Coal is a heterogeneous mineral substance mainly composed of carbon, along with various amounts of other elements. The carbon content is an important and pertinent parameter for coal quality. To achieve the rapid and accurate online measurement of the carbon content in coal, four different calibration strategies are applied to coal analysis by laser-induced breakdown spectroscopy (LIBS). Four calibration models based on support vector regression (SVR), back-propagation training (BP), random forest (RF), and partial least-squares regression (PLSR) were proposed, and the prediction accuracy, prediction precision, model stability, and training velocity of the four calibration models were compared for the quantitative analysis of the carbon content. A total of 65 coal samples were ablated, and the plasma spectra were used as the input data. Among the four calibration models, the results indicate that SVR and BP are the most promising calibration models for finding a better optimized model with a better prediction accuracy and prediction precision, and PLSR has a better prediction stability and a faster training velocity; however, RF has a prediction performance worse than those of the other three models.
Coal is a heterogeneous mineral substance mainly composed of carbon, along with various amounts of other elements. The carbon content is an important and pertinent parameter for coal quality. To achieve the rapid and accurate online measurement of the carbon content in coal, four different calibration strategies are applied to coal analysis by laser-induced breakdown spectroscopy (LIBS). Four calibration models based on support vector regression (SVR), back-propagation training (BP), random forest (RF), and partial least-squares regression (PLSR) were proposed, and the prediction accuracy, prediction precision, model stability, and training velocity of the four calibration models were compared for the quantitative analysis of the carbon content. A total of 65 coal samples were ablated, and the plasma spectra were used as the input data. Among the four calibration models, the results indicate that SVR and BP are the most promising calibration models for finding a better optimized model with a better prediction accuracy and prediction precision, and PLSR has a better prediction stability and a faster training velocity; however, RF has a prediction performance worse than those of the other three models.
Although with the great
demand to reduce CO2 emissions
from fossil fuel combustion has become a major task for every government
to meet the global warming crisis, switching from the traditional
energy system to a renewable one requires time and world-wide efforts.
Fossil fuels still play an important role in the current energy system.
Coal still acts as the dominant fuel for power generation at a global
level, especially for developing countries. The share of coal for
power generation in the world was still 35.1% in 2020.[1] According to the BP Statistical Review of World Energy
2021, the world coal reserves in 2020 stood at 1074 billion tones,
with the top four coal reserve nations being the USA (23%), Russia
(15%), Australia (14%), and China (13%).[1] If the combustion efficiency of the existing power station could
be greatly improved, it would make a great contribution to reducing
CO2 emissions. Therefore, online operation optimization
has become more and more important, while the fuel quality online
monitoring technique has become the short board. Calorific value is
a basic characteristic of fuel, which is very important for combustion
adjustment. The calorific value of coal depends mostly on the carbon
content, and measuring the carbon content is useful for coal quality
analysis. Considering the large amount of coal used in both industry
and power generation, the real-time measurement of the carbon content
of coal is of great significance for combustion optimization, fuel
quality monitoring, and pollution abatement.The development
of laser-based optical technology, namely laser-induced
breakdown spectroscopy (LIBS), as a potential online measurement technology
has received a lot of attention in the field of coal quality analysis.[2−4] LIBS as an optical measurement method has several advantages, such
as simultaneous and fast in situ multielemental analysis, minimal
sample preparation, and better security.[5−7] During the LIBS measurement,
a laser beam is focused on the sample surface to generate a plasma
spark, and the emission spectra are collected during the plasma cooling
process and analyzed.[8] Because of matrix
effects and the fluctuation of experimental conditions,[9] there is not a simple linear relationship between
the carbon content and the signal intensity of carbon.A lot
of analysis work for coal has been conducted using LIBS,
including elemental analysis (C, H, N, and S)[10−13] and proximate analysis (calorific
value, ash content, fixed carbon content, and moisture content).[14−17] To improve the accuracy and precision of the LIBS quantitative analysis,
researchers have carried out a lot of studies on the experimental
setup, operating conditions, and different calibration models to enhance
the spectral signal and improve the accuracy of the quantitative analysis.[18,19] The enhanced spectral signal can increase the signal-to-noise ratio
of the spectrum and thus improve the accuracy of measurement. Main
methods to enhance the spectral signal include ambient conditions,[20,21] microwaves,[22,23] spatial confinement,[24,25] double-pulse,[26,27] etc.Aside from improving
the LIBS signal, the calibration model between
the line intensity and the element content of coal is also important.
Methods used to improve the accuracy of the calibration model include
partial least-squares regression (PLSR), support vector regression
(SVR), principle component analysis (PCA), artificial neutral network
(ANN), etc.[28−30] It is of great significance to evaluate and improve
the performance of different chemometric methods. Wang et al.[31] presented a multivariate model based on the
dominant factor for LIBS that combined the advantages of both the
conventional univariate and PLS models. Zhang et al.[32] compared the modeling efficiencies and prediction accuracies
of four calibration models for the quantitative analysis of ash, volatile
matter, and the calorific value of coal based on PLSR, SVR, ANN, and
PCR and found ANN could offer the best compromise between modeling
efficiency and prediction accuracy. Wei et al.[33] used wavelet neural network (WNN) and ANN for the quantitative
analysis of the major components in coal ash and found that the WNN
model had a better performance than the ANN model. These studies show
that the quantitative analysis of coal quality by LIBS combined with
suitable calibration models can be achieved with a high degree of
accuracy. However, the performance of the calibration model is related
to different input variables and optimization methods. To realize
the real-time measurement of the carbon content of coal, it is necessary
to carry out comparative studies of different calibration models and
select a suitable model to achieve a high measurement accuracy.In this study, a LIBS setup was established, and the spectral data
of 65 coal samples were acquired for the quantitative analysis of
the carbon content of coal. Four calibration models based on SVR,
back-propagation neutral network (BP), random forest (RF), and PLSR
were used to build the relationship between the carbon content and
line intensities, and the performances of the four calibration models
were evaluated and further discussed.
Results
and Discussions
Data Preprocessing
To measure the
carbon content, the carbon atomic line at 247.856 nm (C I) was selected
as the characteristic spectral line of carbon based on information
from the National Institute of Standards and Technology (NIST). The
original LIBS spectrum of a coal sample, which was acquired after
30 laser shots, is shown in Figure .
Figure 1
LIBS spectrum of a coal sample.
LIBS spectrum of a coal sample.Before training the model, the spectral data need to be preprocessed.
To reduce the signal fluctuations due to changes in experimental parameters
and the matrix effect of coal, the input spectral lines were preprocessed
with local spectral normalization to get the normalized line intensities.
In local spectral normalization, the peak area of spectra line was
divided by the integral area of the waveband in which the spectral
line was located. Every waveband has a width of around 3 nm. For the
normalization of the C I 247.856 nm line, the spectral range of the
waveband is between 245.400 and 248.130 nm. As shown in Figure , the correlation coefficients
(R2) of the fitting curve increased from
0.0167 to 0.7892 after preprocessing.
Figure 2
Fitting curve of the carbon content with
the intensity of the CI
247.856 nm line.
Fitting curve of the carbon content with
the intensity of the CI
247.856 nm line.
Selection
of Characteristic Spectral Lines
To improve the prediction
accuracy, we introduced spectral lines
of other elements within the spectral range of 190–350 nm as
input data. The introduction lines selected are shown in Table . In the spectrum
of coal, the main spectral lines in the spectral range of 190–350
nm are carbon lines, Mg lines, Fe lines, and Si lines, followed by
some other lines that are independent, distinguishable, and detectable,
as shown in Figure . PLSR was used to build the linear relationship between the intensity
of the spectral lines and the carbon content. After the introduction
of multiple spectral lines in the spectral range of 190–350
nm, the R2 of the calibration curve increased
from 0.7892 to 0.9271, as shown in Figure .
Table 1
Selected Characteristic
Spectral Lines
of Different Elements for Model Establishment
Predicted results for the carbon content with
input lines in the
spectral range of 190–350 nm.
Predicted results for the carbon content with
input lines in the
spectral range of 190–350 nm.Therefore, the introduction of multiple spectral lines in spectral
range of 190–350 nm is helpful to improve the prediction accuracy
of the calibration models.
Comparison of Different
Models
Comparisons
among the prediction accuracy and the model training velocity of the
four calibration models (SVR, BP, RF, and PLSR) were performed. When
training the four models, we chose 52 samples as the calibration set
and 13 samples as the prediction set. The input data for the four
models were the intensities of the characteristic spectral lines of
C, Si, Mg, Ca, Al, and Fe mentioned in Table and the carbon content of coal samples measured
before the experiment. The output data were the predicted values of
the carbon content. All spectral lines were preprocessed, and the
key parameters of the four models were optimized. To evaluate the
performance of the four calibration models, R2, the root-mean-square error of calibration (RMSEC), the root-mean-square
error of prediction (RMSEP), and the model training times of the four
models were calculated and compared.Figure shows the flowchart of the training process.
For BP and RF, the model with the maximum R2 for the prediction set among the 20 run times was selected as the
final optimized model. The R2 and corresponding
values of RMSEC and RMSEP for the optimized model were calculated
as the final results for BP and RF.
Figure 4
Flowchart of the model training process.
Flowchart of the model training process.To better evaluate the prediction abilities of
the four calibration
models, the results with both the selected random prediction set and
the calibration set were calculated and compared.
Randomly
Selected Calibration Set and Prediction
Set
To better describe the prediction accuracy and stability
of the four calibration models, the calibration set and the prediction
set were randomly selected each time. Every model was run 100 times,
and the R2 and RMSE values of each model
were calculated. The R2, RMSEC, and RMSEP
values of the BP and RF models were calculated as mentioned in the
previous section. After changing the calibration set and the prediction
set, a different distribution of R2, RMSEC,
and RMSEP values for the calibration set and the prediction set can
be seen when different calibration models are used. Figure provides the distribution
of R2 values for the calibration set and
the prediction set of four calibration models in 100 run times. For
a more intuitive view, we counted the maximum, minimum, and average
value of R2 for the 100 run times. The
statistical results of the four calibration models are listed in Table .
Figure 5
Predicted results from
the four different calibration models.
Table 2
Results of the Different Calibration
Models for the Carbon Content under Different Calibration Sets and
Prediction Sets
calibration
set
prediction
set
algorithm
R2 > 0.90 (%)
R2 > 0.80 (%)
Rmax2
Rmin2
RMSECavg
R2 > 0.90 (%)
R2 > 0.80 (%)
R2 > 0.70 (%)
Rmax2
Rmin2
RMSEPavg
SVR
100
100
0.99
0.97
0.04
16
72
90
0.95
0.60
0.24
BP
95
100
0.99
0.85
0.10
47
85
94
0.99
0.61
0.21
RF
97
100
0.94
0.89
0.17
14
58
80
0.97
0.45
0.27
PLSR
69
100
0.95
0.83
0.17
41
90
100
0.97
0.72
0.21
Predicted results from
the four different calibration models.It can be clearly seen from Figure that the R2 values
of
the calibration set were more stable than those of the prediction
set, and the R2 values for the calibration
sets of SVR, BP, and RF were larger than those for the prediction
set in most cases. This may be due to overfitting caused by over training
on the calibration set, resulting an overly complex model. Using more
coal samples can effectively reduce overfitting.R2 values for the calibration sets
of SVR and BP were larger than those of RF and PLSR in general. This
shows that SVR and BP can find a more accurate and complex correlation
between the intensities of multiple lines and the carbon content.
SVR and BP as nonlinear calibration models are superior to the linear
model PLSR. In addition, the average RMSEC and RMSEP values of SVR
and BP were smaller than those of RF. This indicates that SVR and
BP have better prediction precision.From the percentage distribution
of the R2 value for the prediction set
in Table , the R2 value
for the prediction set was larger than 0.80 for 72% of SVR results,
85% of BP results, 58% of RF results, and 90% of PLSR results, showing
that BP and PLSR have prediction performances more stable than SVR
and RF when changing the calibration set and the prediction set. In
addition, 47% of results for the R2 value
of the the prediction set in the BP model were larger than 0.90, with
a maximum value of 0.99, indicating that BP performed better than
other models. The R2 value of the calibration
set in the PLSR model was lower than those in the SVR and BP models.
This means that the prediction ability of the PLSR model is limited.
In the RF model, only 14% results for the R2 value of the prediction set were larger than 0.90, and the minimum
value was 0.45, which was smaller than those of other models. This
indicates that the RF model performed worse relative to other models,
with a lower prediction accuracy and a poorer generalization performance.The PLSR model had the best stability among the four models. This
means that PLSR is less dependent on input data because PLSR is a
linear calibration model and there is a strong positive correlation
between the carbon content and the spectral line intensity of carbon.In summary, BP and PLSR had better model stabilities, SVR and BP
could achieve better training performances, and RF performed worse
than other models when the calibration set and the prediction set
were changed.
Selected Calibration
Set and Prediction
Set
For a more visual analysis, the total 65 samples were
divided into 13 groups according to the carbon content, and one sample
from each group was selected as the prediction set. Then, the rest
were selected as the calibration set. Each of the four models was
trained with the same calibration set and prediction set, and the
results were compared.The final result is shown in Table . In general, the
results with the selected calibration set and prediction set were
in good agreement with the results with a randomly selected calibration
set and prediction set. The R2 values
of the prediction set for all models were above 0.91, among which
SVR and BP performed better. The R2 values
of the calibration set for SVR and BP were above 0.97, which demonstrated
a high degree of fitness. On the other hand, the RMSEC and RMSEP values
of SVR and BP were smaller than those of RF and PLSR. This means that
the prediction precision and prediction accuracy of SVR and BP are
superior to those of RF and PLSR.
Table 3
Results of the Different
Calibration
Models for the Carbon Content with the Same Calibration Set and Prediction
Set
calibration
set
prediction
set
algorithm
R2
RMSEC
R2
RMSEP
SVR
0.99
0.04
0.95
0.17
BP
0.97
0.10
0.95
0.16
RF
0.92
0.18
0.91
0.28
PLSR
0.87
0.19
0.92
0.19
It is worth noting that the R2 value
of calibration set was larger than that of the prediction set for
SVR and BP. Additionally, the R2 value
of the calibration set for PLSR was 0.87, which was lower than other
calibration models.To further evaluate the prediction abilities
of the different calibration
models, the model training time was recorded. The modeling time depends
on the algorithm and the optimization method used in the calibration
models. When training the four calibration models, the model training
time for SVR was 6 s, that for BP was 15 s, that for RF was 14 s,
and that for PLSR was 1 s for each calculation. However, it is difficult
to achieve a good result in just one run for the BP and RF models,
so we ran the BP and RF models 20 times. The model training time for
the BP model changed little when the run time increased 20, but the
model training time for the RF model increased to about 45 s. It can
be seen that PLSR and SVR had faster training velocities, BP ranked
second, and RF was the most time consuming.With this selected
calibration set and prediction set, SVR and
BP performed better than RF and PLSR considering the prediction precision
and prediction accuracy, while SVR and PLSR had faster training velocities.
Among the four models, SVR and BP are more likely to find a better
relationship between the carbon content and line intensities with
a higher prediction accuracy and precision. Considering that BP has
a better prediction stability with an acceptable training velocity,
BP is a better choice for the quantitative analysis of the carbon
content in coal. Meanwhile, when the amount of input data is too small
to train the model well, PLSR can be used to establish a linear relationship
between the carbon content and line intensities with an acceptable
accuracy.
Conclusions
In this
study, a LIBS-based online experimental setup for the analysis
of coal samples was established. Four calibration models (SVR, BP,
RF, and PLSR) were employed for the quantitative analysis of the carbon
content of coal, and the performances of four calibration models were
compared and evaluated. The results show that SVR and BP are more
promising calibration models for finding a better regression between
input line intensities and the carbon content, PLSR has a better prediction
stability and training velocity, and RF has a performance worse than
those of the other three models.In summary, when the amount
of data is small it is more suitable
to choose the PLSR model considering its better stability, and when
the amount of data is large enough it is more suitable to choose BP
model considering its better prediction accuracy and prediction precision.
In this work, four calibration models were built, developed, and compared,
demonstrating that the LIBS technique with appropriate calibration
models was a good way to achieve the online analysis of the carbon
content.
Experiment and Methods
Experimental
Setup
The experimental
system consists of a Q-switched Nd:YAG laser (PRO-250–10H,
Spectra Physics) with an output wavelength of 532 nm. The laser pulse
energy was set to be 115 mJ, the pulse duration was 9 ns, and the
repeat frequency was 10 Hz. The laser beam was focused on the sample
surface using a quartz lens with focal length of 150 mm. The focal
plane was positioned approximately 2 mm under the sample surface.
The plasma emission was collected by a collector and coupled into
the spectrometer (Aryelle Butterfly, LTB) equipped with an electron-multiplying
CCD (EMCCD) camera (Andor) through a SMA fiber. The spectrometer has
a wide wavelength range of 195–950 nm, with a high spectral
resolution of 12 pm in the spectral range of 195–350 nm and
a spectral resolution of 36 pm in the spectral range of 350–950
nm. To improve the signal-to-noise ratio of the spectra, highly purified
argon (99.99%) was used as purge gas with a flow rate of 8 L/min.
The coal sample was placed on a two-dimensional rotating stage. The
schematic of the setup is shown in Figure .
Figure 6
Schematic of the experimental setup.
Schematic of the experimental setup.In total, 65 coal samples were utilized in the experiment.
The
carbon content of these samples is shown in Table . The carbon content of the coal samples
was analyzed according to the national standard of China (GB/T 476-2008).
All coal samples were air-dried, crushed, and sieved to a size of
80–200 mesh. The coal powder was then pressed into pellets
by a hydraulic press. The pressure was set to 25 MPa, and the pellets
were kept under this pressure for 5 min. In total, 30 shots at different
ablation points at the surface of the coal sample were accumulated
for one spectrum, five spectra were obtained for each sample, and
the average spectrum of the five spectra was used as the final spectrum.
In this analysis, 52 coal samples were chosen for calibration and
13 coal samples were chosen for prediction.
Table 4
Carbon
Content of the Coal Samples
sample number
carbon content (%)
sample number
carbon
content (%)
1
70.35
34
51.33
2
63.38
35
56.78
3
68.58
36
64.28
4
59.30
37
57.01
5
65.10
38
63.21
6
64.18
39
50.86
7
58.17
40
62.32
8
76.89
41
62.03
9
76.30
42
40.60
10
72.84
43
60.84
11
71.09
44
61.43
12
66.17
45
68.58
13
64.27
46
59.65
14
76.04
47
53.17
15
75.68
48
41.65
16
81.45
49
42.69
17
79.60
50
56.55
18
74.16
51
55.18
19
68.81
52
53.81
20
74.87
53
54.36
21
75.59
54
47.06
22
81.90
55
51.06
23
79.24
56
49.06
24
78.40
57
46.07
25
76.68
58
49.71
26
76.28
59
42.56
27
68.20
60
53.63
28
50.13
61
52.96
29
74.29
62
49.04
30
72.57
63
48.03
31
70.96
64
44.05
32
65.35
65
45.24
33
54.69
Methods
Support Vector Regression
(SVR)
Support vector regression is a regression algorithm
that works on
the principle of the support vector machine with a few minor differences.
The basic principle is to find a fitting curve from which the distance
to the data point will be minimized. All SVM models in this study
were implemented using the shareware program LibSVM that was developed
by Chih-Chung Chang and Chih-Jen Lin.[34] The radial basis function (RBF) was used as the kernel function
for nonlinear regression, and the key hyperparameters γ and C of the RBF kernel were optimized. Parameters γ and C took values within a certain range and were optimized
by cross-validation. The mean squared error of calibration set with
fivefold cross-validation was calculated to optimize the values of
γ and C. Figure provides the results of the mean squared error for
different values of γ and C. When the mean
square error was at a minimum, the values of γ and C were determined as the optimal parameters.
Figure 7
MSE vs gamma and C for
SVR.
MSE vs gamma and C for
SVR.
Back
Propagation (BP)
The BP neural
network is a multilayer feed-forward network trained according to
an error back-propagation algorithm.[35] In
this study, the obtained optimal architecture of the BP neural network
involved an input layer, a single implied layer, and an output layer.
The learning rate was set to 1, the training times were set to 1000,
the allowable error was 0.001, and the Levenberg–Marquardt
algorithm was used for BP neural network training and prediction.
In this study, the number of neurons (P) in the hidden
layer was decided by an experience formula[36], where m and n are the number
of neurons in the input and output layers, respectively,
and λ is a constant between 1 and 10. In this study, the number
of neurons in the input and output layers were set at 30 and 1, respectively;
therefore, the value of P was between 7 and 16. To
further optimize the number of neurons in the hidden layer, the average
mean squared error of the prediction set was calculated after 15 runs
for each number of neurons in the hidden layer. Figure provides the results for the average mean
squared error of the prediction set with different numbers of neurons.
The number of neurons in the hidden layer was selected when the average
mean squared error of the prediction set was a minimum in each run.
Figure 8
MSE vs
the number of neurons in the hidden layer for BP.
MSE vs
the number of neurons in the hidden layer for BP.
Random Forest (RF)
Random forest
is an ensemble learning algorithm and is commonly used to solve regression
or classification problems. Random forest can handle very high dimensional
data and a nonlinear relationship between predictors. In this study,
we do regression with the TreeBagger in MATLAB to create bag of decision
trees. There are some main parameters that need to be set before training:[37] (1) the number of predictor variables, which
were randomly selected from the data (fboot); (2) the number of decision
trees (ntree); and (3) the optimum terminal nodes (leaf). In this
study, leaf = 5, 10, 15, 20, and 25; ntrees = 50, 100, 200, 250, and
400; and fboot = 0.2, 0.4, 0.6, 0.8, and 1 were assumed, and the model
was run in MATLAB R2019a software to find a best combination. As shown
in Figure , the mean
squared errors obtained by regression for various leaf sizes were
compared to verify the optimal leaf size and ntree values with fboot
set to 1. After the optimal leaf size and ntree valeus was determined,
the mean squared errors obtained by regression for various fboot values
were calculated, as shown in Figure . When the MSE was at the minimum, the optimal leaf,
ntrees, and fboot values were determined and used to construct the
RF model. The best combination of parameters to generate the RF model
is leaf = 5, ntrees = 250, and fboot = 1.
Figure 9
MSE vs the leaf size
for RF.
Figure 10
MSE vs the fboot for RF.
MSE vs the leaf size
for RF.MSE vs the fboot for RF.
Partial Least-Squares Regression (PLSR)
PLSR is a statistical method that integrates advantages of multiple
linear regression analysis, principal component analysis, and typical
correlation analysis. PLSR finds a linear regression model by projecting
the input data into a new space. The number of principal components
is a key parameter of PLSR. In this study, the number of principal
components was selected by the variance explained in the input data
with a fivefold cross-validation, the percentage of variance explained
by the model containing the percentage of variance explained in predictor
variables by each PLS component, and the percentage of variance explained
in response variables. Figure provides the percentage of variance explained in the
input data with different PLS components. When determining the optical
number of principle components, both the cumulative percentage of
variance explained in predictor variables and that in response variables
need to be greater than 0.9.
Figure 11
Percentage of variance vs the component for
PLSR.
Percentage of variance vs the component for
PLSR.
Evaluation
Index for the Calibration Models
To evaluate the performance
of the above-mentioned four models,
the correlation coefficients (R2), the
root-mean-square error of calibration (RMSEC), and the root-mean-square
error of prediction (RMSEP) were employed to represent prediction
accuracy and precision of the calibration models; the model training
time was used to evaluate the model training velocity. R2 and RMSE are defined as follows:where N is the number of
samples, y is the carbon
content of sample i measured before the experiments, is the
average carbon content of the samples,
and is the
predicted carbon content.where n1 is the
number of samples for the calibration set and n2 is the number of samples for the prediction set.R2 reflects the correlation between the carbon
content measured before the experiments and the predicted value of
the carbon content. The RMSE reflects the deviation between the predicted
value and the measured value for the carbon content. The closer R2 is to 1, the closer RMSEC and RMSEP are to
0, and the stronger the prediction ability of the model.
Authors: L B Guo; Z Q Hao; M Shen; W Xiong; X N He; Z Q Xie; M Gao; X Y Li; X Y Zeng; Y F Lu Journal: Opt Express Date: 2013-07-29 Impact factor: 3.894
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11