral bands including $1275 \pm 10$ , $1305 \pm 10$ , $3015 \pm 10$ , and $3095 \pm 10 {cm}^{- 1}$ selected in this study comprise the best spectral combination for the inverse calculation in this study. Reducing the number of uploaded spectral signals or changing the spectral band to reduce reaction time is impractical considering the demand for accurate real-time monitoring of methane gas. (c) The optical background has an obvious influence on inversed results. The variation of dust concentration has a limited effect on inversed results, but the detection distance should be given special attention because the relative error of inversed results would rise sharply when the detection distance is over 60 m in this study. (d) Considering the random disturbance on received transmission signals, the MBID method is still robust and effective in detecting methane gas. Meanwhile, the influence of transmission signal error would be weakened with the increase of methane concentration.

Funding

Fundamental Research Funds for the Central Universities (2014QNB02); National Natural Science Foundation of China (NSFC) (51676206); A project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.

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		Particle Size Distribution (%)
Distance (m)	Dust Concentration ( $mg / m^{3}$ )	$\sim 2 μm$	2–5 μm	5–10 μm	$> 10 μm$
0.1	281.16	17.56	23.44	28.37	30.63
2.0	265.32	21.85	23.34	25.94	28.87
4.0	228.09	24.74	22.65	21.15	31.46
6.0	215.64	20.76	23.67	28.8	26.77
8.0	177.91	29.55	21.13	25.48	23.84
10.0	178.59	35.20	26.97	28.19	9.64

Typical condition	$N_{2}$ (%)	$O_{2}$ (%)	${CO}_{2}$ (%)	$H_{2} O$ (%)	${CH}_{4}$ (%)	Others (%)
Fresh air	76.653	20.599	0.040	2.705	0	0.003
Contaminated air	75.399	19.992	0.039	3.567	1	0.003

Gas Concentration (%)
True Value	Inversed Value	Relative Error (%)	Inversed Coal Dust Concentration ( $mg / m^{3}$ )
0.01	0.0116	16.00	212.41
0.05	0.0487	2.60	202.05
0.1	0.0923	7.70	211.02
0.2	0.1864	6.80	208.99
0.4	0.3858	3.55	206.34
0.6	0.5824	2.93	209.71
0.8	0.7880	1.50	211.91
1.0	0.9907	0.93	210.82
2.0	2.0205	1.03	208.05
3.0	3.0301	1.00	208.32
4.0	4.0200	0.50	208.40
5.0	4.9827	0.35	206.71

MBID Method			Catalytic Combustion Method
	Absolute Error (%)
True Gas Concentration (%)	Positive	Negative	True Gas Concentration (%)	Absolute Error (%)
0.01	0.002 ${CH}_{4}$	$- 0.003 {CH}_{4}$	0–1	$\pm 0.10 {CH}_{4}$
0.1	0.004 ${CH}_{4}$	$- 0.004 {CH}_{4}$
0.2	0.005 ${CH}_{4}$	$- 0.004 {CH}_{4}$
0.6	0.004 ${CH}_{4}$	$- 0.006 {CH}_{4}$
1.0	0.004 ${CH}_{4}$	$- 0.004 {CH}_{4}$	1–2	$\pm 0.20 {CH}_{4}$
3.0	0.002 ${CH}_{4}$	$- 0.003 {CH}_{4}$	2–4	$\pm 0.30 {CH}_{4}$
5.0	0.017 ${CH}_{4}$	$- 0.012 {CH}_{4}$	4–40	$\pm 0.80 {CH}_{4}$

Type	Number of Selected Bands	Wave Number ( ${cm}^{- 1}$ )	Comment
(a)	4	$1275 \pm 10$	Influenced by both gas and dust
		$1305 \pm 10$	Influenced by both gas and dust
		$3015 \pm 10$	Influenced by both gas and dust
		$3095 \pm 10$	Influenced by both gas and dust
(b)	4	$1115 \pm 10$	Influenced by dust
		$1305 \pm 10$	Influenced by both gas and dust
		$2505 \pm 10$	Influenced by dust
		$3095 \pm 10$	Influenced by both gas and dust
(c)	3	$1305 \pm 10$	Influenced by both gas and dust
		$3015 \pm 10$	Influenced by both gas and dust
		$3095 \pm 10$	Influenced by both gas and dust
(d)	3	$1115 \pm 10$	Influenced by dust
		$1305 \pm 10$	Influenced by both gas and dust
		$3095 \pm 10$	Influenced by both gas and dust

Multiband infrared inversion for low-concentration methane monitoring in a confined dust-polluted atmosphere

Abstract

1. INTRODUCTION

2. EXPERIMENTAL SETUP AND NUMERICAL SIMULATION CODE

A. Experimental Setup and Measurement

B. Simulation Code

3. RESULTS

A. Forward Calculation

B. Inverse Calculation

4. DISCUSSION

A. Determination of the Optimized Number of Spectral Bands

B. Influence of Optical Background

C. Robustness of MBID Method under Transmission Signal Errors

5. CONCLUSION

Funding

REFERENCES

Cited By

Figures (11)

Tables (6)

Equations (2)

Applied Optics

	Inversed Gas Concentration with Deviation and Its Maximum Relative Error (%)
Gas Concentration (%)	$γ = 1 %$	Maximum Relative Error (%)	$γ = 2 %$	Maximum Relative Error (%)	$γ = 5 %$	Maximum Relative Error (%)
0.1	$0.1 \pm 0.05$	50	$0.1 \pm 0.07$	70	$0.1 \pm 0.06$	60
0.5	$0.5 \pm 0.05$	10	$0.5 \pm 0.06$	12	$0.5 \pm 0.04$	8
1.0	$1.0 \pm 0.06$	6	$1.0 \pm 0.08$	8	$1.0 \pm 0.05$	5
2.0	$2.0 \pm 0.09$	4.5	$2.0 \pm 0.11$	5.5	$2.0 \pm 0.07$	3.5
5.0	$5.0 \pm 0.03$	0.6	$5.0 \pm 0.01$	0.2	$5.0 \pm 0.01$	0.2