Quantitative Analysis of Calorific Value of Coal Based on Spectral

DOI: 10.1021/acs.energyfuels.7b01718. Publication Date (Web): December 4, 2017 ... The results showed that the quantitative model obtained the best co...
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Quantitative Analysis of Calorific Value of Coal Based on Spectral Preprocessing by Laser-Induced Breakdown Spectroscopy (LIBS) Wenbing Li,†,‡ Jidong Lu,*,†,‡ Meirong Dong,†,‡ Shengzi Lu,†,‡ Jianhua Yu,†,‡ Shishi Li,†,‡ Jianwei Huang,†,‡ and Jing Liu†,‡ †

School of Electric Power of South China University of Technology, Guangzhou 510640, China Guangdong Province Engineering Research Center of High Efficient and Low Pollution Energy Conversion, Guangzhou, Guangdong 510640, China

‡

ABSTRACT: Calorific value is an essential fuel parameter during the process of energy utilization. Forty-four coal samples with different calorific values were quantitatively analyzed by laser-induced breakdown spectroscopy (LIBS) in this paper. The influences of different spectral preprocessing methods such as smoothing, standard normal variate transformation (SNV), multiplicative scatter correction (MSC), mean centering (MC), and derivation by convolution (Savitzky−Golay) on the quantitative model have been analyzed and compared. The results showed that the quantitative model obtained the best comprehensive performance with the application of the 11 points smoothing combined with the second-order derivation. The correlation coefficient of calibration set, correlation coefficient of validation set, RMSECV, and RMSEP were 0.9909, 0.9972, 0.467, and 0.276 MJ/kg, respectively, which were optimized compared with the traditional partial least-squares (PLS) model by 15.9%, 37.7%, 75.1%, and 88.3%, respectively. It indicated the stability and prediction accuracy of the model were greatly improved. This research showed that the spectral smoothing reduced the differences of matrix effects among different samples effectively, and the derivative convolution (Savitzky−Golay) could further eliminate the interelement influences. fluctuation of the heavy ash-forming element (such as iron) greatly. Furthermore, its neutron source causes potential health hazards. The disadvantages of such devices such as technical complexity, costly investment, difficulty in calibration, and radioactive pollution limit its extensive application in the field of coal property analysis. Therefore, it is industrially important to realize the clean and efficient combustion of coal by developing a rapid detection method with wide application prospects. Laser-induced breakdown spectroscopy (LIBS) is a typical atomic emission spectrometry technique. In LIBS, a high temperature plasma is created by focusing a high energy pulsed laser beam at the analytic target and element types and concentrations are analyzed by inspecting the spectrally resolved emissions during the plasma cooling process.6 Cheng7 investigated trace metals in aerosols by laser-induced plasma techniques. De Boni et al.8 monitored a series of transesterification reactions of soy bean oil and methyl alcohol catalyzed by potassium hydroxide with laser spectroscopy. Gaft et al.9 developed a set of test prototype of LIBS measuring coal which was installed on the material conveyor belts. The ash content in the massive coal samples was measured continuously and compared with the results of the PGNAA coal analyzer. The results show that the accuracy of measurement need to be further improved. Zhang et al.10 reported that the development of a coal property fast analyzer prototype which achieved ultimate analysis (C, Ca, Mg, Ti, Si, H, Al, Fe). The relative

1. INTRODUCTION Calorific value is the classification index or auxiliary index of coal classification. It is also the main property index in coal coding system and the main basis for determining the price of fuel for power plants. Calorific value is commonly used to evaluate the energy efficiency of fuel consumed in thermal power plants,1 applied to calculate the thermodynamic efficiency of gasification of entrained-flow gasifier2 and as an important indicator of biodiesel used in diesel engine without any modification.3 Therefore, the timely and accurate analysis of calorific value is an extremely important procedure for combustion optimization and other fuel utilizations. For solid fuels, calorific value is defined as the quantity of heat released from the complete combustion of a unit mass of fuel. It is usually measured by the bomb calorimeter in the laboratory. The traditional detection method of calorific value is analyzed offline after fuel sampling. It usually need take several hours from sampling to the test results reporting, which seriously lag behind the burning of the combustion equipment. And to some extent, it will cause energy waste and not be conducive to the real-time control of combustion equipment and optimize the operation. At present, the rapid analysis device of coal property on the market is mainly the analyzer based on X-ray fluorescence spectrometry technology (XRF)4 or according to prompt gamma neutron activation analysis technology (PGNAA).5 However, XRF has a long measurement period and poor analytical precision. It is only suitable for elements with atomic weights greater than 23 and easily affected by coal, and it requires frequent calibration during the operation. Nonmetallic elements such as C, H, O, and S are detected by PGNAA and used to calculate the calorific value. However, the measurement accuracy is affected by the © XXXX American Chemical Society

Received: June 16, 2017 Revised: November 20, 2017 Published: December 4, 2017 A

DOI: 10.1021/acs.energyfuels.7b01718 Energy Fuels XXXX, XXX, XXX−XXX

Article

Energy & Fuels Table 1. Gross Calorific Value (GCV) of Coal Samples sample no.

GCV (MJ/kg)

sample no.

GCV (MJ/kg)

sample no.

GCV (MJ/kg)

sample no.

GCV (MJ/kg)

#1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11

18.70 20.48 21.05 21.65 21.77 21.86 22.02 22.03 22.50 22.59 22.59

#12 #13 #14 #15 #16 #17 #18 #19 #20 #21 #22

23.36 23.81 23.85 24.29 24.86 25.10 25.13 25.31 25.96 26.40 26.44

#23 #24 #25 #26 #27 #28 #29 #30 #31 #32 #33

26.47 26.63 26.96 27.04 27.29 27.30 27.59 27.98 28.01 28.43 28.47

#34 #35 #36 #37 #38 #39 #40 #41 #42 #43 #44

29.16 29.49 29.62 30.28 30.58 30.76 30.78 30.86 31.49 31.50 32.58

to normalize the spectra using reference signals such as internal standard element,22 spectral area,23 or background intensity.24 The plasma characteristic parameters were also used to compensate for the fluctuation of the spectral signal by Wang et al.25−28 However, to date, the limited quantitative analytical performance due to matrix effects, as well as interference of sample background, overlaps and interferences among spectral lines, still remain. In this work, moving average smoothing was first applied on the same spectrum wavelength of different coal samples to reduce the difference among matrix effects from different samples. Then, scatter correction, spectral interferences correction and enhancement of differences among spectra were investigated. At last, a quantitative analysis model of calorific value was established by utilizing the partial least-squares regression to improve the precisions and accuracies of the calorific value measurement in coal.

standard deviation (RSD) of elemental analysis was about 10%, and RSD of ash analysis was between 2.29% and 13.47%. LIBS is also being gradually developed into a highly competitive coal property rapid detection technology with the advantages of no or little sample preparation, very little damage to the sample, multielement simultaneous rapid detection, and pollution-free operation.11 Yao et al.12 quantitatively analyzed the ash content of coal by partial least-squares (PLS) method and discussed the effects of different spectral ranges on the correlation coefficient of calibration set, the correlation coefficient of validation set, the root-mean-square error of calibration (RMSEC), and the root-mean-square error of cross validation (RMSECV). Dong et al.13 detected the coal samples with different contents of volatile matter by LIBS, and the relevant LIBS spectral information based on coal structural characteristics was extracted by partial correlation and principal component regression. Furthermore, a highly correlative calibration model was established. Yuan et al.14 developed a nonlinear multivariate principal component model based on PLS for quantitative analysis of the ash, volatile matter, and calorific value in coal. They also proposed a spectrum standardization method for the quantitative analysis of C content in bituminous coals by LIBS and the good repeatability and accuracy were obtained.15 In order to further improve the accuracy and precision of coal property analysis, they also combined the two approaches of dominant factor method and spectrum standardization method.16 It has shown great potential in the application of coal property analysis by LIBS. However, matrix effect is the main issue to affect the accuracy of analysis because of the complex composition and structure of coal and the characteristics of LIBS technology.17 And some elements emission lines would be interfered by other elements. Furthermore, the complex and diverse elemental composition of coal coupled with its complex physical and chemical structure lead to more serious interference. Therefore, it is necessary to conduct the spectral preprocessing is necessary for reducing the influence of these disturbances. Yuan18 combined with wavelet transformation and PLS modeling, the quantitative analysis of carbon in coal was performed, and the RMSEP was reduced from 4.18% to 1.94%. Sun et al.19 set thresholds to filter the unwanted spectra and used a polynomial model to estimate continuous background from the residual spectra to achieve the purpose of noise removal. Some others also applied the method of separating overlapping peaks to reduce noise.20,21 In the application of LIBS, it is needed to reduce the data instability in addition to the demand of spectral noise reduction. A common method is

2. MATERIALS AND METHODS 2.1. Samples. Coal samples were collected from different mines across China. The set of samples used consisted of 44 collected coal samples which experienced the grinding, sieving (30 holes per centimeter), and baking into an air-dried base. The gross calorific values (GCVs) of coal samples were determined using a standard offline method, as shown in Table 1. The coal sample was pressed into a 2.5 cm diameter disc-shaped with flat surface. Each kind of coal sample was weighed 3.5 g, the pressure of the tablet press was set to 6.5 t and maintained for 200 s. In order to make the calorific values of the validation set evenly distributed in the calibration set, samples of #3, #7, #11, #15, #19, #23, #27, #31, #35, #39, and #43 were selected as validation samples and the remaining 33 samples were selected for calibration. 2.2. Experimental Setup. The laser-induced breakdown spectroscopy measurements were carried out by a LIBS system shown in Figure 1. The laser source was a Q-switched Nd:YAG pulse laser (Brilliant Eazy, Quantel, France) at 1064 nm, 0−300 mJ adjustable, 6 ns duration. Pulse repetition rate is 1 Hz. The double-channel spectrometer accessorized with two CCD detectors (AvaSpec2048FT-2-RM, Avantes, Netherlands) allowed the recording of the plasma emission in the 230−400 nm and 580−790 nm spectral ranges, with spectral resolution of 0.3−0.4 nm. The laser energy and delay time were optimized to 50.75 mJ and 1.664 μs, respectively. The integration time was set with the minimum integration time of 1.1 ms. With this setting, the signal-to-noise ratio was performed better and the saturation of the detector was not observed. A sample was placed in a chamber which fastened on a motorized X−Y−Z translation stage. Samples were exposed to ambient air during laser ablation. Signal collection was implemented via optical fibers and fused silica collimating lenses set at an about 45° observation angle. Gating of the spectral data collection was achieved by the spectrometer, which was triggered by the digital pulse delay generator (DG535, Stanford, B

DOI: 10.1021/acs.energyfuels.7b01718 Energy Fuels XXXX, XXX, XXX−XXX

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Energy & Fuels 2i − 1

When 1 ≤ i ≤ w ,

xsmooth(i , j) =

1 ∑ xi , j 2i − 1 i = 1

(1) w

When w < i ≤ T − w ,

xsmooth(i , j) =

1 ∑ xi , j 2w + 1 i =−w

xsmooth(i , j) =

1 ∑ xi ,j 2(T − i) + 1 i = 2i − T

(2) T

When T − w < i ≤ T ,

(3) Where xsmooth(i,j) is value of xi,j after smoothing, i is the sample number, j is the number of variable in the spectrum, T is the maximum number of samples. 2w + 1 is the width of the moving window, which can also be interpreted as the number of data points in the window. w is a positive integer. For example, 2w + 1 = 5, it is called five points smoothing. 2.3.2. Surface Scatter Correction. Coal samples selected in this work were subjected to the same sieving but different types of coal have different physical properties. The disc-shaped samples from different types of pulverized coal with same weight and same pressure have different internal density and surface characteristics. Their ablation characteristics are also different, which will disturb the analysis of correlation between calorie value and spectral data. Standard normal variate (SNV) transformation is the standardization of each LIBS spectrum, mainly used to reduce the multiplicative interferences of different solid forms and surface scattering. According to refs 30 and 31 the spectrum of each sample is transformed independently using the following equation:

Figure 1. Diagram of the integrated LIBS system.

USA). The distance between focus position of laser and the surface of each sample should keep the same. In order to achieve this goal, first, laser was focused on the sample surface by adjusting the threedimensional translation stage and adjusting the optical lens to gain the clearest image of sample surface through the CMOS cameras (USB 2.0, Thorlabs, USA). Second, for all samples, when the image is the clearest, the focus point of laser is just on the surface of the sample. Therefore, after the replacement of different thickness samples the laser could be focused on the sample surface, and then the target locations will be obtained by moving the sample stage. The focus position in this paper was optimized to 1 mm below the sample surface. The average intensity of 6 sets spectra from different locations of each sample was obtained to reduce unexpected measurement fluctuations. Each set is an average value of 50 laser shots. 2.3. Methods. A coal plasma is generated by focused a high power laser beam onto the coal sample. The plasma emission decays and emits element-specific radiation which can be resolved spectrally and detected by a spectrometer from the LIBS system. The elemental composition of coal can be detected by analyzing the LIBS spectra. LIBS spectra are generated due to the transitions of atoms between discrete energy levels. Because the transition energy difference is a single value, the LIBS spectra are discrete. In LIBS detection applications, the sample is generally not pretreated or subjected to simple pretreatment. It will inevitably lead to the original spectrum containing matrix effect and other interference information, which will affect the predictive model. Coal contains many kinds of nonmetallic elements and many kinds of metal elements, moreover, the chemical speciations of the same element are also complex and diverse. The chemical structure of coal is very complicated. All these characteristics of coal will affect the state of the laser-induced plasma of coal. It is the reason why matrix effect is always the most critical role which limit the quantitative analytical performance of coal parameters by LIBS. Therefore, the LIBS spectra need to be preprocessed to reduce the adverse effects from interference information in the spectra data. Smoothing, SNV, MSC, MC, and the first and second derivation were applied in this work. In the present work, moving average smoothing was applied on a set spectra of different coal samples to reduce the differences between matrix effects of different samples. In addition, derivation, standard normal variate (SNV) transformation, multiplicative scatter correction (MSC), and mean centering (MC) were used on spectra after smoothing to reduce the other interferences and increasing resolution. 2.3.1. Matrix Effect Correction. Matrix effects play an critical role on the limited accuracy of LIBS measurements. Moving average smoothing method is usually applied on spectrum of each sample to reduce the errors caused by noise signals from instrument and ambient.29 In our work, moving average smoothing was mainly used on the same wavelength of different samples to reduce the influences of the matrix effects from different coal samples. The original spectrum xi,j after smoothing is expressed by the following formula:

xSNV(i , j) =

xi , j − xi m ∑ j = 1 (xi , j

− xi)2 /(p − 1)

(4)

Where xi,j is the original element, xi̅ is the mean value of spectrum xi, xSNV(i,j) is the transformed element, and p is the quantity of variables in the spectrum. 2.3.3. Multiplicative Scatter Correction. Plasma is generated after the high power laser ablating the coal sample. There are atmosphere, plasma and coal particles present on the path for collecting the plasma emission spectrum. And the spectral scattering and other influences caused by the above factors will disturb the collection of effective signals. Similar to the SNV, the multiplicative scatter correction (MSC)32 is mainly to eliminate or weaken the influence of spectral scattering on the experiment resulted from uneven particle size and uneven distribution of the sample particles on the experiment. It is calculated based on the ideal spectral matrix of a group of samples. The ideal spectrum, usually the average spectrum of a representative data set, is used to estimate the scatter of the spectra. The remaining spectra are corrected to have the same scatter level as selected one and each individual spectrum is shifted and rotated so that it fits as closely as possible to the chosen mean spectrum. The fit for the individual and the mean spectrum is achieved by least-squares as followed:

xi = aix ̅ + bi + ei

(5)

Where xi is an original spectrum of sample i, x̅ is the mean spectrum, and ei is the residual spectrum, which ideally represents the chemical information in the data. The fitted constants ai and bi are used to correct each value of the spectrum i as follows: xi ,MSC =

(xi − bi) ai

(6)

Where xi,MSC is the spectrum of xi after MSC. 2.3.4. Differences among Signal Enhancement. The PLS algorithm combines the characteristics of multiple linear regression, principal component analysis and canonical correlation analysis. To establish a spectral analysis model based on multiple linear regression is to analyze the correlation between the changes of the property or compositions to be tested and the fluctuations of spectra rather than the absolute intensities of spectra. The calorific values of coal samples C

DOI: 10.1021/acs.energyfuels.7b01718 Energy Fuels XXXX, XXX, XXX−XXX

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error (RPD).The closer the correlation coefficient to 1, the higher the correlation between the real value and the predicted value. The smaller the values of RMSECV and RMSEP, the better the feasibility of the model and the higher the accuracy of the validation sample prediction. If RPD > 3, it shows that the model calibration is effective, while the robustness is excellent and the prediction accuracy is high. If 2.5 < RPD < 3, the quantitative model is feasible, but the robustness and prediction accuracy need to be improved. When the RPD < 2.5, the model robustness and prediction accuracy are too low to be suitable for quantitative analysis.33 The terms r, RMSEP, RMSECV, and RPD are defined as followed:

selected in this paper are close to each other. In order to improve the robustness and prediction ability of the model, mean centering (MC) was applied to increase the differences between the spectra of the samples. MC is defined as follows: n

1 ∑ x(i , j), n i=1

xMC(i , j) = x(i , j) −

i = 1, 2, ..., n (7)

Where xMC(i, j) is the transformed element, n is the number of samples, and x(i, j) is the original element. 2.3.5. Interferences among Spectral Lines Correction. Deriving spectra is applied to spectra in order to reduce interferences among spectral lines, separate overlapping peaks and improve resolution. In this paper, the first and the second derivative applied is derivation by convolution (Savitzky−Golay) method.31 The derivative spectra xderivative(j) is defined as follows:

n

r=

∑i (yi − y ̅ )(yi ̂ − y ̅ ) n

xderivative(i , j) =

∑

RMSECV =

x(i , t )q(:, j) +w

xderivative(i , j) =

∑

∑i (yi − yi ̂ )2

k

x(i , j + t )q(:, w + 1)

t =−w

RMSEP =

(9)

∑i (yi − yi ̂ )2

L

∑

x(i , t )q(:,2w + 1 − (L − j))

t = L − 2w + 1

SD RPD = = RMSEP

(10)

+w

− yi ̂ )2

(17)

3. RESULTS AND DISCUSSION 3.1. Model of Original Spectra. Calorific value is defined as the amount of heat produced by complete combustion of coal which mainly results from the oxidation of organic compounds. Therefore, nonmetallic elements such as C, H, O, and S have important relationships with calorific value.34 In addition, ash content has been shown to absorb energy during the combustion process since the decomposition of the mineral compound.35 And coal ash is generally composed of various mineral elements such as Ca, Mg, Al, Fe, Na, K, Si, and so on. Based on this physical background, the calorific value of coal is directly or indirectly related to the major, minor, and trace elements. It shows that full spectrum should be used for the quantitative model. Due to the simplification and dimensionality reduction a large number of spectra data, PLS was applied on the quantitative model. First, the invalid signal whose signal-to-noise ratio (SNR) of element spectral intensity is less than three will be removed. The results of the 44 × 4096 raw spectral matrix without preprocessing from coal samples modeled by the PLS algorithm are shown in Figure 2. The rc, rv, RMSECV, and RMSEP values were 0.855, 0.724, 1.89, and 2.36, respectively. The stability and prediction accuracy of the model are very poor because of the interference by excessive noises of raw data and matrix effects of coal samples. In addition, the RPD of the model is 1.5, which indicates that the robustness and prediction accuracy of model are too low to be suitable for quantitative analysis. 3.2. Model of Spectra after Smoothing. Figure 3 shows a typical coal LIBS spectrum with the primarily contained elements marked. The complex and diverse elemental composition of coal coupled with its complexity of physical

⎡ a0 ⎤ ⎢a ⎥ 1 a=⎢ ⎥ ⎢⋮⎥ ⎢ ⎥ ⎣ aw ⎦

(12) The estimated value of a is obtained by fitting with least-squares.

a ̂ = (BTB)−1BTx

k−1 ∑ik (yi

where yi, ŷi are the true and predicted values of coal sample calorific value, respectively. m is the number of cross-validation cycles. k denotes the number of samples of the validation set. y ̅ is the mean true value of coal sample calorific values. y ̂ is the average of the predicted calorific value of coal sample.

normalization factor, H = ∑t =−w ht , and 2w + 1 is the differential width. The convolution derivative under different condition was obtained by applied different column of q according to the above formulas. The purpose of each measurement multiplied by the derivative coefficient is to minimize the influence of the derivative on the useful information. According to the Savitzky−Golay method (also known as polynomial fitting method), q is obtained by fitting with least-squares. For example, q(:,w+1) can be obtained as follows: (11) x = Ba

⎡1 − w ⋯ (− w) p ⎤ ⎥ ⎢ ⋮ ⎥ ⎢⋮ ⋮ ⋯ ⎢ p⎥ ⎢1 − 1 ⋯ (− 1) ⎥ B = ⎢1 0 ⋯ 0 ⎥, ⎥ ⎢ 1 ⎥ ⎢1 1 ⋯ ⎢⋮ ⋮ ⋯ ⋮ ⎥ ⎥ ⎢ ⎣1 w ⋯ w p ⎦

∑ik (yi − y ̅ )2

k

Where xderivative(i,j) is the transformed element, j is number of variables in the spectrum, L is the maximum number of variables in the spectrum, q is the weighting factor matrix with 2w + 1 rows and 2w + 1 h columns, q = H , h refers to the derivative coefficient, H is the

⎡ x −w ⎤ ⎥ ⎢ ⎢ ⋮ ⎥ ⎢ − 1⎥ ⎥ ⎢ where x = ⎢ 0 ⎥, ⎢ 1 ⎥ ⎥ ⎢ ⎢ ⋮ ⎥ ⎢⎣ xw ⎥⎦

(16)

k

When L − w < j ≤ L , xderivative(i , j) =

(15)

m−1

(8)

t=1

When w < j ≤ L − w ,

(14)

m

2w + 1

When 1 ≤ j ≤ w ,

n

∑i (yi − y ̅ )2 ∑i (yi ̂ − y ̅ )2

(13)

Where â is the estimated value of a, and p refers the polynomial order, According to formula 11, the estimated value of x can be derived. Thus, the derivative coefficient and the normalization factor can be obtained. In this paper, the derivation by the convolution (Savitzky− Golay) method with a quadratic polynomial and moving window width of 17 points was used. 2.3.6. Evaluating Parameters of Model. The calibration and validation performances of the model are assessed by the correlation coefficient of calibration set (rc), correlation coefficient of validation set (rv), root-mean-square error of cross validation (RMSECV), rootmean-square error of prediction (RMSEP), and relative percent of D

DOI: 10.1021/acs.energyfuels.7b01718 Energy Fuels XXXX, XXX, XXX−XXX

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Figure 4. Model results of arranging sample #3 in the all positions of the calibration set.

smoothing effects, the smoothing window width from three points to 19 points were selected. The set of graphs in Figure 5

Figure 2. PLS model of the original data.

Figure 5. Comparison of spectrum before and after preprocessing by 11 points smoothing. (a) sample #8 from the calibration set; (b) sample #15 from the validation set; (c) sample #24 from the calibration set.

Figure 3. LIBS spectra of coal sample #1.

and chemical structure lead to the problems of matrix effect and spectral line interference. Before performing other pretreatments on the spectra, the moving average smoothing was applied on the same wavelength of the 44 × 4096 spectral matrix to reduce the interference caused by the matrix effect. Different order of the sample from validation set in calibration set has different effects on the model results. Each validation spectrum was placed in the 34 positions of calibration set respectively and smoothed together with the calibration spectra. The calibration model results after smoothing for each position were compared. And the position with the best model results is the final order used in our work. Figure 4 shows the model results of arranging sample #3 in the all positions of calibration set. The largest rc and the smallest RMSECV were obtained in the third position. Therefore, the final order of sample #3 is the position after the second calibration sample. For the smoothing processing, it is essential to choose the suitable smoothing window width. Too narrow width will cause insufficient smoothing which result in poor denoise effect and model quality. On the contrary, excessive width will lead to excessive smoothing, which causes the missing of much detail information and signal distortion. In order to compare the

show the comparison of spectra before and after preprocessing by 11 points smoothing. The results of samples #8, #24 from the calibration set and sample #15 from the validation set are shown as Figure 5a−c, respectively. It is evidently to show that after the smoothing process, the spectral background of the first channel is almost constant; the spectral background of the second channel with larger background has an increase or decrease, but all the elements in the original spectrum are clearly visible in the smoothed spectrum. The results showed that the spectra smoothing not only significantly reduced the glitches of the spectrum but also made the spectral baselines of different samples closer (consistent with Figure 5a−c), which would decrease the matrix effect among different samples, especially for the second channel. It indicated that the influence of the matrix effect on the model is reduced effectively by smoothing process and the reduction in different samples will also improve the transferability of the model. The matrix effect is one of the main factors which would affect the plasma conditions (plasma temperature, electron density, or ablation quality). Figures 6 and 7 show the comparisons of plasma temperature and electron density from E

DOI: 10.1021/acs.energyfuels.7b01718 Energy Fuels XXXX, XXX, XXX−XXX

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Figure 8. Results of the model after smoothing: (a) correlation coefficient; (b) root-mean-square error.

Figure 6. Plasma temperature of coal samples.

0.9972, respectively, while the smoothing window width changed from 1 to 11 points. The spectral smoothing with appropriate window width reduced the differences among the matrix effects of coal samples, which reduces the interference of the model from the ineffective information and improves the robustness of the model. Furthermore, the number of optimal principal factor was reduced from 10 in the case of nonsmoothing to 7 in the case of 11 point smoothing. It is indicated that the complexity of the model is also significantly reduced. With the further increasing of the smoothing window width, rc is unchanged basically while rv decreases slightly. This is because the main noises have been reduced by 11 point smoothing. As the window width was increased continuously, the noise reduction was not obvious, which indicated that more useful information was removed by the too large window at the same time, resulting in spectral signal distortion and the reduction of model quality. Figure 8b shows that RMSEPV and RMSECV decreased during the increase of the smoothing window width, which means that the effect of the denoising is improved continually. The RMSEP reached the minimum value with 11 point smoothing. As the smooth window width increased, RMSEP began to increase gradually, while RMSECV changed little. This means that the smooth window width was too large and the spectral signal was distorted. As shown in Figure 9, rc and rv values of the model with 11 point smoothing were both above 0.99, and furthermore, RMSECV and RMSEP were 0.481 and 0.305, respectively, which were 74.55% and 87.07% lower than the traditional PLS without preprocessing. The RPD of the model was 11.6, which means that the model has good calibration effect, good robustness, and high prediction precision. Compared with the traditional PLS, the stability of the model and the predictive ability of the validation samples were greatly improved. For quantitative assessment of the calibration model, the value range of the index has to be defined first. The lowest and highest values were determined by the calibration samples. For example, the working range of the model described in this work is 18.70−32.58 MJ/kg. If the index value is outside of the range, the model is not suitable for the prediction. Then the smoothing will have poor performance and even induce larger prediction error. On the other hand, the values of the calibration samples, which used to build models, should be distributed throughout the working range of the model as uniformly and densely as possible. It is one of the principles to

Figure 7. Electron density of coal samples.

original spectra and spectra after smoothing, respectively. The plasma temperature was calculated from Ca I 610.27, 616.22, 643.91, 646.26, and 649.38 nm according to the Boltzmann plot method,36 and the electron density of plasma was derived from HI 656.29 nm.37 The results show that there are huge differences among original spectra both for plasma temperature and electron density of different samples, which would be the reason caused the poor performance of the quantitative analysis model by using the original spectra. While the differences of plasma temperature and electron density from different coal samples were significantly reduced after the spectral smoothing and they show a consistent trend of change both for plasma temperature and electron density. The reducing of differences from temperature and electron density of plasma will significantly improve the quantitative analytical performance of coal property. The results of the PLS model from spectrum after smoothing were shown in Figure 8. The correlation coefficients of calibration set and validation set were significantly increased from nonsmooth (one point smoothing in the figure) to three points smoothing, while the RMSECV and RMSEP were significantly reduced. It was found that the spectral smoothing improved the correlation between the true value and the predicted value, as well as the prediction accuracy. As shown in Figure 8a, the correlation coefficients of validation set and validation set increased from 0.855 and 0.724 to 0.9901 and F

DOI: 10.1021/acs.energyfuels.7b01718 Energy Fuels XXXX, XXX, XXX−XXX

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after smoothing was limited. This is because the grinding, sieving, and pressing improved the inhomogeneity of physical structure and surface characteristics of coal samples. And the plasma emission spectrum is less affected by spectral scattering. Meanwhile, the differences of spectra among samples are big enough because of high sensitivity of LIBS technology. Furthermore, the differences among the influences of different preprocessing methods on the model were not obvious. It was also found that the correlation coefficients and RMSE of the model after smoothing were close to those after smoothing combined with other preprocessing methods. For example, the model results based on smoothing combine with MSC were slightly inferior than smoothing without other preprocessing methods. The cause is that the influence of spectral scattering was not serious, and the preprocessing methods, such as MSC and derivative, increased noise while converted the spectral data.29,38 According to Figure 10, the largest rc and rv of model were obtained by 11 point smoothing combined with second derivative, while the smallest RMSECV and RMSEP were obtained. The results of optimal model are shown in Figure 11,

Figure 9. PLS model with 11 point smoothing.

select the calibration samples, which is helpful for improving the performance of the quantitative model. The more accurate correlation could be established for the calibration samples with uniform and dense distribution. If the values of standards are not distributed uniformly, the spectrum after smoothing can not accurately reflect its value. This will limit the performance of smoothing. 3.3. Model of Spectra after Smoothing Combined with Other Preprocessing Methods. It was evidently to find that the spectra smoothing could reduce the matrix effects among coal samples, but some other factors such as spectral overlap, interferences between spectrum lines would still affect the relationship between the laser-induced breakdown spectrum and the contents of target elements in the samples seriously, as well as the accuracy and stability of the quantitative model. Therefore, it is necessary to perform further interference reduction processing on the spectrum data. Results of the model with 11 point spectral smoothing combined with different preprocessing methods such as SNV, MSC, MC, and first and second derivation were shown in Figure 10. The results showed that the improved degree of SNV and other preprocessing methods applied to the model

Figure 11. PLS model with 11 point smoothing and second derivative.

rc and rv were 0.9909 and 0.9972, respectively, which were 15.9% and 37.7% higher than the traditional PLS model, respectively. Meanwhile the RMSECV and RMSEP were 0.467 and 0.276 MJ/kg which were optimized compared with the traditional PLS model by 75.1% and 88.3%, respectively. The stability and prediction precision were improved by the proposed model compared with PLS model based on dominant factor in literature.14 In particular, RMSEP was reduced by 79.25%, indicating that the prediction ability of the model was greatly improved. The comparisons of the prediction of validation set samples by PLS model with different preprocessing were shown in Table 2. Without any preprocessing, the average relative prediction error of 11 validation samples was 7.16%, and the maximum relative error was 15.24%.With the 11 point smoothing, the average relative prediction error was reduced to less than 1%. And the mean relative prediction error of PLS model based on 11 point smoothing combined with second derivative was 0.87%, which was lower than the 2.71% with the dominant factor PLS model.14 Furthermore, the maximum relative prediction error was only 1.97%. The RPD of the

Figure 10. Results of the model with spectral smoothing combined with different preprocessing: (a) correlation coefficients; (b) rootmean-square error. G

DOI: 10.1021/acs.energyfuels.7b01718 Energy Fuels XXXX, XXX, XXX−XXX

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Energy & Fuels Table 2. Prediction of Validation Samples by PLS Model with Different Preprocessing no. #3 #7 #11 #15 #19 #23 #27 #31 #35 #39 #43 average

real calorific value (MJ/kg)

without preprocessing (MJ/kg)

relative error (%)

11 point smoothing (MJ/kg)

relative error (%)

11 point smoothingand second derivative (MJ/kg)

relative error (%)

21.05 22.02 22.59 24.29 25.31 26.47 27.29 28.01 29.49 30.76 31.5

22.56 23.45 21.74 25.96 27.29 25.66 28.75 30.21 25.13 30.87 26.70

7.18 6.51 3.76 6.86 7.83 3.07 5.35 7.86 14.79 0.36 15.24 7.16

21.02 22.30 22.74 24.45 25.63 26.65 26.79 28.07 29.50 30.25 32.00

0.16 1.26 0.68 0.66 1.25 0.68 1.84 0.21 0.05 1.66 1.59 0.91

20.92 22.43 22.93 24.25 25.81 26.59 27.18 27.95 29.53 30.47 31.91

0.63 1.85 1.51 0.15 1.97 0.45 0.42 0.22 0.13 0.95 1.30 0.87

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ACKNOWLEDGMENTS The work was supported by National Natural Science Foundation of China (No. 51476061 & 51406059); the Guangdong Province Key Laboratory of Efficient and Clean Energy Utilization (2013A061401005); and the Key Laboratory of Efficient and Clean Energy Utilization of Guangdong Higher Education Institutes (KLB10004).

model was 12.9, indicating that the quantitative analysis model had the best robustness, prediction accuracy, and precision. In addition, the average measurement error of the proposed model is 0.22 MJ/kg, which is lower than the national standard error limit.

4. CONCLUSION

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Aiming at the influences of the matrix effects and spectral lines on prediction precision and accuracy of coal quality quantitative analysis model, the PLS quantitative analysis models of coal calorific value were established based on smoothing combined with other preprocessing methods. The moving average smoothing applied on the same variables of different coal samples can effectively reduce the differences of matrix effects among different samples, while the second derivative can further reduce the impacts of the baseline and other backgrounds, overlaps and interferences between spectrum lines. After 11 point smoothing and second derivative, the correlation coefficients of the calibration set and sets of the calorific value model were both above 0.99, which were 15.9% and 37.7% higher than the traditional PLS model by the original spectrum, respectively. Furthermore, the RMSECV and RMSEP of the model were reduced from 1.89 and 2.36 MJ/kg to 0.467 and 0.276 MJ/kg, respectively, while the RPD increased from 1.5 to 12.9, which showed that the excellent robustness and excellent precision and accuracy were obtained for the quantitative model for coal calorific value analysis. The results showed that the combination of smoothing and second derivative processing can greatly improve the robustness and prediction and accuracy of PLS quantitative model. The present work provides a reference for the rapid detection of coal property.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +86-13533770589. Fax: +86-20-87110613. E-mail: jdlu@ scut.edu.cn. ORCID

Jidong Lu: 0000-0003-3351-0456 Shishi Li: 0000-0003-2931-9413 Notes

The authors declare no competing financial interest. H

DOI: 10.1021/acs.energyfuels.7b01718 Energy Fuels XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.energyfuels.7b01718 Energy Fuels XXXX, XXX, XXX−XXX