A correction method for gamma energy spectrum channel shift and peak area variation based on principal component analysis and linear regression

Abstract

The invention discloses a gamma energy spectrum channel shift and peak area change correction method based on principal component analysis and linear regression, which relates to the field of gamma energy spectrum repair technology, including extracting and analyzing FSVD weak information of RO I area of ​​K, U and Th, determining RO I area causing change; using principal component analysis method to RO I area, analyzing background measurement value and value affected by weak information after adding artificial radioactive nuclides, extracting principal components, and determining weights of different channel address counts; based on weight factors, using linear regression analysis to construct a spectrum repair mathematical model; repairing spectrum data after adding artificial radioactive nuclides through the spectrum repair mathematical model; comparing characteristic peak channel addresses and peak areas before and after repair, and verifying the correction results of channel address shift and peak area change. The invention can effectively reduce the peak position shift and peak area change caused by the counting contribution of artificial radioactive nuclides to RO I area of ​​K, U and Th, and improve the accuracy of peak area calculation.

Description

Technical Field

[0001] The present invention relates to the technical field of gamma energy spectrum repair, and in particular to a method for correcting gamma energy spectrum channel deviation and peak area variation based on principal component analysis and linear regression. Background Art

[0002] At present, there are many studies on the correction technology of gamma spectrum channel address shift and peak area change caused by temperature change at home and abroad. The gamma spectrum can be reconstructed according to the temperature change by calculating the change of energy scale. In addition, all channels can be compensated by using external sources and known peaks in the spectrum. The drift correction method based on Gaussian distribution can also be used to correct the offset. The latest research uses simulated and real gamma spectrum data to train neural networks to correctly identify various radioactive isotopes and eliminate the problem of channel position deviation. However, when measuring the ROI area of ​​natural radioactive K, U, and Th, the interference of artificial radioactive nuclides will cause the characteristic peak area of ​​the ROI area of ​​K, U, and Th to change, the characteristic peak position will shift, and the overall count of ROI will be higher than that of non-interference measurement. In the actual measurement process, the background of the instrument itself and the complexity of the measurement environment are important sources of this interference. When calculating the radioactive activity content of K, U, and Th, it leads to a significant increase in the value and cannot be accurately calculated. Especially in the activity calculation during the aerial radioactivity measurement process, the calculation needs to be corrected for the altitude, and the primary influence effect of the interference is cascaded.

[0003] Therefore, it is urgent to provide a method for correcting the gamma energy spectrum channel shift and peak area change based on principal component analysis and linear regression to solve the problem of peak position shift and peak area change in the ROI region of K, U, and Th in natural radioactivity measurement caused by artificial radioactivity, resulting in inaccurate content calculation. Summary of the invention

[0004] The purpose of the present invention is to overcome the above-mentioned shortcomings in the prior art and provide a method for correcting gamma energy spectrum channel shift and peak area change based on principal component analysis and linear regression, which can effectively reduce the peak position shift and peak area change caused by the counting contribution of artificial radioactive nuclides to the ROI area of ​​K, U and Th, and improve the accuracy of peak area calculation.

[0005] In order to achieve the above-mentioned object of the invention, the present invention provides the following technical solutions:

[0006] A gamma energy spectrum channel shift and peak area change correction method based on principal component analysis and linear regression comprises the following steps:

[0007] S1, calibrate the system, obtain background measurement data and measurement data affected by artificial radionuclides, extract and analyze FSVD weak information of ROI areas of K, U, and Th, and determine the ROI area that causes changes;

[0008] S2, using the principal component analysis method for the ROI area, analyzing the background measurement values ​​and the values ​​affected by weak information after adding artificial radionuclides, extracting the principal components, and determining the weight factors of different spectral channel counts;

[0009] S3, based on the weight factor, linear regression analysis is used to construct the energy spectrum repair mathematical model;

[0010] S4, repairing the energy spectrum data after adding artificial radionuclides through the energy spectrum repair mathematical model;

[0011] S5, compare the characteristic peak channels and peak areas before and after repair to verify the correction results of channel offset and peak area change.

[0012] Furthermore, the specific process of step S1 is as follows:

[0013] Measure and obtain the background gamma spectrum matrix B of K, U, and Th without interference from artificial radionuclides;

[0014] Add artificial radioactive nuclide interference and measure and obtain the gamma spectrum matrix A of K, U and Th that are interfered;

[0015] For the background matrix B n×m Perform singular value decomposition to obtain the singular value matrix Λ, take the first r columns of the Λ matrix, ignore the elements of other columns of the Λ matrix, and set them to 0 to reconstruct the background gamma spectrum data matrix B';

[0016] Combine the reconstructed background gamma spectrum B' and the mixed gamma spectrum matrix A to construct the linear regression analysis matrix C n×（m+p） , the Gauss-Markov linear regression method is used to analyze the matrix C and obtain the estimated parameter β. Through the analysis of β, weak information can be extracted and analyzed to determine the ROI area that causes changes in K, U, and Th;

[0017] Among them, the number of β is 1024.

[0018] Furthermore, determining the weights of different spectral channel counts in step S2 includes the following steps:

[0019] Calculate the linear combination coefficient matrix, the formula is: loading matrix / Sqrt(eigen), that is, the loading coefficient divided by the square root of the corresponding characteristic root;

[0020] The formula for calculating the comprehensive score coefficient is: cumulative (linear combination coefficient * variance explanation rate) / cumulative variance explanation rate, that is, the linear combination coefficient is multiplied by the variance explanation rate, then added and divided by the cumulative variance explanation rate;

[0021] The weights of different spectral channel counts are calculated, and the comprehensive score coefficients are normalized to obtain the weight factor values ​​of different spectral channel counts.

[0022] Furthermore, the specific process of step S3 is as follows:

[0023] The weight factor value x1 of different spectral channel counts calculated by S2 and the average value x2 of each spectral channel in the ROI area corresponding to the gamma energy spectrum matrix A of K, U, Th that is interfered with by measurement are used as independent variables, and the average value y of each spectral channel in the ROI area corresponding to the background gamma energy spectrum matrix B of K, U, Th without artificial radionuclide interference by measurement is used as the independent dependent variable;

[0024] By observing the independent variables and dependent variables, linear regression analysis is used to obtain the coefficient b1 of the weight factor value, the coefficient b2 of the average value of each spectral channel in the ROI area corresponding to the gamma spectrum matrix A of the disturbed K, U, and Th, and the constant b3, which are collectively referred to as regression coefficients;

[0025] Constructing a mathematical repair model:

[0026] y=x1×b1+x2×b2+b3.

[0027] Furthermore, the specific process of step S4 is as follows:

[0028] The weight factors of different spectral channel counts and the counts of the background gamma energy spectra of K, U, and Th whose corresponding spectral channels are interfered by artificial radionuclides are substituted into the mathematical repair models x1 and x2 respectively, and the repaired background gamma energy spectra y of K, U, and Th are calculated.

[0029] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0030] The present invention can effectively reduce the peak position shift and peak area change caused by the counting contribution of artificial radionuclides to the ROI area of ​​K, U and Th, and improve the accuracy of peak area calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 The stacked diagram is the measurement results of the ROI area of ​​K, U, and Th based on the CeBr3 detector;

[0032] Figure 2 This is the result of the correlation analysis of the background gamma spectrum measured by the CeBr3 detector;

[0033] Figure 3 The t-test result graph of the ROI peak area counts of K, U, and Th measured 10 times in the background;

[0034] Figure 4 Artificial radionuclides 137Correlation analysis results of Cs interference and background measurement results;

[0035] Figure 5 For 10 background measurements and addition 137 t-test results of ROI peak area counts of K, U, and Th at different Cs distances;

[0036] Figure 6 This is the weak information extraction result diagram of ROI area of ​​K, U, and Th based on the FSVD method;

[0037] Figure 7 Flow chart of the method for correction of channel shift and peak area variation;

[0038] Figure 8 This is the correction result diagram of the spectral channel shift and peak area change in the ROI area of ​​K;

[0039] Fig. 9 This is the correction result diagram of the spectrum channel shift and peak area change in the ROI area of ​​U;

[0040] Fig.10 This is the correction result diagram of the spectrum channel shift and peak area change in the ROI area of ​​Th;

[0041] Fig.11 This is the result of one-way ANOVA of different ROI areas of 10 background measurement data;

[0042] Fig.12 For 10 background measurements and addition 137 The results of one-way ANOVA of ROI area of ​​K, U and Th at different Cs distances;

[0043] Fig.13 is the variance explanation rate diagram;

[0044] Fig.14 is the load factor diagram;

[0045] Fig.15 It is the result graph of linear combination coefficients and weights;

[0046] Fig.16 This is the result of linear regression analysis;

[0047] Fig.17 It is a statistical chart of the channel shift and peak area change results. DETAILED DESCRIPTION

[0048] The present invention is further described in detail below in conjunction with test examples and specific implementation methods. However, this should not be understood as the scope of the above subject matter of the present invention being limited to the following embodiments, and all technologies realized based on the content of the present invention belong to the scope of the present invention.

[0049] This embodiment provides a method for correcting gamma energy spectrum channel shift and peak area change based on principal component analysis and linear regression, including:

[0050] S1, calibrate the system, obtain background measurement data and measurement data affected by artificial radionuclides, extract and analyze FSVD weak information of ROI areas of K, U, and Th, and determine the ROI area that causes changes;

[0051] S2, using the principal component analysis method for the ROI area, analyzing the background measurement values ​​and the values ​​affected by weak information after adding artificial radionuclides, extracting the principal components, and determining the weights of different spectral channel counts;

[0052] S3, based on the weight factor, linear regression analysis is used to construct the energy spectrum repair mathematical model;

[0053] S4, repairing the energy spectrum data after adding artificial radionuclides through the energy spectrum repair mathematical model;

[0054] S5, compare the characteristic peak channels and peak areas before and after repair to verify the correction results of channel offset and peak area change.

[0055] The above embodiment is further optimized, and the specific process of step S1 is as follows:

[0056] Measure and obtain the background gamma spectrum matrix B of K, U, and Th without interference from artificial radionuclides;

[0057] Add artificial radioactive nuclide interference and measure and obtain the gamma spectrum matrix A of K, U and Th that are interfered;

[0058] For the background matrix B n×m Perform singular value decomposition to obtain the singular value matrix Λ, take the first r columns of the Λ matrix, ignore the elements of other columns of the Λ matrix, and set them to 0 to reconstruct the background gamma spectrum data matrix B';

[0059] Combine the reconstructed background gamma spectrum B' and the mixed gamma spectrum matrix A to construct the linear regression analysis matrix C n×（m+p） , the Gauss-Markov linear regression method is used to analyze the matrix C and obtain the estimated parameter β. Through the analysis of β, weak information can be extracted and analyzed to determine the ROI area that causes changes in K, U, and Th;

[0060] Among them, the number of β is 1024.

[0061] Further optimizing the above embodiment, determining the weights of different spectral channel counts in step S2 includes the following steps:

[0062] Calculate the linear combination coefficient matrix, the formula is: loading matrix / Sqrt(eigen), that is, the loading coefficient divided by the square root of the corresponding characteristic root;

[0063] The formula for calculating the comprehensive score coefficient is: cumulative (linear combination coefficient * variance explanation rate) / cumulative variance explanation rate, that is, the linear combination coefficient is multiplied by the variance explanation rate, then added and divided by the cumulative variance explanation rate;

[0064] The weights of different spectral channel counts are calculated, and the comprehensive score coefficients are normalized to obtain the weight factor values ​​of different spectral channel counts.

[0065] The above embodiment is further optimized, and the specific process of step S3 is as follows:

[0066] The weight factor value x1 of different spectral channel counts calculated by S2 and the average value x2 of each spectral channel in the ROI area corresponding to the gamma energy spectrum matrix A of K, U, Th that is interfered with by measurement are used as independent variables, and the average value y of each spectral channel in the ROI area corresponding to the background gamma energy spectrum matrix B of K, U, Th without artificial radionuclide interference by measurement is used as the independent dependent variable;

[0067] By observing the independent variables and dependent variables, linear regression analysis is used to obtain the coefficient b1 of the weight factor value, the coefficient b2 of the average value of each spectral channel in the ROI area corresponding to the gamma spectrum matrix A of the disturbed K, U, and Th, and the constant b3, which are collectively referred to as regression coefficients;

[0068] Constructing a mathematical repair model:

[0069] y=x1×b1+x2×b2+b3.

[0070] The above embodiment is further optimized, and the specific process of step S4 is as follows:

[0071] The weight factors of the counts of different spectral channels and the counts of the background gamma energy spectra of K, U and Th whose corresponding spectral channels are interfered by artificial radionuclides are respectively substituted into the mathematical repair models x1 and x2 to calculate the repaired background gamma energy spectra y of K, U and Th. The present invention can effectively reduce the peak position shift and peak area change caused by the counting contribution of artificial radionuclides to the ROI area of ​​K, U and Th, and improve the accuracy of peak area calculation.

[0072] Artificial radionuclides 137 Explanation of the interference of Cs on K, U, and Th measurements:

[0073] 1. Interference of artificial radionuclides on K, U, and Th measurements

[0074] Based on CeBr3 detector for background (measured 10 times) and 137The measurement of Cs (different detection distances) and the accumulated gamma energy results of the ROI areas of K, U, and Th are as follows: Figure 1 shown.

[0075] In the ROI area of ​​K, 137 Cs is the main nuclide. Figure 1 -a shows that there is no interference from artificial radionuclides in the background data. 40 The background peak of K is 474. 137 When Cs, 40 The peak position of K shifted by 5 channels, and the peak position was 479. Figure 1 -d as shown. Figure 1 -a and Figure 1 -d also has a significant change in the peak area. In the ROI area of ​​U, 214 Bi is the main nuclide. Figure 1 -b shows that there is no interference from artificial radionuclides in the background data. 214 The background peak of Bi is 568. 137 When Cs 214 The peak position of Bi shifted by 5 channels, and the peak position was 573. Figure 1 -e as shown. Figure 1 -b and Figure 1 The peak area in -e also changed significantly.

[0076] In the ROI area of ​​Th, 208 Tl is the main nuclide. Figure 1 -c shows that there is no interference from artificial radionuclides in the background data. 208 The background peak position of Tl is 829. 137 When Cs, 208 The peak position of Tl shifted, and the measurement results shifted by 4 channels, with the peak position at 835. Figure 1 -f as shown. Figure 1 -c and Figure 1 The peak area in -f also changed significantly.

[0077] 2. Peak area deformation analysis

[0078] 2.1 Background Analysis

[0079] (1) Correlation analysis

[0080] The results of 10 background gamma spectrum measurements based on CeBr3 detector and the correlation analysis of peak areas are shown in the figure. Figure 2 shown. Figure 2 -a is a waterfall diagram of 10 background gamma spectrum measurements. Figure 2-b is the peak area correlation analysis result of the full spectrum, with a correlation value of 1. The full spectrum peak area correlation of the 10th background gamma spectrum data is very high.

[0081] The results of correlation analysis of the peak area of ​​ROI region of K are as follows Figure 2 -c shows that the spectral channel analysis boundary of the ROI region of K is 460-500 channels, and the average total peak area of ​​the K peak (i.e., the K peak count, the average value of 10 measurements) is 2284.3, and its overall average correlation value is 0.83313, indicating that the peak area correlation of the ROI region of the 10 background gamma energy spectrum data K is very high.

[0082] The results of the correlation analysis of the peak area in the ROI region of U are as follows Figure 2 -d, the spectral channel analysis boundary of the ROI region of U is 550-590 channels, and its peak area average (i.e., U peak count, taking the average value of 10 measurements) is 671.5, and its overall average correlation value is 0.22375, indicating that the correlation degree of the peak area of ​​the ROI region of the 10 background gamma energy spectrum data U is average.

[0083] The results of correlation analysis of Th ROI peak area are as follows: Figure 2 -e, the ROI region spectrum analysis boundary of Th is 810-860 channels, and its peak area average (i.e., Th peak count, taking the average of 10 measurements) is 443.0, and its overall average correlation value is 0.56816, indicating that the ROI region peak area correlation of Th in 10 background gamma energy spectrum data is high.

[0084] (2) Analysis of channel count deviation

[0085] The counting results of the ROI area of ​​10 background measurement data K, U, and Th were used to check the points that affect the correlation value in each measurement. The analysis results are as follows: Figure 3 shown. Figure 3 -a is the t-test analysis of ROI counts in K. The results show that the larger count value of 30 appeared in the second measurement process. Figure 3 -b is the t-test analysis of the ROI count of U. The results show that the larger count value of 9 appeared in the 1st, 4th, 5th and 10th measurement processes, and the larger count value of 8 appeared in the 9th measurement process. Figure 3 -c is the ROI area count t-test analysis of Th. The results show that in the first measurement process, there are two large count values ​​of 11 and 6, the large count values ​​of the second and third measurements are 9, the large count value of the fourth measurement is 6, the large count value of the fifth measurement is 10, the large count value of the ninth measurement is 9, and the large count values ​​of the tenth measurement are 6 and 9. The large count values ​​in these measurement results are important counting points that cause the peak area correlation value to decrease.

[0086] (3) Qualitative analysis of differences in peak area calculation

[0087] The peak area calculation results of the ROI region of K, U, and Th in the 10 background measurement data were analyzed by single factor variance analysis to determine whether there were significant differences in the measurement results. Fig.11 As shown in Table 4-6. The p-value of the full-segment gamma spectrum is 0.97565, which is higher than the significance level of 0.05, indicating that there is no statistically significant difference in the statistical counting results of the full-segment of the 10 measurements. For the ROI area of ​​K, the p-value (pK) is 0.99382, which is greater than 0.05, indicating that there is no significant difference in the statistical counting results of the 10 measurements in this area. For the ROI area of ​​U, the p-value (pU) is 0.65370, which is greater than 0.05, indicating that there is no significant difference in the statistical counting results of the 10 measurements in this area. For the ROI area of ​​Th, the p-value (pTh) is 0.68135, which is greater than 0.05, indicating that there is no significant difference in the statistical counting results of the 10 measurements in this area.

[0088] In summary, there is generally no difference in the gamma spectrum data of 10 background measurements, the full energy spectrum counts, and the ROI area peak area calculation results of K, U, and Th.

[0089] 2.2. Analysis of interference from artificial radionuclides

[0090] (1) Correlation analysis

[0091] Adding artificial radionuclides 137 The results of the correlation analysis between Cs interference and background measurement results are shown in Figure 4 shown. Figure 4 -a is the energy spectrum waterfall diagram of the measurement results. Figure 4 -b is the peak area correlation analysis result of the full spectrum, the correlation value is 0.92660, indicating that the addition 137 The post-measurement gamma energy spectrum of Cs has a high correlation with the 10 background measurement gamma energy spectra, which are derived from the same experimental measurement conditions.

[0092] The results of correlation analysis of the peak area of ​​ROI region of K are as follows Figure 4 -c shows that the spectral analysis boundary of the ROI region of K is 460 to 500 channels, and its overall average correlation value is 0.84472, indicating that the addition of 137 The correlation degree between the peak area of ​​the ROI region of the post-measurement gamma energy spectrum of Cs and the 10 background measurement gamma energy spectra K is very high.

[0093] The results of the correlation analysis of the peak area in the ROI region of U are as follows Figure 4 -d shows that the spectral analysis boundary of the ROI area of ​​U is 550-590 channels, and its overall average correlation value is 0.33777, indicating that the addition of137 The peak area of ​​the ROI region of the post-measurement gamma energy spectrum of Cs is highly correlated with that of the 10 background measurement gamma energy spectra U.

[0094] The results of correlation analysis of Th ROI peak area are as follows: Figure 4 -e shows that the ROI area spectrum analysis boundary of Th is 810-860 channels, and its overall average correlation value is 0.56093, indicating that the addition of 137 The peak area of ​​the ROI region of the post-measurement gamma energy spectrum of Cs is highly correlated with that of the 10 background measurement gamma energy spectra Th.

[0095] (2) Analysis of channel count deviation

[0096] right 137 The t-test analysis was performed on the gamma spectrum measurement data of Cs at different distances and 10 backgrounds. The results are as follows: Figure 5 The results show that the ROI area counts of K, U, and Th deviate from the results, and the results of the 10 measurements and analyses are consistent with the aforementioned analysis results; 137 Under different measurement distances of Cs, the counting results of the ROI areas of K, U, and Th have no larger (or smaller) values.

[0097] (3) Qualitative analysis of differences in peak area counts

[0098] 10 background measurements and additions 137 The peak area calculation results of the ROI regions of K, U, and Th at different Cs measurement distances were analyzed using a single factor variance analysis to determine whether the measurement results were significantly different. The results are as follows: Fig.12 The p value of the full gamma spectrum is 2.56781E-234, which is lower than the significance level of 0.05, indicating that the 10 measurements and the addition of The statistical counting results of the full-energy segment under different distances are statistically significantly different. For the ROI area of ​​K, the p value (pK) is 3.02955E-74, which is lower than 0.05, indicating that the statistical counting results in this area are significantly different. For the ROI area of ​​U, the p value (pU) is 1.69713E-137, which is lower than 0.05, indicating that there is no significant difference in the statistical counting results of the 10 measurements in this area. For the ROI area of ​​Th, the p value (pTh) is 1.3703E-56, which is lower than 0.05, indicating that the statistical counting results in this area are significantly different.

[0099] In summary, 10 background measurements and adding 137 The gamma spectrum data of Cs at different ranges, the full spectrum counts and the ROI-regioned peak area counts of K, U, and Th have shown significant differences. Especially in the detailed analysis, such as Figure 1 As shown, the spectrum channel shifted and the peak area changed.

[0100] 3. Analysis of Weak Information Impact Based on FSVD Method

[0101] Using FSVD analysis method, 137 Weak information extraction of gamma spectrum data changes in ROI areas of K, U, and Th before and after Cs. The results are as follows Figure 6 As shown in the figure, the larger the negative value of the β value of the corresponding spectral channel in the weak information is, the higher its contribution to the ROI area of ​​K, U, and Th is. Figure 6 -a is the weak information extraction result of ROI area of ​​K. The 476th channel is 137 The contribution count of Cs has a significant impact. Figure 6 -b is the weak information extraction result of ROI area U. The 572nd channel is affected 137 The contribution count of Cs has a significant impact. Figure 6 -c is the ROI area description of Th, 137 The introduction of Cs affects the ROI area counts of K, U, and Th, causing the peak positions of K, U, and Th to shift to the right and the peak areas to change.

[0102] 4. Correction of peak position shift and peak area change

[0103] 4.1. Gamma spectrum correction technology process

[0104] The process of correction of channel shift and peak area change is as follows: Figure 7 As shown in the figure, the system is first calibrated to obtain measurement data, and the FSVD weak information extraction and analysis is performed on the ROI areas of K, U, and Th to determine the ROI area that causes the change. Then, the principal component analysis method is used to analyze the background measurement value and the added 137 Cs after the value of the weak information, extract the main component, determine the weight of different spectral channel counts. Based on the weight factor, linear regression analysis is used to build a mathematical model for energy spectrum repair. 137 Finally, the characteristic peak channels and peak areas before and after the repair are compared to verify the correction results of the channel offset and peak area change.

[0105] 4.2. Restoration results based on principal component extraction and linear regression analysis

[0106] (1) Repair of K’s ROI area

[0107] 1) Principal component extraction

[0108] The principal component extraction analysis results are as follows Fig.13As shown in Table 4-8. The results show that the principal component analysis yielded a single principal component with all eigenvalues ​​greater than 1. The variance explained by this principal component was 87.539%, while the overall variance explained was 87.539%. The analysis yielded 1 principal component, and their weighted variance explained or weights were as follows: 87.539 / 87.539 = 100.00%.

[0109] The information extraction of the principal components and the load relationship analysis results between the principal components and the research items are shown in the figure. Fig.14 As shown in Table 4-9. The analysis results show that the commonality values ​​are all over 0.4, indicating that there is a good correlation between the research items and the principal components.

[0110] The principal component analysis of the load coefficients was used to determine the weights. The results are shown in Fig.15 As shown in Table 4-10. Its calculation includes three stages. First, the linear combination coefficient matrix is ​​calculated by dividing the load coefficient by the square root of the relevant characteristic root. Then, the composite score coefficient is calculated. When the linear combination of the coefficients is multiplied by the variance of the explained rate and divided by the cumulative variance of the explained rate, the two composite scores are equal to 0.7071. Third, the weights are determined. The two weights each account for 50%, which are determined by using the composite score coefficient to standardize the weight of the indicator.

[0111] 2) Linear regression analysis

[0112] CompScore_Cs (composite score in principal component analysis) and 137 The average Cs value was used for linear regression analysis, and the average value of 10 background measurements was used as the dependent variable. The analysis results are shown in Fig.16 The analysis results show that when the constant is 92.231, the model equation 137 The coefficient of the mean value of Cs is -1.054. The R-square value of the model is 1.000, and CompScore_Cs and 137 The average Cs value explained 100.0% of the variation in the average values ​​of the 10 background measurements. When the model was tested using the F test, the result was positive (F(2,48)=9.671646622891367e+28, p=0.000<0.05), indicating that CompScore_Cs and the 6 background measurements were significantly different. 137 At least one of the Cs measurement averages will affect the average of the 10 background measurements.

[0113] In addition, the multiple covariance test of the model showed that its VIF value was greater than 5 but less than 10, indicating that there might be some covariance problems, which could be solved by using ridge regression or stepwise regression. The regression coefficient value of CompScore_Cs was 46.641 (t=290517998632758.400, p=0.000<0.01), indicating that it would have a significant positive impact on the average of the 10 background measurements. 137 The regression coefficient of the mean value of Cs is -1.054 (t=-155253842349445.300, p=0.000<0.01), indicating that the 6 137 There is a substantial inverse correlation between the Cs measurement average and its impact. The survey showed that CompScore_Cs would significantly improve the background measurement average by 10 times. 6 times 137 The average of the Cs measurements will have a significant negative impact on the average of the 10 background measurements.

[0114] 3) Correction of peak position shift and peak area change

[0115] The correction results of the peak position shift and peak area change in the ROI area of ​​K are as follows: Figure 8 shown. Figure 8 -a is at different distances 137 The peak position shift correction results of the ROI area of ​​K in the Cs environment. The results show that 6 The peak position of the different distance measurement results was corrected from 479 to 474, which is consistent with Figure 1 No results found 137 The peak positions of the 10 background measurement results of Cs interference are consistent, and the peak offset correction results are good.

[0116] Figure 8 -b is the ROI area of ​​K 6 times 137 The t-test result of the calculated peak area of ​​Cs at different distances and the average of the calculated peak area of ​​10 background measurements is shown in the figure. The corrected p value is 0.99994, which shows no significant difference at the 0.05 level and no abnormal value. 137 The peak area correction of ROI region of Cs different distance measurement results K is highly correlated with the peak area result of non-interference measurement.

[0117] Figure 8 -c is ROI area of ​​K 6 times 137 Linear correlation analysis of Cs different range measurement results and the average of 10 background measurement results. The results show that the average of 10 background measurements and 6 137The correction result of the average Cs measurement has an overall linear correlation average of 0.96551. The linearity between the correction result and the average of 10 background measurements is very good, which effectively ensures a high linear correlation with the original background measurement data and eliminates 137 Interference of Cs.

[0118] (2) ROI processing results of U

[0119] The correction methods for the peak position shift and peak area change in the ROI region of U and Th are consistent with the above method. The correction results for the spectral channel shift and peak area change in the ROI region of U are shown in Fig. 9 shown. Fig. 9 -a is at different distances 137 The peak position offset correction results of the ROI area of ​​U in the Cs environment. The results show that 6 137 The peak position of Cs different distance measurement results was corrected from 573 to 568. Figure 1 No results found 137 The peak positions of the 10 background measurement results of Cs interference are consistent, and the peak offset correction results are good.

[0120] Fig. 9 -b is the ROI area of ​​U 6 times 137 The t-test result of the calculated peak area of ​​Cs at different distances and the average of the calculated peak area of ​​10 background measurements is shown in the figure. The corrected p value is 0.9953, which shows no significant difference at the 0.05 level and no abnormal value. 137 The peak area correction of ROI region of Cs different distance measurement results U is highly correlated with the peak area result of non-interference measurement.

[0121] Fig. 9 -c is ROI area of ​​U 6 times 137 Linear correlation analysis of Cs different range measurement results and the average of 10 background measurement results. The results show that the average of 10 background measurements and 6 137 The correction result of the average Cs measurement has an overall linear correlation average of 0.70579. The linearity between the correction result and the average of 10 background measurements is good, which effectively ensures a high linear correlation with the original background measurement data and eliminates 137 Interference of Cs.

[0122] (3) ROI processing results of Th

[0123] The correction results of the peak position shift and peak area change in the ROI region of Th are as follows: Fig.10 shown. Fig.10 -a is at different distances 137 The spectral channel offset correction results of Th in ROI area in Cs environment. The results show that 6137 The peak position of Cs different distance measurement results was corrected from 835 to 829. Figure 1 No results found 137 The peak positions of the 10 background measurement results of Cs interference are consistent, and the peak offset correction results are good.

[0124] Fig.10 -b is the ROI area of ​​Th 6 times 137 The t-test result of the calculated peak area of ​​Cs at different distances and the average of the calculated peak area of ​​10 background measurements is shown in the figure. The corrected p value is 0.97228, which is not significantly different at the 0.05 level, and there are no outliers. 137 The peak area correction of ROI region of Cs different distance measurement results U is highly correlated with the peak area result of non-interference measurement.

[0125] Fig.10 -c is 6 times for the ROI area of ​​Th 137 Linear correlation analysis of Cs different range measurement results and the average of 10 background measurement results. The results show that the average of 10 background measurements and 6 137 The correction result of the average Cs measurement has an overall linear correlation average of 0.90248. The linearity between the correction result and the average of 10 background measurements is very good, which effectively ensures a high linear correlation with the original background measurement data and eliminates 137 Interference of Cs.

[0126] 5. Results and Discussion

[0127] The accuracy of weak peak identification is an important guarantee for peak area calculation. The FSVD analysis method can accurately identify the peak position of weak peaks. In this section, the study found that artificial radionuclides caused peak position shifts and peak area changes in the characteristic radioactive isotopes in the ROI area of ​​K, U, and Th. The FSVD analysis method was used to accurately extract the weak information that caused the changes. The principal component analysis method and linear regression analysis method were used to construct a correction model for peak position shift and peak area change. The data were calculated, analyzed, and corrected for the above-mentioned measured data. The statistical results before and after the correction are shown in the figure. Fig.17 As shown in Table 4-12. Through comparative analysis, the following conclusions are drawn:

[0128] (1) 137 The introduction of artificial radioactive nuclide Cs produced counting contributions to the ROI areas of K, U, and Th, causing the peak position of characteristic radioactive isotopes in the ROI area to shift and affecting the peak area, resulting in deviations in the calculation of the content of K, U, and Th in the spectrum channels.

[0129] (2) Before correction, 6 times 137The measurement results of Cs at different distances show that the characteristic peak position of the K region is 479.0 channels, the offset is 5.5 channels, the peak area is 2044.0, and the error is 10.52%; the characteristic peak position of the U region is 573.0 channels, the offset is 5.5 channels, the peak area is 582.0, and the error is 13.48%; the characteristic peak position of the Th region is 834.7 channels, the offset is 6.5 channels, the peak area is 451.7, and the error is 7.00%.

[0130] (3) After correction, 6 times 137 The measurement correction results of Cs at different distances show that the characteristic peak position of K region is 474.0 channels, the offset is 0.5 channels, the peak area is 2296.3, and the error is 1.62%; the characteristic peak position of U region is 567.7 channels, the offset is 0.2 channels, the peak area is 671.4, and the error is 1.79%; the characteristic peak position of Th region is 829.0 channels, the offset is 0.8 channels, the peak area is 439.0, and the error is 4.96%.

[0131] (4) The results before and after correction show that the peak position shift has been effectively repaired, and the maximum channel shift of 0.8 channels is better than the measurement result before correction, and its maximum channel shift is 6.5 channels. The peak area change correction result is good, and the error of the peak area calculation result is effectively reduced. The peak area calculation error in the K zone is reduced from 10.52% to 1.62%, the peak area calculation error in the U zone is reduced from 13.48% to 1.79%, and the peak area calculation error in the Th zone is reduced from 7.00% to 4.96%. The repair model constructed based on principal component analysis and linear regression analysis can effectively reduce artificial radionuclides. 137 The peak position shift and peak area change caused by the counting contribution of Cs to the ROI area of ​​K, U, and Th improved the accuracy of peak area calculation.

[0132] 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 and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for correcting gamma energy spectrum channel shift and peak area change based on principal component analysis and linear regression, characterized in that: The steps include: S1, calibrate the system, obtain background measurement data and measurement data affected by artificial radionuclides, extract and analyze FSVD weak information of ROI areas of K, U, and Th, and determine the ROI area that causes changes; The specific process of step S1 is: Measure and obtain the background gamma spectrum matrix B of K, U, and Th without interference from artificial radionuclides; Add artificial radioactive nuclide interference and measure and obtain the gamma spectrum matrix A of K, U and Th that are interfered; For the background matrix B n×m Perform singular value decomposition to obtain the singular value matrix Λ, take the first r columns of the Λ matrix, ignore the elements of other columns of the Λ matrix, and set them to 0 to reconstruct the background gamma spectrum data matrix B'; Combine the reconstructed background gamma spectrum B' and the mixed gamma spectrum matrix A to construct the linear regression analysis matrix C n×（m+p） , the Gauss-Markov linear regression method is used to analyze the matrix C to obtain the estimated parameter β. Through the analysis of β, weak information extraction analysis is performed to determine the ROI area that causes changes in K, U, and Th; Among them, the number of β is 1024; S2, using the principal component analysis method for the ROI area, analyzing the background measurement values ​​and the values ​​affected by the addition of artificial radionuclides, extracting the principal components, and determining the weight factors of different spectral channel counts; S3, based on the weight factor, linear regression analysis is used to construct the energy spectrum repair mathematical model; The specific process of step S3 is: The weight factor value x1 of the different spectral channel counts calculated in step S2 and the average value x2 of each spectral channel in the ROI area corresponding to the gamma spectrum matrix A of K, U, and Th obtained by measurement and obtained with interference are used as independent variables, and the average value y of each spectral channel in the ROI area corresponding to the background gamma spectrum matrix B of K, U, and Th obtained by measurement and obtained without artificial radioactive nuclide interference is used as the independent dependent variable; By observing the independent variables and dependent variables, linear regression analysis is used to obtain the coefficient b1 of the weight factor value, the coefficient b2 of the average value of each spectral channel in the ROI area corresponding to the gamma spectrum matrix A of the disturbed K, U, and Th, and the constant b3, which are collectively referred to as regression coefficients; Constructing a mathematical repair model: y=x1×b1+x2×b2+b3; S4, repairing the energy spectrum data after adding artificial radionuclides through the energy spectrum repair mathematical model; S5, compare the characteristic peak channels and peak areas before and after repair to verify the correction results of channel offset and peak area change.

2. The method for correcting gamma energy spectrum channel shift and peak area variation based on principal component analysis and linear regression according to claim 1, characterized in that: Determining the weights of different spectral channel counts in step S2 includes the following steps: Calculate the linear combination coefficient matrix, the formula is: loading matrix / Sqrt(eigen), that is, the loading coefficient divided by the square root of the corresponding characteristic root; The comprehensive score coefficient is calculated using the formula: cumulative (linear combination coefficient * variance explanation rate) / cumulative variance explanation rate, that is, the linear combination coefficient is multiplied by the variance explanation rate and then accumulated, and divided by the cumulative variance explanation rate; The weights of different spectral channel counts are calculated, and the comprehensive score coefficients are normalized to obtain the weight factor values ​​of different spectral channel counts.

3. The method for correcting gamma energy spectrum channel shift and peak area variation based on principal component analysis and linear regression according to claim 1, characterized in that: The specific process of step S4 is: The weight factors of different spectral channel counts and the counts of the background gamma energy spectra of K, U, and Th whose corresponding spectral channels are interfered by artificial radionuclides are substituted into the mathematical repair models x1 and x2 respectively, and the repaired background gamma energy spectra y of K, U, and Th are calculated.

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