Uncertainty Analysis Method of Spectral Decomposition Based on Random Sampling

Abstract

The embodiments of the present application relate to the technical field of neutron radiation measurement, and in particular to a method for uncertainty analysis of spectrum decomposition based on random sampling. The method comprises the following steps: S1: placing a plurality of detection foils into a neutron field to be measured for irradiation. S2: taking out the irradiated detection foils and measuring the activity of the detection foils. S3: determining the saturation activity of the detection foils based on the measured activity of the detection foils. S4: determining the energy spectrum of the neutron field to be measured based on the saturation activity and the reaction cross section of the detection foils. S5: determining the factors that lead to the uncertainty of the energy spectrum determined in step S4. S6: performing random sampling processing on the factors determined in step S5 respectively. S7: determining the uncertainty of spectrum decomposition based on the results of the random sampling processing in step S6. The analysis method provided by the embodiments of the present application can obtain uncertainty analysis results of neutron energy spectrum decomposition.

Description

Technical Field

[0001] The embodiments of the present application relate to the technical field of neutron radiation measurement, and in particular to an uncertainty analysis method for spectrum decomposition based on random sampling. Background Art

[0002] The statements herein merely provide background information related to the present application and do not necessarily constitute prior art.

[0003] Neutron spectrum analysis is fundamental to reactor-related research. Accurate interpretation of neutron spectra is crucial for this research. The iterative method is a highly applicable neutron spectrum interpretation method and is currently the most widely used method in reactor neutron spectrum measurement experiments.

[0004] However, the uncertainty assessment of neutron energy spectrum by the iterative method is relatively imperfect, and the uncertainty of the obtained neutron energy spectrum is not accurate enough. Therefore, it is necessary to provide an uncertainty analysis method suitable for the iterative method. Summary of the Invention

[0005] A brief overview of the present application is provided below to provide a basic understanding of certain aspects of the present application. It should be understood that this overview is not an exhaustive overview of the present application. It is not intended to identify key or important portions of the present application, nor is it intended to limit the scope of the present application. Its purpose is simply to present certain concepts in a simplified form as a prelude to the more detailed description that will be discussed later.

[0006] An embodiment of the present application provides an uncertainty analysis method for spectrum interpretation based on random sampling, and spectrum interpretation is to interpret the obtained neutron energy spectrum, which includes the following steps S1 to S7: S1: Place multiple detection foils into the neutron field to be measured for irradiation. S2: Take out the irradiated detection foils and measure the activity of the detection foils. S3: Determine the saturation activity of the detection foils based on the measured activity of the detection foils. S4: Determine the energy spectrum of the neutron field to be measured based on the saturation activity and the reaction cross-section of the detection foils. S5: Determine the factors that cause the uncertainty of the energy spectrum determined in step S4. S6: Perform random sampling processing on the factors determined in step S5. S7: Determine the uncertainty of spectrum interpretation based on the results of the random sampling processing in step S6.

[0007] The analysis method provided in the embodiments of the present application can obtain more accurate uncertainty analysis results of neutron energy spectrum interpretation by randomly sampling factors that cause uncertainty in spectrum interpretation. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] To further illustrate the above and other advantages and features of the present application, the following detailed description of specific embodiments of the present application is provided in conjunction with the accompanying drawings. The accompanying drawings, together with the detailed description below, are incorporated into and form a part of this specification. Elements with the same function and structure are denoted by the same reference numerals. It should be understood that these drawings depict only typical examples of the present application and should not be construed as limiting the scope of the present application.

[0009] Figure 1 It is a flowchart of an analysis method according to an embodiment of the present application.

[0010] It should be noted that the drawings are not necessarily drawn to scale, but are merely shown in a schematic manner that does not affect the reader's understanding. DETAILED DESCRIPTION

[0011] Exemplary embodiments of the present application will be described below with reference to the accompanying drawings. For the sake of clarity and conciseness, not all features of actual implementations are described in the specification. However, it should be understood that many implementation-specific decisions must be made in the process of developing any such actual implementation in order to achieve the developer's specific goals, such as meeting those constraints related to the system and business, and these constraints may vary depending on the implementation. In addition, it should be understood that although the development work may be very complex and time-consuming, it is a routine task for those skilled in the art who benefit from the content of this application.

[0012] It is also necessary to explain here that, in order to avoid obscuring the present application due to unnecessary details, the accompanying drawings only show the device structure and / or processing steps that are closely related to the solution according to the present application, while other details that are not closely related to the present application are omitted.

[0013] The disclosure below provides a plurality of different embodiments or examples for implementing the present application. In order to simplify the disclosure of the present application, the components and methods of specific examples are described below. Of course, they are merely examples and are not intended to limit the present application. In the description of the embodiments of the present application, the meaning of "plurality" is at least two, for example, two, three, etc., unless otherwise specifically defined.

[0014] See also Figure 1 An embodiment of the present application provides an uncertainty analysis method for spectrum decomposition based on random sampling, wherein spectrum decomposition is performed on the obtained neutron energy spectrum, and the method includes the following steps S1 to S7.

[0015] S1: Place multiple detection foils into the neutron field to be tested for irradiation.

[0016] S2: Take out the irradiated detection foil and measure the activity of the detection foil.

[0017] S3: Determine the saturation activity of the detection foil based on the measured activity of the detection foil.

[0018] S4: Determine the energy spectrum of the neutron field to be measured based on the saturation activity and the reaction cross section of the detection foil.

[0019] S5: Determine factors that contribute to the uncertainty of the energy spectrum determined in step S4.

[0020] S6: Perform random sampling on each of the factors determined in step S5.

[0021] S7: Based on the result of the random sampling process in step S6, the uncertainty of the spectrum solution is determined.

[0022] In related technologies, iterative methods are widely applicable to spectrum interpretation, but they introduce a certain degree of uncertainty during the interpretation process. The analysis method provided in the embodiments of the present application can obtain more accurate uncertainty analysis results by randomly sampling the factors that cause uncertainty in the interpretation.

[0023] In some embodiments, in step S4, the saturation activity, the reaction cross section of the detection foil, and the energy spectrum of the neutron field to be measured conform to the following expression (1), wherein the reaction cross section refers to the probability of nuclear reaction occurring when neutrons of different energies collide on a predetermined surface of the activated foil.

[0024]

[0025] Among them, A i To detect the saturation activity of the foil, φ j represents the average neutron flux of the jth group of the neutron spectrum to be measured, σ i,j (E) is the average nuclear reaction cross section of the i-th detection foil in the j-th group neutron energy interval, ΔE j is the energy interval of the jth group of neutrons, and m represents the number of divided energy groups.

[0026] For the detection foil activated in the neutron field, its saturation activity A i Reaction cross section σ with each activated foil i (E) and the neutron energy spectrum to be measured φ(E) satisfy the following expression (2):

[0027]

[0028] Expression (2) is a set of linear integral equations containing n linear equations. By solving this linear integral equation, the neutron energy spectrum of the neutron field to be measured can be obtained. However, due to A iIt is a finite discrete value and it is impossible to determine a unique continuous function φ(E). Therefore, the neutron energy spectrum φ(E) to be measured and the corresponding nuclear reaction cross section σ in expression (2) are i (E) Discretize to obtain expression (1) for mathematical solution. For example, the discretization can be performed by dividing the neutron energy into multiple energy groups.

[0029] Since the number of activated foils n used in actual measurements is very limited, that is, usually m>>n, the solution of expression (1) is not unique. The iterative method is a method to obtain an approximate solution to the measured neutron energy spectrum based on assumptions about the measured neutron field and some constraints.

[0030] Specifically, the principle of the iterative method is to select the initial approximate spectrum φ based on the understanding and assumptions of the neutron field to be measured. 0 (E), the activity value A of the activated foil is calculated according to the expression (1) using the approximate spectrum i (0) , compare the activity value with the actual activity value A obtained by measurement i Compare them and use the difference between the two to correct φ 0 (E), to obtain the first-order approximation spectrum φ (1) (E), and then use the approximate spectrum to calculate the activity value of the activated foil according to expression (1) The activity value is compared with the actual activity value A i Compare and continue to (1) (E) Make corrections and repeat the above process until the difference between the differential spectra of two adjacent iterations is less than the predetermined difference. When the last iteration is the K+1th iteration, φ (K+1) (E) is the solved neutron energy spectrum. The predetermined difference can be obtained, for example, by controlling the standard deviation of the calculated reaction rate and the measured reaction rate, controlling the convergence speed or the maximum iteration speed.

[0031] Combining the above content and expression (1), it can be obtained that the sources of uncertainty in the iterative spectrum solution are activation rate, cross-section covariance and initial spectrum.

[0032] In some embodiments, in step S5, the factor of uncertainty in the determined energy spectrum is the reaction cross section of the detection foil; the method also includes the following steps: determining the covariance matrix of the reaction cross section; decomposing the covariance matrix, and when decomposing, when a negative eigenvalue appears in the covariance matrix, the eigenvalue is set to 0 or a smaller positive number; based on random sampling, the matrix obtained after decomposition is processed to determine the disturbance factor of the reaction cross section; according to the disturbance factor, the reaction cross section after disturbance is determined, and according to the reaction cross section after disturbance, the uncertainty of the spectrum solution is determined.

[0033] Determining the reaction cross section covariance matrix includes storing continuous point cross section values ​​and covariance data between energy groups in a database, and processing the database through a program to obtain cross section information and covariance data for each energy group of each nuclide. The evaluation library can be the ENDF-VIII.8 library, and the program can be the NJOY program, with the data specifically processed through the ERROR module therein.

[0034] In some embodiments, the reaction cross section after disturbance satisfies the following expression (3):

[0035] σ′=P T *μ (3).

[0036] Where σ′ represents the reaction cross section after disturbance, μ is the initial value of the reaction cross section, and P is the disturbance factor of the reaction cross section, which satisfies the following expression (4):

[0037]

[0038] Among them, Y S is a random value that follows a (0,1) normal distribution and is obtained by the Latin hypercube sampling method, Σ r is the covariance matrix, which satisfies the following expression (5):

[0039]

[0040] Where V is the column vector matrix of the symmetric matrix, and D is the diagonal matrix of the eigenvalues ​​corresponding to the eigenvectors.

[0041] The covariance matrix of the multi-group cross section represents the correlation error between each energy group. After the NJOY program processes the database, the relative covariance matrix of each reaction cross section in different energy groups can be obtained. r Σ r Decomposing it, we get the following expression (6):

[0042] Σ r =VDV T (6).

[0043] Where the column vector matrix of V is the eigenvector of the symmetric matrix, and D is the diagonal matrix of the eigenvalues ​​corresponding to the eigenvectors, then It can be expressed as expression (5):

[0044]

[0045] In the process of generating random samples, the eigenvalues ​​of the covariance matrix must be non-negative values, that is, the covariance matrix must be symmetrical and positive definite, but in the actual spectrum solution process, the covariance matrix is ​​likely to be non-positive definite, and there are two reasons affecting the covariance matrix. The first reason is that when linear interpolation generates a new energy group structure, this process will affect the matrix, making it an asymmetric matrix; The second reason is that during the matrix decomposition process, due to the limitation of precision, negative eigenvalues ​​may appear. Therefore, the embodiment of the application adopts principal component analysis (PCA method), and the negative eigenvalues ​​appearing in the matrix decomposition are set to 0 or a smaller positive number. When the spectrum is solved, the main source of uncertainty is the variance of the reaction channel, and the influencing factors occupied by negative eigenvalues ​​and asymmetric elements in the matrix are small, so this treatment has little effect on the result of the final uncertainty analysis.

[0046] Assume that random sampling generates n random variables X=[X1,X2,…X n ] T , can generate multiple groups of cross-sectional perturbation factors, which satisfy expression (4):

[0047]

[0048] where Y S is a random value that follows a (0,1) normal distribution and is obtained by the Latin hypercube sampling method. P is the perturbation factor of the reaction cross section. Then, the perturbed cross section can be obtained by expression (3):

[0049] σ′=P T *μ (3).

[0050] Where σ′ represents the reaction cross section after disturbance, and μ is the initial value of the reaction cross section.

[0051] In some embodiments, in step S5, the factor of the uncertainty of the energy spectrum is determined to be the saturation activity of the detection foil; the source of the uncertainty of the saturation activity of the detection foil is determined, and based on the source, the uncertainty of the saturation activity of the detection foil is determined; based on random sampling, the uncertainty of the saturation activity is processed to determine the saturation activity after disturbance; and based on the saturation activity after disturbance, the uncertainty of the spectrum decomposition is determined.

[0052] Using highly enriched uranium sheets as probe foils, we can measure 235 Taking the reaction rate of U as an example, when measuring the activity, the measured activity A satisfies the following expression (7):

[0053]

[0054] Where C is the measured 103 Total counts of the peak area of ​​γ-rays (497 keV) emitted by Ru;

[0055] I γ for 103 The absolute intensity (branching ratio) of the 497 keV gamma ray emitted by Ru;

[0056] ε is the peak efficiency of the spectrometer measuring 497 keV gamma rays (percentage);

[0057] K is the self-absorption correction coefficient (percentage) of γ-rays with an energy of 497 keV in the sample;

[0058] T M is the measurement time interval, in s;

[0059] τ is the "dead" time (in percent) of the system when measuring the activity of the detection foil.

[0060] λ is 103 Decay constant of Ru, in s -1 ,

[0061] M is the number of uranium nuclei in the detection foil;

[0062] Γ5 is the probe foil 235 U enrichment;

[0063] Y5 is the detection foil 235 U fission production 103 Total output of Ru;

[0064] T s is the irradiation time of the detection foil in the pile, in seconds;

[0065] T w The waiting time between the end of foil irradiation and the measurement time, in seconds;

[0066] It can be concluded from expression (7) that the sources of uncertainty in the saturation activity of the detection foil may include: uncertainty related to the number of nucleons reacting with the detection foil, uncertainty related to time parameters, uncertainty related to the activity measurement value obtained of the detection foil, and uncertainty introduced by the irradiation position deviation of the detection foil and mutual interference between the detection foils.

[0067] In some embodiments, sources of uncertainty in the saturation activity of the probe foil include: uncertainty associated with the number of nuclei reacted by the probe foil, which is 1%; uncertainty associated with a time parameter, which is 1%; and uncertainty associated with the activity measurement value obtained for the probe foil, which is determined by obtaining a peak area of ​​the activity measurement value of the probe foil, wherein the uncertainty of the peak area satisfies the following expression (8):

[0068]

[0069] Where, v C represents the uncertainty of the peak area, C represents the total count of the peak area of ​​a certain specific gamma ray measured, σ C Represents the statistical deviation of the peak area.

[0070] The uncertainty introduced by the deviation of the irradiation position of the detection foil and the mutual interference between the detection foils is between 2% and 4%. The uncertainty of the saturation activity satisfies the following expression (9):

[0071]

[0072] Where, j represents various factors affecting the saturation activity measurement, A is the measured activity, represents the activity uncertainty caused by factor j, and ΔA is the uncertainty of the measured activity. Based on random sampling, the uncertainty of the saturation activity is processed to determine the saturation activity after disturbance.

[0073] The uncertainty associated with the number of nucleons in the probe foil reaction primarily comes from the purity, mass, and enrichment of the probe foil. The probe foil is made of high-purity metal or oxide, with a purity exceeding 99.99%. Therefore, the influence of the probe foil's purity on the uncertainty is negligible. The mass of the probe foil is weighed three times using a high-precision balance with an accuracy of 1 / 10,000g. Therefore, the influence of the probe foil's mass on the uncertainty is less than 0.5%. The enrichment of the probe foil may be inaccurate, which will have a certain impact on the uncertainty. Overall, the uncertainty associated with the number of nucleons in the probe foil reaction is 1%.

[0074] Uncertainties associated with time parameters primarily include those related to irradiation time, waiting time, or measurement time. These times are all measured using a uniformly calibrated clock, and their contribution to the uncertainty is typically less than 1%. Therefore, the uncertainty associated with time parameters is treated as 1% here.

[0075] The uncertainty associated with the activity measurement value obtained for the probe foil includes the uncertainty caused by the peak area of ​​the activity measurement value of the probe foil. The uncertainty of the peak area satisfies the expression (8):

[0076]

[0077] The uncertainty is between 2% and 4%, including the uncertainty caused by the deviation of the irradiation position of the detection foil and the mutual interference between the detection foils.

[0078] Since the various factors containing uncertainty mentioned above are independent of each other and obey the normal distribution, the total measurement uncertainty of the activation rate can be expressed as the root of the sum of squares of the uncertainties. This relationship can be expressed by expression (9):

[0079]

[0080] In some embodiments, the uncertainty associated with the measuring instrument and the uncertainty associated with the decay profile may be further considered as sources of uncertainty in the saturation activity of the detection foil.

[0081] Uncertainties associated with the measuring instrument primarily include the uncertainty of the gamma spectrometer efficiency calibration, including the uncertainty of the calibration of the standard gamma source activity used for the gamma spectrometer efficiency calibration (approximately 3%) and the uncertainty of the efficiency calibration. The gamma spectrometer efficiency calibration is typically performed at least three times, with the efficiency uncertainty at various energies consistently less than 2.5%.

[0082] The uncertainties associated with the decay diagram mainly include the uncertainty of the intensity and branching ratio of gamma rays, the uncertainty of fission yield, and the cascade effect of gamma rays. Among them, the uncertainty of the intensity and branching ratio of gamma rays can be obtained by looking up the table according to the JJG417-2006 gamma spectrometer calibration procedure, and its maximum value is 1.1%. The energy of thermal neutrons is different. When the energy of thermal neutrons is uniformly taken as 0.5MeV, there will be deviations. This deviation will lead to the uncertainty of fission yield, which is 4%. 235 U and 238 U is valid. Since the gamma ray cascade detector is usually more than 5 cm away from the probe, the cascade effect is not obvious and the resulting uncertainty can be ignored.

[0083] In some embodiments, in step S5, the factor of the uncertainty of the determined energy spectrum is the prior spectrum used in the spectrum decomposition process; the method also includes the following steps: using MCNP calculation to obtain the prior spectrum and the calculated relative error of each energy group of the prior spectrum, within the relative error range, using weighted Latin hypercube sampling to obtain N energy spectra, and then respectively bringing the N energy spectra into the spectrum decomposition program as prior spectra for spectrum decomposition, comparing the deviations of all the spectrum decomposition results with the MCNP calculated spectrum, and determining the estimated error of the MCNP calculated spectrum at the maximum deviation; and determining the uncertainty of the spectrum decomposition based on the estimated error.

[0084] The prior spectrum used in the decomposition process is calculated by the MCNP program, which is the average of multiple sampling histories. The MCNP program also provides a relative error in the calculated result. Within this relative error, weighted Latin hypercube sampling is used to obtain N energy spectra. Each of these N energy spectra is then fed into the decomposition program as a prior spectrum for decomposition. The deviations between all the decomposition results and the MCNP calculated spectrum are compared. Through sampling iteration, a more conservative prior spectrum uncertainty that is self-consistent with the decomposition results is obtained.

[0085] In some embodiments, in step S7, the uncertainty of the spectrum solution satisfies the following expression (10):

[0086]

[0087] Where Δσ(R) represents the relative uncertainty of the spectrum solution, and σ(R) represents the uncertainty of the spectrum solution. σ(R) can be obtained by the following expression (11):

[0088]

[0089] Among them, N is the total number of sampling times, and j is the jth sampling.

[0090] For different energy groups of activation reaction, the N groups of data samples generated by Latin hypercube sampling are used for spectrum decomposition calculation, and the response amount samples R = [R1, R2, ... R n ] T .

[0091] Based on the known covariance, the perturbed prior spectrum, activation rate, and reaction cross section obtained by random sampling in step S6 are deconvolution. Based on the deconvolution results, the uncertainty of the deconvolution can be determined. Specifically, in step S6, N samplings are performed. For different energy groups of the activation reaction, N groups of data samples generated by Latin hypercube sampling are used for deconvolution calculation, and the corresponding response quantity samples R for each group are obtained: [R1, R2, ... R n ] T , then the standard deviation of the response quantity σ(R) is the uncertainty of the spectrum solution, and this process is the process expressed by expression (11).

[0092] In some embodiments, N can be determined according to the following expression (12):

[0093]

[0094] in, is the sample mean. When the value of δ·d(x) / σ is within the confidence interval with a confidence level of 95%, the value of N meets the requirements. k is the decomposition result of each group, and δ·d(x) is the standard deviation of the samples.

[0095] During the sampling process, if the number of samples is too small, the results will be inaccurate; if the number of samples is too large, it will lead to a waste of computing power. The minimum value of the number of sample groups N can be determined by studying the variance of the sample activity values. Assuming that the detectors are statistically independent and the theoretical variance of the input activity value x is known, the standard deviation of the sample can be determined by expression (12). When the value of each threshold δ·d(x) / σ is within the confidence interval with a confidence level of 95%, it can be considered that N is sufficiently large and the value of N meets the requirements.

[0096] Regarding the embodiments of the present application, it should also be noted that, in the absence of conflict, the embodiments of the present application and the features therein can be combined with each other to obtain new embodiments.

[0097] The above are only specific implementation methods of the present application, but the protection scope of the present application is not limited thereto. The protection scope of the present application shall be based on the protection scope of the claims.

Claims

1. A method for analyzing uncertainty of spectrum decomposition based on random sampling, wherein the spectrum decomposition is performed on the obtained neutron energy spectrum, characterized in that: It includes the following steps: S1: multiple detection foils are placed in the neutron field to be tested for irradiation; S2: taking out the irradiated detection foil and measuring the activity of the detection foil; S3: determining the saturation activity of the detection foil according to the measured activity of the detection foil; S4: determining an energy spectrum of the neutron field to be measured according to the saturation activity and the reaction cross section of the detection foil; S5: Determine factors that lead to uncertainty of the energy spectrum determined in step S4; S6: According to the factors determined in step S5, random sampling is performed on them respectively; S7: Determine the uncertainty of the spectrum solution based on the result of the random sampling process in step S6; In step S5, the factor of uncertainty of the energy spectrum is determined to be the reaction cross section of the detection foil; The method further comprises the steps of: Determine the covariance matrix of the reaction cross section; Decomposing the covariance matrix, when decomposing, if a negative eigenvalue appears in the covariance matrix, the eigenvalue is set to 0 or a smaller positive number; Based on random sampling, the matrix obtained after decomposition is processed to determine the disturbance factor of the reaction cross section; According to the disturbance factor, the reaction cross section after disturbance is determined. Determining the uncertainty of the spectrum solution according to the reaction cross section after the disturbance; The reaction cross section after the disturbance satisfies the following expression: = ； in, represents the reaction cross section after disturbance, is the initial value of the reaction cross section, P is the perturbation factor of the reaction cross section, T is the matrix transpose symbol, = ； is a random value that follows a (0,1) normal distribution and is obtained by the Latin hypercube sampling method. ； is the covariance matrix, V The column vector matrix is ​​the eigenvector of the symmetric matrix, D is the diagonal matrix of eigenvalues ​​corresponding to eigenvectors; In step S5, the factor of uncertainty of the energy spectrum determined is the saturation activity of the detection foil; Determine the sources of uncertainty in the saturation activity of the probe foil, determining an uncertainty in the saturation activity of the detection foil based on the source; Based on random sampling, the uncertainty of the saturation activity is processed to determine the saturation activity after disturbance; Determining the uncertainty of the spectrum solution according to the saturation activity after the disturbance; Sources of uncertainty in the saturation activity of the probe foil include: The uncertainty associated with the number of nuclei reacted by the probe foil is 1%; The uncertainty associated with the time parameter is 1%; The uncertainty associated with the activity measurement obtained for the probe foil is determined as follows: obtaining the peak area of ​​the activity measurement of the probe foil, The uncertainty of the peak area satisfies the following expression: ； Where, represents the uncertainty of the peak area, It indicates the total count of the peak area of ​​a certain specific gamma ray measured. represents the statistical deviation of the peak area; The uncertainty introduced by the deviation of the irradiation position of the detection foils and the mutual interference between the detection foils is between 2% and 4%; The uncertainty of the saturation activity satisfies the following expression: ， In the formula j Indicates various factors that affect saturation activity measurement, A is the measured activity, Representation factors j The resulting activity uncertainty is is the uncertainty of the measured activity; Based on random sampling, the uncertainty of the saturation activity is processed to determine the saturation activity after disturbance.

2. The method according to claim 1, characterized in that In step S4, the saturation activity, the reaction cross section of the detection foil, and the energy spectrum of the neutron field to be measured conform to the following expression: ，( i =1，2，……， n )， Among them, A i To detect the saturation activity of the foil, Indicates the neutron spectrum to be measured j Group average neutron flux, For the i The detection foil is j The average nuclear reaction cross section within the group neutron energy interval, For the j The energy interval of the neutrons in the group, m Represents the number of energy groups divided.

3. The method according to claim 1, characterized in that In step S5, the uncertainty factor of the energy spectrum is determined to be the prior spectrum used in the spectrum decomposition process; The method further comprises the steps of: The prior spectrum and the relative error of each energy group of the prior spectrum are obtained by MCNP calculation. Within the relative error range, weighted Latin hypercube sampling is used to obtain N energy spectrum, and then N The energy spectrum is taken as a priori spectrum and brought into the spectrum decomposition program for spectrum decomposition. Compare the deviations of all the decomposition results with the MCNP calculated spectrum, determining an estimated error of the MCNP-calculated spectrum at a maximum of the deviation; The uncertainty of the spectrum solution is determined according to the estimated error.

4. The method according to claim 1, wherein In step S7, the uncertainty of the spectrum solution satisfies the following expression: ,in, represents the relative uncertainty of the spectrum solution, ，( = )， represents the uncertainty of the spectrum solution, N is the total number of samplings, j is the jth sampling, For different energy groups of activation reaction, Latin hypercube sampling is used to generate N The data samples are despectralized and the N The response sample corresponding to each group .

5. The method according to claim 4, characterized in that N is determined as follows: = ， in, is the sample mean, is the spectrum solution result of each group, ,when When the value of is within the confidence interval with a confidence level of 95%, N The value meets the requirements.

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