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Abstract
Data analytic methods are required in detecting gas concentrations using spectroscopic techniques, especially for absorption spectra of mixed gases. However the common analytic methods, such as multivariate linear regression, principal component regression etc. are limited to deal with non-linear and uncorrelated variables. In the case of multi-component gases, these methods are able to meet expected accuracy and reliability. In this paper, a simple and effective method is proposed.This method is based on spectral cases of single-component gases, it determines the concentration of each component using linear superposition principle of the spectra in Beer’s law. The experimental results show that the detection error of this method is less than 1% in the known gas mixture case and 3% in the unknown gas mixture case.
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1. Introduction
Gas detection technology has many applications in mines, atmospheric monitoring, medical, food and aerospace [1,2]. This type of technology is in high demand and developed rapidly [3–1]. The concentration detection of a single gas is straight-forward. It can be detected based on specific gas sensor, or by the change in the light intensity at the characteristic wavelength of this gas. In real application environment, pure single gas rarely exists. Multiple gases mixture often coexist. Therefore with a single sensor it is difficult to determine the concentration of the gas [5,6]. In such case, multiple sensors are required to measure multiple signals. Analytical method is therefore applied to decide the concentration of each type of gas based on these measurements.
Currently, the quantitative analysis of multi-component gases is often performed by gas chromatogram [7] (GC) and Gas chromatography-mass spectrometry(GC-MS) methods [8], electrochemical detection [9], and absorbance spectroscopy [10]. GC and GC-MS methods are complex and time-consuming, and cannot meet the needs of real-time automated continuous monitoring. The electrochemical detection method uses a mixture of multiple sensors [11] to detect multiple gases separately and then perform the corresponding processing, such as artificial neural networks, to finally obtain the concentration of each component. However, the limitations of electrochemical detectors lead to their low sensitivity, accuracy and reliability. The spectral analysis technique represented by absorption spectroscopy has high sensitivity, accuracy and reliability [10].Its main implementation method is to emit light of a specific wavelength into the gas chamber filled with the measured gas and analyze its concentration by measuring the attenuation of the light using Beer’s law. This method is suitable for rapid on-site detection and real-time online analysis. The measurements with this method however need to be calibrated by multiple regression models based on chemometric methods, because of the multiple-component spectra cased by the band absorption. Commonly used calibration methods include multivariate linear regression [12] (MLR), principal component regression [13] (principal component regression, PCR), partial least square [14] (PLS), and artificial neural networks [15].
Among them, artificial neural networks require a large amount of data as a training set and cannot be applied on a large scale in practical measurements. Other methods are based on Beer's law, which holds that there is a linear relationship between gas concentration and absorbance. However, Beer’s law is a limiting law and a linear relationship between absorbance and concentration is only established for vanishing absorption [16,17]. At the same time, the nonlinearity of spectrometer response will also affect the measurement results. Therefore, these algorithms are difficult to achieve the required results when dealing with multicomponent gases.
In view of the above problems, this paper proposes a novel method to use the known spectral situation of single component gases to establish the nonlinear relationship between concentration and absorbance, and then use the principle of linear superposition of spectra in Lambert's law to solve the concentration of each component in the gas mixture by considering the absorption spectrum of the gas mixture, as a linear combination of absorption spectra of single gases. The experimental results show that the method has a high accuracy regarding the detection of gas components. It is important that the method can also decide whether a specific gas component exists in the gas mixture. This feature enables the possibility of blind detection of gas mixture.
2. Method of nonlinear analysis for multiple gas components detection
According to Lambert-Beer's law, the results of spectral measurement are shown in the following formula [8]:
Here A is the absorbance, ${I_0}$ is the initial intensity of the light, ${I_1}$ is the intensity after travelling the distance L in the gas and $\delta $ is the molar decadic absorption coefficient.C is the concentration of gas.
The application of Lambert-Beer law to the qualitative and quantitative analysis of absorption spectrum has certain applicable conditions, which requires that the light absorbing material is uniform and free of color difference. It is often difficult to meet in practical application, which will lead to the reflection and scattering of incident light in addition to being absorbed by light absorbing materials, resulting in the inconsistency between the ideal Lambert Beer law model and the reality [16,17].
Take any section perpendicular to the light transmission direction, assuming a minimum thickness DX in Fig. 1, and the light absorbing material is uniform and free of color difference. Then Eq. (1) can be written as
Integrate Eq. (2) in L:
For a gas mixture, the absorbance of a gas mixture at a certain wavelength can be obtained by linearly superimposing the absorbance of its constituents [18], while the absorbance of each constituent is related to the concentration of the constituent and can be expressed as a function of concentration, as shown in Eq. (5).
Due to the different gas components, spectral overlap may occur, resulting in the inability to measure the concentration of a gas using only a single wavelength when measuring a gas mixture. Usually, multiple corresponding absorbances are measured using a known single gas concentration to form a regression equation. In practical measurements the absorbance-concentration curve may be difficult to obtain the analytical formula for Eq.5, which makes it difficult to estimate accurately.The function ${f_i}({\lambda ,{c_i}} )$ is approximated by Taylor’s expansion:
When the measured gas concentration is low, in order to simplify the calculation, the higher-order term is ignored and only the second-order fitting is used
The coefficients in Eq. (3) can be determined by measuring the relationship between single gas concentration and absorbance before measuring the mixed gas.
Then Eq. (5). can be rewritten:
$A({{\lambda_j}} )$ can be obtained by measurement,while the unknowns in the equation are the concentrations of n gases, for a total of n equations, and the concentration of each gas ${c_i}$ can be obtained by solving the set of equations.
3. Experimental results and analysis
The proposed method (Eq. (8) is proved by the experimental by using a gas mixture of $S{O_2},N{O_2}$. Both gases have absorption in the 190-290 nm band. When using spectral absorption for measurements, there is mutual interference. The experimental data in the analysis were taken from the literature [18], where the absorbance at 273.33 nm (the main absorption wavelength of $S{O_2}$) and 231.33 nm (the main absorption wavelength of $N{O_2}$) in the UV spectrum was analyzed using experimental means. The results of the proposed method is compared with the results provided by [19].
3.1 Establishment of absorbance-concentration fitting formula
The $N{O_2}$ absorbance at 100 ppm, 300 ppm and 500 ppm were measured $\textrm{S}{\textrm{O}_2}$ at 273.33 nm and 231.33 nm in Table 1, respectively, and then the quadratic fitting formula was established.
Table 1. Gas absorbance
The coefficients are listed below
Table 2. Fitting coefficients
Using the fitting coefficients in Table 2, the equation for gas concentration versus absorbance was established and substituted into Eq. (8) to obtain
Here ${c_1}$ is the concentration $S{O_2}$ and ${c_2}$ is the concentration $N{O_2}$. $A({273.33} )$ and $A({231.33} )$ are the concentrations of the gas mixture at 273.33 nm and 231.33 nm, respectively.
3.2 Experimental results of gas mixtures
The gas chamber was filled with different concentrations of $S{O_2}$, $N{O_2}$ gas mixture (the specific concentrations are shown in Table 3), and the absorbance at 273.33 nm and 231.33 nm was measured as shown in Table 4.
Table 3. Concentration of each component of the gas mixture
Table 4. Absorbance of the gas mixture
The results of Table 4 are substituted into Eq. (4) and solved. The negative solutions are removed, and the results are shown in Table 5.
Table 5. Gas mixture measurement results
Using the same data, multiple linear regression and partial least squares regression analysis were used, and the results obtained from the analysis are shown in Tables 6 and 7. It can be found that under the same conditions, the errors of these two methods are significantly larger compared with the method in this paper. This is mainly due to the fact that $S{O_2}$ at 231.33 nm isnonlinear [18].
Table 6. Multiple linear regression analysis
Table 7. Partial least squares regression analysis
It is possible to use a specific example, (for example number 5), then it can clearly show the advantage of the proposed method in Fig. 2, Fig. 3 and Table 8.
3.3 Measurement of gas mixtures in case of unknown gas types
In practical measurements, it is often impossible to know whether a gas mixture contains a certain gas or not. However, for certain gases (such as automobile exhaust, coal-fired power plant flue gas, etc.), the possible gas compositions present are known. Before use, the corresponding fitting formula can be established for all possible gases, substituted into Eq. (8) and then the absorbance of the gas mixture is measured to calculate the concentration of various gases.
The four gases $N{H_3}$, $S{O_2}$, $N{O_2}$,and $NO$ were used as possible components of the gas mixture. The absorbance at 273.33 nm, 231.33 nm, 225.88 nm, and 208.23 nm were measured using a spectrometer. The corresponding fitting formula is shown in eq10.Then two of them were chosen to be mixed as the test gases. The corresponding gas concentrations were obtained using calculations, and the results are shown in the following Table 9.
Here ${c_1}$ is the concentration $S{O_2}$, ${c_2}$ is the concentration $N{O_2},{C_3}$ is the concentration $NO$ and ${C_4}$ is the concentration $N{H_3}$. $A({273.33} )$, $A({231.33} ),A({225.88} )$ and $A({208.23} )$ are the concentrations of the gas mixture at 273.33 nm,231.33 nm,225.88 nm and 208.23 nm respectively.
Table 8. Comparison of results
Table 9. Absorbance of the gas mixtureof unknown gas types
Table 10. Measurement results of unknown gas mixture of species (unit: ppm)
As can be seen from Table 10, the calculated results are close to zero when the gas mixture does not contain a certain component, while the error for other gases is less than 3%. It shows that the method in this paper can be used for gas detection of specific gas sources, such as automobile exhaust, coal-fired power plant flue gas, and other gas mixtures with known possible gas components, without considering whether some of them are present.
4. Conclusion
The proposed linear combination method proposed is straightforward and proved to be effective. This method implements multiple measurement by fitting in second degree polynomial equations. It can be used to solve the problem with multiple known gas components as well as unknown gas component gas mixture. The method has high accuracy (with error less than 1% in known components and less than 3% in unknown components cases) and less demanding for computation. It can be used in various real-time applications. It is important that the method can also decide whether a specific gas component exist or not in the gas mixture. This feature enables the possibility of blind detection of gas mixture.
Funding
Natural Science Foundation of Jiangsu Province (BK 2019012).
Acknowledgments
Zhang Jian thanks the National Science Foundation of Jiangsu Province for help.
Disclosures
The authors declare no conflicts of interest
Data availability
Data underlying the results presented in this paper are available in Ref. [19].
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