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Abstract
The identification of steels is a crucial step in the process of recycling and reusing steel waste. Laser-induced breakdown spectroscopy (LIBS) coupled with machine learning is a convenient method to classify the types of materials. LIBS can generate characteristic spectra of various samples as input variable for steel classification in real time. However, the performance of classification model is limited to the complex input due to similar chemical composition in samples and nonlinearity problems between spectral intensities and elemental concentrations. In this study, we developed a method of LIBS coupled with deep belief network (DBN), which is suitable to deal with a nonlinear problem, to classify 13 brands of special steels. The performance of the training and validation sets were used as the standard to optimize the structure of DBN. For different input, such as the intensities of full-spectra signals and characteristic spectra lines, the accuracies of the optimized DBN model in the training, validation, and test set are all over 98%. Moreover, compared with the self-organizing maps, linear discriminant analysis (LDA), k-nearest neighbor (KNN) and back-propagation artificial neural networks (BPANN), the result of the test set showed that the optimized DBN model performed second best (98.46%) in all methods using characteristic spectra lines as input. The test accuracy of the DBN model could reach 100% and the maximum accuracy of other methods ranged from 62.31% to 96.16% using full-spectra signals as input. This study demonstrates that DBN can extract representative feature information from high-dimensional input, and that LIBS coupled with DBN has great potential for steel classification.
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1. Introduction
Steel is an important material applied in many industrial fields, and could be made into different alloys with special performance to meet various industrial needs. Consumption of crude steel worldwide amounted to 1,878 million tons in 2020 and the average growth rate reached 3% in the last five years [1]. A large amount of steel products have been generated due to high consumption of steel. The classification rate of the materials of Cu, Al and Mg is only 86-95% by an optical sorting method [2]. Traditionally, the steel-sorting application is low precision and takes long time, which will influence the quality of steel products made of scrap in the future [3]. To save steel resources and ensure product quality, rapid identification of steel is a crucial step in the process of recycling and reusing steel waste. However, traditional analytical methods, such as atomic absorption spectroscopy (AAS) [4], inductively coupled plasma-mass spectrometry (ICP-MS) [5], and spark discharge optical emission spectroscopy (SD-OES) [4,5], need relatively long analysis time, which is not conducive to the rapid detection of steel in industrial fields [4–6]. Therefore, a more convenient, precise, and rapid classification method for steel is necessary.
Laser-induced breakdown spectroscopy (LIBS), is an atomic emission spectroscopy technique that utilizes laser pulse to create a plasma and the composition of samples could be analyzed by emission lines of the plasma [7,8]. LIBS has great potential prospects in real-time detection of industrial field because it has many advantages, including easy or no sample pretreatment, fast analyzing speed, multi-element analysis capability, and micro damage detection for samples [9,10]. In recent years, some research groups have combined LIBS with machine learning (ML) methods for material classification and obtained meaningful results [11]. For example, Zhang et al. developed LIBS assisted with random forest (RF) to detect nine steel grades and achieved higher performance [12]. Lin et al. used partial least-squares discriminant analysis (PLS-DA) and support vector machine (SVM) classification methods to identify 40 steel alloys, while the identification accuracy was 96.25% and 95%, respectively [13]. Tang et al. used LIBS combined with self-organizing maps (SOM) and K-means algorithm to identify 20 kinds of polymers and the accuracy was 99.2% [14]. During PLS-DA classification model training, Kim et al. applied baseline removal and root-mean-square-based normalization (BR-RMSN) to mitigate the noise effect of LIBS signals, thereby improving the classification accuracy from 91.2% to 95.5% for all five metal types [15]. Eden et al. proposed a metal scrap classification based on LIBS coupled with the pre-cluster-based regression and PLS-DA for same-base alloys; the results indicated that the proposed method is better than conventional classification algorithms [16]. Campanella et al. developed the application of back-propagation artificial neural networks (BPANN) to LIBS analysis for non-ferrous automotive scraps, which obtained satisfactory performance for the on-line classification of Al alloys [17]. Evelyne et al. used soft independent modeling of class analogy (SIMCA) to classify the alloy species, and the results indicated that the model was robust [18]. Jeyne et al. achieved the discrimination of 80 metal samples by applying multivariate normalization method combined with k-nearest neighbor (KNN) [19]. However, limitations remain in that most of the aforementioned methods need to identify the composition of samples in advance to determine and select feature information as input by using different selection principles.
In general, the classification accuracy is greatly affected by the quality of input. However, some uncertainty factors of spectral signal remain in sample measuring progress such as self-absorption [20] and spectral interference [21]. Meanwhile, only a nuanced difference is observed in the intensity of spectral lines due to the similarities in composition of steel products, which increases the uncertainty of LIBS signals and the uncertainty may lead to the poor accuracy of multivariable model [22]. In some cases, to avoid the problem of the hard spectral line selection, spectral interference, and less input information, the LIBS full-spectra signals with a large amount of available variables were used as input for the classification model [23]. For example, Soichi et al. proposed a signal preprocessing method that takes the full spectra of pelletized hydrothermal deposits into an appropriate form as input for artificial neural network (ANN), which improves the identification accuracy to 90.1% [24]. However, besides the spectral lines of the element analyzed, the full-spectra signals also contain much redundant information such as spectral noise and background, which may increase the difficulty of extracting feature information. Thus, we need to solve the complex non-linear properties in LIBS signals by applying an ML method with strong adaptive capacity and higher precision.
Deep learning can extract the important feature information automatically from large and complex sets of data by utilizing hierarchical architectures, which is a more accurate and efficient method [25]. As a representative of deep learning, deep belief network (DBN) is suitable to deal with the nonlinear problem for classification in industrial application that depends on the model structure. Composed of several restricted Boltzmann machines (RBMs), DBN is a randomly generated neural network that can learn probability distribution through input data [26]. In general, increasing hidden layers can learn high-level features from input and improve the DBN model performance, but the high-level features are not easy to encode in DBN with a deeper hidden layer [27], which may increase the computational cost and leads to a negative effect of classification performance. Recently, Vrábel et al. compared the performance of principal component analysis (PCA) and RBM for dimension reduction in large data of soil powders mixed with gypsum, and the results show that RBM is better than PCA in terms of less training time, applicability to large datasets, and extensibility of the method [28]. Zhao et al. applied LIBS combined with DBN to classify the contaminated soil and achieved satisfactory classification [29]. However, to the best of our knowledge, publications on LIBS combined with DBN algorithm for steel classification are rarely reported.
In this study, the structures of DBN model were designed and optimized to improve the classification accuracy. To evaluate the performance of LIBS coupled with DBN, the predicted accuracy of 13 steel types by DBN were compared with other methods (SOM, LDA, KNN, and BP) when full-spectra signals (8400 variables) were used as input. Meanwhile, the same evaluation procedure was conducted by using intensities of characteristic spectra lines (84 variables) as input. Finally, the results of two different inputs indicate that LIBS coupled with DBN has better application prospects in steel classification.
2. Experimental setup and methodology
2.1 Experimental setup
The schematic of the mobile LIBS setup used in this study is illustrated in Fig. 1(a). A compact Q-switch Nd:YAG laser (Ultra 50, Bigsky Co. Ltd., US) operating at a center wavelength of 532 nm and the repetition rate of 10 Hz with a maximum of 29 mJ per pulse. The pulse duration is 7 ns. The laser beam is transmitted through by a special optical fiber (core diameters: 1 mm), reflected by a dichroic mirror and then focused onto the surface of the sample to generate plasma by a plano-convex lens (focal length = 100 mm, Φ = 25.4 mm). Then the emission of LIBS plasma was collected into a compact spectrometer (AvaSpec-ULS2048-6-USB2) by using an optical fiber (core diameter: 400 µm). The spectrometer, equipped with six 2048-pixel CCD cameras (Sony 554), has six channels with a spectral resolution of 0.08 ∼ 0.11 nm in the wavelength range of 291 ∼ 1020 nm. The delay time between the laser pulse and the spectrometer was set as 1.3 µs and the integration time of 1.1 ms was used in this work. The used mobile LIBS setup is shown in Fig. 1(b), which is composed of the main case and the probe. The compact laser, spectrometer, circuit system, optical system, control system, and power system are integrated into the main case (size: 40 × 50 × 70 cm, weight: 50 kg). The probe (size: 22 × 15 × 10 cm, weight: 2 kg) is equipped with lens, optical fibers and dichroic mirror. Experimental environment: Intel CoreTM i5-6200U CPU (2.30 GHz) with 8 GB of computer memory.
2.2 Sample preparation
A total of 39 samples from 13 different brands of special steel (Inner Mongolia North Heavy Industries Group Corp. Ltd.) were used in this study. The matrix element of all samples is Fe with a concentration higher than 90%. The reference concentrations of trace elements of 13 steel brands are listed in Table 1, which are measured by their physicochemical laboratory using inductively coupled plasma-atomic emission spectrometry (ICP-AES) and ICP-MS. For each sample, 30 spectra were collected from different positions on the surface, and each spectrum was an average of 10 measurements, resulting in 1170 spectra for the 39 samples of the 13 steel brands for LIBS analysis.
Table 1. Concentration information (wt.%) of certified elements in 13 brands of steel tube
2.3 Deep belief network (DBN)
A DBN consists of two procedures: (1) utilizing the strategy of training RBMs layer by layer to construct the deep network preliminarily, and (2) fine-tuning the weight parameters of the entire network by back propagation (BP). The structure of DBN is adjusted by the feature of input data. The number of neurons in the output layer is consistent with the number of steel brands. The schematic of DBN is shown in Fig. 2(a). The DBN model was implemented in MATLAB ver. R2017a (MathWorks Corporation, USA).
Input: The intensity value at each wavelength of LIBS data is used as an input variable.
Pre-training: The purpose of pre-training procedure is to obtain proper values of the entire network. DBN, which is utilized RBMs as learning modules, is a significant advance in deep learning [26]. RBM is an energy-based model that is directly inspired by statistical physics. It is a two-layer network with visible neurons vi = {0,1} and hidden neurons hj = {0,1}. The schematic of RBM is shown in Fig. 2(b). The energy function of RBM can be written as follows:
Fine-tuning: As described above, we obtain the proper initialization of the DBN model in the pre-training step. To use the DBN as a classifier, we add an output layer to predict the label of training sets. Then, all parameters in different layers of the network are adjusted by the supervised learning algorithm such as BP. The dimension of LIBS spectra is reduced by DBN to obtain representative feature information from training sets, and BP was later applied to the classification model, which was useful to improve the classification accuracy. This fine-tuning progress is performed over training sets for a certain number of epochs or until the classification accuracy is no longer improved. Using this mechanism, the features with high correlations between neurons in the lower layers can be captured in deeper layers of the DBN model [32], which is beneficial to extract important feature information from large and complex sets of LIBS data.
Compared with ANN, DBN uses a layer-by-layer unsupervised learning to pre-train the networks, which is beneficial to set the proper initial weights of the networks. DBN has the advantages to improve the model performance by avoiding over-fitting and enhancing the model generalization [33]. However, it is difficult to optimize the structure of the DBN model. The calculation time is significantly influenced by the quality of input and the structure of the DBN model. The number of layers and neurons of DBN is adjusted by the features of the LIBS data. Therefore, to improve the modeling efficiency, the number of hidden layers and neurons in each layer is optimized to establish a suitable DBN model in the following sections.
3. Results and discussion
3.1 Data pre-treatment
As mentioned in section 2.1, the LIBS full spectra ranged from 291 nm to 1020 nm, and the intensity of a spectrum has 11,022 variables. The LIBS spectra are shown in Fig. 3 and spectra lines have weak intensity in the wavelength range over 800 nm. To reduce the irrelevant variates from LIBS data and accelerate the training time, the spectrum with 8400 variables in the range of 291 ∼ 797 nm is used as full-spectra signals. To avoid obvious order of magnitude difference in input variables, the intensities of these signals were normalized to the 0–1 range. The normalized computational formula was written as follows:
where the X and Y is the original value and normalized value of the intensity of spectral lines; Xmax and Xmin is the maximum and minimum value of X, respectively. One-ninth of the spectra of each steel brand was randomly chosen as test set and the remaining spectra were randomly divided into training and validation sets in 4:1 proportion. The spectra from different steel samples were evenly distributed in each dataset. Figure 4(a) and (b) shows the LIBS spectrum with specified lines and the first two principal components (PCs) from the training sets of 13 different brands, respectively. The contribution rates of first two PCs accounted for 79.81% of the total variability. It can be seen that the spectra of different steel samples were difficult to classify. Therefore, 832 spectra (training sets), 208 spectra (validation sets), and 130 spectra (test sets) were used to evaluate the performance of the DBN classification model. The results are obtained by after five-fold cross-validations.
Fig. 4. (a) LIBS spectrum with specified lines; (b) the score of the first two PCs from the training sets
3.2 Data pre-treatment
The classification depends on the difference of LIBS full-spectra or several spectral lines corresponding to the composition of steels. However, the LIBS full-spectra often have much unnecessary redundant information, which interferes with the quality of input data and increases the difficulty for rapid classification. Moreover, Shin et al. [34] proved that compared with feature information of full-spectra signals extracted by PCA, the modeling time of using some characteristic spectral line in peak values as input could be reduced by a factor of 20 or more, without losing any precision.
Thus, in this study, we compare the performance of the classification model under two different inputs (full-spectra signals and characteristic spectral lines in peak values) respectively. The results are used as a standard to verify the suitable input for LIBS combined with DBN model for the steel classification. In the selection of spectral lines, the spectral lines information of matrix element Fe has little difference in different samples and is not helpful to classify the brand of samples. In addition, the spectral peak intensity values of Fe are much higher than the values of spectral lines of trace elements in LIBS measurements. To avoid obvious order of magnitude difference in input variables, Fe lines are not used in this work. Based on the National Institute of Standards and Technology (NIST), considering little or no self-absorption and few spectral interferences, the intensities of 17 detected characteristic spectral lines (including 5 data points around each spectral line) of trace elements are selected as input variables and the data dimension is reduced to 84. The spectral lines used for the classification are listed in Table 2.
Table 2. Main spectral lines of special steels
3.3 Influence of various DBN constructions
The DBN model can extract more representative features than the original input [35]. Under the limitation of computer hardware, the performance of the DBN model is closely related to the number of hidden layers and neurons in the hidden layer. However, selecting the optimal parameters for DBN is difficult and the selection is heuristic or based on previous experience [28]. To explore the influence of neurons and hidden layers for the DBN model, after five-fold cross-validations, the accuracy of three different datasets and the training time were adopted to evaluate the performance of the DBN model.
The number of hidden layers (1, 2, 3, 4, and 5) and neurons (30, 40, 50, 60, and 70) in one hidden layer is set in turn for each experiment. The value of other parameters, namely, number of epochs, momentum, and learning rate input variable are 200, 0.05, and 0.5 respectively.
The performance of different neurons (30, 40, 50, 60, and 70) for the DBN model with one hidden layer were evaluated and shown in Fig. 5(a). As shown in Fig. 5, the uncertainty of the results is obtained with five-fold cross-validations and this is represented by the error bar. Under some parameters, the calculated results do not change, and the error bar is 0. The probable reason is that after trained with a large number of epochs, a certainly and hardly optimized value of classification accuracy could be obtained by DBN model. As the neurons in the hidden layer increased, the accuracy of the model could be improved basically while the training time was increasing. However, DBN is constructed by RBMs, and RBM is a probability distribution model. Due to random of network in computational process, the DBN model with 50 neurons might get trapped in relatively poor local minima, which leaded the longer training time than the model with 60 and 70 neurons. These results demonstrate that the best accuracy of all datasets (including training, validation, and test sets) was 99.61% and the training time was 216.68 s. When the number of neurons is over 60, the performance of the DBN model almost did not change with the growing number of neurons. Increasing the numbers of neurons in first hidden layer is beneficial to set a large network. Generally, the classification performance of the DBN model depends on the size of network structure such as the number of hidden neurons and hidden layers. The DBN model with large and complex network structure could achieve high classification results for training data, but leaded to more long training time. Considering the dimension-reduction performance and the reliability of the DBN model, the neurons in the first hidden layer was set as 70 to guarantee that more representative features can be extracted from high-dimensional full-spectra signals by the DBN model with multilayers.
Fig. 5. Optimization of DBN model of different parameters: the number of (a) neurons and (b) hidden layers
Additionally, we used different DBN structures (including 8400-70-13, 8400-70-40-13, 8400-70-60-40-13, 8400-70-60-40-30-13, and 8400-70-60-40-40-30-13) for evaluation in the same datasets, the results of which are shown in Fig. 5(b). When the DBN structure was 8400-70-40-13, the best accuracy (99.92%) could be obtained and the training time was the shortest (234.6 s). Meanwhile, a larger number of hidden layers would not only increase the training time, but also may lead to unsatisfactory predictability of the deep network, such as the accuracy of the DBN with 5 hidden layers decreasing to 95.3%. The possible reason is that the more hidden layers significantly increase the number of parameters and increase the difficulty of parameter adjustment in the training process. Obtaining a proper convergence state for the deep network is difficult. To maintain a balance between accuracy and training time, the number of hidden layers is set to 2. In summary, compared with the best accuracy of the DBN with 1 hidden layer in the training, validation, and test sets, the accuracy of the DBN with 2 hidden layers was improved from 99.69%, 99.61%, and 99.23% to 99.92%, 99.9%, and 100%, respectively. Moreover, the results show that compared with 1 hidden layer, the training time of the DBN with 2 layers is not significantly increased. The reason may be that the training time, most of which is caused by the fine-tuning progress, is influenced by the size of structure of DBN model. However, the DBN model with large network structure could achieve high classification accuracy and the more suitable pre-trained network could reduce the time of fine-tuning by BP algorithm. Therefore, the training time could be reduced with more neurons and more hidden layers under specific conditions. Using full-spectra data, the DBN with 2 hidden layers has good feature expression ability, which is beneficial for classification of unknown samples. Thus, 8400-70-40-13 was selected as the structure of the DBN model in this study.
3.4 Comparison with input of characteristic spectral lines
In this experiment, a comparison of new input variables, which were the spectral lines listed in Table 2, was conducted. The same parameter tuning progress was conducted and the dimension of the input layer of the model is adjusted to 84 (the dimension of characteristic spectral lines). As the dimension of input is significantly reduced, the training time in the training progress of 500 epochs are all decreased near the range from 20 s to 30 s, where the difference is negligible. As shown in Fig. 6(a), the performance of the DBN model with one hidden layer reaches 99.88% and is less affected by the number of neurons in the range from 30 to 70. However, Fig. 6(b) shows that the DBN model with multiple hidden layers not only needs to take large epochs to improve the accuracy, but also reduces the value of the maximum accuracy range from 99.88% to 91.54%. Moreover, the DBN model with 5 hidden layers is too complex for the input date with low dimension and cannot converge to a proper state to predict the label of samples. Compared with full-spectra data, using the spectral lines as input, the DBN model (structure: 84-30-13) can achieve high accuracy and reduce the training time significantly, which is beneficial for the classification of known samples with certified elements.
Fig. 6. Optimization of DBN model by using characteristic spectral lines as input: the number of (a) neurons and (b) hidden layers
The best result of the DBN model for the test set is presented in Fig. 7. The circle represents the actual label, and the scatter represents the predicted label by the DBN model. The result demonstrates that the spectra of 42CrMo (sample label: 10) and 42CrMoA (sample label: 5) was easily mutually misclassified. 42CrMoA is an upgrading steel of 42CrMo and can be considered as the same steel brands. The probable reason is that the samples of 42CrMo and 42CrMoA are the nearest neighbor type listed in Table 1 and have similar content of main trace elements (Mn, Cr, and Cu) with rich spectra lines, thereby resulting in difficulty of classification.
3.5 Comparison with other ML methods
To further evaluate the predictive abilities of the DBN for steel classification, the results are compared with those of other ML models such as KNN, SOM, BP, and LDA, which are all widely applied in LIBS analysis. The k value and distance metric of KNN model is set to 10 and Euclidean respectively. The number of neurons and iterations of SOM model were set to 36 and 1000, respectively. The network structure of BP model was set as 8400-70-40-13 and 84-30-13, respectively. The Mahalanobis distances was used for LDA model to classify the type of spectra data. Then, 5-fold cross-validation was conducted and the cross-validation results of other methods by using two different input variables (full spectra: 8400 variables, spectra lines: 84 variables) are shown in Table 3. By using spectra lines as input, the accuracies of other classification models were improved significantly, as shown by the test results in Fig. 8. Figure 8(a) presents the result of the SOM in which 16 spectra of the 4 steel brands were misclassified and the test accuracy reached 87.69%, which was the worst performance in all methods. The accuracy of the LDA model was improved to 92.31%, while 10 spectra of the 3 steel brands were misclassified, as shown in Fig. 8(b). In Figs. 8(c) and (d), the results of the KNN and BP models show that 1 spectrum and 2 spectra of the 2 steel brands were misclassified, respectively. Although KNN reaches high accuracy that only 1 spectrum of 15NiCuMoNb5 was misidentified as 25#, the two samples have obvious content difference in elements of Mn (1.05% and 0.65%), Ni (1.17% and 0%), and Cu (0.605% and 0%). These results illustrate that KNN may have poor discrimination for various steel brands. In particular, BP only mistook the spectra of 42CrMoA and 42CrMo, the result of which was consistent with the DBN model.
Table 3. Performance of different methods in two inputs
Figure 8 and Table 3 show that when the characteristic spectra lines were selected as input, other ML methods, such as KNN and BP, could also obtain better classification, and the performance of DBN was not significantly different. When the full spectra was used as input, DBN could classify the sample perfectly in test sets, but the accuracies range of other ML methods are decreased from (87.69% ∼ 99.23%) to (62.31% ∼ 96.16%). A similar phenomenon compared with spectra lines, the identification model performed better by using the full spectra as input, which can be found in other studies [36,37]. The reason may be that the subtle differences of similar steel samples, such as unique matrix effects, only could be found in the full-spectra with all variables, thereby leading to better performance [37]. The results demonstrate that DBN can extract representative information from complex and high-dimensional LIBS datasets and has great ability in classifying special steel with similar compositions. To sum up, the DBN model presented the best classification accuracy compared with all the other methods.
4. Conclusions
In this study, a novel method of identification for 13 steel brands by using mobile LIBS coupled with DBN was developed and applied. To improve the modeling efficiency, the different structures of DBN were optimized to evaluate the identification performance. The optimized results show that the neurons in the first hidden layer has less influence on accuracy and the classification performance can be improved by selecting the appropriate numbers of hidden layers for the DBN model. Otherwise, depending on the dimension size of input, more hidden layers reduce the accuracy and cost long training time. By using two inputs (full-spectra signals and characteristic spectra lines), after five-fold cross-validations, the test accuracies of the DBN model with the optimized structure (8400-70-40-13 and 84-30-13) could reach 100% and 98.46%, respectively, while the training times were 234.6 s and 18.71 s, respectively. Moreover, compared with the accuracies range (62.31% ∼ 96.16%) of other ML methods in test sets, only the DBN model can reach an accuracy over 99% in each dataset when the input was full-spectra signals. This result shows that DBN has great feature-extraction abilities for complex and high-dimensional LIBS datasets and exhibited better performance for steel classification. Furthermore, as a deep learning method, DBN can be applied in transfer learning for more similar samples by using the parameters of the model trained early and improving the modeling efficiency in industrial applications, especially online platforms with large datasets.
Funding
Natural Science Foundation of Xiaogan City (XGKJ2021010003); Hubei Provincial Department of Education (T201617); Natural Science Foundation of Hubei Province (2021CFB607); National Natural Science Foundation of China (61705064).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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