Machine learning-based kernel data verification method

Abstract

The invention discloses a machine learning-based kernel data verification method, which comprises the following steps of: firstly, obtaining simulated effective proliferation factors and actually measured effective proliferation factors of a plurality of kernel experiment references, and calculating to obtain a difference value; 2, calculating nuclear data sensitivity characteristics of each experimental reference, wherein the nuclear data sensitivity characteristics comprise a sensitivity coefficient for a nuclear reaction cross section and experimental metadata; thirdly, constructing a machine learning model based on a random forest, and performing training by taking the kernel data sensitivity characteristics as input and the effective multiplication factor difference value as output; and finally, carrying out model feature importance analysis, and identifying kernel data sensitivity features which have significant influence on effective proliferation factor differences. The nuclear data verification method based on machine learning is established for the first time, and is used for identifying potential defects in nuclear reaction data or deviation of experimental references.

Description

Technical Field

[0001] The present invention relates to the technical field of nuclear data verification, and in particular to a nuclear data verification method based on machine learning for identifying potential defects or experimental benchmark deviations in nuclear reaction data. Background Art

[0002] Nuclear data is a set of key parameters that describe the interaction between neutrons and atomic nuclei, mainly including neutron-induced nuclear reaction cross sections (such as fission, scattering, and absorption), fission neutron yield, fission neutron energy spectrum, resonance parameters, etc. These data are basic input parameters for nuclear reactor design, nuclear fuel cycle analysis, and other nuclear fields. Their accuracy directly determines the reliability of simulation calculations. In nuclear reactor criticality safety analysis, k eff If the calculation error of (effective proliferation factor) exceeds 500 pcm, it may lead to incorrect judgment of critical state and cause serious safety accidents.

[0003] The complexity of nuclear data stems from its high dependence on neutron energy, target nuclear isotope, and reaction type. Experimental measurements are also subject to extreme conditions, resulting in some data relying on extrapolation from theoretical models. Therefore, nuclear databases are generally validated against nuclear experimental benchmarks. Measuring the effective proliferation factor of these benchmarks indirectly reflects the overall matching of the nuclear data.

[0004] Existing nuclear data verification mainly relies on expert experience and sensitivity analysis, which has the following problems: the correlation of high-dimensional data is difficult to track, and the nonlinear coupling effect of hundreds of thousands of nuclear data makes manual analysis almost impossible; low-sensitivity vulnerabilities are easily overlooked, and experts usually prioritize verifying highly sensitive nuclear data, but materials with low sensitivity that are widely present may lead to significant deviations due to the accumulation of small errors; compensating for error risks by adjusting single nuclear data to force matching a specific nuclear test benchmark may undermine the predictive ability of other nuclear test benchmarks. Summary of the Invention

[0005] In order to solve the problems existing in the above-mentioned prior art, relying on the random forest machine learning model and SHAP feature importance interpretation technology, the purpose of the present invention is to propose a nuclear data verification method based on machine learning to solve the problems that traditional methods are difficult to track the correlation of high-dimensional nuclear data, cannot detect low-sensitivity nuclear data, and have low efficiency in sensitivity analysis.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

[0007] A nuclear data verification method based on machine learning, comprising the following steps:

[0008] Step 1: Obtain the simulated effective proliferation factors and measured effective proliferation factors of multiple nuclear experimental benchmarks, and calculate the difference between the two;

[0009] Step 2: Calculate the nuclear data sensitivity characteristics of each experimental benchmark, including the sensitivity coefficient to the nuclear reaction cross section and experimental metadata;

[0010] Step 3: Build a random forest-based machine learning model, using the nuclear data sensitivity features as input and the effective proliferation factor difference value as output for training;

[0011] Step 4: Perform model feature importance analysis to identify nuclear data sensitivity features that significantly influence the differences in effective proliferation factors.

[0012] Preferably, in step 1, both the simulated effective proliferation factor and the measured effective proliferation factor contain uncertainty, and the standardized difference index between the two is calculated using the following formula:

[0013]

[0014] Where:

[0015] δk eff — Standardized difference indicators;

[0016] - Simulated effective multiplication factor for nuclear experimental benchmarks;

[0017] -- the measured effective proliferation factor of the nuclear experimental benchmark;

[0018] — Uncertainty in the simulated effective multiplication factor of the nuclear test benchmark;

[0019] —Uncertainty in the measured effective multiplication factor of the nuclear test benchmark;

[0020] The standardized difference value is calculated for each nuclear experimental benchmark to obtain the effective proliferation factor standardized difference value data set.

[0021] Preferably, in step 2, the sensitivity coefficient of the nuclear reaction cross section in the nuclear data sensitivity characteristics includes at least one of the following: sensitivity coefficients of neutron induced fission cross section, neutron elastic scattering cross section, neutron inelastic scattering cross section, neutron radiation capture cross section, average total fission neutron number and fission neutron energy spectrum;

[0022] The purpose of calculating the sensitivity coefficient is to determine the changing pattern of the simulated effective proliferation factor with respect to the sensitivity characteristics of nuclear data. The calculation formula is as follows:

[0023]

[0024] Where:

[0025] —Sensitivity coefficient of nuclear data characteristics with respect to simulated effective proliferation factors;

[0026] σ0 – nominal value of the nuclear data characteristic;

[0027] k eff,0 — the nominal value of the effective proliferation factor calculated from the nominal value of the nuclear data characteristics;

[0028] ——The change in effective proliferation factor calculated after the nuclear data characteristics change;

[0029] — the amount of change in nuclear data characteristics;

[0030] The experimental metadata includes at least one of the following: laboratory, experimental year, nuclide composition, geometric configuration, moderator type, fuel concentration and experimental uncertainty.

[0031] Preferably, in step 3, the effective proliferation factor standardized difference data set is divided into a training set and a test set at an 8:2 ratio, and the RandomForestRegressor module of the Scikit-learn library in the Python language is used for training, and the loss function is the mean square error; the hyperparameters of the random forest machine learning model are optimized by grid search, and the cross-validation fold k = 5 is selected. When the mean square error is less than the uncertainty of the effective proliferation factor measured by the nuclear experimental benchmark, the model training is completed.

[0032] Preferably, in step 4, the importance analysis of nuclear data sensitivity features is performed using the SHAP library in the Python language. The SHAP indicator is based on the Shapley theory in cooperative game theory, and quantifies the marginal contribution of each nuclear data sensitivity feature to the model prediction to analyze its impact on the difference value of the effective proliferation factor.

[0033] When using the SHAP indicator for feature importance analysis, in order to avoid the importance dispersion caused by high-dimensional correlation, different aggregation strategies are adopted, and finally a global importance ranking and individual case explanations are generated to identify nuclear data with potential defects.

[0034] Compared with the prior art, the present invention has the following advantages:

[0035] (1) Through feature grouping and random forest (RF) ensemble learning, the problem that traditional methods are difficult to track the correlation of high-dimensional kernel data is solved.

[0036] (2) Through the SHAP interpretability technology, the contribution of low-sensitivity nuclear data features to the difference value is quantified, solving the problem that traditional methods cannot detect low-sensitivity nuclear data.

[0037] (3) The automated training and analysis process can complete the analysis of thousands of benchmarks within a few hours, and simultaneously output a list of suspicious nuclear data and an experimental outlier report, solving the problem of low efficiency of sensitivity analysis of traditional methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 It is a flow chart of the method of the present invention.

[0039] Figure 2 It is a disturbance 238 Graph of feature importance ranking of machine learning models using the U neutron elastic scattering cross section.

[0040] Figure 3 It is a disturbance 238 A plot of the feature importance ranking of the machine learning model when considering the U neutron radiation capture cross section. DETAILED DESCRIPTION

[0041] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0042] The present invention is a nuclear data verification method based on machine learning. Figure 1 As shown, the method of the present invention comprises the following steps:

[0043] Step 1: Obtain the simulated effective proliferation factors and measured effective proliferation factors of multiple nuclear experimental benchmarks, and calculate the difference between the two;

[0044] Both the simulated effective proliferation factor and the measured effective proliferation factor contain uncertainties, and the standardized difference index is calculated using the following formula:

[0045]

[0046] Where:

[0047] δk eff — Standardized difference indicators;

[0048] - Simulated effective multiplication factor for nuclear experimental benchmarks;

[0049] -- the measured effective proliferation factor of the nuclear experimental benchmark;

[0050] — Uncertainty in the simulated effective multiplication factor of the nuclear test benchmark;

[0051] —Uncertainty in the measured effective multiplication factor of the nuclear test benchmark;

[0052] Calculate the standardized difference value for each nuclear experimental benchmark to obtain the effective proliferation factor standardized difference value data set;

[0053] Step 2: Calculate the nuclear data sensitivity characteristics of each experimental benchmark, including the sensitivity coefficient to the nuclear reaction cross section and experimental metadata;

[0054] In the nuclear data sensitivity characteristics, the sensitivity coefficient to the nuclear reaction cross section includes at least one of the following: neutron induced fission cross section (n,f), neutron elastic scattering cross section (n,el), neutron inelastic scattering cross section (n,inl), neutron radiation capture cross section (n,γ), average total fission neutron number and fission neutron spectrum (χ tot ) sensitivity coefficient;

[0055] The purpose of calculating the sensitivity coefficient is to determine the variation law of the effective proliferation factor of the simulation system with respect to the sensitivity characteristics of the nuclear data. The calculation formula is as follows:

[0056]

[0057] Where:

[0058] —Sensitivity coefficient of nuclear data characteristics with respect to simulated effective proliferation factors;

[0059] σ0 – nominal value of the nuclear data characteristic;

[0060] k eff,0 — the nominal value of the effective proliferation factor calculated from the nominal value of the nuclear data characteristics;

[0061] ——The change in effective proliferation factor calculated after the nuclear data characteristics change;

[0062] — the amount of change in nuclear data characteristics;

[0063] The experimental metadata includes at least one of the following: laboratory, experimental year, nuclide composition, geometric configuration, moderator type, fuel concentration, and experimental uncertainty;

[0064] Step 3: Build a random forest-based machine learning model, using the nuclear data sensitivity features as input and the effective proliferation factor difference value as output for training;

[0065] Nuclear data sensitivity features are high-dimensional, nonlinear, and some features are highly correlated. Compared with machine learning models such as linear regression and support vector machines (SVM), random forest (RF) reduces the risk of overfitting by integrating multiple decision trees, and performs better in scenarios with complex nuclear data feature correlations.

[0066] The standardized difference dataset of effective proliferation factors was split into training and test sets with an 8:2 ratio. Training was performed using the RandomForestRegressor module of the Scikit-learn library in Python, with the mean squared error (MSE) as the loss function. The hyperparameters of the random forest machine learning model were optimized using grid search (GridSearchCV), with a cross-validation fold of k = 5. Model training was considered complete when the mean squared error (MSE) was less than the uncertainty of the measured effective proliferation factor of the nuclear experimental benchmark.

[0067] Step 4: Perform model feature importance analysis to identify nuclear data sensitivity features that significantly influence the differences in effective proliferation factors;

[0068] The SHAP library in Python was used to perform an importance analysis of nuclear data sensitivity features. The SHAP (ShapleyAdditive exPlanations) metric is based on the Shapley theory in cooperative game theory. It quantifies the marginal contribution of each nuclear data sensitivity feature to the model prediction and analyzes its impact on the difference value of the effective proliferation factor.

[0069] When using the SHAP indicator for feature importance analysis, in order to avoid the importance dispersion caused by high-dimensional correlation, different aggregation strategies are used, such as by nuclide ( 239 Pu, 14 N), energy range (hot zone, fast zone) or neutron reaction type, and finally generate a global importance ranking and individual case explanation to identify nuclear data with potential defects.

[0070] Examples of machine learning-based nuclear data validation methods

[0071] To verify the effectiveness of the method of the present invention, we first simulated and calculated 1081 nuclear benchmark experiments based on the ENDF / B-VIII.0 evaluation nuclear database, and used the obtained effective proliferation factors as the measured effective proliferation factors. Then, we perturb the original database to simulate the defects or problem data in the nuclear data features. In this example, 238 The neutron elastic scattering cross section (n,el) and neutron radiative capture cross section (n,γ) of U were each perturbed upward by 5%. Simulations using the perturbed data yielded simulated effective multiplication factors. The calculated standardized difference values ​​were used as samples to train a random forest machine learning model using the aforementioned method. Feature importance analysis was performed to see if the model could capture the perceived "defect" in the nuclear data.

[0072] The calculation results are as follows Figure 2 and Figure 3 As shown:

[0073] from Figure 2The results show that when human disturbance 238 When the neutron elastic scattering cross section of U is calculated, the SHAP interpretation model will be 92238.80c_elastic (i.e. 238 U neutron elastic scattering) features were ranked first, and it was considered to be strongly correlated with the difference value of effective proliferation factor; Figure 3 The results show that when human disturbance 238 When the neutron radiation capture cross section of U is calculated, the SHAP interpretation model will be 92238.80c_n,gamma (i.e. 238 The U neutron radiation capture feature was ranked first and was found to be strongly correlated with the difference in effective proliferation factors. This demonstrates that the proposed machine learning-based nuclear data verification method has a good ability to identify nuclear data feature defects and can screen and identify potentially high-impact nuclear data features within high-dimensional nuclear data features.

Claims

1. A nuclear data verification method based on machine learning, characterized by: The following steps are involved: Step 1: Obtain the simulated effective proliferation factors and measured effective proliferation factors of multiple nuclear experimental benchmarks, and calculate the difference between the two; Step 2: Calculate the nuclear data sensitivity characteristics of each experimental benchmark, including the sensitivity coefficient to the nuclear reaction cross section and experimental metadata; Step 3: Build a random forest-based machine learning model, using the nuclear data sensitivity features as input and the effective proliferation factor difference value as output for training; Step 4: Perform model feature importance analysis to identify nuclear data sensitivity features that significantly influence the differences in effective proliferation factors.

2. The nuclear data verification method based on machine learning according to claim 1, characterized in that: In step 1, both the simulated effective proliferation factor and the measured effective proliferation factor contain uncertainty, and the standardized difference index between the two is calculated using the following formula: Where: δk eff — Standardized difference indicators; - Simulated effective multiplication factor for nuclear experimental benchmarks; -- the measured effective proliferation factor of the nuclear experimental benchmark; — Uncertainty in the simulated effective multiplication factor of the nuclear test benchmark; —Uncertainty in the measured effective multiplication factor of the nuclear test benchmark; The standardized difference value is calculated for each nuclear experimental benchmark to obtain the effective proliferation factor standardized difference value data set.

3. The nuclear data verification method based on machine learning according to claim 1, characterized in that: In step 2, the sensitivity coefficient of the nuclear reaction cross section in the nuclear data sensitivity characteristics includes at least one of the following: sensitivity coefficients of neutron induced fission cross section, neutron elastic scattering cross section, neutron inelastic scattering cross section, neutron radiation capture cross section, average total fission neutron number and fission neutron energy spectrum; The purpose of calculating the sensitivity coefficient is to determine the changing pattern of the simulated effective proliferation factor with respect to the sensitivity characteristics of nuclear data. The calculation formula is as follows: Where: —Sensitivity coefficient of nuclear data characteristics with respect to simulated effective proliferation factors; σ0 – nominal value of the nuclear data characteristic; k eff,0 — the nominal value of the effective proliferation factor calculated from the nominal value of the nuclear data characteristics; ——The change in effective proliferation factor calculated after the nuclear data characteristics change; — the amount of change in nuclear data characteristics; The experimental metadata includes at least one of the following: laboratory, experimental year, nuclide composition, geometric configuration, moderator type, fuel concentration and experimental uncertainty.

4. The nuclear data verification method based on machine learning according to claim 1, characterized in that: In step 3, the standardized difference dataset of the effective proliferation factor is divided into a training set and a test set with an 8:2 ratio. The training is performed using the RandomForestRegressor module of the Scikit-learn library in the Python language, and the loss function is the mean square error. The hyperparameters of the random forest machine learning model are optimized through grid search, and the cross-validation fold k = 5 is selected. When the mean square error is less than the uncertainty of the effective proliferation factor measured by the nuclear experimental benchmark, the model training is completed.

5. The nuclear data verification method based on machine learning according to claim 1, characterized in that: In step 4, the SHAP library in Python is used to perform an importance analysis of the nuclear data sensitivity features. The SHAP indicator is based on the Shapley theory in cooperative game theory. It quantifies the marginal contribution of each nuclear data sensitivity feature to the model prediction and analyzes its impact on the difference value of the effective proliferation factor. When using the SHAP indicator for feature importance analysis, in order to avoid the importance dispersion caused by high-dimensional correlation, different aggregation strategies are adopted, and finally a global importance ranking and individual case explanations are generated to identify nuclear data with potential defects.

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