Instrument mass fractionation correction method for secondary ion mass spectrometer based on multiple regression

Abstract

The application discloses a secondary ion mass spectrometer instrument mass fractionation correction method based on multiple regression, comprising alternately measuring standard samples and unknown samples in an analysis sequence, synchronously collecting isotope ratio measurement values, analysis time, primary ion beam current intensity and secondary ion signal intensity at each analysis point to obtain measurement data; the preprocessing comprises calculating single-point instrument measurement deviation of the standard samples, performing outlier rejection and variable centering; the measurement data is preprocessed, a multiple linear regression model containing time drift, beam current effect and secondary ion yield effect is established; the multiple linear regression model is solved according to the measurement data by using an iterative reweighted least squares method to obtain optimal model parameters; the unknown samples are corrected one by one by using the optimal model parameters, and mass fractionation correction results are output.

Description

Technical Field

[0001] This invention relates to the field of mass fractionation calibration of mass spectrometers, and more particularly to a method for mass fractionation calibration of secondary ion mass spectrometers based on multiple regression. Background Technology

[0002] Secondary ion mass spectrometry (SIMS) is one of the most effective tools for in-situ isotope analysis in micro-areas, and is widely used in geology, materials science, and biological sciences. However, significant instrumental mass fractionation (IMF) is a common problem in SIMS analysis. IMF refers to the deviation between the isotope ratios measured by the instrument and the true ratios of the sample, and it is affected by a variety of instrument parameters.

[0003] Existing techniques typically employ a cross-calibration method of "standard sample-unknown sample-standard sample," assuming that the IMF is linear or constant over a short period. However, this traditional method has the following drawbacks: 1. Neglecting non-time-dependent drift: Traditional methods primarily correct for linear drift over time, but ignore the nonlinear fractionation effects caused by fluctuations in primary beam intensity (Ip) and secondary ion signal intensity (Is). In practical applications, instability of the ion source can lead to fluctuations in Ip, and minute differences in sample surface conditions (such as smoothness and conductivity) can also cause changes in Is. Both of these can significantly affect the IMF through space charge effects, dead time effects, or changes in instrument transmission efficiency. 2. Limited accuracy: In long-term analyses or when there are minor fluctuations in instrument conditions, time calibration alone cannot completely eliminate errors, making it difficult to achieve the analytical accuracy required for high-precision studies. 3. Low data utilization: The lack of effective outlier removal and diagnostic mechanisms results in abnormal data points lowering the overall calibration quality.

[0004] Therefore, there is an urgent need for a high-precision IMF calibration method that can simultaneously consider the influence of multiple instrument parameters and has stronger robustness. Summary of the Invention

[0005] The purpose of this invention is to provide a method for mass fractionation correction of a secondary ion mass spectrometer based on multiple regression.

[0006] To achieve the above objectives, the present invention is implemented according to the following technical solution: This invention includes the following steps: In the analytical sequence, standard samples and unknown samples are measured alternately. At each analytical point, the isotope ratio measurement value, analysis time, primary ion beam intensity, and secondary ion signal intensity are collected simultaneously to obtain measurement data. The preprocessing includes calculating the single-point instrument measurement deviation of the standard sample, performing outlier removal, and variable centering. The measured data were preprocessed to establish a multiple linear regression model that includes time drift, beam effect and secondary ion yield effect; The iterative reweighted least squares method is used to solve the multiple linear regression model based on the measured data to obtain the optimal model parameters; the optimal model parameters are then used to correct the unknown samples one by one, and the mass fractionation correction results are output.

[0007] Furthermore, the single-point instrument measurement deviation and the method for performing outlier removal include: Calculate the single-point instrument measurement deviation of the standard sample: ,in Let be the measured value of the i-th standard sample. This is the recommended true value for the standard sample; In secondary ion mass spectrometry analysis, for data points with sample surface inclusions, electron gun charge neutralization momentary failures, or circuit noise: calculate the average IMF value of the standard sample sequence. and standard deviation According to the statistical law of normal distribution, Data points outside the range are marked as outliers and removed.

[0008] Furthermore, the method for obtaining the centralization of the variable includes: Analysis time Primary ion beam intensity Secondary ion signal intensity The transformation is performed, and the expression is: ; ; ; in This is the arithmetic mean of the analysis times corresponding to the standard sample sequences. This is the arithmetic mean of the ion beam current intensities corresponding to a single test of the standard sample sequence. This is the arithmetic mean of the secondary ion signal intensities corresponding to the standard sample sequence. For the centered analysis time variable, The primary ion beam intensity variable after decentralization. The intensity of the secondary ion signal changes after centering.

[0009] Furthermore, the method for constructing the multiple linear regression model includes: A multiple linear regression model incorporating time drift, beam effect, and secondary ion yield effect is established, expressed as follows: ; in For random residuals, For the intercept term, The influence coefficient of time drift. The influence coefficient of the primary beam. This is the influence coefficient of the secondary ion yield. For the centered analysis time variable, The primary ion beam intensity variable after decentralization. The intensity variable of the secondary ion signal after centering; Define the weighted sum of squared residuals as the objective function, expressed as: ; ; in Let be the vector of regression coefficients to be determined. Let i be the weight of the i-th observation point. Let be the objective function. Let be the feature vector of the i-th sample. For the i-th analysis time variable after centralization, Let i be the decentralized primary ion beam intensity variable. The signal intensity variable of the i-th secondary ion after centering. This represents the total number of samples. For the i-th sample, Let i be the residual of the i-th sample. As an adjustment constant, The absolute median of the residuals. The residual threshold; The pseudo-weighted loss function, converted to matrix form, is expressed as follows: ; in It is a diagonal weight matrix. This is the transpose of the matrix. A column vector of the actual observations. It is a column matrix of eigenvectors; By differentiating the vector of regression coefficients and setting the derivative to zero, we obtain the weighted normal equation, and then solve for the weighted least squares estimator. ; This is the column vector of the optimal regression coefficients.

[0010] Furthermore, the method for obtaining the optimal model parameters includes: Obtain a standardized training dataset based on the measurement data. ;in Let be the feature vector of the i-th sample. For the i-th sample, This represents the total number of samples. Use the ordinary least squares solution as the initial value for iteration. Calculate the initial residual vector and initial scale ;in The column matrix of eigenvectors, This is the initial regression coefficient vector. Let this be the residual vector of the 0th iteration. This represents the predicted value vector of the multiple linear regression model. For the initial robust scaling estimate, The median of the residuals. The median of the absolute deviation; Calculate new weights based on the current residuals. Construct a diagonal weight matrix ;in Let i be the weight of the i-th sample in the k-th iteration. For the first The residual vector of the next iteration For the first Robust scaling estimation in the next iteration This is the Tukey double-weighted kernel function. Construct operators for diagonal matrices; Solving the weighted least squares problem Closed-form solutions are obtained through weighted normal equations. ;in Let be the optimal regression coefficient vector for the k-th iteration. For the weighted sum of squared residuals, For the weighted covariance matrix, It is the inverse of the weighted covariance matrix. This is a weighted cross term vector; Update residual vector and robust scalar estimation Calculate the relative rate of change of parameters If satisfied If the value is less than the convergence threshold, the iteration terminates and the output is given. Otherwise, update the weight matrix and continue iterating; where Let be the residual vector of the k-th iteration. This is the vector of model predictions for the k-th iteration. For the robust scaling estimate of the k-th iteration, After the iteration converges, the asymptotic covariance matrix of the parameter estimates is calculated. and parameter standard error ;in Here is the weight matrix at convergence. For the final robust scalar estimation; Construct a t-statistic to test the significance of each coefficient. For a given significance level ,like If the j-th predictor variable has no significant contribution to the IMF, it is removed. This process is repeated until all coefficients have been traversed to determine the optimal multiple linear regression model dimension. ; Calculate the weighted variance inflation factor for each variable. ,like Then the multiple linear regression model, through collinearity diagnosis, accepts the current parameter estimates; if If moderate multicollinearity exists, the composite variable method should be preferred, and the following definition should be used: Replace the original variable pairs and re-execute the iterative reweighted least squares algorithm; if If severe collinearity exists, the variable with the largest WVIF and relatively minor physical significance is removed, and the iterative reweighted least squares algorithm is re-executed; where The coefficient of determination is the weighted regression of the remaining variables with the j-th variable as the dependent variable. After convergence and significance screening using the iterative reweighted least squares algorithm, the final model parameter set is determined. ;in This is the set of valid variable indexes.

[0011] Furthermore, the method of correcting the unknown samples one by one using the optimal model parameters includes: The arithmetic mean of the standard sample sequences must be used. The measurement variables of the current unknown sample are centered. The multiple linear regression model is based on a coordinate system with the standard sample mean as the origin; Calculate for the th Centralized variables for unknown sample points: , , ;in Let be the original time variable for the u-th unknown sample. Let u be the time variable after centering the u-th unknown sample. Let be the ion beam current variable after centering the u-th unknown sample. Let be the initial primary ion beam current variable for the u-th unknown sample. Let be the original secondary ion yield variable for the u-th unknown sample. Let be the secondary ion yield variable after centering the u-th unknown sample; Will , , Substitute into the optimal model, calculate the first Prediction bias for unknown sample points: in Let be the predicted IMF bias for the u-th unknown sample; Calculate the corrected true value: in This represents the corrected true isotope ratio for the u-th unknown sample. The original measured isotope ratio of the u-th unknown sample. denoted as the systematic bias of the u-th unknown sample in the multiple linear regression model.

[0012] The beneficial effects of this invention are: This invention is a method for mass fractionation correction of a secondary ion mass spectrometer based on multiple regression. Compared with the prior art, this invention has the following technical advantages: This invention effectively eliminates additional fractionation errors caused by minor fluctuations in instrument status by introducing beam intensity and secondary ion signal intensity correction, improving the external precision of isotope analysis from >0.5‰ to <0.2‰, meeting the needs of high-precision geochemical research. The inclusion of secondary ion signal intensity further reveals subtle instrument fractionation caused by changes in sample surface condition or instrument transmission efficiency, making the correction model closer to physical facts and improving its explanatory power. Through centering preprocessing, 3σ outlier removal, and stepwise regression screening mechanisms, the model is ensured to be insensitive to outliers and can automatically adapt to major error sources under different instrument conditions, making it suitable for long-term, large-scale automated analysis sequences. Attached Figure Description

[0013] Figure 1 This is a flowchart of the steps of the secondary ion mass spectrometer instrument mass fractionation correction method based on multiple regression of the present invention; Figure 2 This is a three-dimensional correlation analysis diagram of the IMF with the primary beam intensity and the secondary ion signal intensity in the embodiments of this specification; Figure 3 This is a comparison of the distribution of instrument mass fractionation data before and after calibration in the embodiments of this specification. Detailed Implementation

[0014] The present invention will be further described below through specific embodiments. The illustrative embodiments and descriptions herein are used to explain the present invention, but are not intended to limit the present invention.

[0015] The present invention provides a method for mass fractionation calibration of a secondary ion mass spectrometer based on multiple regression, comprising the following steps: like Figure 1 As shown, this embodiment includes the following steps: In the analytical sequence, standard samples and unknown samples are measured alternately. At each analytical point, the isotope ratio measurement value, analysis time, primary ion beam intensity, and secondary ion signal intensity are collected simultaneously to obtain measurement data. The preprocessing includes calculating the single-point instrument measurement deviation of the standard sample, performing outlier removal, and variable centering. The measured data were preprocessed to establish a multiple linear regression model that includes time drift, beam effect and secondary ion yield effect; The iterative reweighted least squares method is used to solve the multiple linear regression model based on the measured data to obtain the optimal model parameters; the optimal model parameters are then used to correct the unknown samples one by one, and the mass fractionation correction results are output. In the actual assessment, a set of zircon silicon isotope analysis data was corrected. To ensure the representativeness and authority of the experimental data, the standard sample selected was homogeneous mantle zircon (Mud Tank) as reported in the literature. Recommended true value: -0.38‰; Experimental conditions and data acquisition: Instrument: SHRIM V secondary ion mass spectrometer; Detection target: and ; Collect 30 standard sample points (Std) and 20 unknown sample points (Unk); Variable monitoring: Analysis time Record relative timestamp (h); one beam A Cs+ ion source was used, with the beam current set to 3.0 nA; secondary ion signal intensity... The average count rate is approximately cps; Data preprocessing: Centralized: h, nA, cps; Constructing variables: .

[0016] Regression results: (Time): p=0.04 (significant); (Beam): p < 0.001 (highly significant); (Yield): p=0.03 (significant, indicating that yield fluctuations still affect the IMF under constant beam current); ; VIF check: and The VIF is 3.2 (<5), indicating that although the two are correlated, the collinearity is within an acceptable range, and the model parameter estimation is reliable. Verification of calibration effect and comparison of accuracy improvement: Bivariate model: includes only time ( The primary beam intensity is used as a correction factor; model formula: ; Correction result: 2SD = 0.18‰. This is a significant improvement compared to univariate time correction, but some unexplained errors remain. Three-variable model: The complete model proposed in this invention further incorporates secondary ion signal intensity. Model formula: Correction result: 2SD = 0.12‰; Conclusion: Introducing secondary ion signal intensity ( After that, the fluctuations in ionization efficiency caused by minute differences on the sample surface were further corrected, pushing the analytical precision to the limits of the instrument.

[0017] In this embodiment, the single-point instrument measurement deviation and the method for performing outlier removal include: Calculate the single-point instrument measurement deviation of the standard sample: ,in Let be the measured value of the i-th standard sample. This is the recommended true value for the standard sample; In secondary ion mass spectrometry analysis, for data points with sample surface inclusions, electron gun charge neutralization momentary failures, or circuit noise: calculate the average IMF value of the standard sample sequence. and standard deviation According to the statistical law of normal distribution, Data points outside the interval are marked as outliers and removed.

[0018] In this embodiment, the method for centralizing variables includes: Analysis time Primary ion beam intensity Secondary ion signal intensity The transformation is performed, and the expression is: ; ; ; in This is the arithmetic mean of the analysis times corresponding to the standard sample sequences. This is the arithmetic mean of the ion beam current intensities corresponding to a single test of the standard sample sequence. This is the arithmetic mean of the secondary ion signal intensities corresponding to the standard sample sequence. For the centered analysis time variable, The primary ion beam intensity variable after decentralization. The intensity variable of the secondary ion signal after centering; In actual evaluation, after variable centering, the model intercept... It directly represents the baseline IMF value under average instrument conditions, which includes average time, average beam current, and average yield.

[0019] In this embodiment, the method for constructing the multiple linear regression model includes: A multiple linear regression model incorporating time drift, beam effect, and secondary ion yield effect is established, expressed as follows: ; in For random residuals, For the intercept term, The influence coefficient of time drift. The influence coefficient of the primary beam. This is the influence coefficient of the secondary ion yield. For the centered analysis time variable, The primary ion beam intensity variable after decentralization. The intensity variable of the secondary ion signal after centering; Define the weighted sum of squared residuals as the objective function, expressed as: ; ; in Let be the vector of regression coefficients to be determined. Let i be the weight of the i-th observation point. Let be the objective function. Let be the feature vector of the i-th sample. For the i-th analysis time variable after centralization, Let i be the decentralized primary ion beam intensity variable. The signal intensity variable of the i-th secondary ion after centering. The total number of samples. For the i-th sample, Let i be the residual of the i-th sample. As an adjustment constant, The absolute median of the residuals. The residual threshold; The pseudo-weighted loss function, converted to matrix form, is expressed as follows: ; in It is a diagonal weight matrix. This is the transpose of the matrix. A column vector of the actual observations. It is a column matrix of eigenvectors; By differentiating the vector of regression coefficients and setting the derivative to zero, we obtain the weighted normal equation, and then solve for the weighted least squares estimator. ; This is the column vector of the optimal regression coefficients.

[0020] In this embodiment, the method for obtaining the optimal model parameters includes: Obtain a standardized training dataset based on the measurement data. ;in Let be the feature vector of the i-th sample. For the i-th sample, This represents the total number of samples. Use the ordinary least squares solution as the initial value for iteration. Calculate the initial residual vector and initial scale ;in The column matrix of eigenvectors, This is the initial regression coefficient vector. Let this be the residual vector of the 0th iteration. This represents the predicted value vector of the multiple linear regression model. For the initial robust scaling estimate, The median of the residuals. The median of the absolute deviation; Calculate new weights based on the current residuals. Construct a diagonal weight matrix ;in Let i be the weight of the i-th sample in the k-th iteration. For the first The residual vector of the next iteration For the first Robust scaling estimation in the next iteration This is the Tukey double-weighted kernel function. Construct operators for diagonal matrices; Solving the weighted least squares problem Closed-form solutions are obtained through weighted normal equations. ;in Let be the optimal regression coefficient vector for the k-th iteration. For the weighted sum of squared residuals, For the weighted covariance matrix, It is the inverse of the weighted covariance matrix. This is a weighted cross term vector; Update residual vector and robust scalar estimation Calculate the relative rate of change of parameters If satisfied If the value is less than the convergence threshold, the iteration terminates and the output is given. Otherwise, update the weight matrix and continue iterating; where Let be the residual vector of the k-th iteration. This is the vector of model predictions for the k-th iteration. For the robust scaling estimate of the k-th iteration, After the iteration converges, the asymptotic covariance matrix of the parameter estimates is calculated. and parameter standard error ;in Here is the weight matrix at convergence. For the final robust scalar estimation; Construct a t-statistic to test the significance of each coefficient. For a given significance level ,like If the j-th predictor variable has no significant contribution to the IMF, it is removed. This process is repeated until all coefficients have been traversed to determine the optimal multiple linear regression model dimension. ; Calculate the weighted variance inflation factor for each variable. ,like Then the multiple linear regression model, through collinearity diagnosis, accepts the current parameter estimates; if If moderate multicollinearity exists, the composite variable method should be preferred, and the following definition should be used: Replace the original variable pairs and re-execute the iterative reweighted least squares algorithm; if If severe collinearity exists, the variable with the largest WVIF and relatively minor physical significance is removed, and the iterative reweighted least squares algorithm is re-executed; where The coefficient of determination is the weighted regression of the remaining variables with the j-th variable as the dependent variable. After convergence and significance screening using the iterative reweighted least squares algorithm, the final model parameter set is determined. ;in For the set of valid variable indices; In actual evaluation, the convergence threshold is 10. -6 , It is 0.05.

[0021] In this embodiment, the method of correcting the unknown samples one by one using the optimal model parameters includes: The arithmetic mean of the standard sample sequences must be used. The measurement variables of the current unknown sample are centered. The multiple linear regression model is based on a coordinate system with the standard sample mean as the origin; Calculate for the th Centralized variables for unknown sample points: , , ;in Let be the original time variable for the u-th unknown sample. Let u be the time variable after centering the u-th unknown sample. Let be the ion beam current variable after centering the u-th unknown sample. Let be the initial primary ion beam current variable for the u-th unknown sample. Let be the original secondary ion yield variable for the u-th unknown sample. Let be the secondary ion yield variable after centering the u-th unknown sample; Will , , Substitute into the optimal model, calculate the first Prediction bias for unknown sample points: in Let be the predicted IMF bias for the u-th unknown sample; Calculate the corrected true value: in This represents the corrected true isotope ratio for the u-th unknown sample. The original measured isotope ratio of the u-th unknown sample. denoted as the systematic bias of the u-th unknown sample in the multiple linear regression model.

[0022] Figure 2 The figure shows a three-dimensional correlation analysis of IMF with primary beam intensity and secondary ion signal intensity. The figure displays the response surface of IMF (Z-axis, color depth) as it changes with primary beam intensity (X-axis) and secondary ion signal intensity (Y-axis). Grayscale mapping is used in the figure to represent the magnitude of IMF values ​​(black / dark color represents low value, white / light color represents high value). IMF is not only affected by a single variable, but also exhibits a significant multiple linear correlation with Ip and Is, which intuitively verifies the necessity of establishing a multiple regression model. Figure 3Left figure (before calibration): Shows the IMF distribution of the original measurement data. The gray dots indicate large data dispersion, significantly affected by instrument status fluctuations, with an external precision (2SD) of only 0.41‰ (shaded area within the gray dashed box). Right figure (after calibration): Shows the data after calibration using the multivariate regression model of this invention (including three variables: time, primary beam intensity, and secondary ion signal intensity). The black triangle significantly converges to near the true baseline (solid line), and the external precision (2SD) is greatly improved to 0.12‰ (shaded area within the black solid box), with a variance improvement rate of 91.4%. The calibration model used is: ;in , All parameters were significant (p<0.05).

[0023] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for mass fractionation correction of a secondary ion mass spectrometer based on multiple regression, characterized in that, Includes the following steps: In the analytical sequence, standard samples and unknown samples are measured alternately. At each analytical point, isotope ratio measurements, analysis time, primary ion beam intensity, and secondary ion signal intensity are collected simultaneously to obtain measurement data. Preprocessing includes calculating single-point instrument measurement bias of standard samples, performing outlier removal, and variable centering. The measured data were preprocessed to establish a multiple linear regression model that includes time drift, beam effect, and secondary ion yield effect; including: A multiple linear regression model incorporating time drift, beam effect, and secondary ion yield effect is established, expressed as follows: ； in For random residuals, For the intercept term, The influence coefficient of time drift. The influence coefficient of the primary beam. This is the influence coefficient of the secondary ion yield. For the centered analysis time variable, The primary ion beam intensity variable after decentralization. The intensity variable of the secondary ion signal after centering; Define the weighted sum of squared residuals as the objective function, expressed as: ； ； in Let be the vector of regression coefficients to be determined. Let i be the weight of the i-th observation point. Let be the objective function. Let be the feature vector of the i-th sample. For the i-th analysis time variable after centralization, Let i be the decentralized primary ion beam intensity variable. The signal intensity variable of the i-th secondary ion after centering. This represents the total number of samples. For the i-th sample, Let i be the residual of the i-th sample. As an adjustment constant, The absolute median of the residuals. The residual threshold; The pseudo-weighted loss function, converted to matrix form, is expressed as follows: ； in It is a diagonal weight matrix. This is the transpose of the matrix. A column vector of the actual observations. It is a column matrix of eigenvectors; By differentiating the vector of regression coefficients and setting the derivative to zero, we obtain the weighted normal equation, and then solve for the weighted least squares estimator. ; This is the column vector of optimal regression coefficients; The iterative reweighted least squares method is used to solve the multiple linear regression model based on the measured data to obtain the optimal model parameters; the optimal model parameters are then used to correct the unknown samples one by one, and the mass fractionation correction results are output.

2. The method for mass fractionation correction of a secondary ion mass spectrometer based on multiple regression according to claim 1, characterized in that, The single-point instrument measurement deviation and the method for performing outlier removal include: Calculate the single-point instrument measurement deviation of the standard sample: ,in Let be the measured value of the i-th standard sample. This is the recommended true value for the standard sample; In secondary ion mass spectrometry analysis, for data points with sample surface inclusions, electron gun charge neutralization momentary failures, or circuit noise: calculate the average IMF value of the standard sample sequence. and standard deviation According to the statistical law of normal distribution, Data points outside the range are marked as outliers and removed.

3. The method for mass fractionation correction of a secondary ion mass spectrometer based on multiple regression according to claim 1, characterized in that, The variable centralization method includes: Analysis time Primary ion beam intensity Secondary ion signal intensity The transformation is performed, and the expression is: ； ； ； in This is the arithmetic mean of the analysis times corresponding to the standard sample sequences. This is the arithmetic mean of the ion beam current intensities corresponding to a single test of the standard sample sequence. This is the arithmetic mean of the secondary ion signal intensities corresponding to the standard sample sequence. For the centered analysis time variable, The primary ion beam intensity variable after decentralization. The value represents the intensity variable of the secondary ion signal after centering.

4. The method for mass fractionation correction of a secondary ion mass spectrometer based on multiple regression according to claim 1, characterized in that, The method for obtaining the optimal model parameters includes: Obtain a standardized training dataset based on the measurement data. ;in Let be the feature vector of the i-th sample. For the i-th sample, This represents the total number of samples. Use the ordinary least squares solution as the initial value for iteration. Calculate the initial residual vector and initial scale ;in The column matrix of eigenvectors, This is the initial regression coefficient vector. Let this be the residual vector of the 0th iteration. This represents the predicted value vector of the multiple linear regression model. For the initial robust scaling estimate, The median of the residuals. The median of the absolute deviation; Calculate new weights based on the current residuals. Construct a diagonal weight matrix ;in Let i be the weight of the i-th sample in the k-th iteration. For the first The residual vector of the next iteration For the first Robust scaling estimation in the next iteration This is the Tukey double-weighted kernel function. Construct operators for diagonal matrices; Solving the weighted least squares problem Closed-form solutions are obtained through weighted normal equations. ;in Let be the optimal regression coefficient vector for the k-th iteration. For the weighted sum of squared residuals, For the weighted covariance matrix, It is the inverse of the weighted covariance matrix. This is a weighted cross term vector; Update residual vector and robust scalar estimation Calculate the relative rate of change of parameters If satisfied If the value is less than the convergence threshold, the iteration terminates and the output is given. Otherwise, update the weight matrix and continue iterating; where Let be the residual vector of the k-th iteration. This is the vector of model predictions for the k-th iteration. For the robust scaling estimate of the k-th iteration, After the iteration converges, the asymptotic covariance matrix of the parameter estimates is calculated. and parameter standard error ;in Here is the weight matrix at convergence. For the final robust scalar estimation; Construct a t-statistic to test the significance of each coefficient. For a given significance level ,like If the j-th predictor variable has no significant contribution to the IMF, it is removed. This process is repeated until all coefficients have been traversed to determine the optimal multiple linear regression model dimension. ; Calculate the weighted variance inflation factor for each variable. ,like Then the multiple linear regression model, through collinearity diagnosis, accepts the current parameter estimates; if If moderate multicollinearity exists, the composite variable method should be preferred, and the following definition should be used: Replace the original variable pairs and re-execute the iterative reweighted least squares algorithm; if If severe collinearity exists, the variable with the largest WVIF and relatively minor physical significance is removed, and the iterative reweighted least squares algorithm is re-executed; where The coefficient of determination is the weighted regression of the remaining variables with the j-th variable as the dependent variable. After convergence and significance screening using the iterative reweighted least squares algorithm, the final model parameter set is determined. ;in This is the set of valid variable indexes.

5. The method for instrument mass fractionation correction of a secondary ion mass spectrometer based on multiple regression according to claim 1, characterized in that, The method for correcting the unknown samples one by one using the optimal model parameters includes: The arithmetic mean of the standard sample sequences must be used. The measurement variables of the current unknown sample are centered. The multiple linear regression model is based on a coordinate system with the standard sample mean as the origin; Calculate for the th Centralized variables for unknown sample points: , , ;in Let be the original time variable for the u-th unknown sample. Let u be the time variable after centering the u-th unknown sample. Let be the ion beam current variable after centering the u-th unknown sample. Let be the initial primary ion beam current variable for the u-th unknown sample. Let be the original secondary ion yield variable for the u-th unknown sample. Let be the secondary ion yield variable after centering the u-th unknown sample; Will , , Substitute into the optimal model, calculate the first Prediction bias for unknown sample points: in Let be the predicted IMF bias for the u-th unknown sample; Calculate the corrected true value: in This represents the corrected true isotope ratio for the u-th unknown sample. The original measured isotope ratio of the u-th unknown sample. denoted as the systematic bias of the u-th unknown sample in the multiple linear regression model.

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