1. Introduction

Carbon dioxide (CO₂) is the primary greenhouse gas, and there have been intense research efforts to reduce its emissions by CO₂ capture, storage, and reuse [1–3]. Considerable amount of carbon emissions is from combustion-based power plants; thus, flue gas monitoring is important to ensure operating regimes that can mitigate the production of particulate matter and other toxic byproducts as well as to evaluate the amount of carbon emissions to the atmosphere. A monitoring system primarily consists of three components: a flow meter, temperature sensor, and gas analyzer; familiar choices of gas analyzers are a gas chromatograph or electrochemical sensor array. However, these methods require gas sampling, which inevitably causes a time lag between the actual and measured gas compositions.

Tunable diode laser absorption spectroscopy (TDLAS) [4–6] and laser-induced breakdown spectroscopy (LIBS) [7,8] have been proposed as real-time monitoring methods for carbon emissions. TDLAS has the advantage of directly measuring CO₂ concentration; however, it is often difficult to determine the exact concentration because the signal is a function of the target gas concentration and temperature, and the measurement path. Thus, accurate concentration measurement requires the acquisition of the whole concentration and temperature fields through multipath measurements and numerical tomographic reconstructions. LIBS, on the other hand, is a local measurement based on emission spectroscopy of gas discharges produced by focusing a high-energy pulsed laser beam. As all molecules break into atoms, and the spectrum consists of the emission lines of atoms, this method has been a tool for chemical element analysis [9,10]. Although the method has been used mainly for material identification and local equivalence ratio measurement [11–15], it has also been applied to carbon emission monitoring based on the fact that the majority of carbon (C)-containing species in the flue gas is carbon dioxide (e.g., concentrations of other C-containing species, such as carbon monoxide, are as low as hundreds of parts per million).

LIBS has been very successful in measuring relative concentrations, especially in the field of reacting flows, and signal quantification has been achieved via univariate analysis after mapping the peak intensity ratios (PIRs) between different chemical elements to relevant species concentrations [9–15]. Nevertheless, in practice, the plasma state depends on the gas density immediately after laser irradiation (i.e., pressure and temperature) because the energy coupling efficiency between the plasma and laser changes [16,17]. In the early stage of the plasma, molecules are not decomposed into atoms yet, and emission occurs mostly through the bremsstrahlung process, which appears as a broadband continuum in the spectrum [11]. The process then decays rapidly, and the spectrum consists mainly of the emission lines of the atoms resulting from molecular dissociation. Therefore, owing to the difficulties in quantifying the broadband signal and the temporal change in the plasma state with changes in the gas density and optical settings, the emission spectra are often recorded under conditions where the density remains almost constant and the broadband emission is almost completely attenuated.

The flue gas density varies with temperature, and can significantly affect the accuracy of the measured species concentration. The strength of the bremsstrahlung process, in which energetic free electrons lose energy and emit photons as they are deflected by ions, is proportional to the product of the electron and ion densities, and therefore increases with the gas density [16]. Recently, J Lee et al. [18] proposed a machine learning-based quantification method for laser-induced breakdown emission spectra containing broadband continua, and discrete emission lines. The spectra used were recorded 100 ns after laser irradiation with an exposure time of 10 ns; thus, for a given chemical composition, each spectrum can be specified by a single pressure and temperature. The data-driven model could accurately predict both the local equivalence ratio and pressure (e.g., coefficients of determination of 0.99996 and 0.99975, respectively); however, the acquisition of the spectra requires an expensive intensified camera, which reduces the practicality of this method.

In this study, we propose a novel method to accurately predict both CO₂ concentration and gas temperature based on LIBS using a portable spectrometer equipped with a charge-coupled device (CCD) line array detector that is not capable of fast gating. Unlike previous studies [13–15], the time delay at which the spectra are recorded was set shorter because the broadband continuum spectra depend on gas density, such that the acquired spectra can contain some degree of the broadband continuum. Density changes cause changes in the laser absorption efficiency and plasma lifetime, which in turn cause changes in spectral shapes. Thus, because it is difficult to find analytical relationships between spectral line intensities and broadband continuum intensity, the predictive model was derived by training the spectra. As the study intends to develop a technique to monitor the CO₂ concentration of flue gases, LIBS spectra were collected for varying CO₂ concentrations and temperatures from 294 to 498 K and from 0 to 30 vol%, such that the ranges cover the typical ranges of CO₂ concentration and temperature for flue gases [19]. A convolutional neural network (CNN) was employed as a model; in this model, CO₂ concentration and temperature were outputs, and the spectra were used as inputs. The prediction accuracies were evaluated in terms of the coefficient of determination, and gradient-weighted regression activation mapping (Grad-RAM) analysis was performed on the acquired model to investigate the spectral features exploited by the model in the predictions.

2. Experimental setup

Figure 1 shows a schematic of the experimental setup of the laser-induced breakdown spectroscopy for monitoring carbon emissions. The 10 Hz pulsed output of a Q-switched 532 nm Nd:YAG laser (Nano LG 300-10, Litron Lasers) was used as the source of the periodic breakdown. The 6 mm-diameter laser with a beam energy of 25 mJ per pulse was focused using a plano-convex lens with a focal length of 50 mm to induce gaseous breakdown at the exit of a pencil-type air heater. Plasma emission was then collected at a location perpendicular to the laser direction using a fiber equipped with a collimator and connected to an optical spectrometer (Avaspec-2048L, AVANTES). The emission spectrum was obtained using an optical spectrometer with a detection range and spectral resolution of 200-1100 nm and 2.3 nm, respectively. The exposure time of the spectrometer was set to 1.05 ms, and time synchronization between the laser firing and spectrometer was achieved using a delay generator (9520 Series pulse generator, Quantum Composers). Specifically, the laser was set to trigger the delay generator, which triggered the spectrometer; therefore, the detailed timing between these devices was achieved by delaying the emission capture window until the optical signal appears; this is because of the internal delays within the delay generator and spectrometer. Spectrum acquisition was performed at 5 Hz, and the measurement was repeated while increasing the time delay (with reference to the laser firing) from 500 ns to 2100 ns.

 

Fig. 1. A schematic of an experimental setup for the generation of laser-induced plasma in N₂-O₂-CO₂ mixtures, and the collection of plasma emission spectra while varying CO₂ concentration and gas temperature.

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The mixtures of CO₂, N₂, and O₂ were injected into a pencil-type air heater, and their flow rates were controlled using mass flow controllers (i-300CV-S4, i-600CV-S6, FACTORS) after calibration using a dry gas meter (DV-2C-M, Shinagawa Corporation). The air heater was used to supply a continuous hot gas flow, and the flow gas temperature was controlled using a proportional integral derivative (PID) controller (K-DAC-1, JOOWON H&C) connected to a type-K thermocouple installed near the heater nozzle outlet. The heater had an outer diameter of 12.5 mm, so the breakdown plasma was positioned 2 mm above the nozzle outlet to prevent the gas from being affected by the entrained air. Additionally, a perforated steel plate was attached to the heater outlet to ensure a uniform temperature field immediately downstream of the heater outlet. The LIBS measurements were performed by changing the CO₂ concentration from 0 vol% to 30 vol% in 3 vol% increments, and the gas temperature from 294 K to 498 K in 25 K increments, while maintaining a 7:3 volume ratio between nitrogen and oxygen within the injection flow. Five hundred spectra were captured for each condition and delay time, and 50 spectra averaged over 10 spectra were used as the data.

3. Data

The continuum spectrum is mostly a consequence of the bremsstrahlung process, and the emission coefficient of this bremsstrahlung radiation (i.e., energy emitted per volume, time, and wavelength), ${\varepsilon _\nu }$ is given as [20]

Equations (4) and (5) are the integrals of Eqs. (1) and (2) for the spectrum acquisition delay, ${t_d}$, and exposure time, τ, respectively.

Figure 2(a) and (b) show the emission spectra obtained with a 500 ns acquisition delay by varying the CO₂ concentration and temperature, respectively. The temperature was 298 K for Fig. 2(a), and the concentration was 30 vol% for Fig. 2(b). All the spectra were normalized to the peak intensity of N⁺ at 500 nm. The spectra consisted of atomic emission lines for N (746 nm), O (777 nm), N⁺ (500 nm), and C (247 nm), and CN bands near 385 nm, in addition to the broadband continuum. As seen in previous studies [7,8], as shown in Fig. 2(a), the intensities of the C line and CN bands increase proportionally with increasing CO₂ concentration. As shown in Fig. 2(b), once normalized to the N + line, the broadband emission intensity decreased with increasing gas temperature. Notably, the intensities of the atomic lines decreased more rapidly as the temperature increased, which is expected owing to the faster decay of plasma at a lower density.

 

Fig. 2. (a,b) Emission spectra collected 500 ns after the laser fire for various CO₂ concentrations at a fixed gas temperature of 298 K, and for various gas temperatures at a fixed CO₂ concentration of 30 vol%, respectively. (c,d) Emission spectra collected 2,100 ns after the laser fire for various CO₂ concentrations at a fixed gas temperature of 298 K, and for various gas temperatures at a fixed CO₂ concentration of 30 vol%, respectively. The spectra in (a,b) are normalized by the intensity at 500 nm, while the spectra in (c,d) are normalized by the intensity at 777 nm.

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Figure 2(c) and (d) show the emission spectra obtained with a 2100 ns acquisition delay by varying the CO₂ concentration and temperature, respectively. All the spectra were normalized to the peak intensity of O at 777 nm. Compared to the spectra with a 500 ns delay, the broadband continuum was almost suppressed, so the spectra consisted mostly of atomic lines and CN bands. From Fig. 2(c), the peak intensities of the C line and CN bands are proportional to the CO₂ concentration at a given temperature. However, from Fig. 2(d), it can be confirmed that these relative spectral intensities do not remain the same with changes in gas temperature certainly because of the different behavior of the plasma, even in the late stages of plasma extinction.

4. Methodology

4.1 Limitations of traditional LIBS analysis

In a conventional univariate analysis, the continuum spectrum was removed and then normalized to a reference atomic line (whose species are relatively invariant) to correlate the emission intensity ratios between the species to their relative concentrations [9]. The plasma is extremely hot in its early stages (< 200 ns after plasma formation), so the fate of C in CO₂ is a C atom. As the plasma cools, these atoms then combine with N atoms to form CN. Thus, the CO₂ concentration had been correlated with the peak intensities of the C and N lines and CN bands [7,8]. Ratios between the spectral lines were obtained after subtracting the continuum spectrum. Figure 3(a) and (c) show the CN-to-N intensity ratios, and Fig. 3(b) and (d) show the C-to-N intensity ratios obtained in the gas temperature range of 294–498 K for each time delay. Although there was a linear trend between the CO₂ concentration and the ratios of each test temperature, they all had different slopes at different temperatures. The slope increased with increasing temperature, and this is because the overall plasma temperature decreases as the ambient density decreases, considering the upper state energies of C, CN and N, which are 7.7, 3.2, and 12 eV, respectively [21,22]. Importantly, as these ratios become a function of both the concentration and density, it can be found that one of the parameters has to be determined before choosing the slope to be used for the determination of the other parameter.

 

Fig. 3. (a,c) CN-to-N intensity ratios from spectra obtained with 500 and 2,100 ns time delays, respectively, for temperatures ranging from 294 to 498 K. (b,d) C-to-N intensity ratios from spectra obtained with 500 and 2,100 ns time delays, respectively, for temperatures ranging from 294 to 498 K.

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4.2 Methodology of this study

The advantage of machine learning is that, once there is a sufficient amount of relevant data, a machine learning model can identify repetitive but subtle changes in spectral samples and can use these changes as features to predict a numeral indicating a desired property, without knowing or requiring detailed physics [23]. Therefore, this study attempts to obtain a data-driven model that simultaneously predicts CO₂ concentration and gas temperature using the entire emission spectrum, containing both broadband emission and atomic emission lines.

As the strength of the broadband emission becomes a function of gas density (see Eq. (3)), specifically in this study, the emission spectra were set to be acquired with delays shorter than those used in previous studies [13–15], allowing the spectra to include some degree of continuum spectrum, in addition to the atomic emission lines. Since the laser-induced plasma emission lasts for a few microseconds [11] and we adopted a portable spectrometer with a CCD line array to improve the practicality of the method, the delay was varied within a few microseconds while fixing the CCD array exposure time to a minimum value. We found that more 532 nm scattered laser light started appearing in the spectrum at shorter delays, but without much scattered laser light, the spectrum still contained a significant amount of broadband continuum at 500 ns delay. Therefore, the emission spectra were collected by shortening the delay from 2100 ns to 500 ns. Results from the spectra with 500 and 2100 ns delays are presented herein, each representing the case of spectra with a significant contribution from broadband emission and that with little contribution from broadband emission.

5. Model structure, model acquisition, and model analysis scheme

5.1 Structure of ML model

Convolutional neural networks (CNN) are most commonly used when input data are images because they can find the correlation and its collective meaning between spatially separated pixels and map these acquired features to the desired output as a complex non-linear function [24]. By viewing the emission spectrum as an image of 1-by-spectrum length in this study, a CNN was employed as a model to predict the CO₂ concentration and gas temperature.

The structure of the CNN used is shown in Fig. 4. A typical CNN is composed of a series of convolutional layers followed by fully connected layers, and an activation layer and a pooling layer are usually placed between the convolutional layers to impose nonlinearity on the output and reduce the dimension of the feature space. Each convolutional layer consists of a number of convolutional kernels (also called filters) used to compute feature maps. The feature maps after the l^th convolution layer are given as

 

Fig. 4. Detailed structure of the CNN model used in the study.

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5.2 Model acquisition

Training, validation, and test datasets were prepared for model acquisition; each dataset was used for training the model, optimization of the model hyper parameters, and evaluation of the model performance, respectively. We note that all data are from individual measurements averaged over 10 laser shot results, and most importantly, data obtained under the same experimental conditions as the data included in the test dataset were not included in the training and validation datasets because the problem this study is addressing is regression prediction. As the data in the test datasets are from experimental conditions and not analyzed through the training and validation datasets, the scheme allows us to estimate the generalization ability of the model, in addition to the predictive performance. More specifically, data from 67% of the experimental conditions in the entire dataset were allocated to the training set. The remaining 22% and 11% of the conditions were assigned to the test and validation sets, respectively. When distributing the experimental conditions across the datasets, the conditions in the training datasets were spread out over the entire range of experimental conditions such that the training data space covers the spaces of the validation and test data.

Critical hyper parameters of CNNs that are kernel size, number of filters, number of epochs, batch size, and initial learning rate, were first selected heuristically and then optimized through the grid-search [25] for all the parameters, and Bayesian optimization [26], especially for the batch size and initial learning rate. As a result of the optimization, the training epochs, batch size, and initial learning rate were determined to be 105, 32, and 0.008, respectively. To find the global minimum, a cosine annealing method that periodically increases the learning rate between the user-specified minimum and maximum learning rates was used as a learning rate scheduler [27]. All the weights and biases in the CNN were updated using the Adam optimizer. Meanwhile, the mean squared error (MSE) was employed as a loss function, and the training proceeded to reduce the function loss using the strategy of the optimizer. The MSE can be formulated as follows

5.3 Gradient-weighted regression activation mapping (Grad-RAM)

Gradient-weighted class activation mapping (Grad-CAM) is a technique that produces a visual map that highlights regions in the image that are key to decisions, especially in a classification problem with CNN models [28]. The importance of spatial features is evaluated based on the gradients of an output with respect to the feature maps of a convolutional layer of interest, which is given as

Although classification is performed based on differences in the combinations of spatial features, in a regression problem, features are shared, and changes in the relative intensities of these features lead to changes in the output values. In addition, both the positive and negative influences of these features on the prediction are important. Thus, as in previous studies [29,30], we calculated the score maps of the positive and negative influences for regression prediction (we call the procedure gradient-weighted regression activation mapping, Grad-RAM) as:

6. Result and discussion

6.1 Prediction results

Figure 5(a) and (b) show a comparison between the predicted and expected values of CO₂ concentration and temperature using the spectra with 500 and 2100 ns time delays, respectively. The slopes of the linear fit were 0.998 and 1.001 for the two time delays in the CO₂ concentration prediction and 1.000 and 0.982 for the temperature prediction. The coefficients of determination (R²) for the CO₂ concentration prediction were 0.9994 and 0.9986 for the two time delays, respectively, and the R² values for the temperature prediction were 0.9968 and 0.9776, respectively. As indicated by the results, the model trained with the shorter time delay spectra (i.e., spectra containing more of the broadband continuum) exhibited a better predictive performance for both concentration and temperature. In particular, the predictive performance for temperature degraded faster than for CO₂ concentration with increasing delay time (i.e., with decreasing contribution of the broadband continuum to the spectra).

 

Fig. 5. (a) Predictive performances of the model trained with the spectra data obtained with 500 ns time delay for CO₂ concentration and gas temperature. (b) Predictive performances of the model trained with the spectra data obtained with 2,100 ns time delay for CO₂ concentration and gas temperature. (c) Prediction error distributions of the models for CO₂ concentration and gas temperature.

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To quantitatively evaluate the prediction accuracy, the distribution of the predictive errors for each model is shown in Fig. 5(c). The Gaussian curves obtained through non-linear least-squares fitting to a normal distribution are also shown in Fig. 5(c). It was found that with a 96% prediction probability (i.e., probability to be within two times σ the standard deviation), the model trained with 500 ns time delay spectra can predict the CO₂ concentration within ±0.4427 vol% and the temperature within ±7.3321 K, whereas the model trained with 2100 ns time delay spectra predicted the CO₂ concentration within ±0.5134 vol%, and a temperature within ±16.9162 K.

6.2 Grad-RAM analysis results

Filters in the first convolutional layer detect the rising and falling (e.g., edges of a 2-D image) of various patterns in a 1-by-225 array. Filters in the second layer then detect higher-order features, such as spectral intensity and shape, expressed as a combination of features from the first layer. The layers essentially extract features that have more collective meanings between pixels in different spatial locations, while losing the location information of those features in an image. We performed a Grad-RAM analysis on the feature maps from the second convolutional layer to visualize the spatial features used by the model and their degree of negative and positive influence on the prediction. The features after the first convolutional layer were composed of too low-level semantics, whereas the spectral resolution in the features after the third convolutional layer was too coarse (i.e., it lost too much spatial information). The Grad-RAM results of predictions for concentration and temperature using the model trained with 500 ns delay time spectra are shown in Fig. 6. For easier interpretation, the results were rescaled and piecewise cubic fitted to the size of the spectrum, as the size of the feature map did not match the size of the spectrum. A Grad-RAM result is specific to each spectrum; thus, results at three different concentrations of 6, 15, and 24 vol% at a fixed temperature of 423 K and three different temperatures of 348, 423, and 498 K at a fixed concentration of 15 vol% are displayed to identify the contributions of each spectral feature to concentration and temperature predictions. First and foremost, peaks of positive and negative influences are located not only on the spectral lines (i.e., 247, 746, and 777 nm) or bands (i.e., 385 nm) but also on the broadband continuum regions (i.e., 400-700 nm). The model tends to predict concentrations by focusing on the relative intensity changes of the CN bands at 385 nm and the O line at 777 nm. The model estimated higher concentrations as the intensities of the CN bands increased but as the O line intensity decreased. As shown in Fig. 3(a), to correct for the effect of gas density on these relative intensity changes, the model predicts lower concentrations with increasing broadband spectral intensities in the wavelength region of 400-500 nm and 540-600 nm. It can be seen from Fig. 6(d), (e), and (f) that, for temperature predictions, the model still utilizes the intensities of the CN bands and O line but utilizes more of the broadband spectrum for prediction. The model estimated higher temperatures with increasing broadband spectral intensity in the wavelength region of 540-700 nm.

 

Fig. 6. (a,b,c) Normalized Grad-RAM scores of spectra obtained with 500 ns time delay at CO₂ concentrations of 6, 15, and 24 vol%, respectively, at a fixed temperature of 423 K. (d,e,f) Normalized Grad-RAM scores of spectra obtained with 500 ns time delay at temperatures of 348, 423, and 498 K, respectively, at a fixed CO₂ concentration of 15 vol%.

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Figure 7 shows the Grad-RAM results of predictions for concentration and temperature, using the model trained with 2100 ns delay time spectra. Again, the results were for 6, 15, and 24 vol% at 423 K and 348, 423, and 498 K at 15 vol%, and were rescaled and cubic-fit to the size of the spectrum. From Fig. 5(b), we can see that the model still predicts both the concentration and temperature well, despite the disappearance of most of the broadband continuum. The analysis shows that the model still uses the broadband continuum but noticeably utilizes the C line at 247 nm in the predictions. The line was small and, therefore, not exploited meaningfully in the model trained with spectra with strong broadband emission. The model estimated higher concentrations as the intensities of the C line and CN bands increased but as the O line intensity decreased. Again, correcting for the effect of gas density on relative intensity changes is essential for accurate prediction, and the correction appears to occur through the different relationships between two of these three spectral intensities. For temperature prediction, from Fig. 7(d), (e), and (f), the model also relies on the intensities of the CN bands, and O and C lines. The model estimated higher temperatures as the intensities of the O line and CN bands increased but as the C line intensity decreased. However, the temperature prediction was noticeably more inaccurate than the concentration prediction (see Fig. 5(a) and (b)). The reason was that the changes in the intensity of these spectral lines and bands result mostly from changes in concentration, and intensity changes due to changes in gas temperature are relatively subtle. Importantly, the model trained with spectra with strong broadband emission was superior in prediction accuracy at both concentration and temperature, although the model was still able to accurately predict concentrations by exploiting differences in the relationships between the atomic line intensities of the three different species.

 

Fig. 7. (a,b,c) Normalized Grad-RAM scores of spectra obtained with 2,100 ns time delay at CO₂ concentrations of 6, 15, and 24 vol%, respectively, at a fixed temperature of 423 K. (d,e,f) Normalized Grad-RAM scores of spectra obtained with 2,100 ns time delay at temperatures of 348, 423, and 498 K, respectively, at a fixed CO₂ concentration of 15 vol%.

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7. Summary and conclusions

The traditional univariate analysis that used the peak intensity ratios suffered from errors in concentration prediction owing to the changes in these ratios with changes in gas density. Therefore, considering that the intensity and shape of the broadband continuum are functions of the gas density for a given optical setup, in this study, a novel method to predict both the temperature and CO₂ concentration using peak intensities, as well as the broadband continuum, was proposed. Furthermore, because the analytical quantification of this broadband spectrum is not trivial, the identification and quantification of features were achieved by employing machine learning, using spectra data obtained experimentally by varying the gas temperature and concentration.

The models in the form of a convolutional neural network (CNN) were acquired using spectra data with and without broadband emission obtained with short and long-time delays, respectively. We found from the model evaluation and gradient-weighted regression activation mapping (Grad-RAM) analysis that:

On the other hand, the model obtained using the data without broadband spectra also showed reasonable prediction performance, although not as good as that of the model using the data with broadband spectra. This is notable because the data-driven training process allows the model to utilize three or more emission lines that exhibit different sensitivities to temperature changes (i.e., gas density).