2018 International Conference on Sensor Network and Computer Engineering (ICSNCE 2018) 

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Research and Application of SO2 Concentration Monitoring Algorithm in Flue Gas  

Wang Qinqin 

School of Computer Science and Engineering 

Xi’an Technological University 

Xi’an, 710021, China 

e-mail: 1466122350@qq.com 

Su Xiaohui 

School of Computer Science and Engineering 

Xi’an Technological University 

Xi’an, 710021, China 

e-mail: 287099144@qq.com 

 

Abstract—This paper mainly focuses on the concentration 

calculation of SO2 in flue gas. There are many methods for 

smoke detection. First of all, this paper mainly introduces 

the basic Differential Optical Absorption Spectroscopy 

technology. Then, in order to solve the problem of 

overlapping absorption between different gases in the flue 

gas, this paper use cyclic iteration algorithm to measure the 

concentration of SO2. It is concluded that the basic DOAS 

algorithm has a large error for the concentration 

measurement of mixed gas with overlapping absorption, the 

he error is above 25%. However, the cyclic iterative 

algorithm has a good effect on processing with it which can 

get a more stable result after three iterations, and the 

measurement error can be controlled finally within 2%. 

Keywords-Differential Optical Absorption Spectroscopy; 

SO2 Monitoring; Mixed Gas; Spectral Overlap Absorption; 

Cyclic Iterative Algorithm 

I. INTRODUCTION 

With the rapid development of industrialization and 

human destruction, their pollution is becoming more and 

more serious. Therefore, monitoring the harmful gases of 

the atmosphere is the primary prerequisite for controlling 

and treating pollution. 

At present, people mainly use portable gas analysis 

equipment to carry on flue gas analyze, and The 

Differential Optical Absorption Spectroscopy (DOAS) is 

the most commonly and effective method which is used to 

real-time detect gas concentrations in the atmosphere by 

characteristic absorption of absorbable molecules in the 

near ultraviolet region[1]. The traditional DOAS algorithm 

exist large errors for the gas concentration measurement of 

short path and low concentration. In order to decrease limit of 

detection and enhance environment adaptability of the portable 

flue gas analyzer, to improve measurement accuracy, Wang 

Kunpeng completed the research and design of portable gas 

analyzer based on AVR micro-controller, and increase it’s 

detection accuracy and environmental adaptability[2]. Deng 

Meng developed the portable gas analyzer based on the non- 

dispersive ultraviolet absorption, and has improved resolution 

and stability in high humidity and low concentration of SO2 gas 

monitoring[3].Wang Jing designed concentration calculation 

method based on the least square method on the basis of DOAS 

algorithm, which is used in the short optical path and a low SO2 

calculation[4]. Zhou Mi proved the monitoring accuracy of 

Fourier infrared method for the low concentration SO2 in straw 

burning flue gas[5]. Yan Yue’s experiment has proved that BP 

neural network based on adaboost optimization algorithm has a 

good effect in monitoring concentration of SO2 gas with 

interference[6]. In order to separate and calculate the gas 

concentration from the absorption spectrum signal of the mixed 

gas, Xu Shuping designed the portable smoke analyzer based 

on the cyclic iteration algorithm. It conclude that the method 

can simultaneously calculate various gas concentration and has 

strong anti-interference ability[7]. Wang Yingjian designed 

Strong independence and multi-scale wavelet discrete 

decomposition method, and obtained accurate concentration of 

SO2 with NO gas absorption interference [8]. 

In the paper, a portable flue gas analyzer is used as an 

experimental instrument to study the method of measuring the 

SO2 content in the exhaust emission of the factory. The 



2018 International Conference on Sensor Network and Computer Engineering (ICSNCE 2018) 

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experiment mainly research on the DOAS absorption 

model and the cyclic iterative algorithm. It can get the 

efficient method on SO2 concentration measurement in 

the mixed gas. So, it can provide the best technical 

support for the factory exhaust emission monitoring and 

reduce the air pollution. 

II. DIFFERENTIAL ABSORPTION SPECTROMETRY 

Differential absorption spectroscopy is proposed by 

U.Platt of the Institute of environmental physics at 

Heidelberg University in Germany. The basic principles 

are as follows: Firstly, It need irradiate the tested 

substance with a beam of light, ten, select the 

corresponding absorption wavelength of the gas, lastly, 

calculate the gas absorbance and then get its concentration. 

The theory is based on the Lambert-Bee law.  

A. Lambert-Beer Law 

The basic principle of Lambert-Beer law: when abeam 

of parallel monochromatic light through a certain 

absorbable material in the vertical direction and generate 

transmission, the medium itself will absorbs a part of light, 

so, the original intensity weakened, and the thicker the 

medium, the higher the concentration, the greater 

decreases the light intensity [9]. The specific expression is 

as follows:  

KLC
I

I
A 

1

0log



Among them, A is absorbance, I0 is the intensity of 

incident light, I1 is transmission light intensity, Kis 

constant, absorption coefficient, Lis the thickness of 

medium, C is the concentration of absorption material. Set 

I0(λ) as the original light intensity, I(λ) as receiving light 

intensity and σ(λ) as the  absorption cross section of the 

gas to be measured, then the mathematical model of the 

spectral absorption of a single gas can be expressed as:  

)](exp[)()(
0

  CLI I 

Lambert-Beer law is used only for the concentration 

measurement of single gas and it requires no interference in the 

experimental environment. However, in the actual 

measurement process, the measured material is usually a 

mixture materials which concluding kinds of interfere with the 

impurities such as sols and solid particles.  

B. Actual Spectral Absorption Model 

Due to the uneven refractive index, when the light incident 

into the uneven medium, it will produce scattered light and 

reduce the transmittance of light, including Rayleigh scattering 

and Mie scattering which are show broadband absorption and 

narrowband absorption in the optical spectrum chart. Therefore, 

it is necessary to establish a spectral absorption model under 

actual conditions. Set i as the type of gas, and introduce the 

extinction coefficient of gas including  R and  M . The model 

of the gas absorb light is as follows:  

      ]exp[)()(
0

  MRiiCLII   

When analyzing and calculating, the absorption cross 

section will be decomposed into fast parts and slow parts. So, 

The High pass filtering will avoid the influence of Rayleigh 

scattering and Mie scattering. Set the absorbance of the gas to 

be measured is D, the actual absorbance model is finally as 

follows: 

  )(])()(ln[
0

  iiCI LID  

From the formula 4, It can be known that the difference 

optical density  D is linear with the differential absorption 

cross section  i in a certain concentration range.  

Although the differential absorption method can accurately 

calculate the concentration of most of the gases, the loss of the 

slow change absorption spectrum information in the filtering 

process will lead to produce some wrong results for gas 

concentration measurement. Therefore, it is necessary to study 

other methods of concentration inversion to improve the 

measurement precision of gas composition. 



2018 International Conference on Sensor Network and Computer Engineering (ICSNCE 2018) 

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III. CYCLIC ITERATIVE ALGORITHM 

The absorbance has Superposition property. When the 

gases is used as a mixture, the total absorbance is equal to 

the sum of the absorbance of each component in the 

mixture if each kind of gas has a absorption of the light in 

a particular wavelength[10]. According to the 

superposition property of absorption spectrum, the cyclic 

iteration algorithm can gradually eliminates the 

interference between gas molecules through successive 

cycle calculation, and finally approach the real 

concentration of the gas.  

C. The Model of Cyclic Iterative Algorithm 

The paper mainly research the concentration 

measurement of SO2 of mixed gases with overlapping 

absorption characteristics. The experiment only consider 

the interference of NO2 on spectral absorption of SO2 in 

the range of 200nm~300nm band of the near ultraviolet 

region. Two standard gases of SO2 and NO2 are added 

one by one, the absorption spectra of two kinds of gases 

are shown in Figure 1. 

190 200 210 220 230 240 250 260 270 280 290 300
0

10000

20000

30000

40000

50000

60000

In
te

n
si

ty
(c

o
u

n
ts

)

Wavelength(nm）

 零气线
 NO2
 SO2

 

Figure 1.  Absorption spectrogram of SO2 and NO2. 

As shown in Figure1, although both NO2 and SO2 

have the absorption of light at wavelength 230nm and 

270nm, the absorption intensity is very different. The 

absorbance of NO2 at 230nm is much greater than that of 

its absorbance at 270nm, while the absorbance of SO2 at 

270nm is much greater than that of its absorbance at 

230nm [9]. Therefore, at 230nm, the absorption of NO2 

can be seen as the main absorption and the absorption of 

SO2 as an interference. On the contrary, at the wavelength of 

270nm, the absorption of SO2 can be seen as the main 

absorption, and the absorption of NO2 as the interference of the 

main absorption of SO2. The basic calculation steps of the 

cyclic iteration method are as follows:  

At 230nm, the total absorbance (A1) is considered as the 

absorbance of NO2 (AS1). 

Step 1, at 230nm,according to AS1, it can obtain the 

concentration of NO2 (CS1) by looking up the table; 

Step 2, at 270nm, according to Cs1. it can obtain was to the 

absorbance of NO2 (AS2); 

Step 3, at 270nm, the total absorbance (A2) minus AS2 is 

equal to the absorbance of SO2 (AN2); 

Step 4, at 270nm, it can obtain the concentration of SO2 

(CN2) by looking up the table; 

Step 5, at 230nm,according to CN2, it can obtain the 

absorbance of SO2 (AN1) by looking up the table; 

Step 6, at 230nm, A1 minus AN1is equal to the absorbance 

of NO2 (AS1); 

Repeat steps one to six, it can get the exact values of SO2 

concentration. 

The above algorithm flow can not only calculate the 

concentration of each component of the mixture gases which 

include SO2 and NO2, but also it is suitable for concentration 

measurement of any mixed gas.  

IV. DESIGN OF EXPERIMENTAL SYSTEM 

The experimental system is mainly composed of light 

source, spectrometer, optical fiber and computer. Firstly, open 

the light source, and the emitted light of the optical fiber pass 

through a double convex lens, after that, it becomes parallel 

light and pass through the measured gas. Next, the light enters 

into the spectrometer after focusing through the focusing lens. 

Lastly, the spectrometer converts the optical signal into 

electrical signal and sends it to the computer to collect and 

process the spectral signal. The specific experimental device 

and system flow are shown in Figure 2 and Figure 3. 



2018 International Conference on Sensor Network and Computer Engineering (ICSNCE 2018) 

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Figure 2.  Experimental device diagram. 

Gas entry 

Air chamber

Exhaust fume 

Spectrometer 

Computer 

UV light source Optical fiber 

Data line 

Optical fiber 

 

Figure 3.  Flow chart of the experimental system. 

In the experiment. Firstly, it measured the dark 

spectrum when the light source does not pass into the 

spectrometer. Then, add the gas and open the light source, 

so that the light can enter the air chamber through the 

optical fiber. After the gas was absorbed, the number of 

photons will decrease correspondingly, and the number of 

absorbed photons will change with the change of gas 

concentration. Finally, the transmission light goes into the 

spectrometer, converts the light signal into the electrical 

signal, and sends it to the computer to display the 

spectrum. It can obtain original absorption spectrum after 

calculation the average value of absorption spectrum for 

many times. From the original spectra deducted the data 

of dark spectrum, it can get the actual spectrum. 

V. EXPERIMENTAL RESEAECH AND RESULT ANALYSIS 

In order to verify the feasibility and practicability of 

DOAS and cyclic iteration algorithm, we will compare 

the result and accuracy of them through experiments, and 

summarize the advantages and disadvantages of each 

algorithm. 

D. Research on Curve Fitting 

Lambert-Beer law provides a linear relationship 

between gas absorbance and concentration. In practice, 

the linear relationship is not always true due to the 

influence of various factors. Therefore, the curve fitting method 

is used to fit the measured data. In order to improve the 

efficiency of the algorithm, the number of photons absorbed by 

the experiment is first converted into the absorption intensity. 

Because the dark spectrum is included in the spectrum after the 

light is passed into the light source, therefore, In calculating the 

absorbance and concentration of the substance to be measured, 

the dark spectrum should be removed from the original 

spectrum. The calculation model of absorbance is as follows: 





DS

DR
A




 lg



Among them, A is an absorbance, R is a number of incident 

photons, S is a number of transmitted photons,  is a 

wavelength, D is a dark noise. 

In this paper, the effect of NO2 on the absorption spectrum 

of SO2 is only considered. The mixture of NO2 and SO2 is used 

in the experiment, and there are two kinds of standard gas 

concentration, such as 100ppm and 500ppm. It can fit the 

concentration and absorbance curves of each gas at a certain 

wavelength by the measured gas absorption spectra, and then 

obtain the fitting data relation table of each gas. The fitting 

formula is as follows: 

 PCCC
C

A
CA

i

i

i 
 2i2i2i2i



Among them, p is the change rate of average absorbance 

along with increasing concentration, Ci+2 is the gas 

concentration, 2iA  is a absorbance of gas to be measured. As 

long as there are two points ii CA   1i1i  CA  on the measured 

curve, the relationship between concentration and absorbance 

can be fitted. At 230nm and 270nm,the relationship figures 

between concentration and absorbance of SO2 and NO2 can be 

obtained by using excel, respectively. As shown in Figure 4 

and 5 (horizontal coordinate is concentration, ordinate is 

absorbance). 



2018 International Conference on Sensor Network and Computer Engineering (ICSNCE 2018) 

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Figure 4.  Data relationship between concentration and absorbance of 

NO2. 

 

Figure 5.  Data relationship between concentration and absorbance of 

SO2. 

E. Experimental Results and Analysis 

In the experiment, firstly, we should turn off the light 

source and measure the dark spectrum. Then, measure the 

original spectrum. Finally, two kinds of mixed gas with 

different ratio of SO2 and NO2 are introduced to measure the 

spectral data. The mixed concentrations of SO2 are 301ppm 

and 102ppm, respectively. The mixed concentrations of NO2 

are 199ppm and 498ppm, respectively. Then, the concentration 

of the measured spectral data is respectively calculated by 

using DOAS and cyclic iterative algorithm. The SO2 

concentration under the interference of NO2 as shown in Table 

I. The iterative results of cyclic iteration algorithm are shown 

in Table II. 

 

 

 

 

TABLE I.  THE COMPARISON OF MEASURED CONCENTRATION WITH ACTUAL VALUES OF SO2 

Computational 

Method 

Standard Value 301 Standard Value 102 

Measured value Measured deviation(%) Measured value Measured deviation(%) 

DOAS 368.35      22.3% 128.07      25.5% 

Cyclic iterative 

algorithm 
298.71      0.7% 100.46        1.5% 

TABLE II.  THE RESULTS OF CYCLIC ITERATIVE ALGORITHM 

Iterations 1st time 2nd time 3rd time 4th time 

FirstGroup 

SO2 (ppm) 310.24 299.86 299.71 299.71 

NO2 (ppm) 193.83 201.47 201.47 201.47 

Second Group 

SO2 (ppm) 134.71 101.90 101.46 101.46 

NO2 (ppm) 487.62 497.36 497.64 497.64 

In the experiment, DOAS and cyclic iteration 

algorithms are used to invert the concentration of SO2 in 

the mixture gas respectively. According to Table I, under 

the interference of NO2 gas, with the increase of NO2 

concentration, the greater the deviation, the lower the 

measurement accuracy. It is shown that the error is more 

than 25% when the DOAS method is used to measure the 

SO2 concentration in the mixed gas. Combined with Table I 

and Table II, the results show that the inversion effect of 

DOAS method for the mixture gas concentration with 

overlapping absorption is not satisfactory. On the contrary, the 

accuracy of the cyclic iteration algorithm is the highest, and the 

content of the mixed components can be accurately measured 



2018 International Conference on Sensor Network and Computer Engineering (ICSNCE 2018) 

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by only three cycles, and the measurement deviation is 

finally within 2%. 

VI. SUMMARY OF THE PAPER 

In order to find a method with high detection accuracy 

and good calculation efficiency, this paper mainly study 

the concentration monitoring method of SO2 in flue gas. 

First, the advantages and disadvantages of the current 

equipment and algorithm of smoke composition detection 

can be obtained. Then, the basis theoretical and 

calculation principle of DOAS are introduced in detail. 

Next, according to the actual detection environment, a 

cyclic iterative algorithm is designed for the spectral 

absorption characteristics of measured gas. Finally, the 

spectral data are obtained through experiments, and use 

the DOAS method and cyclic iteration algorithm to 

calculate the concentration of SO2. It is concluded that the 

cyclic iteration algorithm is superior to the content 

monitoring of SO2 in flue gas, and greatly reduces the 

calculation deviation, finally control the error within 2%.  

The cyclic iteration algorithm is not only suitable for 

the concentration monitoring of the gas in the paper. It 

has a high accuracy for the detection of exhaust gas 

emissions in industrial production, especially for the 

concentration measurement of the of various components 

in the mixed gases with overlapping absorption spectra. 

The study results provide a good technology for industrial 

development and environmental protection. It make the 

factory exhaust gas to reach the safety target, and reduce the air 

pollution. 

ACKNOWLEDGMENT 

Provincial Science and Technology Project, Shaan’xi 

Provincial Education Department Project (15JF019). 

 

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