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Abstract
The spectral analysis based on laser-induced breakdown spectroscopy (LIBS) is an effective approach to carbon concentration monitoring. In this work, a novel LIBS-based method, together with a system designed independently, was developed for carbon monitoring. The experiments were conducted in two modes: static and dynamic. In static monitoring, gases in three scenarios were selected to represent different carbon concentrations, based on which measurements of carbon concentrations were performed through a mathematical model. Then, K-nearest Neighbors (KNN) was adopted for classification, and its accuracy could reach 99.17%, which can be applied for the identification of gas composition and pollution traceability. In dynamic monitoring, respiration and fossil fuel combustion were selected because of their important roles in increasing carbon concentration. In addition, the simulation of combustion degree was performed by the radial basis function (RBF) based on the spectral information, where the accuracy reached 96.41%, which is the first time that LIBS is proposed to be used for combustion prediction. The innovative approach derived from LIBS and machine learning algorithms is fast, online, and in-situ, showing far-reaching application prospects in real-time monitoring of carbon concentrations.
© 2021 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Global climate change has become one of the biggest challenges to human development and poses a major threat to human society, which has greatly promoted the global political consensus and major actions on climate change [1,2]. The October 2018 report of the Intergovernmental Panel on Climate Change (IPCC) concluded that the world must limit global warming to 1.50 degrees Celsius in order to avoid extreme harm. This will be possible only if the entire world achieves net zero greenhouse gas emissions and carbon neutrality by the middle of the 21st century [3,4].
Real-time monitoring of carbon concentrations is of great importance to the control of carbon emissions. However, no perfect system that can fully meet the needs for real-time carbon monitoring has been developed. Komhyr et al. measured carbon dioxide in the atmosphere with a combination of fast Fourier transform and low pass filtering [5]; yet, the sampling in the Fourier domain and frequency domain will have the absence of effective values and difficult to eliminate the complex noise interference, which means poor anti-interference ability. Li et al. designed a fiber-optic carbon dioxide sensor [6], which, however, failed to avoid the huge interference caused by background noise. Similarly, other researches including a sampling estimate based on land area of Cacho [7], carbon monitoring satellite of Buchwitz [8], and scale remote sensing of Hoover all have gained noticeable achievements [9]. Still, no one successfully developed a system satisfying the needs of applications in terms of real-time monitoring, accuracy and reliability.
Meanwhile, other applications based on carbon concentration monitoring are yet to be developed. Qi et al. achieved classification of aerosols using dual-polarization lidar, but the recognition of common gas components is low [10]. However, gas identification and classification based on LIBS would have better adaptability. In addition, the prediction of combustion processes is currently only on the modeling of the material's own indicators, such as the large eddy simulation of Akaotsu [11], and the environmental effects are often ignored. In this work, attempts were made to quantitative detect carbon concentration through mathematical models and machine learning rather than just confirm the existence of carbon. And two modes of detection were set with establishment of model in static mode, test of model and further discussion in dynamic mode. Such model and research idea can serve as references to researchers in relevant fields.
LIBS is a spectral measurement method, which could quickly extract the spectrum of substances and has been considered as a perfect method for component analysis of gas [12], soil [13], minerals [14], etc. Compared to other techniques such as X-ray fluorescence (XRF) and atomic absorption spectrometry (AAS), minimum sample size, contactless analysis and rapid real-time analysis were possessed by LIBS. So far, LIBS has been widely used in biology [15], medicine [16], environment and other fields [17]. Radial basis function (RBF) is a basis which could accurately fit nonlinear function. RBF network in machine learning could approximate almost all nonlinear functions and process the system with fuzzy rules with good generalization ability. It is a suitable choice for the prediction of carbon concentration. RBF has been successfully applied to time series analysis [18], data classification [19], pattern recognition [20], and fault diagnosis, etc. K-nearest Neighbors (KNN) is a supervised learning method. As a well-established and widely applicable theory, KNN is one of the most commonly used machine learning classification algorithms, which could determine the classification of samples based on the dfferences between different attributes of samples.
Herein, LIBS was employed to conduct static spectral analysis of air in three scenarios: indoor air, air exhaled by humans and gas generated by fossil fuel combustion. And based on these spectra, the work of classification and source tracing with high accuracy was realized by adopting KNN. Specifically, a qualitative analysis was carried out based on the characteristics of the corresponding spectra and quantitative analysis was performed to determine the carbon concentration. Then, based on the model, we also added the studies on the LIBS real-time monitoring of combustion process into our work, and the prediction of carbon content in combustion process was achieved with high accuracy by neural network. Furthermore, the influence of spectral range on the prediction results was also studied, which has hardly been discussed in the past. These conclusions have important reference value for further research.
2. Experiment
2.1 Experiment setup
The experimental scheme of LIBS was illustrated in Fig. 1. To ensure the reliability of this research, all present elements in the analyte should be fully excited. Therefore, a high-power Q-switch neodymium-doped yttrium aluminum garnet (Nd: YAG) laser exhibiting a wavelength of 1064 nm was employed. One single pulse duration of the laser was 10 ns, with the frequency of 10 Hz, pulse energy of 200 mJ with fluctuation ratio of 7.3%. The size of the laser spot was 7 ± 0.1 mm, and its irradiance could reach 5.3×107 W/cm2.
The gas to be measured was kept between the light probe and lens, and the gas molecules were then ablated into a plasma state by the Nd: YAG laser. Then, the optical signal was received by a detector and transmitted via a coupled fiber bundle (AvaSpec-ULS 2048-4 Channel-USB 2.0, Avantes) [21]. The range of wavelength was 200 nm ∼ 890 nm and spectral resolution in this study reached 10−2 nm. In order to synchronize the detector with the Nd: YAG laser, a delay controller was employed to transmit the control signal between the laser and spectrometer. Having considering past experience and current devices, the delay of time was set to 1.35 µs [22]. Gas molecules were sampled by raster mode.
2.2 Sampling modes
In the experiment, in order to simulate two modes: static and dynamic, the sampling method of the spectrometer was set in two types. Under the static condition, 200 spectral data were measured every 1 minutes for 20 seconds, i.e., each spectral data took 0.1 seconds and a total of 5 groups were measured. In the dynamic case, 100 spectral data were obtained at 10-second intervals of 1 minute, its number of groups to be measured depending on actual needs.
2.3 Scenario preparation
To verify the reliability and adaptability of the monitoring system, two monitoring modes, static and dynamic, were built. Indoor air, air exhaled by humans and gas produced by fossil fuel combustion were used as monitoring targets. Indoor air was not detailed here. To obtain stable air exhaled by humans, the experimenter was required to breathe at a constant rate into one end of a hose, the other end of which illuminated by the laser. The rate of respiration was maintained at eight seconds each time, four for inhalation and four for exhalation. Afterwards, kerosene was ignited through a cotton core and kept burning until the gas concentration reached equilibrium. It was followed by static spectral detection. Gases generated in two scenarios, i.e., respiration and kerosene combustion, were measured in the dynamic mode. In the former case, the time detected was changed from the exhalation time to the full length of respiration; in the latter case, the whole combustion was conducted in a confined space and then detected.
3. Static carbon concentration monitoring
3.1 Analysis of spectrum
Having considered the characteristics and applicability of LIBS, the spectra exhibited by different types of air were analyzed. In this section, air in three scenarios were selected as the experimental objects to conduct the spectral analysis. With references of the National Institute of Standard and Technology (NIST) and related data [23], the result of the monitoring of element concentration could be well presented in certain range of wavelength. In order to conduct experiments to monitor carbon concentration, indoor air, exhaled air of human and gas of fossil fuels combustion were picked out for their differences in carbon concentration.
Spectral information of three gases is illustrated in Fig. 2, where the spectral lines of major elements, i.e., C I 247.86 nm and CN 388.18 nm, are marked in red dashed lines. As observed, indoor air has the lowest carbon concentration and exhaled air has a higher carbon concentration than indoor air; the highest one comes from the gas generated by combustion, which is almost twice that of the air exhaled. In addition, from the CN spectral line, it can be found that the content of CN increases with the rising carbon concentration and the spectral intensity of CN reaches stable when the carbon concentration reaches a certain value. This might be attributed to the content of N as a constant. It reveals certain relationships between the content of CN and both C and N, which deserves further research.
In the wavelength range of 640 nm to 880 nm, as shown in Fig. S1 in Supplement 1, spectral lines of H, O and N are dominant in the spectrum of indoor air, in line with the fact that air is a mixture of O2, N2, CO2, water vapor and other substances. Characteristic peaks of N mainly are observed in three ranges of wavelength: 742 ∼747 nm, 815∼818 nm and 856∼875 nm; those of O are at 777.54 nm, 822.18 nm and 844.10 nm. The intensities of all these spectral signals are both high, with several spectral lines out of range. For instance, O I 777.54 nm remains high and unchanged, thus becoming an invalid value. Also, changes in the contents of N, O and Ar with carbon concentrations can be observed at the wavelengths of 740 ∼ 750 nm, 794.82 nm, 821.63 nm and 844.10 nm. Another finding is the trend that the O and N contents decrease with the increasing carbon concentration.
3.2 Precise measurement of carbon concentration
Intensity of spectral lines could be measured with great precision, which laid the foundation for quantitative measurement of carbon concentration. In previous study, it can be considered that an explicit relationship exists between material concentration and spectral signal intensity [24,25]. The relationship between the slope of the curve and the substance concentration is calibrated by Eq. (1).
Thus, the relation between spectral intensity and element content can be assumed with Eq. (2).
where KC is the slope of calibration curve; IC is the spectral signal intensity of carbon; m is the slope of KC and lognC; α and β are constants under experimental conditions and nC is the carbon concentration. In the ideal case, other disturbances such as self-absorption of spectral lines are ignored, which makes m = 0, KC = 1. Therefore, there exists a linear relationship between logIC and lognC.
According to previous studies, the carbon element in normal air can be considered to come entirely from carbon dioxide, and the concentration of carbon dioxide in the room is 300 ± 1.4 ppm [26]. Since the change of carbon concentration in respiration and combustion processes simulated in this experiment is much greater than this fluctuation therefore the fluctuation can be ignored here and the carbon concentration in general air is considered to be 0.03%. The indoor air spectral lines were obtained by the LIBS system for a continuous period of 10 minutes, and the statistics of the carbon spectral line intensity values (C I 247.86 nm) were obtained: the mean value is 334 with a variance of 37.5433. According to Rochon's test [27], the significance test of this set of data can be achieved, and the test results prove that there is no significant difference between the sample and population, which means that the intensity of the carbon spectral line in the general air can be expressed as 334. In the same way, the intensity of the carbon spectrum corresponding to the concentration of elemental carbon in human exhaled air can be obtained [28], that is, the carbon concentration in exhaled air was 4.0%, spectral line signal intensity value was 4902. Therefore, β could be calculated to be -0.451 and α is 10.2624. The final mathematical model of carbon concentration can be illustrated by Eq. (3).
For example, spectral intensity value of gas of combustion that could be measured was 10194.38. Thus, the carbon concentration in gas of combustion could be measured as 15.24% through this experimental system.
To more accurately describe the model we developed, the accuracy of the model was calculated based on the carbon spectral line data used for the modeling. With the amount of data being 1000, which can be obtained by Section 2.2, standardization and data outlier troubleshooting were first carried out to ensure minimal noise interference and error. Then the value of uncertainty is calculated to be 3.1748% by Eq. (4).
where UA is the value of uncertainty; Si is intensity value of carbon spectral line (C I 247.86 nm) in the tested samples; S0 is the carbon concentration in general air, i.e., 0.03%; n is sample size after standardization and data outlier troubleshooting.
3.3 Identification of three scenario
Having obtained the spectrum of three scenarios, due to the lengthiness and cumbersomeness of spectral data, only relevant spectral information of carbon elements was used for the next step of identification (wavelength range: 247∼249 nm and 380∼390 nm), which included 317 data points in one spectrum and 200 samples were selected for identification in each scenario. Meanwhile, the principal component analysis (PCA) algorithm was used to perform dimensionality reduction on the spectral data of carbon elements [29]. Theoretically speaking, when the cumulative contribution rate reaches 85%, all the data could be considered sufficient to be identified by these components [30], which are called principal components (PC).
The normalized spectral data of carbon from the above experiment were used in PCA, 24 components calculated out. Cumulative contribution rate of PC1, PC2 and PC3 was up to 89.03% as shown in Fig. 3.
To confirm the results of PCA, statistical tests were of great significance, among which combination tests of KMO and Bartlett are always the most persuasive one [31]. Value of KMO sampling suitability variables should exceed 0.5, and the significance in Bartlett's sphericity test needs to be less than 0.05. As is shown in Table 1, the result was solid enough.
Table 1. KMO and Bartlett test
Having confirmed the validity, one three-dimensional map and three two-dimensional maps were contained in Fig. 4 to illustrate the relationships between three PCs. Obviously seen in Fig. 4 PC1, PC2 and PC3 could give a relatively specific boundary between indoor air and exhaled air, which might be difficult for any two PCs, while gas of combustion could be distinguished easily. In consequence, these three PCs could be applied for identification of indoor air, exhaled air and gas of combustion.
PC1, PC2 and PC3 of air in three scenarios and their categories were then used as the training set and labels for KNN. Data was standardized; KNN adopted Euclidean distance; number of adjacent points was 1; Distance weight adopted equal distance [32]. The classification accuracy was 99.17%, which means that only 5 samples were classified wrongly in all of 600 samples. Therefore, more air or gas in different scenarios could be classified correctly via spectral data of C with KNN.
4. Dynamic carbon concentration monitoring
4.1 Analysis of respiration dynamic monitoring
After the static measurement, dynamic measurement was carried on over the whole process of respiration. Relatively stable 36 seconds were selected for analysis. Then a three-dimensional curved surface was created with X-axis represents time, Y-axis represents wavelength, and Z-axis represents spectral intensity. With intention of highlighting the pattern of change in the image, the curved surface was projected onto the two-dimensional plane of X and Y, and only 246 nm to 249 nm, 374 nm to 390 nm and 730 nm to 790 nm of wavelength were taken here for analysis.
The change rule of carbon spectrum line (C I 247.86 nm and CN 388.18 nm) was illustrated in Fig. 5. The upper broken line chart reflects the change of peak value of spectrum line with time; diagram on the right shows the difference between exhaled and inhaled air. It could be seen that this spectral line clearly conforms to the regularity of breathing, and the spectral intensity of carbon and CN in exhaled air is higher than that in inhaled one. Through this example, it can be seen that LIBS has far-reaching application value for dynamic monitoring of carbon concentration.
4.2 Analysis of combustion dynamic monitoring
In the current real-time monitoring of carbon concentrations, the importance should be attached to fossil fuel combustion. Therefore, kerosene, a typical fossil fuel, was selected for combustion in a confined space. Based on the spectral information of the gas in the space, the change of element content in the combustion process of kerosene was obtained. And several methods were applied to mitigate combustion chemiluminescence in this work: relative wide gate width, detection away from chemiluminescence and opaque barrier.
With a similar method detailed in Section 4.1, the spectral lines of carbon and CN were obtained. As seen in Fig. 6 (a), the spectral intensity of carbon increases with the combustion time and reaches almost stable after about 500 s, which is contrary to common sense. Indeed, the combustion did not stop, but got weakened to a certain extent at that time. This might be attributed to the existence of some minor gaps in the experimental sealing device. At a low level of combustion intensity, the carbon-contained gas generated by combustion connected the outside air to reach a dynamic balance, thus maintaining carbon concentrations unchanged.
The spectral line variation of CN is depicted in Fig. 6 (b) where the change of CN spectral intensity is consistent with that of carbon. Differently, the former has a strong step-change feature. A steep change in the spectral signal intensity can be observed at the combustion time of about 200 s and 410 s. Meanwhile, the time for the spectral intensity of CN reaching stable is earlier than that of carbon, which may be another manifestation of the step-change feature. A similar phenomenon was found in Mousavi’s LIBS based CN spectroscopic study [33]. In the future, more research efforts are needed to explore the spectral characteristics of CN.
For a detailed illustration of the combustion process, an analysis of the spectral lines of N and O and their spectral identities were performed, with the results in Fig. 7. Their change trends, however, are not in line with reality. In such a confined space, the concentrations of nitrogen and oxygen should remain constant, so should their spectral intensity.
To explain this phenomenon, two hypotheses were proposed. First of all, the reduction in the spectral intensity of N and O originated from their decreasing concentrations, which might be triggered in two aspects. For one thing, because kerosene combustion produced a large number of new gases containing little or even no N and O, other gases containing N and C were pushed to the space, thus becoming undetectable by a spectral detector. For the other, the existence of leaks in the confined space allowed the newly produced gases to push the original air out of the space. Second, the reduction in spectral intensity might also come from a change in the existing form of elements. Originally, N and O were mainly existed in the form of nitrogen and oxygen, i.e., completely composed of respective elements. The spatial distribution of these elements after they were excited into plasma was dense, resulting in high spectral intensity. After new gases were produced during the combustion, the existing form of elements changed, reducing the plasma density of the same element and then weakening spectral intensity.
4.3 Prediction of the combustion degree
The prediction of the degree of combustion is also a very important object to study. After obtaining the spectral data of carbon elements, it could be found from which the spectral information corresponding to each combustion time was different. And a certain pattern of this variation can be seen in Fig. 7. Therefore, there exists the possibility of using the spectral information of C to predict the combustion degree of kerosene under specific conditions. This relationship is clearly nonlinear, which is exactly the scope of the RBF algorithm. The radial basis function used in this paper was a Gaussian kernel function and the distance used was the Euclidean distance [34,35]. Equation (5) illustrates its functional form.
where x is the input spectral data, c is the center of the kernel function, and σ is the width parameter of the function, which controls the radial range of action of the function.The basic idea of RBF networks is that the kernel function is used as the “base” of the hidden unit to form the implicit layer space, so that the input vector is mapped directly to the hidden space without the need for a power connection. In this way, the mapping of the network from input to output is nonlinear, while the network output is linear with respect to the adjustable parameters. The network weights can then be solved directly from the linear system of equations. The activation function of the neural network can be expressed as the Eq. (6).
After obtaining the trained neural network, the predicted results can be expressed in Eq. (7) by inputting the spectral data at the corresponding combustion level.
In this study, 70% of the spectral data were used to train the neural network and 30% were used for testing. In order to obtain the most desirable prediction results, sampling radius of wavelength was adjusted to obtain the corresponding accuracy centered on the spectral peak of C, as shown in Fig. 8. It could be found that the highest accuracy of 96.41% was achieved when the sampling radius is 0.64 nm. Therefore, it can be concluded that the degree of combustion of kerosene can be predicted using the spectral information of elemental carbon, and the wavelength range used is centered on the carbon spectral peak with a radius of 0.64 nm. Also, this method can be applied to the combustion of other fossil fuels by simply adjusting the wavelength sampling range.
4.4 Verification of LTE
Since the LTE state of laser-induced plasma is the precondition of quantitative analysis, it is necessary to certify whether plasma could match this condition [36]. On the basis of McWhirter conditions [37], Eq. (9) gives the requirement that the plasma in the LTE state should obey.
ne is the density of electron number, TP is the plasma temperature, and ΔE is the difference of energy between the upper and the lower level of the transitions.In this series of experiments, TP was 12496 K, which can be calculated by the equation of Saha-Boltzmann [38]. Among the characteristic spectral lines of C (247.856 nm), N (742.364 nm, 744.229 nm, 746.831 nm) and O (777.194 nm, 777.417 nm, 777.539 nm), the maximum difference between the upper and lower level is 35.1211 eV, and it can calculate that ne is about 7.748 × 1018 cm-3. The maximum difference of energy levels and ne of other related elements are shown in Table 2. According to Dong who did the study about Time-resolved LIBS of atomic and molecular carbon from coal in air, argon and helium [39], the plasma of element C, N and O satisfy the McWhirter conditions.
Table 2. The maximum difference of energy levels and ne of related elements
However, McWhirter criterion is only a necessary but not sufficient condition. According to Cristoforetti [40]. For calculation purposes, it is assumed that the plasma in the experiment conforms to homogenous and transient. Therefore, the experiments in this work should also satisfy the conditions given by Eq. (10).
where τrel can be expressed by Eq. (11).
Meanwhile, Δf of C, N and O could be obtained in Cristoforetti’s work: ΔfC≈3.7×10−2, ΔfN≈4.5×10−2 and ΔfO≈5.2×10−2 with temperature calculated by LIFBASE [41]. The values of Eq. (10) for different elements range from 10−3∼10−5, which can be considered much less than 1 in this experiment.
5. Conclusion
In this work, a novel monitoring system was developed for carbon concentration monitoring in two modes, static and dynamic. The gases used in the static mode were indoor air, air exhaled by humans and gas produced from the combustion of fossil fuels in a confined space, representing three levels of carbon concentrations. The carbon concentrations of indoor air and air exhaled by humans were obtained previously, which could help to calculate the unknown carbon concentration of the rest gas. For gas traceability and classification, KNN was used to process the carbon signal in the spectrum and the accuracy of classification finally reached 99.17%. In the subsequent dynamic mode, the air exhaled by humans and the gas produced from the combustion of fossil fuels in a confined space were applied to dynamic monitoring as two more meaningful scenarios. The whole process of respiration was monitored. Spectral lines of C and CN were obtained and analyzed, results of which confirmed the feasibility of dynamic carbon concentration monitoring based on LIBS technology. For further exploring this experimental system, kerosene was selected and ignited in a confined space. The change rule of element concentrations of gas in the space was obtained through the monitoring of the whole combustion process. Specifically, C, CN, N and O were selected for spectral analysis. On the one hand, the concentrations of C and CN shows an upward trend, and their spectral signals remain unchanged at a certain value of intensity. In addition, the spectral change of CN increases sharply at about 200 nm and 420 nm, revealing a step-change feature, which is worthy of further study. On the other hand, the concentrations of N and O show a downward trend, which conflicts with the theory. Two hypotheses were then put forward to explain this phenomenon. Furthermore, RBF was employed to predict the degree of combustion with spectral information of C, where an accuracy of 96.41% were obtained. Eventually, the LTE state of laser-induced plasma was verified by the criterion of both McWhirter and Cristoforetti, confirming the reliability of above research. With the fast real-time detection of LIBS and an efficient algorithm, the developed system displays the work efficiency that meets the requirement of practical applications. This paper presents novel insights into the application of the spectral information of C and concludes that the combination of LIBS technology and various algorithms will have promising applications.
Funding
National Natural Science Foundation of China (U1932149); Qinglan Project of Jiangsu Province of China; National College Students' innovation and entrepreneurship training program and NUIST Students' Platform for Innovation and Entrepreneurship Training Program (202110300049Z).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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