SVM-based liquid flash spectrometer alpha and beta discrimination method
By using the SVM model for αβ discrimination in liquid scintillation spectrometers, the problem of insufficient αβ discrimination accuracy in existing technologies is solved, and a stable and reproducible high-precision αβ discrimination effect is achieved.
Patent Information
- Application Number
- CN202511752467.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-26
- Publication Date
- 2026-03-27
AI Technical Summary
The lack of efficient αβ discrimination methods in existing technologies leads to insufficient accuracy of liquid scintillation spectrometers when measuring the activity of low-energy β radionuclides.
The α-β discrimination is performed using a support vector machine (SVM) model. By using the Gaussian kernel trick, low-dimensional nonlinear data is implicitly mapped to a high-dimensional space to establish an α-β prediction model. The model is then learned using a large amount of training data to reduce the probability of misjudgment and improve the discrimination accuracy.
The results of αβ discrimination by liquid scintillation spectrometer are stable and reproducible, with noise robustness and high data accuracy, reducing the probability of misjudgment and improving the accuracy of αβ discrimination.
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Figure CN121741808A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the field of radioactivity measurement, in particular to a liquid scintillation spectrometer alpha-beta discrimination method based on SVM. BACKGROUND
[0002] Liquid scintillation spectrometer (also known as liquid scintillation counter) is widely used in customs, nuclear power plants, nuclear industry, environmental monitoring, nuclear medicine, life science research, radiation protection and other fields, mainly used for measuring H-3, C-14 and other low-energy beta radionuclide activity. It is mainly composed of a detector, a multi-channel pulse amplitude analyzer, a high-voltage module, a transmission device, a shielding system, a computer and the like.
[0003] At present, there is no efficient alpha-beta discrimination (i.e. alpha-beta nuclide separation) method, and how to improve the alpha-beta discrimination and activity detection precision is a technical problem to be solved at present. SUMMARY
[0004] In order to solve the problems of the prior art, the present application provides a liquid scintillation spectrometer alpha-beta discrimination method based on SVM, which implicitly maps low-dimensional nonlinear data to high-dimensional space by Gaussian kernel skill to realize linear separability, without the need for explicit high-dimensional calculation, suitable for alpha / beta discrimination of this kind of binary feature classification problem, capable of reducing the interference of pulse width outliers, and capable of learning through a large number of training set data, greatly reducing the possibility of misjudgment and improving the discrimination precision.
[0005] The present application provides the following scheme:
[0006] The present application provides a liquid scintillation spectrometer alpha-beta discrimination method based on SVM, the method comprising:
[0007] S1, standard solution samples of A nuclides with alpha radioactivity and standard solution samples of B nuclides with beta radioactivity with known activity are respectively subjected to liquid scintillation determination, and the pulse signals corresponding to the two nuclides are obtained;
[0008] S2, the pulse width and rise time of the pulse signal are taken as two-dimensional feature values, the two-dimensional feature values are standardized, and a standardized data set is formed, each sample in the standardized data set contains a nuclide type label and two-dimensional feature values;
[0009] S3, an SVM model is established, and the standardized data set is trained to obtain an alpha-beta prediction model;
[0010] S4, a mixed solution standard source containing A nuclides and B nuclides with known activity is subjected to liquid scintillation determination, and the pulse signals obtained by liquid scintillation determination are classified by using the alpha-beta prediction model to obtain the number N α of alpha pulse signals corresponding to A nuclides and the number N β of beta pulse signals corresponding to B nuclides., and the standard source B nuclide counting efficiency E α and the standard source B nuclide counting efficiency E β ;
[0011] S5, liquid scintillation measurement is performed on the mixed sample to be measured containing the A nuclide and the B nuclide, pulse data samples are collected, prediction classification is performed by using an alpha-beta prediction model, and a category label is recorded, so as to obtain the number N αs of alpha pulse signals corresponding to the A nuclide and the number N βs of beta pulse signals corresponding to the B nuclide, and the A nuclide activity C α of the sample to be measured and the B nuclide activity C β of the sample to be measured are further calculated.
[0012] Further, the step S1 includes the following process:
[0013] S1.1, a standard solution sample of the A nuclide and a standard solution sample of the B nuclide with known activities are configured respectively;
[0014] S1.2, the two standard solution samples are placed into a liquid scintillation spectrometer, pulse signal collection is performed by using a digital multi-channel, a group of alpha pulse signals corresponding to the A nuclide and a group of beta pulse signals corresponding to the B nuclide are obtained.
[0015] Further, the step S3 includes the following process:
[0016] S3.1, an optimization objective function of the SVM model is established:
[0017] ,
[0018] wherein K(x i ,x j ) is a Gaussian radial basis kernel function, , x i is a pulse width feature of the i-th sample in the standardized data set, x j is a rise time feature of the j-th sample in the standardized data set, and γ is a hyperparameter; α represents a vector composed of Lagrange multipliers corresponding to each sample, α i is a Lagrange multiplier corresponding to the i-th sample, and α j is a Lagrange multiplier corresponding to the j-th sample;
[0019] The constraint condition is:
[0020] ,
[0021] wherein C is a regularization parameter, y i is a nuclide type label corresponding to the i-th sample, and takes a value of +1 or -1, and n is the number of samples;
[0022] S3.2, 70% of the samples in the standardized data set are taken as a training set, and the other 30% of the samples are taken as a test set, the SVM model is trained and verified, and the trained SM model is taken as an alpha-beta prediction model.
[0023] Further, the hyperparameters in step S3.1 are calculated by the following formula:
[0024] ,
[0025] Where n features is the number of two-dimensional feature values in the standardized data set, and X.var is the average of the variance of the two-dimensional feature values of all samples.
[0026] Further, the regularization parameter C in step S3.1 is set to 1.
[0027] Further, the verification in step S3.2 refers to evaluating the prediction effect by statistics of the precision, recall and F1 score of the prediction result.
[0028] Further, step S4 calculates the standard source A nuclide counting efficiency E α and the standard source B nuclide counting efficiency E β by the following formula:
[0029] ,
[0030] ,
[0031] Where t m represents the effective counting time of the standard source, A α and A β represent the activities of the A nuclide and the B nuclide respectively, λ1 and λ2 represent the decay constants of the A nuclide and the B nuclide respectively, and t represents the time from the activity calibration date of the standard source to the measurement time.
[0032] Further, step S5 calculates the A nuclide activity C α of the sample to be measured and the B nuclide activity C β of the sample to be measured by the following formula:
[0033] ,
[0034] ,
[0035] Where t s represents the effective measurement time of the mixed sample to be measured.
[0036] The application has the beneficial effects of the technical scheme in that:
[0037] (1) This invention uses an SVM classifier model for αβ discrimination of liquid scintillation spectrometers. By using the Gaussian kernel trick, low-dimensional nonlinear data is implicitly mapped to a high-dimensional space to achieve linear separability, eliminating the need for explicit high-dimensional computation. This model is well-suited for binary feature classification problems like αβ discrimination. Moreover, the SVM model has high parameter flexibility, and the decision boundary is determined only by the support vectors. Combined with the regularization constraint of C, overfitting and local optima are avoided. The αβ discrimination results of liquid scintillation spectrometers under this model are stable and reproducible.
[0038] (2) Compared with traditional single-feature pulse width discrimination or amplitude-pulse width 3D spectrum methods, this invention has better noise robustness and data accuracy. Traditional methods use linear classification, which has a high probability of misjudgment and is difficult to apply to complex datasets. This invention uses the soft-margin mechanism of the SVM model and Gaussian kernel locality to perform nonlinear classification of data, reducing the interference of pulse width outliers. At the same time, it can learn from a large amount of training data, which greatly reduces the possibility of misjudgment and improves the discrimination accuracy. Attached Figure Description
[0039] To more clearly illustrate the technical solutions in the embodiments of this specification or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this specification. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0040] Figure 1 This is a schematic flowchart of an SVM-based liquid scintillation spectrometer αβ discrimination method provided by the present invention.
[0041] Figure 2 This is a schematic diagram of a single pulse signal.
[0042] Figure 3 This is a schematic diagram of multiple sets of original pulse signals.
[0043] Figure 4 This is a schematic diagram of pulse signals with the same amplitude.
[0044] Figure 5 This is a schematic diagram of the original data distribution.
[0045] Figure 6 This is a schematic diagram of the standardized data distribution.
[0046] Figure 7 This represents the data distribution after Gaussian kernel function transformation.
[0047] Figure 8 The data distribution after classifying the test set.
[0048] Figure 9 This is a schematic diagram of the decision-making plane. Detailed Implementation
[0049] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention are within the protection scope of the embodiments of the present invention.
[0050] Reference Figure 1 This embodiment provides an SVM-based αβ discrimination method for liquid scintillation spectrometers, the method comprising:
[0051] S1. Perform liquid scintillation measurements using standard solution samples of nuclide A and nuclide B with known activity to obtain the pulse signals corresponding to the two nuclides.
[0052] This embodiment takes Am-241 and Sr-90 / Y-90 as examples, and includes the following process:
[0053] S1.1 Preparation of Am-241 and Sr-90 / Y-90 standard solution samples with known activities: Take a clean and uncontaminated 20mL polyethylene bottle or polytetrafluoroethylene bottle, add 0.5mL of standard solution, ensuring that the activity of each series of samples in each bottle is within the range of 10Bq-100Bq, then add 7.5mL of uncounted pure water and 12mL of scintillation fluid, tighten the cap and shake well, finally obtaining one bottle each of Am-241 and Sr-90 / Y-90 standard samples.
[0054] S1.2. Place the standard sample into the liquid scintillation spectrometer and use digital multichannel to acquire pulse signals. Acquire 100 raw pulse signals for each sample vial. A single pulse signal is as follows: Figure 2 As shown. Multiple sets of original pulse signals are as follows. Figure 3 As shown, it includes 100 groups of A signals (α pulse signals) + 100 groups of B signals (β pulse signals).
[0055] Since the α spectrum is a discrete spectrum with single energy, but the β spectrum is a continuous spectrum, the α / β ratio only needs to be discussed as follows: Figure 4 The same amplitude case is shown.
[0056] S2. Calculate and summarize the characteristic parameters of the pulse signal, such as amplitude, pulse width, integral area, and rise time. Take the pulse width and rise time of the pulse signal as two-dimensional characteristic values, as shown in the distribution diagram. Figure 5 As shown.
[0057] Standardizing the two-dimensional feature values results in an overall distribution shape similar to the original data, but with a changed numerical range, which is beneficial for subsequent model training. The distribution is as follows: Figure 6As shown, each sample in the standardized dataset contains a nuclide type label and two-dimensional feature values.
[0058] S3. Establish an SVM model and train it using a standardized dataset to obtain an α-β prediction model, including the following steps:
[0059] S3.1 Establish the optimization objective function for the SVM model:
[0060] ,
[0061] Where K(x) i ,x j ) is the Gaussian radial basis kernel function. x i To standardize the pulse width feature of the i-th sample in the dataset, x j To standardize the rise time feature of the j-th sample in the dataset, ||x i - x j || represents the Euclidean distance between two points, which can be understood as the magnitude of a vector. γ is a hyperparameter that controls the range of the Gaussian kernel. The larger the γ value, the more complex the model; the smaller the γ value, the smoother the model. It can be calculated based on the number of features and variance of the training data. The following formula can achieve the best separation effect:
[0062] ,
[0063] Where, n features X is the number of features (i.e., the number of columns in the dataset, excluding the target variable), and X.var is the average variance of all features of the training data X.
[0064] α represents the vector composed of the Lagrange multipliers corresponding to each sample. i Let α be the Lagrange multiplier corresponding to the i-th sample. j Let be the Lagrange multiplier corresponding to the j-th sample.
[0065] The constraints are:
[0066] ,
[0067] Where C is the regularization parameter, controlling the degree of penalty for classification errors. A smaller C value results in stronger regularization, allowing for more classification errors, a simpler model, and prevention of overfitting. A larger C value results in weaker regularization, a heavier penalty for classification errors, and potentially a more complex model. In this embodiment, the regularization parameter is set to 1.
[0068] α i Let be the Lagrange multiplier corresponding to the i-th sample, measuring the sample's influence on the decision boundary, when α iWhen ξ = 0, the sample has no influence on the boundary and is a non-support vector; when 0 < ξ i < C, the sample is a support vector and is located within the classification margin; ξ i = C, the sample is a support vector and is located within the soft margin.
[0069] y i is the nuclide type label corresponding to the i-th sample, taking values of +1 or -1, representing group B or group A respectively, and is used to determine the sample category direction. n is the number of samples.
[0070] The set of all standardized two-dimensional eigenvalue is transformed through the Gaussian kernel function to obtain the following data distribution as Figure 7 shown.
[0071] S3.2. Take 70% of the samples in the standardized dataset as the training set, and the other 30% of the samples as the test set, train and validate the SVM model, and obtain the trained SM model as the α-β prediction model. The prediction results on the test set are as Figure 8 shown. Thus, the decision plane is obtained as Figure 9 shown. The figure shows the classification results and decision boundary of the Gaussian kernel SVM. The blue dots represent group A, the red dots represent group B, and the dots with green borders are support vectors. Through this figure, the classification effect of the model and the position of the decision boundary can be intuitively seen.
[0072] The statistical results based on 60 samples in the test set are shown in the following table:
[0073]
[0074] Perform confusion matrix analysis on the statistical results: For class a (corresponding to group A), the model correctly predicted 30 samples, and there was no case of mispredicting as class b. For class b (corresponding to group B), the model correctly predicted 21 samples, and 9 samples were mispredicted as class a.
[0075] Classification results: The precision rate of class a is 0.77, the recall rate is 1.00, and the F1 score is 0.87. The model can identify samples of class a accurately and comprehensively. The precision rate of class b is 1.00, the recall rate is 0.70, and the F1 score is 0.82. It shows that the model's prediction for class b is accurate, but some samples are missed. The overall accuracy rate is 0.85, and the indicators of macro-average and weighted average are also around 0.85, indicating that the overall performance of the model is good, but there is still room for improvement in the recall rate of class b.
[0076] S4. Perform liquid scintillation measurement on the mixed solution standard source containing known activities of nuclide A and nuclide B, use the α-β prediction model to classify the pulse signals obtained from the liquid scintillation measurement, and obtain the number N of α pulse signals corresponding to nuclide A in itα The number N of β pulse signals corresponding to the B nuclide β The counting efficiency E of standard source A nuclide is calculated using the following formula. α and the standard source B nuclide counting efficiency E β (unit:%):
[0077] ,
[0078] ,
[0079] Among them, t m Indicates the effective counting time of the standard source (unit: min), A α and A β λ1 and λ2 represent the activities of nuclide A and nuclide B, respectively (unit: DPM), λ1 and λ2 represent the decay constants of nuclide A and nuclide B, respectively, which are calculated from the nuclide half-life, and t represents the time from the standard source activity calibration date to the measurement time.
[0080] S5. Perform liquid scintillation measurement on a mixed sample containing nuclides A and B, collect pulse data samples, use the α-β prediction model for prediction and classification, and record the category labels to obtain the number N of α pulse signals corresponding to nuclide A. αs The number N of β pulse signals corresponding to the B nuclide βs The activity C of nuclide A in the test sample is calculated using the following formula. α and the activity of nuclide C in the sample to be tested B β (Unit: DPM):
[0081] ,
[0082] ,
[0083] Among them, t s Indicates the effective measurement time of the mixed test sample (unit: min).
[0084] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.
[0085] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.
[0086] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.
Claims
1. A liquid scintillation spectrometer αβ discrimination method based on SVM, characterized in that, The method includes: S1. Perform liquid scintillation measurements on standard solution samples of α-radioactive nuclide A with known activity and standard solution samples of β-radioactive nuclide B with known activity to obtain the pulse signals corresponding to the two nuclides. S2. Take the pulse width and rise time of the pulse signal as two-dimensional feature values, standardize the two-dimensional feature values to form a standardized dataset. Each sample in the standardized dataset contains a nuclide type label and a two-dimensional feature value. S3. Establish an SVM model and train it using a standardized dataset to obtain an α-β prediction model; S4. Perform liquid scintillation measurements on a standard source containing a mixed solution of nuclides A and B with known activities. Classify the pulse signals obtained from the liquid scintillation measurements using an α-β prediction model to obtain the number N of α pulse signals corresponding to nuclide A. α The number N of β pulse signals corresponding to the B nuclide β Further calculations yielded the standard source A nuclide counting efficiency E. α and the standard source B nuclide counting efficiency E β ; S5. Perform liquid scintillation measurement on a mixed sample containing nuclides A and B, collect pulse data samples, use the α-β prediction model for prediction and classification, and record the category labels to obtain the number N of α pulse signals corresponding to nuclide A. αs The number N of β pulse signals corresponding to the B nuclide βs Further calculations yielded the activity C of nuclide A in the sample to be tested. α and the activity of nuclide C in the sample to be tested B β .
2. The SVM-based liquid scintillation spectrometer αβ discrimination method according to claim 1, characterized in that: Step S1 includes the following processes: S1.1 Prepare one bottle each of standard solution samples of nuclide A and nuclide B with known activity; S1.2 Place the two standard solution samples into a liquid scintillation spectrometer and use digital multichannel to acquire pulse signals to obtain a set of α pulse signals corresponding to nuclide A and a set of β pulse signals corresponding to nuclide B.
3. The SVM-based liquid scintillation spectrometer αβ discrimination method according to claim 1, characterized in that: Step S3 includes the following processes: S3.1 Establish the optimization objective function for the SVM model: ， Where K(x) i ,x j ) is the Gaussian radial basis kernel function. x i To standardize the pulse width feature of the i-th sample in the dataset, x j To standardize the rise time feature of the j-th sample in the dataset, γ is a hyperparameter; α represents the vector composed of the Lagrange multipliers corresponding to each sample. i Let α be the Lagrange multiplier corresponding to the i-th sample. j Let j be the Lagrange multiplier corresponding to the j-th sample; The constraints are: ， Where C is the regularization parameter, y i is the nuclide type label corresponding to the i-th sample, with a value of +1 or -1, and n is the number of samples; S3.
2. Use 70% of the samples in the standardized dataset as the training set and the other 30% as the test set to train and validate the SVM model, and obtain the trained SM model as the α-β prediction model.
4. The SVM-based liquid scintillation spectrometer αβ discrimination method according to claim 3, characterized in that: The hyperparameters mentioned in step S3.1 are calculated using the following formula: ， Where n features X.var is the number of two-dimensional feature values in the standardized dataset, and X.var is the average variance of the two-dimensional feature values of all samples.
5. The SVM-based liquid scintillation spectrometer αβ discrimination method according to claim 3, characterized in that: The regularization parameter C mentioned in step S3.1 is set to 1.
6. The SVM-based liquid scintillation spectrometer αβ discrimination method according to claim 3, characterized in that: The verification described in step S3.2 refers to evaluating the prediction effect by statistically analyzing the precision, recall, and F1 score of the prediction results.
7. The SVM-based liquid scintillation spectrometer αβ discrimination method according to claim 1, characterized in that: Step S4 calculates the standard source A nuclide counting efficiency E using the following formula. α and the standard source B nuclide counting efficiency E β : ， ， Among them, t m Indicates the effective counting time of the standard source, A α and A β λ1 and λ2 represent the activities of nuclide A and nuclide B, respectively, λ1 and λ2 represent the decay constants of nuclide A and nuclide B, respectively, and t represents the time from the standard source activity calibration date to the measurement time.
8. The SVM-based liquid scintillation spectrometer αβ discrimination method according to claim 7, characterized in that: Step S5 calculates the activity C of nuclide A in the sample to be tested using the following formula. α and the activity of nuclide C in the sample to be tested B β : ， ， Among them, t s This indicates the effective measurement time for the mixed sample to be tested.