A spectrum analysis method for multi-sphere neutron spectrometer based on parameterized energy spectrum

Abstract

The present invention relates to a multi-sphere neutron spectrometer spectrum analysis method based on parameterized energy spectrum. On the basis of making full use of the distribution law of neutron energy spectrum in certain energy bands, such as the near-Gaussian distribution in the thermal neutron zone, the "platform zone" of 1eV-10keV, etc., the parameterized energy spectrum is used as the initial energy spectrum, and these parameters are revalued through calculation and analysis to minimize the total error level between the detector count and the solution result, and a continuous neutron energy spectrum with a clear physical image is obtained. By using the multi-sphere neutron spectrometer spectrum analysis method based on parameterized energy spectrum disclosed by the present invention, the shape of each segment of the neutron energy spectrum obtained has a high degree of consistency with the actual physics, which can greatly reduce the reliance on the strict initial spectrum in the spectrum analysis process of the multi-sphere neutron spectrometer, and has a wide range of applications and strong practicality.

Description

Technical Field

[0001] The invention belongs to the technical field of file analysis, and in particular relates to a multi-sphere neutron spectrometer spectrum analysis method based on parameterized energy spectrum. Background Art

[0002] The multi-sphere neutron spectrometer can measure a wide energy range and can be used to measure the energy spectrum of fast neutrons from thermal neutrons to tens of MeV. It is widely used in the fields of site monitoring and personal dose monitoring. The key to the multi-sphere neutron spectrometer is to analyze and convert the detector technology into an energy spectrum. The spectrum analysis methods commonly used internationally include the following:

[0003] Least square method: This method uses the least square method to establish the least square operation relationship between the measured data, the response function, the neutron energy spectrum (spectral injection) to be determined, and its covariance. Under given constraints, the covariance is minimized, and then some assumptions, approximations, and transformations are used to obtain the energy spectrum to be determined through repeated iterations. This method is currently commonly used for spectrum analysis, and different algorithms such as SAND-Ⅱ, GRAVEL, FERDOR, DIFBAS, and LEPRICON have been developed based on it.

[0004] The Monte Carlo method adopts the maximum entropy principle, that is, under given constraints, a multivariate probability density distribution function related to the neutron energy spectrum to be determined is established, so as to find the neutron energy distribution when the information entropy reaches the maximum value. This distribution is the distribution with the maximum estimate of uncertainty (maximum degree of freedom). Currently, the more mature programs developed on this basis include MIEKE, MAXED and its improved versions.

[0005] Genetic algorithm, the basic idea of ​​this method is: put all hypothetical solutions in the environment of solving the problem, select individuals that adapt to the environment through fitness function and given constraints and penalty conditions for replication, and then generate a new generation of individuals that are more adaptable to the environment through genetic operations such as crossover and mutation, so that it continues to evolve and finally converges to an individual that is most adaptable to the environment. At present, the more mature programs developed on this basis include BONDI-97, ANDI-03, etc.

[0006] For most decomposition methods, the decomposition results are strongly dependent on the initial spectrum. An initial spectrum needs to be input and the decomposition is performed based on the initial spectrum. Improper selection of the initial spectrum may cause the decomposition results to deviate seriously from the actual situation. In many cases, it is difficult to give a suitable initial spectrum, especially for the first analysis and measurement of an unknown specific neutron field. Even when a suitable initial spectrum is given, the decomposition results may not match the actual situation due to measurement errors and other reasons. The current decomposition methods also have the defect of not being able to fully utilize the known neutron distribution in certain energy segments of the neutron energy spectrum, resulting in low decomposition efficiency. Summary of the invention

[0007] In view of the defects existing in the prior art, the purpose of the present invention is to provide a multi-sphere neutron spectrometer spectrum interpretation method based on parameterized energy spectrum. On the basis of making full use of the distribution law of neutron energy spectrum in certain energy bands, such as the near-Gaussian distribution in the thermal neutron region, the "platform region" of 1eV-10keV, etc., the parameterized energy spectrum is used as the initial energy spectrum, and these parameters are re-valued through calculation and analysis to minimize the total error level between the detector count and the solution result, so as to obtain a continuous neutron energy spectrum with a clear physical image.

[0008] To achieve the above purpose, the technical solution adopted by the present invention is: a multi-sphere neutron spectrometer spectrum analysis method based on parameterized energy spectrum, the method comprising the following steps:

[0009] S1. Simulate and calculate to obtain the response function of the detector to neutrons of different energies after adding different moderators;

[0010] S2, dividing the neutron energy spectrum to be measured into n neutron energy groups with specific functional distribution forms, calculating the response functions of m detectors to neutrons in each energy group, and obtaining the response coefficient matrix A;

[0011] S3. Calculate the matrix B and vector according to the following formula

[0012] The elements of matrix B are:

[0013]

[0014] vector The weight is:

[0015]

[0016] The response coefficient matrix A has m rows and n columns, and the element A ij is the response of the i-th (i=1,m) detector to the j-th (j=1,n) energy neutron, the vector represents the detector count rate, y i is the counting rate of the ith detector during the neutron field measurement, σ i is the count rate y of the i-th detector i The error of

[0017] S4. Solve linear equations Conclusion That is, the values ​​of each energy spectrum parameter are obtained;

[0018] S5. According to the energy spectrum parameter values ​​obtained in step S4, output the energy spectrum and perform error analysis to calculate detector count, dose, and injection information.

[0019] Furthermore, in step S1, Monte Carlo software is used to perform simulation calculations to obtain the response function of the detector to neutrons of different energies after adding different moderators.

[0020] Furthermore, the specific function is a triangular function.

[0021] Furthermore, the specific function is a cosine function.

[0022] Furthermore, the specific function is a Gaussian distribution.

[0023] Furthermore, the specific function is Maxwell distribution.

[0024] Furthermore, the number of energy groups n is less than the number of detectors m.

[0025] Furthermore, the value range of the energy group number n is: 5≤n≤7.

[0026] The effect of the present invention is that: a multi-sphere neutron spectrometer decomposition method based on parameterized energy spectrum disclosed in the present invention is adopted, on the basis of making full use of the distribution law of neutron energy spectrum in certain energy bands, such as the near-Gaussian distribution in the thermal neutron region, the "platform region" of 1eV-10keV, etc., the parameterized energy spectrum is used as the initial energy spectrum, and these parameters are re-valued through calculation and analysis, so that the total error level between the detector counting rate and the solution result is minimized, and a continuous neutron energy spectrum with a clear physical image is obtained. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 It is a schematic diagram of the equivalent linear function neutron energy spectrum of a multi-sphere neutron spectrometer spectrum decomposition method based on parameterized energy spectrum according to an embodiment of the present invention;

[0028] Figure 2 This is a comparison diagram of the analysis results of the Am-Be neutron spectrum in the multi-sphere neutron spectrometer decomposition method based on parameterized energy spectrum described in an embodiment of the present invention and the standard spectrum. DETAILED DESCRIPTION

[0029] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments.

[0030] Embodiment 1

[0031] like Figure 1 As shown, a multi-sphere neutron spectrometer spectrum analysis method based on parameterized energy spectrum disclosed in the present invention comprises the following steps:

[0032] S1. Use Monte Carlo software to simulate and calculate, and obtain the response function of the detector to neutrons of different energies after adding different moderators;

[0033] S2. Perform a preliminary analysis on the neutron energy spectrum to be measured and describe it approximately with a piecewise continuous linear function. For example, the energy spectrum can be approximately expressed with a continuous linear function with n+1 segments, where the left side of the first segment and the right side of the last segment are set to zero, then the neutrons can be divided into n energy groups, and the neutron spectrum in each energy group is distributed in a triangular manner. Calculate the response coefficient matrix A of the m detectors to the neutrons in each energy group based on the triangular distribution.

[0034] According to the near-Gaussian distribution in the thermal neutron region and the "platform region" of 1eV-10keV, a triangular function is chosen to equivalently calculate the response coefficient matrix A of m detectors to neutrons of each energy group. During the response function calculation process, the height of the triangle is taken as 1, and the response coefficient matrix A of each detector to these triangularly distributed neutron spectra is calculated.

[0035] In this embodiment, an example is given of using only a triangular function distribution to equivalently calculate the response matrix A of m detectors to neutrons in each energy group. Of course, cosine function distribution, Gaussian distribution, Maxwell distribution or other function forms can also be used to calculate the response matrix A of m detectors to neutrons in each energy group, and there is no limitation to this.

[0036] When the neutron spectrum to be measured is divided into n energy groups for spectrum analysis, n unknown parameters need to be calculated. According to the results measured by m detectors, m equations can be established. When the number of unknown parameters n is greater than the number of equations m, it is a minor spectrum analysis problem, and a reliable solution cannot be obtained at this time; when the number of unknown parameters n is less than the number of detectors m, it is possible to obtain its optimal solution. For the spectrum analysis problem of a multi-sphere neutron spectrometer with a sufficient number of detectors, some constraints can be used to transform it into a situation where the number of equations is greater than the number of unknowns for solution, such as using the continuity of the neutron energy spectrum and the definite spectrum shape in certain energy ranges. Therefore, a series of parameters can be used to mathematically describe the neutron energy spectrum, such as the inflection points and their coordinate values ​​in the piecewise continuous linear neutron energy spectrum, and the corresponding algorithms can be used to solve these parameters, that is, the parameterized energy spectrum analysis method.

[0037] When measuring with a multi-sphere neutron spectrometer, the number of detectors m generally selected is less than 20, and the value of m is usually between 5 and 13. The number of unknown parameters of the linearly independent equation that can be obtained through mathematical processing is no more than the number of detectors m. The number of unknown parameters n of the linearly independent equation is the number of independent parameters that need to be determined in the spectrum solution process, which must be less than the number of detectors m. When using a piecewise linear continuous function energy spectrum to describe the actual neutron energy spectrum to be measured, the number of segments n of the energy spectrum needs to be less than the number of detectors m. For the field neutron energy spectrum, five to seven segments can generally be selected. When seven segments are selected, the energy spectrum obtained by analysis is already highly consistent with the actual energy spectrum. The energy spectrum analyzed with more than 10 segments is prone to distortion.

[0038] In this embodiment, a piecewise continuous linear function is used to describe the neutron energy spectrum. Figure 1 As shown in the figure, the black solid line gives the neutron energy spectrum composed of 6 linear functions. For the convenience of processing, 5 triangular functions can actually be used to be equivalent to it. The triangular functions are surrounded by dotted lines and the horizontal axis. These triangular functions all have a certain inflection point as the vertex, and the line connecting two adjacent inflection points is the base (the value is zero). Obviously, the superposition of these triangular functions is exactly the neutron energy spectrum of this piecewise continuous linear function.

[0039] S3. Calculate the matrix B and vector according to the following formula

[0040] The elements of matrix B are:

[0041]

[0042] vector The weight is:

[0043]

[0044] A is the coefficient matrix of the detector's response to neutrons of different energy groups after adding moderators of different sizes, with m rows and n columns, and the element A ij is the response of the i-th (i=1,m) detector to the j-th (j=1,n) energy neutron, cm 2 The detector count rate is expressed as a vector Indicates that y i is the counting rate of the ith detector during the neutron field measurement, σ i is the count rate y of the i-th detector i of error.

[0045] S4. Solve linear equations Conclusion Each component of corresponds to the height of each neutron energy zone distributed in a triangle, that is, the value of each parameter is obtained, and the spectrum decomposition process is completed;

[0046] is the neutron energy spectrum vector, n elements, S j is the injection rate of neutrons of the jth energy in the neutron energy spectrum.

[0047] The process of spectrum decomposition is to determine the actual heights of these triangles. Finally, the neutrons in each energy range are accumulated to obtain the desired neutron energy spectrum. The process of spectrum decomposition is completed by determining the heights of these triangles through spectrum decomposition.

[0048] S5. Based on the parameter values ​​obtained through analysis and calculation, the energy spectrum is output and error analysis is performed, and the calculated detector count, dose, injection amount and other information are obtained.

[0049] Matrix B and vector The derivation process is as follows: Let A be the coefficient matrix of the detector's response to neutrons of different energies after adding moderators of different sizes, with m rows and n columns, and the element A ij is the response of the i-th (i=1,m) detector to the j-th (j=1,n) energy neutron, cm 2 . is the neutron energy spectrum vector, n elements, S j is the neutron flux rate of the jth energy in the neutron energy spectrum. The detector count rate is expressed by the vector Indicates that y i is the counting rate of the ith detector during the neutron field measurement process, then the three satisfy the relationship:

[0050]

[0051] The process of solving the above equations is called spectrum solving. In fact, all measured data have errors. Suppose the count rate of the i-th detector is y i The error σ i When m≥n, the solution of the system of equations can be expressed as finding a set of S j The value is set so that the error F between the calculated counting rate result and the experimental value is minimized, such as:

[0052]

[0053] The above formula is for injection rate s k Find the partial derivative, and we get

[0054]

[0055] To minimize the error F, it should satisfy

[0056]

[0057] Therefore, formula (4) can be written as

[0058]

[0059] Further sorting can be obtained

[0060]

[0061]

[0062] The spectral solution process is transformed into the solution of a linear system of equations with n unknowns and n equations given by equation (5), expressed by matrix multiplication:

[0063]

[0064] The elements of B are:

[0065]

[0066] vector The weight is

[0067]

[0068] According to formulas (7), (8) and (9), the neutron energy spectrum vector is calculated

[0069] like Figure 2 As shown, the energy spectrum obtained by performing energy spectrum analysis on the measurement data of the Am-Be neutron source using the method shown in the embodiment of the present invention is compared with the actual energy spectrum. It can be seen from the figure that the energy spectrum has a high degree of overlap. Although the energy spectrum of the Am-Be neutron source is complex, the analysis result using this method has a high degree of consistency with the standard spectrum, indicating that the spectrum analysis method has a low level of error and high reliability.

[0070] It can be seen from the above embodiments that the multi-sphere neutron spectrometer decomposition method based on parameterized energy spectrum disclosed in the present invention can greatly reduce the dependence on strict initial spectrum in the decomposition process of the multi-sphere neutron spectrometer, has a wide range of applications, and is highly practical. The shapes of the neutron energy spectra of each segment obtained are highly consistent with physical reality, and can be applied to neutron energy spectrum analysis of neutron sources and sites.

[0071] The method described in the present invention is not limited to the embodiments described in the specific implementation manner. Those skilled in the art may derive other implementation manners based on the technical solution of the present invention, which also fall within the technical innovation scope of the present invention.

Claims

1. A multi-sphere neutron spectrometer spectrum analysis method based on parameterized energy spectrum, the method comprising the following steps: S1. Simulate and calculate to obtain the response function of the detector to neutrons of different energies after adding different moderators; S2, dividing the neutron energy spectrum to be measured into n neutron energy groups with specific functional distribution forms, calculating the response functions of m detectors to neutrons in each energy group, and obtaining the response coefficient matrix A; S3. Calculate the matrix B and vector according to the following formula The elements of matrix B are: vector The weight is: The response coefficient matrix A has m rows and n columns, and the element A ij is the response of the i-th detector to the j-th energy neutron, where i = 1······m, j = 1······n, and element A ik is the response of the ith detector to the kth energy neutron, where i = 1······m, k = 1······n, y i is the counting rate of the ith detector during the neutron field measurement, σ i is the count rate y of the i-th detector i The error of S4. Solve linear equations Conclusion That is, the values ​​of each energy spectrum parameter are obtained; S5. According to the energy spectrum parameter values ​​obtained in step S4, output the energy spectrum and perform error analysis to calculate detector count, dose, and injection information.

2. The multi-sphere neutron spectrometer spectrum interpretation method based on parameterized energy spectrum according to claim 1, characterized in that: In step S1, Monte Carlo software is used to perform simulation calculations to obtain the response function of the detector to neutrons of different energies after adding different moderators.

3. The multi-sphere neutron spectrometer spectrum analysis method based on parameterized energy spectrum according to claim 1, characterized in that: The specific function is a triangular function.

4. The multi-sphere neutron spectrometer spectrum analysis method based on parameterized energy spectrum according to claim 1, characterized in that: The specific function is a cosine function.

5. The multi-sphere neutron spectrometer spectrum analysis method based on parameterized energy spectrum according to claim 1, characterized in that: The specific function is Gaussian distribution.

6. The multi-sphere neutron spectrometer spectrum analysis method based on parameterized energy spectrum according to claim 1, characterized in that: The specific function is Maxwell distribution.

7. The multi-sphere neutron spectrometer spectrum analysis method based on parameterized energy spectrum according to claim 1, characterized in that: The number of energy groups n is less than the number of detectors m.

8. The multi-sphere neutron spectrometer spectrum interpretation method based on parameterized energy spectrum according to claim 7, characterized in that: The value range of the energy group number n is: 5≤n≤7.

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