Combination of the internal standard and dominant factor PLS for improving long-term stability of LIBS measurements

Abstract

Improving long-term stability is an important issue for large-scale applications of laser-induced breakdown spectroscopy (LIBS). Unlike laboratory instruments, many applications of LIBS instruments are in harsh outdoor environments, where instrument drift can lead to deterioration of long-term stability, hindering the use of LIBS technology in applications with high-precision requirements. In this work, based on the designed LIBS sensor for molten steel, we analyzed the spectral drift problem of different day measurements, on the basis of which we proposed a drift correction method combining the internal standard and the dominant factor partial least squares (PLS) regression. In this method, spectra are first preprocessed to build an internal standard model of the elemental concentration ratios to spectral line intensity ratios. Then the PLS regression is utilized to construct a corrected model between the spectral intensity and the drift value of the intensity ratio. Finally, elemental concentration predictions are made by using the established internal standard model with modified spectral line intensity ratios. The method was tested on low alloy steel samples. In the experiment, the detection spectra were recorded for 9 days for quantitative analysis and drift correction of the major elements C, Si, Cr, Ni, Cu, and Mn in alloy steels. Compared with the uncalibrated internal standard method, for the prediction of unknown samples over a long period of time, the RMSE values of C, Si, Cr, Ni, Cu, and Mn decreased by 48.74%, 50.00%, 73.30%, 72.15%, 72.57%, and 18.23%, respectively, and the RSD decreased by 27.71%, 42.97%, 35.17%, 38.95%, 55.58%, and 23.40%, respectively. Furthermore, several typical drift correction methods were also studied for comparison, and the proposed method achieved the best results for different test sets.

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1. Introduction

Laser-induced breakdown spectroscopy (LIBS) is a multi-element atomic emission spectroscopy analysis technique characterized by minimal sample damage, no or only simple sample preparation required, and rapid analysis.^1–6 It is particularly suitable for in situ analysis in industrial sites or extreme environments,⁷ such as the metallurgical industry,^8,9 coal industry,^10,11 deep-sea exploration,^12,13 and deep-space exploration.^14,15 However, the relatively low stability of the measurement limits the further development of LIBS technology, which hinders the large-scale application of LIBS technology. The stability of LIBS can be categorized into short-term and long-term stability. Short-term stability refers to the repeatability of spectral intensity within a single measurement process, while long-term stability is the repeatability of spectral intensity of different measurements taken some time apart, where the time interval between measurements is usually measured in hours or days.¹⁶

Currently, there is extensive research focused on improving the short-term stability of LIBS spectra, which can be broadly categorized into three types: optimization of system parameters, modulation of the plasma, and correction using algorithms. Wang et al.¹⁷ systematically reviewed the calibration methods for short-term stability in LIBS. In terms of optimizing system parameters, spectral signals with higher intensity and better stability could be obtained by setting optimal experimental parameters such as laser energy, spectral acquisition delay, and acquisition gate width. Shabanov et al.¹⁸ emphasized the importance of the appropriate position and orientation when using lenses or optical fibers to collect spectra. System parameter optimization is a prerequisite for the instrument to carry out measurement applications, and this step is essential no matter which method is used later to further improve the stability.

Plasma modulation involves controlling the generation process of plasma through hardware measures to make the evolution of the plasma more stable. Cui et al.¹⁹ found experimentally that in co-linear long-short pulse LIBS, when the short pulse arrived in the middle of the long pulse, the long pulse served to preheat the sample and maintain the plasma. In comparison to other pulse-delay dual-pulse LIBS and single-pulse LIBS, the combination of long and short pulses can achieve a more stable plasma, providing consistent spectra even under different environmental temperatures. Hou et al.²⁰ transformed a Gaussian beam into a circular flat-top beam, resulting in a more uniform and stable plasma, thereby enhancing the stability of the LIBS spectral signal.

Improving stability through data processing and calibration algorithms offers a more flexible and easily implementable approach. The internal standard method, full spectrum normalization, and segmented spectrum normalization are commonly used methods to improve short-term repeatability. Zhang et al.²¹ proposed a method combining internal standards with plasma image features, significantly improving measurement repeatability. Particularly, when the distance to the target changes, this method could mitigate the impact of spectral fluctuations on measurements to some extent. Wang et al.²² introduced a method that combined the partial least squares (PLS) method with a physically based dominant factor. The intensity of the characteristic spectral lines of the characteristic elements was used to construct the dominant factor to reflect the concentration of the major elements, and the PLS method was used to construct a correction model between the spectral intensity and the deviation of the predicted concentration. Test results on brass samples showed that compared to the traditional PLS method using full spectral information, the RMSEP of the dominant factor-based PLS model decreased from 5.25% to 2.33%. Zhang et al.²³ integrated plasma images with dominant factor-based PLS to assess and compensate for self-absorption in liquid samples. Parameters such as plasma intensity, plasma area, and brightness contrast were inverted from plasma images and utilized to estimate self-absorption factors for spectral intensity correction. Nie et al.²⁴ proposed a novel method called spectral standardization based on plasma image-spectrum fusion (SS-PISF). This approach utilized information from plasma images and spectra to correct variations in total number density, plasma temperature, and electron number density, thereby enhancing spectral stability. When compared to the full spectrum normalization method and the simplified spectral standardization method, results on aluminum alloy, alloy steel, and ore samples indicated a significant improvement in the R² of the calibration curves after correction with SS-PISF, accompanied by a reduction in standard deviation.

While the above studies have been on short-term reproducibility, little attention has been paid to the long-term stability of LIBS. Unlike laboratory instruments, many applications of LIBS instruments occur in harsh outdoor environments. Environmental temperature, humidity, mechanical structure stress, vibration and many other factors can lead to the drift of the measurement spectrum of the analytical instrument, which ultimately poses challenges to the long-term stability of measurements, hindering the use of LIBS technology in applications with high-precision requirements. In instruments like spark direct-reading spectrometers or inductively coupled plasma atomic emission spectrometers, the two-point calibration method is commonly used for instrument drift calibration.^25,26 However, it is difficult for the two-point calibration to take into account the wide range of calibrations for all elements, and this aspect will be further analyzed later in the research process. Liu et al.¹⁶ proposed a method for correcting spectral intensity based on the intensity distribution of the laser beam. This method preprocessed the laser beam intensity distribution profile and spectral intensity, and then used PLS regression to model the relationship between the relative deviation of the beam and spectral intensity. As a result, the long-term RSD for copper and silicon samples decreased from 13.5% and 10.7% to 4% and 6.5%, respectively. Additionally, Liu et al.²⁷ investigated the influence of ambient humidity on LIBS spectra. The impact of environmental humidity on the spectral intensity of copper samples was elucidated, providing evidence that ambient humidity was one of the factors affecting the long-term reproducibility of LIBS. However, these studies only considered the influence of individual factors on the long-term stability of the spectra, and in practical applications, it is challenging to analyze the effects of various drift factors comprehensively. Dissecting the factors influencing drift one by one is exceptionally challenging, and obtaining general rules is difficult.

The experimental work in this work was conducted on a LIBS molten steel sensing system. The design objective of this sensor is to measure the composition of molten steel online, and therefore it incorporated a 1.5 meter-long probe and a Paschen–Runge spectrometer with a spectral radius of 0.5 meters. The long-distance optical transmission and high-resolution spectrometer system necessitate the consideration and correction of spectral drift issues before the sensor's final application.

Initially, we analyzed the impact of spectral drift over different day measurements and constructed quantitative analysis models based on internal standards. On the basis of this, we employed the concept of dominant factor PLS to create a correction model for the spectral intensity and intensity ratio drift values. Finally, we utilized the established internal standard models along with drift-corrected spectral line intensity ratios for elemental concentration predictions. Testing was conducted on low-alloy steel samples, and the results indicated that this method effectively enhanced the long-term stability of LIBS measurements. In comparison to several commonly used calibration methods, optimal results were achieved with this approach.

2. Method

2.1 Combination of the internal standard with dominant factor PLS (ID-PLS)

The predominant idea of this method is to predict the drift value of the intensity ratios using a PLS model. First, through measurements over multiple days, an estimation of the expected non-drifted spectra is obtained. Subsequently, an internal standard model for elemental concentration and spectral intensity ratios is constructed based on the expected spectra to obtain the baseline intensity ratio. Following this, a PLS prediction model for intensity ratio drift is built on the foundation of the internal standard model.

2.1.1 The internal standard model of the expectation spectrum. We define the expected spectra as ideal spectra without any drift. The estimation of the expected spectra can be obtained by averaging the spectra from measurements over multiple days. Since the internal standard method can correct the spectral fluctuations to some extent, the internal standard model is considered to obtain the baseline intensity ratio. Using detection spectra from different samples on multiple days as the training set, denoted as S_ijz, the expected spectrum B_j for sample j is calculated using the following formula:where j represents the sample index, j = 1, 2, …, A (number of samples in the training set), M is the number of measurements over a long-time interval (e.g., detection days), N is the number of measurements over a short time interval (e.g., continuous measurements), i denotes the i-th measurement over a long-time interval, and z denotes the z-th measurement over a short time interval. Based on the expected spectrum B_j, the characteristic spectral line intensity I^s_j for the analyte elements and the characteristic spectral line intensity I^s_IS_j for the internal standard elements can be obtained. The ratio of their intensities, R^s_j, is given by:where s represents different elements, s_IS represents the internal standard element for element s, and the meaning of j is the same as in eqn (1). The reference sample concentration ratio P^s_j is given by:where C^s_j represents the concentration of the analyte element in sample j, and C^s_IS_j represents the concentration of the internal standard element in sample j. A curve fitting of P^s_j and R^s_j for all samples is performed to obtain the internal standard model for various elements:

P^s = f_p(R^s) (4)

where f_p represents the internal standard model function, generally a linear or quadratic function.

2.1.2 PLS regression model for intensity ratio drift. By substituting the reference concentration ratio P^s_j of sample j into the inverse function of eqn (4), the expected spectral intensity ratio for that sample can be obtained as follows:

R_B^s_j = f⁻¹_p(P^s_j) (5)

where f⁻¹_p represents the inverse function of f_p. Considering R_B^s_j as the baseline intensity ratio, the formula for calculating the intensity ratio drift value R_D^s_ijz is as follows:

R_D^s_ijz = R_S^s_ijz − R_B^s_j (6)

where i, j, and z have the same meanings as in eqn (1), and R_S^s_ijz represents the characteristic spectral line intensity ratio for element s obtained on the detection spectrum S_ijz, i.e., R_S^s_ijz = I^s_ijz/I^s_IS_ijz.

After obtaining the intensity ratio drift values for the training set through eqn (6), the PLS method is applied to model the relationship between the detection spectra and intensity ratio drift values in the training set. This results in the PLS regression model for intensity ratio drift, expressed as:

R_D^s_ijz = f_d(S_ijz) (7)

where f_d represents the PLS regression model for intensity ratio drift.

Through the above steps, a PLS regression model for intensity ratio drift is constructed. In practical applications, this model can be used to predict intensity ratio drift, subsequently correcting the experimentally obtained spectral intensities. The formula for calculating the calibrated intensity ratio R_B̂^s_ijz is as follows:

R_B̂^s_ijz = R_S^s_ijz − R_D^s_ijz (8)

Finally, by substituting the calibrated intensity ratio R_B̂^s_ijz into the internal standard model, concentration predictions can be made. Fig. 1 illustrates the application process of this method.

Fig. 1 Application flow of ID_PLS: (a) model training flow and (b) model testing flow.

2.2 Comparison methods

2.2.1 Mean internal standardization method (MIS). The mean internal standardization method constructs an internal standard model using the ideal expected spectra, as shown in the previous eqn (4), without applying any correction to the measurements on each day.

2.2.2 Direct PLS model for spectral intensity (PLS). A direct PLS model for spectral intensity and elemental concentration is built using spectra obtained from multiple days. The formula is as follows:

C^s_j = f_c(S_ijz) (9)

where C^s_j represents the concentration of the analyte element in sample j, S_ijz represents the detection spectrum, and f_c represents the PLS regression model for elemental concentration.

2.2.3 Two-point standardization method (TPS). The two-point standardization method selects two samples from the training set as high and low standard samples. The internal standard model established with the first-day data in the training set serves as the baseline model. Before each day's measurement, high and low standard samples are measured, and the slope correction coefficient and intercept correction coefficient are determined using the measured intensity ratio values of the high and low standard samples. The slope correction coefficient α and intercept correction coefficient β can be calculated using the following formulas:

α = (I_Hr − I_Lr)/(I_Hm − I_Lm) (10)

β = I_Lr − αI_Lm (11)

where I_Hr and I_Lr are the reference intensity ratios for the high and low calibration samples on the baseline model, and I_Hm and I_Lm are the measured intensity ratios for the high and low calibration samples. The corrected intensity ratio I_c using the two-point method is given by:

I_c = αI_m + β (12)

where I_m is the measured intensity ratio of the analyzed element.

These comparison methods provide benchmarks for evaluating the performance of the proposed approach.

2.3 Evaluation indexes

The determination coefficient (R²) and root mean square error (RMSE) are crucial indicators for evaluating the calibration performance of different methods. Their expressions are as follows:^28,29where n is the number of measurements, ŷ_i is the predicted concentration for the i-th measurement, y_i is the reference concentration for the i-th measurement, and ȳ is the average of y_i for n measurements.

In this experiment, due to the concentration of different samples varying greatly, resulting in large differences in RSD from sample to sample, it is considered to evaluate the overall degree of dispersion by the ratio of the mean value of the SD of the predicted concentrations of all samples (SD_mean) to the mean value of the predicted concentrations of all samples (Con_mean). Let RSD be:

where A is the number of samples, n is the number of measurements for each sample, ŷ_ab is the b-th predicted concentration for sample a, and ȳ_a is the average of n predicted concentrations for sample a.

3. Experimental

3.1 Experimental setup

The apparatus for LIBS detection and quantitative spectral analysis is illustrated in Fig. 2. The plasma-exciting light source employed was a Nd : YAG nanosecond laser with an output wavelength of 1064 nm, a pulse energy of 104.8 mJ, and a pulse frequency of 10 Hz. After beam shaping through an optical path, the laser beam was reflected downward by a 45° perforated mirror, and then focused through a 200 mm lens. The generated plasma was coaxially collected by a lens, passed through the aperture in the perforated mirror, and was subsequently focused into the slit of the spectrometer. The spectrometer utilized was a Paschen–Runge grating spectrometer with a spectral radius of 0.5 meters with a resolution of approximately 0.02 nm, from NCS Testing Technology Co., Ltd. The spectrometer was equipped with nine CCD detectors covering a wavelength range from 175 nm to 420 nm, with the pixel dimension of each CCD being 1 × 3648. The focusing lens and perforated mirror were housed in a 1.5 m-long probe. During the experiment, both the spectrometer and the probe were filled with argon gas to maintain the efficiency of ultraviolet light collection.

Fig. 2 Schematic of the setup.

3.2 Experimental data collection

Using the device depicted in Fig. 2, measurements were conducted on 10 standard samples of low-alloy steel continuously for 9 days (from June 9, 2023, to June 17, 2023), with 10 consecutive measurements each day (N = 10). In each measurement, the laser was continuously excited 200 times, and the average spectrum of 200 spectra was obtained as one measurement spectrum. A total of 900 spectra (M = 9, A = 10, N = 10) were obtained over the 9 days. During each measurement, the sample was placed on a two-dimensional rotating stage to rotate, ensuring that the laser struck different positions.

3.3 Sample preparation and division

The primary elemental composition and concentration values of the 10 low-alloy steel samples used in the experiment are shown in Table 1. Before detection, the samples were polished with sandpaper and then cleaned with alcohol to ensure a clean surface for LIBS measurement. The calibration samples for TPS were sample 2 and sample 9.

Table 1 Concentration of each element in low alloy steel samples

Sample no	C (%)	Si (%)	Mo (%)	Ni (%)	Cu (%)	Mn (%)	Fe (%)
1	0.0009	0.001	0.001	0.01	0.01	0.01	0.999
2	0.1	0.6	0.5	0005	0.07	0.15	0.937
3	0.149	0.4	0.4	0.1	0.69	0.75	0.938
4	0.21	0.06	0.3	0.5	0.11	2	0.937
5	0.26	0.25	0.092	1.05	0.4	1.6	0.937
6	0.34	0.34	0.2	1.55	0.49	1.29	0.937
7	0.5	0.3	0.6	2.02	0.2	1.02	0.936
8	0.64	0.15	1.02	2.53	0.3	0.51	0.937
9	0.8	0.2	0.82	3.26	0.17	0.31	0.938
10	0.99	0.11	0.059	4.06	0.05	0.1	0.937

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In order to investigate the predictive ability of different methods for unknown samples, two samples were selected out during the modeling process and the remaining eight samples were used to train the model. The samples that did not participate in the modeling were noted as samples-untrain and those that did participate in the modeling were noted as samples-train. The experiment spanned 9 days of data collection, with data from the first seven days serving as the training set. To facilitate the analysis of different methods' predictive capabilities for unknown samples, the test set was divided into Testset1 and Testset2. Testset1 represented data from the 8th and 9th days of samples-train, while Testset2 included data from all 9 days of samples-untrain. Fig. 3 illustrates the sample division.

Fig. 3 Sample division.

4. Results and discussion

4.1 Repeatability of LIBS quantitative analyses

Fig. 4 illustrates the local average spectra of different elements in sample 7 on the first day, the third day, and the first seven days. During the 9 days measurement process, potential interfering factors were eliminated by checking laser energy, focusing and light collection positions, surface smoothness of samples, and room temperature before each measurement, ensuring consistent system parameters for each measurement.

Fig. 4 Localized average spectra of different elements at different times, 7 days: average spectra of the first seven days; day3: average spectra of the third day; day1: average spectra of the first day. (a) C; (b) Mo, Si; (c) Cu, Ni; (d) Mn.

As an internal standard quantification model is utilized, it is essential to select characteristic spectral lines for both the analyte and internal standard elements. In the selection of characteristic spectral lines, neutral atomic or singly ionized persistent lines of the analyte elements were chosen to weaken spectral interference and self-absorption. Neutral atomic weak lines of iron were selected as internal standard spectral lines, representing the spectral lines of the major component of samples with intensity that remained approximately constant across all samples. Meanwhile, internal standard spectral lines are chosen as closely as possible to characteristic spectral lines of the analyte elements to ensure similar fluctuation patterns between the two. The chosen characteristic spectral lines are presented in Table 2.

Table 2 Characteristic spectral lines of elements used for internal standard analysis

Analysis elements	Wavelength (nm)	Reference element	Wavelength (nm)
C I	193.09	Fe II	192.60
Si I	288.16	Fe I	293.69
Mo II	281.61	Fe II	275.57
Ni II	227.02	Fe II	232.74
Cu II	224.26	Fe II	232.74
Mn I	257.55	Fe II	260.71

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4.1.1 Repeatability of original measurements. Fig. 5 shows the internal standard models established for the detection of carbon (C) on the first day, the third day, and the first seven days. The models established using data from the first day were referred to as day-1, those from the third day as day-3, and those from the first seven days as 7 days. The curves fitted for different days exhibited significant variations in slope, indicating that internal standard models established by LIBS over an extended period did not exhibit good repeatability.

Fig. 5 Repeatability of element C measurements (a) internal standard model for the first day, day-1; (b) internal standard model for the third day, day-3; (c) internal standard model for the first seven days, 7 days.

Models established using data from the same day showed better performance, with both day-1 and day-3 achieving an R² exceeding 0.99. In comparison, 7 days had an RSD twice as large as day-1 and day-3, with RMSE increasing to 0.0446%, and R² dropping from over 0.99 to 0.97. This suggests that as the measurement period extends, the fluctuations in detected values increase significantly, leading to data degradation. Therefore, correction for the long-term stability of LIBS is crucial. Similar long-term stability issues were observed similarly for other elements besides carbon.

4.1.2 Prediction results of the internal standard method (IS) in the test set. For each sample in the training set, the spectra obtained on the first day were averaged, resulting in one average spectrum per sample. An internal standard quantification model was established based on these average spectra, and this model was used to predict concentrations in the test set. Fig. 6 displays the prediction results for different elements using the internal standard method in the test set. Directly predicting concentrations in the test set using the IS method yielded R² values below 0.9 for molybdenum (Mo) and copper (Cu), with only manganese (Mn) achieving an R² of 0.98. Testset1 samples participated in model training and had only 2 days of data, while Testset2 samples did not participate in model training and had 9 days of data, and the internal standard method performed better overall on Testset1. On Testset1, only manganese (Mn) had an R² exceeding 0.98. Meanwhile, for all other elements in Testset1, the RSD exceeded 5%, and silicon (Si) even reached 11.31%. However, on Testset2, the RSD for all elements exceeded 8%, with copper (Cu) and silicon (Si) reaching over 10%, and silicon (Si) even reaching 13.01%. Additionally, from Fig. 6, it was evident that the predicted concentrations of samples fluctuated significantly. This is closely related to the poor long-term stability of the LIBS detection system. The internal standard model established on the first day exhibits significant instrument drift issues when measurements are made after a certain period, leading to a gradual decrease in measurement accuracy.

Fig. 6 Relationship between predicted and true concentrations of different elements in the test set, (a) C; (b) Si; (c) Cr; (d) Ni; (e) Cu; (f) Mn.

4.2 Comparison of calibration results

Calibrations were conducted using PLS, TPS, MIS, and ID-PLS, with Fig. 7–12 illustrating the calibration effects of these four methods on the test set for the elements C, Si, Mo, Ni, Cu, and Mn, respectively. Fig. 13 presents the RMSE and RSD of the internal standard method compared to the four methods in different test sets, while Fig. 14 depicts the R² values for the entire test set for the internal standard method and the four approaches.

Fig. 7 Effectiveness of different methods in predicting elemental C concentration in the test set.

Fig. 8 Effectiveness of different methods in predicting elemental Si concentration in the test set.

Fig. 9 Effectiveness of different methods in predicting elemental Mo concentration in the test set.

Fig. 10 Effectiveness of different methods in predicting elemental Ni concentration in the test set.

Fig. 11 Effectiveness of different methods in predicting elemental Cu concentration in the test set.

Fig. 12 Effectiveness of different methods in predicting elemental Mn concentration in the test set.

Fig. 13 Comparison of the internal standardized method with four calibration methods on different test sets, (a) RMSE for Testset1; (b) RSD for Testset1; (c) RMSE for Testset2; (d) RSD for Testset2.

Fig. 14 Comparison of R² of different methods for all data in the test set.

Regarding the direct PLS method, for a given element under analysis, the input spectral lines for PLS encompassed all the spectral lines on the CCD corresponding to the selected characteristic spectral line of the given element in Table 2. The appropriate number of latent variables for the direct PLS method was determined through eight-fold cross-validation. Its effectiveness in enhancing short-term continuous measurements is evident. In Testset1, except for the C element, PLS showed lower RMSE than the internal standard method, and RSD was only higher in the case of C and Mn elements. However, the calibration performance of PLS is less ideal for long-term predictions of unknown samples. In Testset2, compared to the internal standard method, PLS exhibited a significant increase in RMSE for Ni and Mn elements, especially for Mn, where the RMSE increased from 0.062% to 0.1898%, three times that of the internal standard method. PLS is prone to overfitting, where predictions for concentrations of unseen samples deviate significantly from actual concentrations. PLS directly learns the relationship between spectral intensity and concentration, and given the multitude of spectral features, during the model training process, spectra corresponding to the same concentration are obtained multiple times for each sample. This results in multiple distinct input features mapping to the same output. In such cases, the model may overly adapt to this mapping relationship, overlooking the diversity of input features, making generalization difficult on unseen data. Fig. 10 and 12(a) depict the relationship between predicted and actual concentrations for Ni and Mn elements using the PLS method in the test set. Compared to predictions on Testset1, predictions on Testset2 notably deviated from actual concentrations. Moreover, at lower concentrations, where the feature spectral lines are weak, the elemental information might be overshadowed by background noise, leading to a deterioration in the prediction performance of PLS. In comparison to other calibration methods, the PLS method demonstrated a more significant deviation from actual concentrations in predicting low-concentration samples.

Regarding the widely used TPS method in current instruments, its performance on most elements is not satisfactory. In Testset1, compared to the internal standard method, the RMSE for Mo and Mn elements not only did not decrease but increased from 0.0859%, 0.0602% to 0.1028%, 0.1082%, respectively. Moreover, the RSD for multiple elements, including C, Mo, Cu, Mn, also increased. In Testset2, compared to the internal standard method, the RMSE increased for the Mn element, and the RSD increased for Cu and Mn elements. The two-point standardization method has three challenging limitations. First, when using the two-point standardization method for detecting multiple elements, it is challenging to simultaneously calibrate all elements using two samples. This is because it is difficult to ensure that both samples contain multiple elements with both high and low concentrations. For instance, in this study, samples 2 and 9 were used as calibration samples, but they did not meet the high and low concentration requirements for Mo, Mn, and Cu simultaneously. Insufficient concentration differences can lead to significant deviations from the expected calibration line. Taking Cu as an example, Fig. 15(a) shows the internal standard quantification model (Day-8), considered as the target internal standard model for calibration and the internal standard model calibrated using the two-point standardization method (TPS-Line). Since the Cu content in the calibration samples for Cu was relatively low, the TPS calibration resulted in a smaller slope of the internal standard curve, thereby amplifying the concentration prediction error for high-concentration samples. Second, when the measured values of the two calibration samples deviate from the expected calibration curve, it can lead to an overall bias in the calibration effect. Using Mo as an example, Fig. 15(b) shows the internal standard quantification model for Mo using data from the eighth day (Day-8), considered as the ideal internal standard model, and the internal standard model calibrated using the two-point standardization method (TPS-Line). Due to the deviation of the measured values of the two calibration samples from the Day-8 model, the curve corrected by the TPS method naturally deviated from Day-8, resulting in an increased calibration deviation. Third, the two-point standardization method assumes a linear correlation between the intensity of calibration samples and their previously measured intensity, making it challenging to calibrate non-linear models. Taking Mn as an example, its internal standard model used a quadratic model, leading to the TPS method being less effective for calibrating Mn compared to the internal standard method without any calibration.

Fig. 15 TPS method for Cu and Mo elemental calibration on day 8.

The mean internal standardization method (MIS) adopts an averaging approach, taking the average of data from multiple days to establish an internal standard quantification model. This model, serving as the expected model, exhibits greater representativeness compared to models established using only the data from the first day. For most elements, there is an improvement in long-term stability. However, fundamentally, this method lacks corrective capabilities for drift, and its performance in enhancing long-term stability is limited.

Regarding the ID-PLS method, the processing method for the input spectral lines and the selection for latent variables were the same as the direct PLS method. In comparison with the Internal Standard method (IS) and the other three calibration methods, the ID-PLS method achieved the highest R² and the smallest RMSE on all elements in both Testset1 and Testset2. For C, Ni, and Mn elements, the R² reached 0.99. Particularly in Testset2 predictions, compared to the uncalibrated internal standard method, the RMSE for C, Si, Cr, Ni, Cu, and Mn decreased by 48.74%, 50.00%, 73.30%, 72.15%, 72.57%, and 18.23%, respectively. The RSD also decreased by 27.71%, 42.97%, 35.17%, 38.95%, 55.58%, and 23.40%, respectively. Therefore, it is evident that this method outperforms others in the long-term measurement stability of unknown samples. The ID-PLS method, while retaining the stability of the MIS model, corrects measured intensity ratios by predicting drift values, aligning the intensity ratios to the baseline intensity ratio for enhanced spectral long-term stability. As this method calibrates around the baseline intensity ratio, similar to the dominant factor PLS method proposed by Wang,²² it restricts the PLS prediction range to a small interval, thereby enhancing the model's robustness and generalization ability.

5. Conclusions

To address the issue of long-term instability in LIBS spectra, this study proposes a method combining internal standardization with dominant factor PLS (ID-PLS). The approach initially establishes an internal standard model for the expected spectra and subsequently constructs a PLS model between the detection spectra and intensity ratio drift values, effectively calibrating spectral fluctuations. To validate the effectiveness of this method, it is compared with several typical drift correction methods. Results for low-alloy steel samples across different test sets consistently demonstrate that the proposed method yields superior comprehensive calibration performance for C, Si, Cr, Ni, Cu, and Mn elements compared to typical drift correction methods. In comparison with the uncalibrated internal standard method, the long-term predictions for unknown samples using ID_PLS exhibited significant improvements with RMSE reductions of 48.74%, 50.00%, 73.30%, 72.15%, 72.57%, and 18.23% for C, Si, Cr, Ni, Cu, and Mn, respectively. The RSD also decreased by 27.71%, 42.97%, 35.17%, 38.95%, 55.58%, and 23.40%. ID-PLS significantly enhances the long-term stability of LIBS. Thus, utilizing the ID-PLS method to improve LIBS analytical performance represents a promising avenue, but further in-depth research is needed in the future.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This research was supported by the National Key R&D Program of China (grant no. 2021YFB3202402).

Notes and references

1. J. Yan, Z. Hao, R. Zhou, Y. Tang, P. Yang, K. Liu, W. Zhang, X. Li, Y. Lu and X. Zeng, Anal. Chim. Acta, 2019, 1082, 30–36.
2. J. Huang, M. Dong, S. Lu, Y. Yu, C. Liu, J. H. Yoo and J. Lu, Analyst, 2019, 144, 3736–3745.
3. Q. Wang, A. Chen, H. Qi, W. Xu, D. Zhang, Y. Wang, S. Li, Y. Jiang and M. Jin, Phys. Plasmas, 2019, 26, 073302.
4. S. A. Davari, P. A. Taylor, R. W. Standley and D. Mukherjee, Talanta, 2019, 193, 192–198.
5. J. Junwei, F. Hongbo, H. Zongyu, W. Huadong, N. Zhibo and D. Fengzhong, Plasma Sci. Technol., 2018, 21, 034003.
6. X. Liu, Q. Lin, Y. Tian, W. Liao, T. Yang, C. Qian, T. Zhang and Y. Duan, J. Anal. At. Spectrom., 2020, 35, 188–197.
7. L. Guo, D. Zhang, L. Sun, S. Yao, L. Zhang, Z. Wang, Q. Wang, H. Ding, Y. Lu, Z. Hou and Z. Wang, Front. Phys., 2021, 16, 22500.
8. T. Chen, L. Sun, H. Yu, P. Zeng and L. Qi, Spectrochim. Acta, Part B, 2023, 106821.
9. J. Li, L. Guo, N. Zhao, X. Yang, R. Yi, K. Li, Q. Zeng, X. Li, X. Zeng and Y. Lu, Talanta, 2016, 151, 234–238.
10. C. Yan, J. Qi, J. Liang, T. Zhang and H. Li, J. Anal. At. Spectrom., 2018, 33, 2089–2097.
11. W. Zhu, R. Sun, Y. Yan, M. Yuan, X. Meng, X. Li, X. Yu and X. Ren, Combust. Flame, 2022, 244, 112237.
12. T. Takahashi, S. Yoshino, Y. Takaya, T. Nozaki, K. Ohki, T. Ohki, T. Sakka and B. Thornton, Deep Sea Res., Part I, 2020, 158, 103232.
13. G. Lu, L. Sun, Z. Cong and T. Chen, Talanta, 2023, 125531.
14. P. Beck, P. Meslin, A. Fau, O. Forni, O. Gasnault, J. Lasue, A. Cousin, S. Schröder, S. Maurice and W. Rapin, Icarus, 2024, 408, 115840.
15. T. Delgado, F. Fortes, L. Cabalin and J. Laserna, Spectrochim. Acta, Part B, 2022, 192, 106413.
16. J. Liu, W. Song, W. Gu, Z. Hou, K. Kou and Z. Wang, Anal. Chim. Acta, 2023, 1251, 341004.
17. Z. Wang, M. S. Afgan, W. Gu, Y. Song, Y. Wang, Z. Hou, W. Song and Z. Li, TrAC, Trends Anal. Chem., 2021, 143, 116385.
18. S. Shabanov, I. Gornushkin and J. Winefordner, Appl. Opt., 2008, 47, 1745–1756.
19. M. Cui, Y. Deguchi, Z. Wang, Y. Fujita, R. Liu, F.-J. Shiou and S. Zhao, Spectrochim. Acta, Part B, 2018, 142, 14–22.
20. Z. Hou, M. S. Afgan, S. Sheta, J. Liu and Z. Wang, J. Anal. At. Spectrom., 2020, 35, 1671–1677.
21. P. Zhang, L. Sun, H. Yu, P. Zeng, L. Qi and Y. Xin, Anal. Chem., 2018, 90, 4686–4694.
22. Z. Wang, J. Feng, L. Li, W. Ni and Z. Li, J. Anal. At. Spectrom., 2011, 26, 2289–2299.
23. Y. Zhang, Y. Lu, Y. Tian, Y. Li, W. Ye, J. Guo and R. Zheng, Anal. Chim. Acta, 2022, 1195, 339423.
24. J. Nei, Y. Zeng, X. Niu and D. Zhang, J. Anal. At. Spectrom., 2023, 38, 2387–2395.
25. N. R. McQuaker, P. D. Kluckner and G. N. Chang, Anal. Chem., 1979, 51, 888–895.
26. V. B. Thomsen, Modern Spectrochemical Analysis of Metals: an Introduction for Users of Arc/spark Instrumentation, ASM International, 1996.
27. J. Liu, Z. Hou and Z. Wang, J. Anal. At. Spectrom., 2023, 38, 2571–2580.
28. R. Yuan, Y. Tang, Z. Zhu, Z. Hao, J. Li, H. Yu, Y. Yu, L. Guo, X. Zeng and Y. Lu, Anal. Chim. Acta, 2019, 1064, 11–16.
29. A. P. Rao, P. R. Jenkins, J. D. Auxier, M. B. Shattan and A. K. Patnaik, J. Anal. At. Spectrom., 2022, 37, 1090–1098.

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