CN113092447B - LIBS quantitative analysis method for screening nonlinear PLS based on cyclic variables - Google Patents

Abstract

The invention relates to the field of spectral analysis, in particular to a laser-induced breakdown spectroscopy quantitative analysis method based on cyclic variable screening nonlinear partial least squares. Aiming at the problems of data redundancy caused by overhigh dimensionality of spectral data and nonlinearity caused by self-absorption and matrix effect, the LIBS analysis method based on the cyclic variable screening nonlinear PLS is provided to improve the quantitative analysis precision. The method comprises the following specific steps: (1) selecting a p-th-order polynomial form of analysis line intensity and full spectrum data from the training samples to perform PLS modeling; (3) circularly screening characteristic spectral line data according to the magnitude of the regression coefficient absolute value, and searching optimal spectral line data according to the root mean square error of the check set; (4) and establishing a nonlinear PLS model after the variables are circularly screened by using the determined optimal variables. The invention provides a solution to the problem of nonlinearity caused by reducing data dimensionality and self-absorption and matrix effect, and improves the analysis precision.

Description

LIBS quantitative analysis method for screening nonlinear PLS based on cyclic variables

Technical Field

The invention relates to the field of spectral analysis, in particular to a laser-induced breakdown spectroscopy quantitative analysis method based on cyclic variable screening nonlinear partial least squares.

Background

The current methods commonly used for analyzing the composition of a substance generally include chemical analysis and XRF fluorescence analysis. The chemical analysis method has high analysis precision, but the method has complex operation, long analysis period and low analysis efficiency, and cannot realize real-time online detection. XRF fluorescence analysis enables on-line detection, but on-line detection fails to detect elements up to atomic number 20, and X-rays are radioactive and potentially hazardous. Laser Induced Breakdown Spectroscopy (LIBS) is a new detection method, and has the advantages of wide range of analyzable elements, low requirements on the form and sample preparation of a substance to be detected, real-time online detection, simultaneous analysis of multiple elements and the like, and is paid more and more attention by researchers.

When the laser-induced breakdown spectroscopy technology is used for quantitative analysis, the spectral data contains a large amount of noise interference and is simultaneously influenced by self-absorption and matrix effect, so that the single-variable quantitative analysis precision is not ideal. As a multivariate linear regression method, the Partial Least Squares (PLS) method has the advantages of simplicity, rapidness, high quantitative accuracy and the like, is a quantitative analysis method widely applied at present, and is particularly suitable for processing the problems of small sample size, high variable dimension and multiple collinearity among variables. As a linear processing method, the traditional PLS model cannot solve the nonlinear influence of self-absorption and matrix effect on spectral data, so that the further improvement of the quantitative analysis precision of the method is limited. The researchers put forward a multivariate nonlinear PLS model which can improve the accuracy of quantitative analysis, but the dimensionality of modeling data is too high, and the model is complex. With the continuous improvement of the resolution of the spectrometer, the data dimension is higher and higher, wherein the data dimension comprises a large amount of redundant information which is useless for component analysis, the modeling complexity is increased, and overfitting is easily caused if the full spectrum data is modeled. By means of a dimension reduction method such as feature extraction, the dimension of the spectral data is reduced, and the modeling complexity is reduced.

In the quantitative analysis of LIBS using PLS, existing studies are to separately improve on dimensionality reduction and nonlinear correction using line feature selection, respectively. In order to simultaneously reduce data dimension, reduce interference of redundant information and correct the non-linear problem of data, the invention provides a LIBS model for screening non-linear PLS based on cyclic variables to improve the accuracy of quantitative analysis.

Disclosure of Invention

The invention aims to solve the problems of data redundancy and overfitting brought to PLS modeling by overhigh dimensionality of spectral data and nonlinearity caused by self absorption and matrix effect influence of laser-induced breakdown spectroscopy during composition analysis, and provides a LIBS analysis method for screening nonlinear PLS based on cyclic variables to improve the accuracy of quantitative analysis.

Therefore, the invention is realized by adopting the following technical scheme: a LIBS quantitative analysis method for screening nonlinear PLS based on cyclic variables comprises the following steps:

acquiring original full spectrum data of a laser-induced breakdown spectrum of a substance to be detected, and carrying out normalization and noise reduction treatment to obtain a multi-dimensional spectral line data set;

dividing a multi-dimensional spectral line data set into a training set, a check set and a test set;

performing PLS modeling by using training set data and check set data, performing loop iteration screening on model parameters, determining loop screening times, and obtaining an optimal nonlinear PLS model;

and inputting the data of the test set into the established nonlinear PLS model, and automatically acquiring the concentration of the element to be analyzed.

The training set, the checking set and the testing set are divided according to the proportion; and when the check sample and the test sample are divided, the check sample and the test sample are uniformly distributed in the concentration range of the total sample, so that the effect of most fully evaluating the model performance is realized.

The PLS model parameters include: regression coefficients of elements to be analyzed, regression coefficients of interference elements and regression coefficients of filtered spectral lines.

The establishment of the optimal nonlinear PLS model specifically comprises the following steps:

step a, selecting a nonlinear form of the intensity of a spectral line to be analyzed and full spectrum data from training set data to perform PLS modeling, and obtaining a regression coefficient variable of the intensity of the spectral line to be analyzed;

b, arranging all regression coefficient variables of the PLS model from large to small according to absolute values, circularly screening the regression coefficient variables, modeling the PLS again until a preset termination condition is met, and stopping iteration so as to determine the number of circularly screening times;

step c, inputting the data of the check set into the PLS model in the step b, and calculating the root mean square error of the concentration of the element to be detected in the check set;

and d, establishing a nonlinear PLS model after circularly screening the variables according to the corresponding variables and the corresponding principal component numbers when the root mean square error is minimum.

The total number of samples of the multi-dimensional spectral line data set is N, N _ val samples are selected as check samples, N _ tes samples are selected as test samples by utilizing parameters of the sample optimization model and used for evaluating the prediction precision of the final model, and the rest N _ tra samples are used as training samples for modeling.

The spectral lines to be analyzed are m characteristic spectral lines of an element E1 to be analyzed and h characteristic spectral lines of an interference element E2.

The obtained optimal nonlinear PLS model is as follows:

wherein C is the element concentration, p is the highest power, m is the number of selected element E1 element spectral lines to be analyzed, and alpha_i,jFor the element to be analyzed, E1 linear regression coefficient, I is the power of spectral line intensity, j is the serial number of the selected E1 element spectral line, I_E1Is the E1 spectral line intensity, h is the number of selected interfering element E2 element spectral lines, beta_i,qIs the regression coefficient of interference element E2 spectral line, q is the serial number of the selected E2 element spectral line, I_E2The intensity of the E2 spectral line, u the number of spectral lines screened from the full spectrum, k the number of spectral lines screened from the full spectrum, γ_kTo screen the regression coefficients of the lines, I_kThe intensity of the spectral line after screening.

The non-linear form of the selected characteristic line is a p-th order polynomial form.

The cyclic variable screening removes a spectral line intensities with the minimum regression coefficient absolute value each time; and the termination condition of the cyclic variable screening is that the number of the regression coefficient variables is less than a set value n _ min.

A LIBS quantitative analysis system for screening nonlinear PLS based on cyclic variables comprises a spectrum acquisition equipment module, a data preprocessing module, a data set dividing module, a PLS modeling optimization module and a test module;

the spectrum acquisition equipment module is used for acquiring original full spectrum data of laser-induced breakdown spectrum of the substance to be detected;

the data preprocessing module is used for carrying out normalization and noise reduction on the original full spectrum data of the laser-induced breakdown spectrum of the collected substance to be detected to obtain a multi-dimensional spectral line data set;

the data set dividing module is used for dividing the multi-dimensional spectral line data set into a training set, a check set and a test set and storing the training set, the check set and the test set in the memory;

the PLS modeling optimization module is used for performing PLS modeling by using training set data and check set data in a cyclic iteration mode to obtain model parameters, cyclic screening times and an optimal nonlinear PLS model;

and the test module is used for inputting the data of the test set into the established nonlinear PLS model, automatically acquiring the concentration of the element to be analyzed and outputting the concentration.

The invention has the beneficial effects that:

according to the invention, the nonlinear PLS model is established through cyclic variable screening to carry out quantitative analysis of the components based on LIBS, so that the modeling complexity caused by data redundancy and the nonlinear interference caused by self-absorption and matrix effect are reduced, and the precision of quantitative analysis is improved.

Drawings

FIG. 1 is a flow chart of the present invention.

Fig. 2 is an original spectrum of a laser-induced breakdown spectrum of iron ore concentrate pulp.

FIG. 3 is a diagram of the relationship between the number of principal components of the nonlinear PLS model and the root mean square error RMSE of the check set.

FIG. 4 is a graph of variable screening times versus check set root mean square error RMSE.

FIG. 5 is a diagram showing the relationship between the number of principal components after variable screening and the root mean square error RMSE of the check set.

Figure 6 is a graph comparing predicted values with actual values for iron concentrate pulp.

Detailed Description

The technical scheme of the invention is further explained by combining an LIBS grade analysis example of the iron ore concentrate pulp.

Example (b): a LIBS iron ore pulp quantitative analysis method for screening nonlinear PLS based on cyclic variables. The flow chart is shown in fig. 1, and is specifically described as follows: in order to reduce the influence of self absorption on quantitative analysis of the elements to be analyzed, the characteristic spectral line intensities of m elements E1 to be analyzed are selected, and in order to reduce the interference of other elements, the characteristic spectral line intensities of h main interference elements E2 are selected. Adding the p-th polynomial form of the (m and h spectral line intensities) into the modeling of the PLS to approximately correct the nonlinear influence caused by self-absorption and matrix effect, and simultaneously determining the optimal variable by a cyclic variable screening mode in order to reduce the interference of variable redundant information and reduce the model complexity, wherein the model expression is as follows:

c is the element concentration, p is the highest power, m is the number of selected element E1 element spectral lines to be analyzed, alpha_i,jFor the element to be analyzed, E1 linear regression coefficient, I is the power of spectral line intensity, j is the serial number of the selected E1 element spectral line, I_E1Is the E1 spectral line intensity, h is the number of selected interfering element E2 element spectral lines, beta_i,qIs the regression coefficient of interference element E2 spectral line, q is the serial number of the selected E2 element spectral line, I_E2The intensity of the E2 spectral line, u the number of spectral lines screened from the full spectrum, k the number of spectral lines screened from the full spectrum, γ_kTo screen the regression coefficients of the lines, I_kThe intensity of the spectral line after screening. The method specifically comprises the following steps:

(1) and (4) preprocessing data. The obtained original graph of the laser-induced breakdown spectrum of the iron ore concentrate pulp is shown in figure 2, the dimension is 6116, full spectrum and normalization are carried out, and two layers of wavelet denoising treatment are carried out.

(2) And dividing a training set, a check set and a test set. The total sample number is 95, 15 samples are selected as verification samples, parameters of the sample optimization model are utilized, 20 samples are used as test samples for evaluating the prediction accuracy of the final model, the verification samples and the test samples are uniformly distributed in the concentration range of the total samples when being divided, so that the effect of most fully evaluating the performance of the model is achieved, and the rest 60 samples are used as training samples for modeling.

(3) And selecting a 3 rd-order polynomial form of analysis line intensity and full spectrum data from the training samples to perform PLS modeling. The element to be analyzed of the iron ore concentrate pulp is Fe element, the main interference element is Si, therefore, 10 characteristic spectral lines of the element to be analyzed Fe and 5 characteristic spectral line intensities of the main interference element Si are selected, a 3-degree polynomial form and full spectrum data (6161 dimension in total) are subjected to PLS modeling, the principal component number is determined through a checking set minimum root mean square error RMSE, and the relation between the principal component number and the checking set root mean square error is shown in figure 3.

(4) The variables are ranked from large to small by the absolute value of the regression coefficients. And (4) arranging the 6116-dimensional data from large to small according to the magnitude of the absolute value of the regression coefficient.

(5) And removing the 50 variables with the minimum regression coefficient absolute values, performing PLS modeling on the remaining variable data, and recording the root mean square error of the check set.

(6) And (5) repeating the step (4) until the number of modeling variables is less than the set minimum number of variables of 100. The relationship between the variable screening times and the check set root mean square error RMSE is shown in fig. 4.

(7) And determining a final variable for establishing a nonlinear PLS model according to the root mean square error of the check set, establishing the nonlinear PLS model after circularly screening the variables, determining the number of principal components through the minimum root mean square error of the check set, and showing the relationship between the number of the principal components after screening the variables and the root mean square error of the check set in figure 5.

A LIBS quantitative analysis system for screening nonlinear PLS based on cyclic variables comprises a spectrum acquisition equipment module, a data preprocessing module, a data set dividing module, a PLS modeling optimization module and a test module;

the spectrum acquisition equipment module is used for acquiring original full spectrum data of laser-induced breakdown spectrum of the substance to be detected; the spectrum acquisition equipment module is a laser or a spectrometer. Such as Nd used in the examples; a YAG double pulse laser, such as the AvaApec-2048 spectrometer used in the examples.

The data preprocessing module is used for carrying out normalization and noise reduction on the original full spectrum data of the laser-induced breakdown spectrum of the collected substance to be detected to obtain a multi-dimensional spectral line data set;

the data set dividing module is used for dividing the multi-dimensional spectral line data set into a training set, a check set and a test set and storing the training set, the check set and the test set in the memory;

the PLS modeling optimization module is used for performing PLS modeling by using training set data and check set data in a cyclic iteration mode to obtain model parameters, cyclic screening times and an optimal nonlinear PLS model;

and the test module is used for inputting the data of the test set into the established nonlinear PLS model, automatically acquiring the concentration of the element to be analyzed and outputting the concentration.

And (5) result verification:

FIG. 6 is a diagram showing the comparison between the predicted values and the true values of the check set and the test set obtained by the method.

TABLE 1

TABLE 2

Table one is the analysis line for the selected element Fe to be analyzed and the main interfering element Si. Table two compares the results of the method of the present invention, which achieves the lowest predicted root mean square error RMSEP and the highest coefficient of determination R, with conventional PLS and the nonlinear PLS method of adding 3 rd order polynomials in the spectra of the principal analysis elements and the interference elements². The method has obvious effects on the quantitative analysis of the data with higher dimensionality, spectral data dimensionality reduction, self absorption reduction and nonlinear influence brought by matrix effect reduction.

The embodiment adopts iron ore concentrate pulp, is only a preferred embodiment, and can carry out analysis according to different application objects during specific implementation, and the types and the number of the selected analysis lines are adjusted.

The above-described embodiments are intended to illustrate the present invention, but not to limit the present invention, and any modifications, equivalents, improvements, etc. made within the spirit of the present invention and the scope of the claims fall within the scope of the present invention.

While the foregoing is directed to the preferred embodiment of the present invention, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention as defined in the appended claims.

Claims (6)

1. A LIBS quantitative analysis method for screening nonlinear PLS based on cyclic variables is characterized by comprising the following steps:

acquiring original full spectrum data of a laser-induced breakdown spectrum of a substance to be detected, and carrying out normalization and noise reduction treatment to obtain a multi-dimensional spectral line data set;

dividing a multi-dimensional spectral line data set into a training set, a check set and a test set;

performing PLS modeling by using training set data and check set data, performing loop iteration screening on model parameters, determining loop screening times, and obtaining an optimal nonlinear PLS model;

inputting the data of the test set into the established nonlinear PLS model, and automatically acquiring the concentration of the element to be analyzed;

the establishment of the optimal nonlinear PLS model specifically comprises the following steps:

step a, selecting a nonlinear form of the intensity of a spectral line to be analyzed and full spectrum data from training set data to perform PLS modeling, and obtaining a regression coefficient variable of the intensity of the spectral line to be analyzed;

b, arranging all regression coefficient variables of the PLS model from large to small according to absolute values, circularly screening the regression coefficient variables, modeling the PLS again until a preset termination condition is met, and stopping iteration so as to determine the number of circularly screening times;

step c, inputting the data of the check set into the PLS model in the step b, and calculating the root mean square error of the concentration of the element to be detected in the check set;

d, establishing a nonlinear PLS model after circularly screening variables according to the corresponding variables and the corresponding principal components when the root mean square error is minimum;

the total number of samples of the multi-dimensional spectral line data set is N, N _ val samples are selected as check samples, N _ tes samples are selected as test samples by utilizing parameters of a check sample optimization model and used for evaluating the prediction precision of a final model, and the rest N _ tra samples are used as training samples for modeling;

the spectral lines to be analyzed are m characteristic spectral lines of an element E1 to be analyzed and h characteristic spectral lines of an interference element E2;

the cyclic variable screening removes a spectral line intensities with the minimum regression coefficient absolute value each time; and the termination condition of the cyclic variable screening is that the number of the regression coefficient variables is less than a set value n _ min.

2. The method of claim 1, wherein the training set, the check set and the test set are divided into a scale; and when the check sample and the test sample are divided, the check sample and the test sample are uniformly distributed in the concentration range of the total sample, so that the effect of most fully evaluating the model performance is realized.

3. The method of claim 1, wherein the PLS model parameters comprise: regression coefficients of elements to be analyzed, regression coefficients of interference elements and regression coefficients of filtered spectral lines.

4. The LIBS quantitative analysis method for cyclic variable based nonlinear PLS screening, as claimed in claim 1, wherein the obtained optimal nonlinear PLS model is:

wherein C is the element concentration, p is the highest power, m is the number of selected element E1 element spectral lines to be analyzed, and alpha_i,jFor the element to be analyzed, E1 linear regression coefficient, I is the power of spectral line intensity, j is the serial number of the selected E1 element spectral line, I_E1Is the E1 line intensity, h is the selected stemNumber of spectral lines, beta, of disturbing element E2 element_i,qIs the regression coefficient of interference element E2 spectral line, q is the serial number of the selected E2 element spectral line, I_E2The intensity of the E2 spectral line, u the number of spectral lines screened from the full spectrum, k the number of spectral lines screened from the full spectrum, γ_kTo screen the regression coefficients of the lines, I_kThe intensity of the spectral line after screening.

5. The method of claim 4, wherein the nonlinear form of the selected characteristic line is a p-th order polynomial.

6. A LIBS quantitative analysis system for screening nonlinear PLS based on cyclic variables is characterized by comprising a spectrum acquisition equipment module, a data preprocessing module, a data set dividing module, a PLS modeling optimization module and a test module;

the spectrum acquisition equipment module is used for acquiring original full spectrum data of laser-induced breakdown spectrum of the substance to be detected;

the data preprocessing module is used for carrying out normalization and noise reduction on the original full spectrum data of the laser-induced breakdown spectrum of the collected substance to be detected to obtain a multi-dimensional spectral line data set;

the data set dividing module is used for dividing the multi-dimensional spectral line data set into a training set, a check set and a test set and storing the training set, the check set and the test set in the memory;

the PLS modeling optimization module is used for performing PLS modeling by using training set data and check set data in a cyclic iteration mode to obtain model parameters, cyclic screening times and an optimal nonlinear PLS model;

and the test module is used for inputting the data of the test set into the established nonlinear PLS model, automatically acquiring the concentration of the element to be analyzed and outputting the concentration.

Images