High-precision coal classification using laser-induced breakdown spectroscopy (LIBS) coupled with the CST-PCA-based ISSA-KELM

Abstract

As one of the main energy sources in human production and life, the accurate and rapid classification of coal is of great significance to industrial production and the control of pollution emissions. However, the complex composition and highly similar elemental composition of coal with different physical properties and chemical composition lead to a high degree of similarity in coal spectral data measured by laser-induced breakdown spectroscopy (LIBS), which poses a great challenge to accurate classification and identification work. In this paper, based on LIBS technology, we integrate the chi-square test (CST) and principal component analysis (PCA) to construct a quadratic dimensionality reduction network (CST-PCA), and for the first time, we propose a new improved sparrow search algorithm (ISSA) by introducing spatial pyramid matching (SPM) chaotic mapping, adaptive inertia weights (w) and Gaussian mutation, and combine it with kernel based extreme learning machine (KELM) to construct an ISSA-KELM data classification model to classify and identify seven types of coal samples. Firstly, 2520 12248-dimensional coal spectral data were preprocessed using a combination of the chi-square test (CST) and principal component analysis (PCA). The KELM was hyper-parameter optimised using ISSA. By comparing with the unoptimized model, the accuracy of coal classification reaches 99.773%. The experimental results show that the CST-PCA-based ISSA-KELM algorithm effectively optimizes the parameters, improves the classification accuracy of coal, and provides a new data processing scheme for accurate qualitative analysis of coal.

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1 Introduction

Coal is an important energy source for human survival and is widely used in various fields, such as power generation, steel production, and construction.¹ The diversity of coal varieties in different regions is due to the differences in the original coal-forming materials, the age of coal formation, the degree of reduction, and the type of genesis. The organic matter of coal mainly consists of carbon, hydrogen, oxygen, nitrogen, and sulfur, among which carbon, hydrogen, and oxygen are the main bodies of organic matter in coal. As coalification proceeds, the carbon content increases while the hydrogen and oxygen content decreases. Furthermore, fundamental indices including volatile matter (V), fixed carbon (FC), and total sulfur (St) differ across various coal samples. In industrial production, by understanding the characteristics of coal, such as calorific value, volatile matter, and ash content, it is possible to effectively improve combustion efficiency, reduce sulfur oxide emissions, extend equipment life, etc. Therefore, identification and analysis of coal with different physical properties and chemical compositions are of great significance for improving combustion efficiency and reducing environmental pollution. However, traditional coal classification methods commonly include two types: manual classification, which is quick but less accurate, and chemical analysis, and chemical analysis, which offers high accuracy but suffers from high costs and time inefficiency, leading to delayed coal quality data. These traditional methods of coal classification are no longer able to meet the requirements for accuracy and cost control to satisfy the current level of industrial production, so it is necessary to develop a new method for rapid coal identification.

Laser-induced breakdown spectroscopy (LIBS) is a widely utilized multi-element analytical technique that employs high-energy laser-induced plasma to generate emission spectra, enabling the determination of a sample's elemental composition and content.^2–7 LIBS is widely used in the field of geological,^8,9 alloy,¹⁰ nuclear material,¹¹ food,^12,13 explosives,¹⁴ and other material testing and analysis.

Recently, advancements in LIBS technology and intelligent optimization algorithms have enabled researchers to apply it alongside multivariate statistical methods in substance analysis. Xinmeng Luo et al.¹⁵ used the optimized back-propagation (BP) neural network model of the sparrow search algorithm (SSA) to achieve the rapid detection of Cd, Cu, and Pb in Fritillaria thunbergii, which provided a basis for the application of LIBS technology to the quantitative analysis of heavy metal content in traditional Chinese medicine. Haorong Guo et al.¹⁶ used LIBS in combination with four machine learning models: support vector machines (SVM), particle swarm optimization for support vector machines (SVM-PSO), least squares support vector machine (LSSVM) and particle swarm optimization for least squares support vector machine (LSSVM-PSO), which were successfully applied to classify six alloys and can be effectively used as a real-time, nondestructive, and multi-element on-line analytical method for aerospace alloys classification. Tianbing Chen et al.¹⁷ used particle swarm optimization-support vector machine (PSO-SVM) to achieve quantitative prediction of heavy metals in pork. Jing Liang et al.¹⁸ used particle swarm optimization algorithm (PSO) optimised kernel extremum learning machine (KELM) on 15 samples of Salvia miltiorrhiza to achieve better classification results. Yarui Wang et al.¹⁹ applied high repetition rate laser-ablation spark-induced breakdown spectroscopy (HRR LA-SIBS) with particle swarm optimization algorithm (PSO) optimization-extreme learning machine (ELM) model to achieve high-precision quantitative elemental analysis of aluminum alloys.

In this study, LIBS was used to classify different coal samples. Due to the complexity of the elemental composition of the coal samples and the sophistication of the spectrometer, the obtained spectra often show many intensity lines. Therefore, extracting meaningful information from raw multidimensional spectral data and downscaling it is a challenging task. To address this problem, this study employs feature selection and dimensionality reduction techniques to eliminate irrelevant and redundant features from spectral data, aiming to reduce computational costs and improve learning performance.

Regarding the application of feature selection methods in LIBS, Chunhua Yan et al.²⁰ proposed a hybrid feature selection method based on the Wootton, Sergeant, Phan-Tan-Luu's algorithm-unsupervised variable reduction-particle swarm optimization (V-WSP-PSO) to reject irrelevant and redundant features and verified the effectiveness of the method using LIBS spectral data from different coal samples. Xiangjun Xu et al.²¹ adopted a method combining spectral preprocessing and feature selection to improve the robustness of the SVM classification model and proved the feasibility of the proposed plastic classification and recycling method. Peng Lu et al.²² proposed a hybrid feature selection method combined with wavelet transform (WT) to analyze the heat value of coal by laser induced breakdown spectroscopy (LIBS), which can effectively reduce the calculation time and improve the performance of the model. Tong Chen et al.²³ proposed a weakly supervised feature selection method based on raw spectral data – the spectral distance variable selection method to improve the prediction accuracy of iron content in slurries. On the other hand, the purpose of dimensionality reduction is to map the original data from a high-dimensional space to a low-dimensional component subspace. Hui Lu et al.²⁴ used partial least squares (PLS) and principal component analysis (PCA) to perform dimensionality reduction and variable screening on electrolyte spectral data, which provided a temporary new method for the testing of the molecular ratios of electrolytes. Hongda Li et al.²⁵ used the UMAP data dimensionality reduction algorithm and support vector machine classification algorithm to classify hyperspectral remote sensing images, which improved the accuracy of recognition and classification. P. N. Senthil Prakash et al.²⁶ proposed a hybrid local fisher discriminant analysis (HLFDA) method for dimensionality reduction of the medical data, which improves the prediction accuracy. Jing Liu et al.²⁷ proposed a kernel-supervised machine learning spectral downscaling framework based on the Mahalanobis distance in hyperspectral imaging remote sensing with good performance in spectral dimensionality reduction.

Intelligent optimisation algorithms, feature selection methods and dimensionality reduction methods show significant advantages in LIBS substance analysis, and this study proposes an ISSA-KELM classification model based on CST-PCA quadratic dimensionality reduction network. Firstly, the elemental spectral data of the coal samples were obtained by ablating the surface of the coal sample preparation by the LIBS system, and the data were subjected to feature selection and dimensionality reduction by using the chi-square test (CST) and principal component analysis (PCA). Subsequently, an improved sparrow search algorithm (ISSA) was proposed by introducing spatial pyramid matching (SPM) chaotic mapping, adaptive inertia weights w and Gaussian mutation. The parameters of the Kernel Extreme Learning Machine (KELM) are also optimised by ISSA and 5-fold cross-validation to determine the optimal model parameters. Finally, the ISSA-KELM qualitative analysis model was applied to classify seven coal samples, and the performance was compared with the unoptimized model. The results show that combining LIBS with the CST-PCA-based ISSA-KELM algorithm model is an effective tool for discriminating and analyzing coals with different physical properties and chemical compositions.

2 Materials and methods

2.1 LIBS experimental setup

The schematic diagram of the LIBS setup used is shown in Fig. 1. The LIBS experimental equipment is a ChemReveal integrated benchtop laser-induced breakdown spectrometer designed and manufactured by TSI, USA. The instrument features a 1064 nm, 10 ns laser light source (Quantel CFR 200) and a seven-channel CCD spectrometer with 0.1 nm resolution. Laser light emitted from the source is focused onto the sample surface via a 1-inch diameter quartz lens. Subsequently, laser-induced plasma spectra are captured by an optical acquisition spectroscopy assembly and transmitted to the spectrometer, enabling the acquisition of full LIBS spectra ranging from 190 to 950 nm. The instrument includes ChemLytics spectral data analysis software, which integrates periodic table and NIST databases to facilitate rapid analysis of LIBS spectra.

Fig. 1 Schematic diagram of the LIBS device.

2.2 Sample preparation

The seven coal samples used in this study were provided by Jinan Zhongbiao Technology Co. Ltd, and their details are presented in Table 1. The raw coal was pre-selected, naturally dried, crushed, blended, and then sieved through an 80-mesh screen before being blended again. Each sample was weighed to 2 g. A tablet press was used to compress each sample at 20 MPa for 130 seconds to produce a tablet with a diameter of 32 mm.

Table 1 Certified values and uncertainties of 7 coal samples

Sample number	Carbon (%)	Hydrogen (%)	Nitrogen (%)	Full sulfur (%)	Volatile matter (%)
ZBM102A	62.30 ± 0.36	3.11 ± 0.10	1.02 ± 0.06	1.53 ± 0.05	12.86 ± 0.22
ZBM104A	78.97 ± 0.38	3.33 ± 0.12	0.96 ± 0.06	4.10 ± 0.12	10.13 ± 0.22
ZBM105	52.69 ± 0.40	2.58 ± 0.10	0.72 ± 0.06	6.35 ± 0.18	14.18 ± 0.50
ZBM106	72.07 ± 0.38	4.46 ± 0.12	1.25 ± 0.06	0.57 ± 0.04	29.70 ± 0.40
ZBM107	79.89 ± 0.38	3.33 ± 0.10	1.21 ± 0.06	1.54 ± 0.05	9.32 ± 0.22
ZBM108A	78.45 ± 0.38	3.27 ± 0.12	1.06 ± 0.07	0.59 ± 0.04	11.72 ± 0.22
ZBM111C	77.14 ± 0.38	4.59 ± 0.12	1.23 ± 0.06	0.92 ± 0.04	31.29 ± 0.36

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2.3 Integrated quadratic dimensionality reduction network based on chi-square test and principal component analysis

2.3.1 Chi-square test. CST is a filtered feature selection method based on statistical theory.²⁸ The main idea is to use the hypothesis validation method to judge the relevance of features to labels by calculating the chi-square value between the actual value and the expected value. The basic formula for chi-square validation is shown in eqn (1).where A represents the actual value and E represents the expected value. Eqn (1) is used to calculate the chi-square value, the larger the chi-square value, the stronger the correlation between the feature and the label, and the features with small chi-square values are removed by sorting through the size of the chi-square value of each feature. To better define the effective range, p-values can be obtained based on the chi-square value and degrees of freedom. P-values generally use 0.01 and 0.05 as the significance level. In this paper, coal sample data were analyzed, and features with p-values less than 0.01 were selected for better removal of uncorrelated features from coal sample spectra and to improve the speed of subsequent qualitative analysis.

2.3.2 Principal components analysis. PCA is an unsupervised learning algorithm for dimensionality reduction, where the main idea is to transform multiple correlated variables into a small number of uncorrelated variables, which are called principal components.²⁹ Each principal component is a linear combination of mutually uncorrelated original variables. PCA reduces the dimensionality of the data by picking these principal components and retaining the main features of the data, avoiding the effects of data redundancy and invalid information. The expression for PCA error can be given in eqn (2).

In this paper, the spectral features after CST feature selection are extracted, and the four principal components are selected to make the error less than 0.05 to complete the secondary dimensionality reduction and achieve the original data information represented by a few variables.

2.4 Kernel based extreme learning machine

KELM is a single hidden layer feed-forward neural network illustrated in Fig. 2. Its core concept involves employing kernel mapping, rather than stochastic mapping, to convert the intricacies of low-dimensional space into a high-dimensional inner product operation, facilitating linear analysis in this expanded space.³⁰ Its kernel matrix and kernel function are shown in eqn (3) and (4). In this paper, the kernel function of the KELM model is set to the radial basis kernel function.

P_ELM = HH^T = h(x_i)h(x_j) = K(x_i,x_j) (3)

K(x_i,x_j) = exp(−γ‖x_i − x_j‖²) (4)

where x_i, x_j are the input vectors. γ is an adjustable parameter that controls the width of the RBF kernel. ‖x_i − x_j‖ is the euclidean distance between two data points. Where x_i, y_i are model input vectors. And the objective function is as in eqn (5).where K(x,x_i) is the kernel function, H is the hidden layer output matrix, C is the regularization coefficient, β is the output weight, and I is the unit matrix. The algorithm is influenced by both the regularization coefficient C and the kernel function parameter S, making it susceptible to local optima. Therefore, it is essential to employ a suitable optimization algorithm to identify the optimal parameters.

Fig. 2 KELM schematic diagram.

2.5 KELM optimization based on improved sparrow search algorithm

2.5.1 Sparrow search algorithm. SSA is an optimization algorithm inspired by the biological traits of sparrows for iterative search.³¹ In SSA, the sparrow population is categorized into discoverers and followers, with a random distribution of vigilantes introduced via a vigilante mechanism. Initialization involves setting up the population and adjusting the positions of discoverers, followers, and vigilantes based on adaptation benefits. The algorithm concludes by identifying the optimal positions of sparrows.

The discoverer's position update formula is shown in eqn (6).

where t is the number of current iterations, t_max is the maximum number of iterations, α is a uniform random number between (0,1), the variable Q obeys a Gaussian distribution, L is a matrix whose elements are all of size 1, R₂ is the warning value, and ST is the safety value.

The follower's position update formula is shown in eqn (7).

where A⁺ = A^T(AA^T)⁻¹, Z^t+1_i,d is the position of the sparrow in dimension i at the t + 1th iteration, A is a 1 × d dimensional matrix, w^t_d is the worst position of the sparrow in dimension d at the t-th iteration of the population, and b^t+1_d is the optimal position of the sparrow in dimension d at the t + 1th iteration of the population.

The vigilante's position update formula is shown in eqn (8).

where Z^t_g denotes the current global optimal position, K is a uniform random number between (−1,1). β is a step control parameter. f_i is the optimal fitness value of the sparrow. f_w is the worst fitness value. f_g is the global optimal fitness value and ε is the smallest constant, which avoids the division by zero error.

The sparrow search algorithm demonstrates robust search capabilities in practical applications for solving global optimization problems. However, it suffers from two primary disadvantages:

• The initial population is generated randomly, making the generated population unevenly distributed and poorly traversed.

• The stagnation phenomenon may occur at the late stage of the algorithm iteration due to the single population, and it is difficult to obtain the global optimal solution.

To address these shortcomings of the sparrow search algorithm, the traditional sparrow search algorithm is improved by using SPM chaotic sequences, adaptive inertia weights (w), and Gaussian mutation.

2.5.2 ISSA optimization KELM algorithm implementation process. In the application of KELM, the selection of kernel function, kernel function parameter S, and regularization coefficient C determine the accuracy of KELM classification. The optimal regularization coefficient C and kernel function parameter S are selected as the model parameters of KELM by the improved SSA model to achieve the recognition of different coal samples. The parameters of the improved sparrow search algorithm to optimize the kernel extreme learning machine include the number of populations, the maximum number of iterations, the dimensionality, and the fitness function. The improvements to the sparrow search algorithm are as follows:

(1) SPM initialization improvements. In typical SSA model, the sparrow population is generated by using the function of generating random numbers, which generates a random population within the upper and lower bounds, therefore, the population distribution has inhomogeneity. SPM mapping is a common form of chaotic mapping, which has the characteristics of randomness and traversal.³² In this paper, SPM mapping is used to generate chaotic sequence initialization populations to improve the quality of the initial solutions, which makes the initial solutions as uniformly distributed as possible and enhances the global search ability. The SPM mapping expression is shown in eqn (9).

where r is a random number in the range (0, 1) and the system is in a chaotic state when the control parameter η, μ ∈ (0, 1).

Combined with the chaotic sequence X(i), the sequence of locations of the primed sparrow individuals in the search area Z^k_n is further generated as in eqn (10).

Z^k_n = Z^k_n,min + X(i)(Z^k_n,max − Z^k_n,min) (10)

Z^k_n,max is the maximum value of the individual position sequence Z^k_n of the first generation sparrow, and Z^k_n,min is the minimum value of the individual position sequence of the first generation sparrow.

Fig. 3 illustrates the distribution of chaotic sequences generated by SPM chaotic mapping. Additionally, this study employs the Tent chaotic mapping function to perturb individual values chaotically, aiming to prevent them from converging to local optima.

Fig. 3 Sequence distribution of SPM chaotic mapping (a) scattered distribution map (b) distribution histogram.

(2) Adaptive inertia weights (w). In the SSA algorithm, the finder locates food for the entire population. Eqn (6) reveals that the finder's own position is not fully utilized, leading to inefficient searching and neglect of the position. Additionally, the discoverer's aggressive search behavior and subsequent convergence of other sparrows to the optimal solution reduce population diversity, making the algorithm prone to local optima. To address this, incorporating the dynamically changing weights w into the updating equation of the discoverer can further optimize the search approach and balance the global and local search. Eqn (12) shows that the weight w is larger in the early stage of the algorithm to achieve stronger global search performance, and w gradually decreases as the number of iterations increases. Thus, the position of the discoverer is dynamically adjusted to give the sparrow population a greater global search capability³³ The updated formula for the discoverer's position is presented in eqn (11).

where t is the current number of iterations, and t_max is the maximum number of iterations.where ω_start is the initial inertia weight, ω_end is the inertia weight at the maximum number of iterations, and i_iter,max is the maximum number of iterations.

(3) Gaussian mutation. In the later stages of the SSA algorithm iteration, the searching individuals rapidly converge to one or a few locations, which increases the likelihood of encountering local optimal stagnation. When the fitness value of the sparrow individual is less than the average fitness value of the sparrow population, it indicates that the “aggregation” phenomenon occurs and Gaussian mutation begins. To address this problem, a Gaussian mutation strategy is proposed.³⁴ When performing the variation, a normally distributed random number with mean μ and variance σ² is used to replace the original parameter values. The Gaussian variation operator is formulated as in eqn (11).

Z_g = Z × (1 + N(0,1)) (13)

where Z_g is the value after gaussian variation, Z is the original parameter value. And N(0,1) is a normally distributed random number with an expectation 0 and standard deviation of 1.

The properties of the normal distribution suggest that the gaussian mutation has superior local search capabilities, concentrating on a specific neighborhood around the original individual. This focus improves the algorithm's efficiency in finding global minima.

(4) Specific steps for ISSA optimisation of KELM. Step 1: initialize the parameters of the ISSA, including the number of populations (pop), the number of iterations (Max_iter), the upper and lower bounds of the variables (lb, ub), the dimensions of the variables (dim), and the objective function for optimization (fobj). Additionally, predefine the proportion of discoverers (PD) and the proportion of sparrows aware of the danger (SD);

Step 2: initialize the population using the SPM chaotic mapping strategy;

Step 3: calculate the fitness value of each individual within the initial population and subsequently sort the population based on these fitness values;

Step 4: update the weights based on the number of iterations;

Step 5: update the location of discoverers, followers, and alerts;

Step 6: determine whether the mutation condition is satisfied or not, if it is satisfied, then perform a gaussian mutation to update the optimal sparrow position, otherwise go to the next step;

Step 7: judge whether the termination condition is satisfied or not, if so, proceed to the next step of decoding to get the optimal parameters C and S, otherwise return to step three.

The entire qualitative analysis process of building the KELM model for ISSA optimization is shown in Fig. 4.

Fig. 4 ISSA-KELM model flowchart.

The model was evaluated through model evaluation metrics (e.g., accuracy, precision, sensitivity, and F1),^35–37 calculated as follows.

where TP is the correct prediction for the positive category, TN is the correct prediction for the negative category, FP is the incorrect prediction for the positive category, and FN is the incorrect prediction for the negative category.

3. Results and discussion

3.1 LIBS spectra

In the experiment, the laser energy was set to be 200 mJ, the laser spot size to be 10 μm, the repetition frequency to be 2 Hz, and the acquisition delay time to be 0.03 μs. 20 presses were prepared for each coal sample, and 18 spectra were acquired for each coal press. A total of 360 spectra were acquired for each coal sample, and the LIBS spectra of different coal samples are shown in Fig. 5.

Fig. 5 Characteristic spectra of different coal samples.

3.2 Analysis of coal samples by CST-PCA

CST was used to select features from the 2520 12248-dimensional spectral data of seven coal samples. The features with p-values less than 0.01 were sorted according to the chi-square value, the spectral features with background and noise were removed, and 7642 features were finally selected. And the major elements were identified according to the National Institute of Standards and Technology (NIST) standards, as shown in Fig. 6, where the spectra of ZBM107 were used, and it can be seen that the typical elemental features in the coal samples were selected.

Fig. 6 Schematic representation of the spectral features selected by the CST method.

The optimal features identified by CST are used as inputs to the PCA model. Since the PCs are new linear combinations of the original wavelength variables, the similarity between the spectra can be visualized by mapping the scores of the first two or three PCs. Fig. 7 shows the visualized 2D and 3D plots of seven coal samples using PCA and CST-PCA downscaling, respectively. In Fig. 7(a), it can be found that there is a serious overlap between ZBM102A and ZBM108A, and the same between ZBM106 and ZBM111C. While in Fig. 7(c), a few samples have a smaller overlap, the differentiation of each sample is better. In Fig. 7(b), there is a serious overlap between ZBM105 and ZBM111C, and the other samples are weakly distinguished. In contrast, Fig. 7(d) shows that each sample has a higher degree of differentiation. By comparing the CST-PCA quadratic dimensionality reduction network with the classical PCA method, it can be found that CST-PCA improves the differentiation between the seven coal samples, which is more conducive to the subsequent classification task.

Fig. 7 Scatter plots of seven coal samples visualized (a) 2D plots of the first two PCs of PCA (b) 3D plots of the first three PCs of PCA (c) 2D plots of the first two PCs of CST-PCA (d) 3D plots of the first three PCs of CST-PCA.

To achieve a significant recognition effect, the optimal features identified by CST were downscaled using PCA. By constructing cumulative plots of principal components from both PCA and CST-PCA, the contributions and cumulative contributions of their respective principal components were determined, as illustrated in Fig. 8. The results show that by using CST-PCA to extract 4 principal components (PCs), the cumulative contribution reaches 96.39%, exceeding the 95% threshold. However, the cumulative contribution does not increase notably with more PCs, suggesting that additional components have limited explanatory power for the dataset. Thus, these 4 PCs capture the majority of the information from the original spectral data and effectively represent the spectral characteristics of the entire coal sample. The cumulative contribution rate of 4 PCs extracted by the PCA model alone only reached 91.43%, which could not represent the sample spectra well, and 11 PCs were needed to be extracted if we wanted to reach the selection threshold of 95%, so the combination of the CST model and PCA model for the secondary dimensionality reduction well simplified the computation of the subsequent qualitative analyses.

Fig. 8 Cumulative contribution of PCA principal components.

3.3 Qualitative analysis study of coal samples based on ISSA-KELM

The KELM parameters were optimized using the improved sparrow search optimization algorithm, as outlined in the optimization method shown in Fig. 4. The parameters for the improved sparrow search algorithm (ISSA) in ISSA-KELM were set as follows: the population size was 30; the maximum number of iterations was 100; the regularization coefficient (C) ranged from 0.01 to 150; the kernel function parameter (S) ranged from 0.01 to 150; the warning value was set to 0.6; the proportion of finders was set to 0.7; and the proportion of at-risk sparrows was set to 0.2. Firstly, the 4-dimensional LIBS spectral data after the secondary dimensionality reduction by CST-PCA was used as input to the ISSA-KELM qualitative analysis model. The analyzed spectral data contained 2520 sets of data, with 360 sets of spectral data for each coal sample, and the spectral data of each coal sample was divided into two groups (252 spectral data for the training set and 108 spectral data for the test set). Then, after ISSA optimization and through five-fold cross-validation, the optimal regularization coefficient C of the KELM model was obtained as 3.9386, and the kernel function parameter S was obtained as 37.0884. Finally, the ISSA-KELM was used to classify the spectral data of seven coal samples. The results show that the classification accuracy of ISSA-KELM can reach 99.773%.

Fig. 9 shows the convergence curves of ISSA and SSA, from which it can be seen that in terms of convergence speed, ISSA converges faster than SSA, with stronger search capability. In addition, the optimal fitness searched by ISSA is also more ideal, with the characteristic of not easily falling into local optimality. The significant advantage of the model's improved performance is well verified.

Fig. 9 Convergence curves for SSA and ISSA.

In order to further illustrate the superiority of CST-PCA-ISSA-KELM classification models in identifying coal types, KELM and SSA-KELM models were constructed, respectively. The performance of KELM, SSA-KELM, and ISSA-KELM qualitative analysis models under different downscaling networks of CST-PCA and PCA was compared under the same training and test sets, and the model confusion matrices in different cases are shown in Fig. 10, which shows that only ZBM102A predicted incorrectly 4 samples for the CST-PCA-ISSA-KELM model. The rest of the samples are predicted with fewer errors, while the number of prediction errors for the unoptimized model is significantly higher.

Fig. 10 Classification confusion matrix for different model test sets (a) PCA-based KELM (b) PCA-based SSA-KELM (c) PCA-based ISSA-KELM (d) CST-PCA-based KELM (e) CST-PCA-based SSA-KELM (f) CST-PCA-based ISSA-KELM.

The results of the evaluation indexes of different models for seven different numbered coal samples (ZBM102A, ZBM104A, ZBM105, ZBM106, ZBM107, ZBM108A, and ZBM111C) are shown in Table 2. It can be seen that the CST-PCA-based ISSA-KELM has the highest classification performance for different coal samples. In order to further observe the performance differences between various classification algorithm models, the values of accuracy, recall, precision, and F1 value of seven coal samples were averaged to obtain the evaluation indexes of various classification algorithm models, as shown in Table 3. It can be seen that the values of accuracy, recall, precision, and F1 value of the CST-PCA-based ISSA-KELM are improved when compared with other unoptimized models.

Table 2 Evaluation indicators for different coal numbers^a

Sample	Dimensionality reduction network and models		Classification performance evaluation index
			Accuracy	Recall	Precision	F1 value
a Bold indicate that the evaluation indexes (precision, recall, F1 score, or accuracy) of the proposed method are the highest compared to other methods.
ZBM102A	PCA	KELM	0.96164	0.93519	0.69655	0.79842
		SSA-KELM	0.98413	0.92593	0.96154	0.94340
		ISSA-KELM	0.98810	0.91667	1	0.95652
	CST-PCA	KELM	0.96296	0.96296	0.81250	0.88135
		SSA-KELM	0.98942	0.96296	0.96296	0.96296
		ISSA-KELM	0.99471	0.96296	1	0.98113
ZBM104A	PCA	KELM	0.97090	0.79630	1	0.88660
		SSA-KELM	1	1	1	1
		ISSA-KELM	1	1	1	1
	CST-PCA	KELM	0.98810	0.91667	1	0.95652
		SSA-KELM	1	1	1	1
		ISSA-KELM	1	1	1	1
ZBM105	PCA	KELM	0.99339	0.95370	1	0.97630
		SSA-KELM	0.99868	0.99074	1	0.99535
		ISSA-KELM	0.99868	0.99074	1	0.99535
	CST-PCA	KELM	0.99339	0.95370	1	0.97630
		SSA-KELM	0.99735	0.98148	1	0.99065
		ISSA-KELM	0.99868	0.99074	1	0.99535
ZBM106	PCA	KELM	0.99471	0.97222	0.99057	0.98131
		SSA-KELM	0.99735	0.99074	0.99074	0.99074
		ISSA-KELM	0.99868	1	0.99083	0.99539
	CST-PCA	KELM	0.99471	0.97222	0.99057	0.98131
		SSA-KELM	0.99735	0.99074	0.99074	0.99074
		ISSA-KELM	0.99868	1	0.99083	0.99539
ZBM107	PCA	KELM	0.99603	0.97222	1	0.98591
		SSA-KELM	1	1	1	1
		ISSA-KELM	1	1	1	1
	CST-PCA	KELM	0.99603	0.97222	1	0.98591
		SSA-KELM	1	1	1	1
		ISSA-KELM	1	1	1	1
ZBM108A	PCA	KELM	0.97751	0.91667	0.92523	0.92093
		SSA-KELM	0.98413	0.97222	0.92105	0.94595
		ISSA-KELM	0.98677	1	0.91525	0.95575
	CST-PCA	KELM	0.98677	0.95370	0.95370	0.95370
		SSA-KELM	0.98942	0.97222	0.95455	0.96331
		ISSA-KELM	0.99339	1	0.95575	0.97737
ZBM111C	PCA	KELM	0.99471	0.96296	1	0.98113
		SSA-KELM	0.99868	0.99074	1	0.99535
		ISSA-KELM	0.99868	0.99074	1	0.99535
	CST-PCA	KELM	0.99603	0.98148	0.99065	0.98605
		SSA-KELM	0.99735	0.99074	0.99074	0.99074
		ISSA-KELM	0.99868	0.99074	1	0.99535

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Table 3 Evaluation metrics for different algorithmic models^a

Dimensionality reduction network	Models	Accuracy	Recall	Precision	F1 value
a Bold indicate that the evaluation indexes (precision, recall, F1 score, or accuracy) of the proposed method are the highest compared to other methods.
PCA	KELM	0.98413	0.92989	0.94462	0.93294
	SSA-KELM	0.99471	0.98148	0.98190	0.98154
	ISSA-KELM	0.99584	0.98545	0.98658	0.98548
CST-PCA	KELM	0.98828	0.95899	0.96392	0.96016
	SSA-KELM	0.99584	0.98544	0.98557	0.98549
	ISSA-KELM	0.99773	0.99206	0.99237	0.99208

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In summary, compared with other unoptimized classification algorithm models, the CST-PCA-based ISSA-KELM algorithm model has significant advantages over other unoptimized models, and the accuracy is 99.773%.

4 Conclusion

For the LIBS spectral data of coal samples with complex and highly similar elemental compositions, this study proposes a CST-PCA quadratic dimensionality reduction model for in-depth processing of the data, and the experimental results show that the cumulative contribution rate of the preprocessed spectral data reaches up to 96.39%, which demonstrates a more excellent performance of dimensionality reduction than that of the classical PCA method, significantly reduces the spectral background noise, and improves the efficiency of the model computation. Then, in this study, an improved sparrow search algorithm is proposed for the first time by combining SPM chaotic mapping, adaptive inertia weights (w), and Gaussian variation, and further combined with KELM to construct the ISSA-KELM high-precision coal classification model. And through five times of cross-validation, the model achieves the optimal classification effect with an accuracy of 99.773% under the condition that the regularization coefficient C is set to 3.9386 and the kernel function parameter S is set to 37.0884. Compared with the unoptimized models (KELM, SSA-KELM), this improved strategy significantly enhances the model classification performance. The significant advantages of this method in complex multi-dimensional spectral data processing are verified by the high-precision identification and classification of seven different coal samples. This study provides a novel and efficient solution to the problem of high-dimensional data processing and classification based on LIBS technology, which has high academic value and application potential. Meanwhile, in industrial production, the research results of this paper have important reference value for improving combustion efficiency and reducing environmental pollution.

Data availability

Due to legal and ethical confidentiality, the raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work is grateful for the funding of the National Natural Science Foundation of China (No. 52075504), Shanxi Province key Research and Development Program Projects (No. 202302150101016), State Key Laboratory of Quantum Optics and Optical Quantum Devices (Shanxi University) Open project (No. KF202301), the Open Project Program of Shanxi Key Laboratory of Advanced Semiconductor Optoelectronic Devices and Systems (No. 2023SZKF11), Postgraduate Scientific Research Innovation Project of Shanxi Province in 2023 (No. 2023KY608), and Postgraduate Scientific Research Innovation Project of Shanxi Province in 2023 (No. 2023KY584).

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