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Abstract
There are many challenges in the determination of elements in complex matrix such as soil, coal and minerals by laser induced breakdown spectroscopy (LIBS) method. Due to the influence of matrix effect, instability of laser plasma and fluctuation of laser parameters, the repeatability and accuracy of quantitative results are always not satisfactory. In order to improve the accuracy, high-energy laser (30mJ-100mJ) with precise control was utilized in many laboratories. In this paper, quantitative analysis of copper in copper concentrate by low-energy (10µJ) LIBS is studied. In order to reduce the influence of matrix effect and other factors, a partial least square regression method based on double genetic algorithm (DGA-PLS) is proposed. The detail operations are as follow: the reference spectral lines are automatically selected by GA as the optimal internal standard for spectral normalization. Then the GA is used to select variables from the normalized spectra for PLS. The results showed that, for univariate model, the coefficient of determination (R2) was improved from 0.6 to 0.97 by the optimal internal standard normalization. Compared with tradition PLS, the root mean square error of cross validation (RMSECV) and root mean square error of prediction (RMSEP) of PLS trained by the normalized spectral data decreased from 1.4% and 0.42% to 0.9% and 0.29% respectively. Compared with the normalized PLS, the RMSECV and RMSEP of the DGA-PLS trained by the normalized and feature selected spectral data decreased from 0.9% and 0.29% to 0.26% and 0.21% respectively. The results show that DGA-PLS can significantly reduce matrix effect, improve prediction accuracy and reduce the risk of overfitting in determination of copper in copper concentrate.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Copper concentrate is the main raw material in the copper smelting industry. It is a substance with higher copper concentration (generally 18∼28%) obtained by enrichment and extraction of minerals with lower copper concentration. The higher the copper concentration is, the greater the value of copper concentrate will be, so quantitative analysis of copper concentration in copper concentrate is necessary in the process of production and procurement. In Chinese copper smelting factory, the general analysis process is based on the national standard: Firstly, sample multiple times from different positions in the carrier which transport bulk copper concentrate [1,2]. Then the samples are sent to the laboratory or testing center for pretreatment like grinding, sieving, etc. Finally, iodometric method is used to determine the concentration of copper [3]. What is more, the iodometric method require a series of sample pretreatment steps and many kinds of chemical reagents are needed. This may cause other serious problems, such as secondary pollution, complicated operation, long time-consuming, slow speed of analysis [4]. Although ICP-AES can also be used to analysis copper concentrate, but sample pretreatment is still required [5]. And the ICP-AES instrument is expensive and bulky, so it always be used in lab only. Therefore, it is of great significance to study and develop high accuracy and convenient analysis method for copper concentrate determination.
Laser-induced breakdown spectroscopy (LIBS) is a promising elemental analysis method with many advantages such as fast, micro-destructive, no sample pretreatment, in-situ and multi-element simultaneous analysis [6,7]. Therefore, LIBS has received much attention, and developed rapidly in many fields like geochemistry, archaeology, coal property analysis, metal recycling, environmental protection, health care and so on [8–13]. Meanwhile these studies found that there are many difficulties for LIBS in the quantitative analysis of elements in complex matrixes such as soil, coal, minerals, etc. The repeatability and accuracy of the results are poor. The reasons for poor results include matrix effect, instability of laser-induced plasma, laser parameters fluctuation and so on [14,15]. The matrix effect of LIBS refers to that the matrix of a material can influent the intensity of the plasma emission of the measured element. There are three situations of matrix effect of LIBS. First, the physical properties of the sample, such as particle size and hardness, affect the emission intensity of the measured element [16]. Second, under the same condition of excitation source, the intensities of plasma emission of the measured element are different in different matrixes, even if the concentrations of the measured element are same [17]. Furthermore, if the relative concentrations of multiple elements are different from sample to sample, the correlation between the intensities of plasma emission and the concentrations of the measured element will also be different from sample to sample [18].
In order to eliminate the matrix effect of LIBS while building calibration model, a widely used method is to normalize the spectra using the intensity of one emission spectrum line of an element or the sum of the intensities of a continuous background, which is called internal standardization method. For example, Łukasz et al. used LIBS to measure Ag, Co, and V in copper concentrate, using a continuous background as an internal standard. the linearity of the single variate calibration model obtained by this method were 0.93 to 0.9848 [19]. One of the problems in using the internal standard method is that it is time-consuming and laborious to choose the internal standard manually in complex spectra, and it is difficult to find the optimal choices based on experience. To solve this problem, Kong et al. used genetic algorithm to automatically select spectral peaks of iron as internal standard to achieve quantitative analysis of trace elements in steel [20].
The second strategy to eliminate matrix effects is based on multivariate analysis methods, such as partial least squares method, artificial neural network, which have been used for the analysis of rocks, soil, coal, etc. [21–24]. Multivariate analysis is able to extract latent variables from the full spectrum information automatically. However, in the case of small sample number and severe matrix difference, multivariate analysis often cannot extract correct information which represent the concentrations of measured element, resulting in under-fitting or over-fitting [25]. One solution for this problem is to use variable selection algorithm to eliminate interference variables and noises before multivariate analysis, so as to improve prediction accuracy [26–29].
The composition of copper concentrate is complex, generally mixed with pyrite, silicate and carbonate. Therefore, the major elements of copper concentrate include Cu, Fe, S, Si, Ca, Mg, Al, etc. The trace elements mainly include As, Zn, Pb, Au, Ag, etc. The relative concentrations of major elements such as Fe, Ca and Mg are various from sample to sample. The changes in the concentrations of these elements affect the intensities of the plasma emission of Cu, resulting in severe matrix effects. The calibration error caused by these matrix effects cannot be eliminated by selecting a single element spectral line as the internal standard. In the case of a small number of samples used for calibration, simply using the common multivariate analysis method cannot completely eliminate the matrix difference from sample to sample, and the result of over-fitting or under-fitting is inevitable.
In this paper, the high accuracy method of quantifying copper in copper concentrate by LIBS is studied. In order to improve the accuracy and efficiency of quantitative analysis, a partial least square regression method based on double genetic algorithm (DGA-PLS) is proposed. In this method, the reference spectral lines are automatically selected by GA as the internal standard for spectral normalization. In this step, the reference spectral line is selected as the internal standard among the spectral lines of all elements except Cu, instead of being selected only in the spectral line of iron in [20]. Further, the GA is used to select variables for PLS. The results show that the internal standardization selected by GA significantly improves the linearity of the univariate model and the prediction accuracy of PLS. The use of GA for feature selection further improves the prediction accuracy and avoids over-fitting for PLS model.
2. Experimental
2.1 LIBS setup
The block diagram of LIBS system is shown in Fig. 1. A low power 1064 nm Diode Pump Solid State (DPSS) laser (actively Q-switched Nd: YAG, 10µJ/pulse, 10 ns pulse duration, 8 kHz repetition rate, power fluctuation <2%) is focused onto the target samples. And the diameter of the focused spot is10µm. The plasma emission spectra are collected by two self-designed C-T spectrometers covering the wavelength range of 252∼373 nm and 445∼550 nm with a resolution of 0.1∼0.2nm, which are equipped with 2048 pixels linear CCD. A software was developed to operate laser and spectrometers. Spectra pre-treatment and calibration were done in MATLAB (MathWorks, 2016).
2.2 Copper concentrate samples
Copper concentrate samples were offered by Zijin Mining Group Co. Ltd (Fujian, China). In this paper, 11 samples tagged “TJK” were used for calibration and prediction. These copper concentrate samples were sampled from bulk copper concentrate which exploited in a same mine and then purchased by the smelter. The accurate copper concentrations of these samples determined by iodimetry are shown in Table 1 [3].
Table 1. Concentrations of Cu of the “TJK” samples
2.3 Measurement procedures
To realize high quality LIBS measurements, the copper concentrate powders were compressed into compact pellet using a compressor under a pressure of 6 MPa and then transported to the sample stage. Keeping Each sample moving during measurement to obtain a signal enhancement. In the situation of 8 kHz laser repetition rate and 65 ms integration time, one spectrum was an accumulation of 520 laser shots. The copper concentrate pellet and the spectrum were shown in Fig. 2.
2.4 Evaluation of homogeneity of the sample
A certified standard sample of copper concentrate “ZBK388C” (provided by Zhongbiao Technology Co., Ltd, Jinan, China) was used to compare sample homogeneity.
The standard sample and actual copper concentrate samples were repetitively measured 3 times. The relative standard deviations (RSDs) of peak intensity of the Cu I 521.82 nm were utilized to evaluate the sample heterogeneity, shown in Fig. 3. The procedure of one measurement are the following: 1. Acquire N spectra at different position on the sample surface. 2. Average N spectra to one spectrum for later analysis according to the following:
Fig. 3. The RSDs of the Cu I 521.82 nm peak intensity. The RSDs were calculated from three repeated measurements. One measurement averages 20 spectra here.
In Fig. 3, the RSDs of the actual samples were 1.5∼2 times that of the reference sample. The result indicated that there might be no significant differences between actual samples and reference sample in repeatability of LIBS measurement.
LIBS spectra of No. 6 sample were measured to investigate the relationship between the RSD of the peak intensity of Cu I 521.82 nm and the average number of spectra, shown in Fig. 4. When the average number reaches 60, the RSD reduction rate is quite low. The RSD may reach saturation because of laser energy fluctuation and the change in sample-to-lens distance. Considering measurement repeatability and time cost, we defined a result of one measurement as the average of 40 spectra. Due to the high repetition rate of the laser, one measurement only costs 4∼5 seconds. Each sample was measured 3 times. With this setting, the influences induced by laser energy fluctuation and sample-to-lens distance variation have been reduced to an acceptable scale. Thus, we can discuss the influence induced by matrix effects on the peak intensity of Cu in the following sections.
2.5 Evaluation of the matrix difference
Principal Components Analysis (PCA) was performed to evaluate matrix differences of copper concentrates. PCA is a powerful tool for multivariate analysis and searching differences between spectra [30]. For ease to read, the approximate areas of each category were artificially drawn. In Fig. 5(a), samples tagged “TJK” were significantly distinguished from ASK sample and ZBK388C sample. The sample tagged “ASK” was exploited from another mine. In Fig. 5(b), samples tagged “TJK” were partially differentiated from each other. The results of PCA might prove that the matrix differences exist not only in the samples from different mines, but also in the samples from the same mine.
Fig. 5. (a) Plot of PCA scores of samples from different mines; (b) Plot of PCA scores of samples from one mine. Each point represents one spectrum of corresponding sample.
Figure 6 shows the peak intensities of Cu, Ca, Fe, Zn, Si, and Mg in the spectra of 11 samples tagged “TJK”. The error bars are the standard deviations of 3 repeated measurements. The matrix differences were implied in LIBS spectra as the peak intensities of each element are fluctuating from sample to sample. It is noted that the peak intensities of Cu exhibit a weak correlation with the concentrations.
Fig. 6. Peak intensities of different element in samples No.1∼11. The error bars are the standard deviations of 3 repeated measurements. One measurement was averaged by 40 spectra. The LIBS peak used here are Cu I 521.82 nm, Ca II 317.933 nm, Fe I 371.993 nm, Zn I 481.053 nm, Si I 288.157 nm, Mg II 279.553 nm.
3. Results and discussion
3.1 Data set and model evaluation
The 11 samples tagged “TJK” were divided into a calibration set and a prediction set. The calibration set contained No.1, 2, 4, 5, 6, 8, 9, 11 and the prediction set was No.3, 7, 10, which contained 24 and 9 spectra, respectively.
To evaluate the calibration model, the coefficient of determination (R2) was applied. The root mean square error of prediction (RMSEP) and the relative error of prediction (REP) were applied to evaluate the prediction accuracy of the calibration model. The relative standard error (RSD) was used to evaluate the precision of the calibration model. In the case of cross validation, the root mean square error of cross validation (RMSECV) and the relative error of cross validation (RECV) were applied. All the cross validations mentioned in this paper are Leave-one-out-cross-validation (LOOCV).
3.2 Univariate calibration
As showed in Fig. 7, three univariate calibration methods were discussed in this study. The peak of Cu I 521.82 nm was analyzed in these models. The R2 of the unnormalized model, whole spectrum normalization model, and multi-internal standards model were 0.6379, 0.758, 0.9344, respectively. The multi-internal standards model exhibited a much better result of R2. These internal standard lines were chosen manually according to the researcher's priori knowledge, including 3 emission lines of Ca, Fe, and Zn. In all the figures of calibration models in this paper, the ideal fit is depicted as the solid line with slope 1 and intercept 0.
Fig. 7. (a) univariate model of non-normalization. (b)whole spectrum normalization. (c) multi-internal normalization, the intensity of Cu I 521.82nm is normalized by the sum intensity of Fe I 492.044 nm, Ca II 317.933 nm and Zn I 330.268 nm.
3.3 Quantitative analyses using traditional PLS
A traditional PLS model was developed and investigated, shown in Fig. 8. The complete spectrum without normalization and feature selection was set as the input variable. Though the R2 is very high, there is high risk of over fitting in this model [31]. The RMSECV is 1.4012% and the RMSEP is 0.4214%. RMSECV is much higher than RMSEP, which suggest that it is difficult for traditional PLS model to extract correct latent variables from the original spectra. And the prediction accuracy of traditional PLS model is lower than that of multi-internal standards normalization model presented in Fig. 7(c).
3.4 Internal standard chosen by genetic algorithm
The genetic algorithm (GA) is a global optimization method based on natural selection [32,33]. It could be applied to choose the optimal internal standard from large amount of different combinations of reference lines. The detail steps of using GA to choose reference lines or spectral segment could be found in literature [20,26,29,32,33].
A total of 135 emission lines were extracted from the spectrum for GA. The fitness function was set as RECV of the univariate model, which is the optimized goal of GA and is obtained by LOOCV.
The results are shown as follows. 25 emission spectrum lines were chosen by GA as the internal standard. 22 of them were recognized according to the NIST database [34] and LIBS Info [35], as listed in Table 2. The results of univariate model with GA internal standard normalization is shown in Fig. 9(a). The R2 of the univariate model was increased from 0.9344 to 0.9739, compared with the result of Fig. 7(c).
Fig. 9. Calibration regression curve of univariate model (a) and PLS model (b) with the GA internal standard normalization.
Table 2. Spectral lines selected by GA as internal standard
A PLS model was built using the spectra normalized by the GA selecting internal standard (GA-ISN-PLS), shown in Fig. 9(b). The RMSECV was reduced from 1.4012% to 0.9164%, and the RMSEP was reduced from 0.4214% to 0.2927%, compared with the result of tradition PLS.
The results show that the matrix effects from sample to sample were significantly reduced by the optimal internal standard selected by GA. The tradition normalization method failed because the concentration of other elements in copper concentrate fluctuated greatly, and the single spectral line could not be used as an internal standard. And the result of full-spectrum normalization is approximate to that of internal standard with iron lines. The reason is that there were much more emission lines of iron than that of other elements in the range covered by our set-up. However, the optimal internal standard of GA could strike a balance among all elements, by choosing different number of lines in different elements, which is equivalent to giving each element a weight in the internal standard. Therefore, the GA optimal internal standard has better stability than the full spectrum or single line.
We observe that GA internal standard normalization improves the prediction accuracy of PLS model. The weights of PLS models are shown in Fig. 10. After GA internal standard normalization, the weights of Cu line at 510.55 nm and 521.82 nm increase significantly, which indicates that the Cu lines peak intensity positively correlate with the Cu concentration.
Fig. 10. Black line is the LIBS spectrum. Red line is the weights obtained by traditional PLS model. Blue line is the weights obtained by GA-ISN-PLS model.
3.5 Variables chosen by genetic algorithm
In this part, GA is applied to select variables of the spectra normalized by the GA-internal standard in section 3.4. The RECV of PLS model was set as the optimization target. 4 pixels of the spectra, which are a FWHM of the spectrometer, were set as a segment. Hence, 4080 pixels of single spectrum is encoded as a chromosome containing 1020 genes.
The optimization process of the two GAs is shown in Fig. 11. And the result of DGA-PLS is shown in Fig. 12.
Fig. 11. The optimization process of choosing internal standard (a) and choosing variables for PLS (b).
This GA variable selection was also performed on the original spectra. The PLS model training by this spectral data could be called as GA feature selection PLS (GA-FS-PLS). The results of the four PLS models (traditional PLS, GA-FS-PLS, GA-ISN-PLS, and DGA-PLS) are shown in Table 3.
Table 3. Comparison between four PLS models
Compared with the GA-ISN-PLS, the RMSECV and RMSEP of the DGA-PLS trained by the normalized and feature selected spectral data decreased from 0.9% and 0.29% to 0.26% and 0.21%, respectively. The feature selection eliminated the variables containing noises and less related to the Cu concentration, which made the model more robust [29].
We tried another 3 different prediction sets. In the first situation, the prediction set includes sample 2, 7, 10, the rest samples are set as calibration set. In the second situation, the prediction set includes 4, 6, 9, and the third is 2, 4, 6. It should be noted that we totally retrain the GA normalizations, GA variable selections and PLS models, not just change the data set. The results of the models are shown in Table 4, Fig. 13 and Fig. 14. In these three cases, sample 2 and 4 which have severe matrix effects are included in prediction sets.
Fig. 13. Calibration regression curve of GA-ISN-univariate model. (a) prediction set: sample 2, 7, 10. (b) prediction set: sample 4, 6, 9. (c) prediction set: sample 2, 4, 6.
Fig. 14. (a) Traditional PLS with prediction set of sample 2, 7, 10; (b) DGA-PLS with prediction set of sample 2, 7, 10; (c) Traditional PLS with prediction set of sample 4, 6, 9; (d) DGA-PLS with prediction set of sample 4, 6, 9; (e) Traditional PLS with prediction set of sample 2, 4, 6; (f) DGA-PLS with prediction set of sample 2, 4, 6.
Table 4. RMSECV and RMSEP of models of different prediction sets
Analyzing the results shown in Table 3 and Table 4, we observe that the GA internal standard normalization mainly increase the prediction accuracy of PLS model, and GA selecting variables mainly increase the modeling accuracy. Since DGA-PLS combines the two procedures, it could significantly increase modeling accuracy and prediction accuracy at the same time.
The results also show that DGA-PLS can increase the prediction accuracy of sample 2 and 4, indicating that DGA-PLS could be a feasible algorithm for reducing matrix effects in copper concentrates.
4. Conclusions
This study presented a new algorithm which use GA twice to optimize the PLS model to eliminate the influence of matrix effects and overcome the fluctuations of experimental parameters in a low-cost, low-energy and compact LIBS system. The DGA-PLS model for quantitative analysis of Cu in copper concentrate samples was established, and RMSEP, RMSECV and RSDP are 0.2116%, 0.2631%, and 0.630%, respectively. The results suggest that DGA-PLS could be a feasible algorithm for determining the concentration of elements in complex matrixes with LIBS systems of low cost and low energy.
Funding
National Key Scientific Instrument and Equipment Development Projects of China (No. 2012YQ180132); National Natural Science Foundation of China (No. 61775133).
Disclosures
The authors declare no conflicts of interest.
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