CN114117870A - Feedback type radiation shielding analysis method, system, terminal and medium - Google Patents
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Abstract
The invention discloses a feedback type radiation shielding analysis method, a system, a terminal and a medium, relating to the technical field of radiation shielding, and the key points of the technical scheme are as follows: acquiring a forward solution of forward transport and an accompanying solution of accompanying transport of a radiation region by a determinism method based on an initial multi-group section library; determining a required variance reduction parameter calculated by an MC method according to a forward solution and a concomitant solution of a radiation area; counting and analyzing the forward transport count of the MC method to generate nuclear reaction macroscopic cross sections of the materials in each space area, feeding the nuclear reaction macroscopic cross sections back to the initial multi-group cross section library, and forming an updated multi-group cross section library in the same format; and (4) carrying out forward transport and accompanying transport calculation again according to the updated multi-group section library, and outputting a radiation field spatial distribution result obtained by forward transport calculation of the MC method after iteration for multiple times. The invention can avoid the problems of rough calculation results caused by using a determinism method alone and no counting or technical non-convergence in the deep penetration problem by using an MC method alone.
Description
Technical Field
The invention relates to the technical field of radiation screens, in particular to a feedback type radiation shielding analysis method, a feedback type radiation shielding analysis system, a feedback type radiation shielding analysis terminal and a feedback type radiation shielding analysis medium.
Background
In the fields of scientific research and engineering practice, the accurate and efficient radiation shielding analysis method has important research value and engineering application value. For the deep penetration radiation shielding problem, the determinism method has rough calculation results due to the accuracy problem of a plurality of groups of section libraries, the calculation results of the Monte Carlo (MC) simulation method of continuous energy are accurate, but the problem that the concerned area has no count or the count is not converged occurs in the deep penetration problem solving process. In order to realize accurate deep penetration radiation shielding analysis, a great deal of research work is carried out in the field at home and abroad.
In 1963, Kalos indicated that there was an importance function that could direct MC sampling to make the statistics zero variance. Based on different understandings of the importance function, several important variance reduction techniques are proposed: (1) in 1998, Wagner et al proposed a CADIS method, which is applicable to source-detector problems and source-local solution problems, and calculates the adjoint function of the problem by a deterministic method, and designs corresponding weight window parameters to guide MC simulation to accelerate convergence at the detector; (2) in 2001, Cooper proposed a flat sampling technique for the global solution problem, which considers that the statistics converge in all phase space cells, requiring that the intra-cell MC particle density be sufficiently high and controlling the dispersion of the intra-cell particle weights; (3) in 2007, Wagner et al combined the global variance reduction idea of Cooper with the CADIS method, and proposed an FW-CADIS method suitable for global solution problem; (4) in 2009, based on forward calculation results of determinants, Becker proposes a Global Flux Weight Window (GFWW) method and a Global Response Weight Window (GRWW) method, and generalizes the global variance reduction method of Cooper from standard flux to an energy-space cellular level; (5) in the same year, Becker estimates a target weight window through a particle value flow calculated by a deterministic theory, makes an assumption that the standard flux is positively correlated with the particle density, and develops flux deviation flattening and response deviation flattening technologies; (6) in 2016, Berkeley university popularized the FW-CADIS method from energy-space cells to energy-space-angle cell level, which was very high in both memory requirements and computational cost.
The above-described hybrid computation variance reduction techniques have a common theoretical basis, namely that deterministic computations are used to generate importance functions that can be used to guide the computation of MC. However, in practice, the deterministic method can only use a plurality of groups of section parameters, which are different from the MC method in which the core sections of continuous energy are used, so that the importance function generated by the deterministic calculation is not matched with the MC method calculation model, and the calculation accuracy and the analysis capability of the hybrid method in the deep penetration shielding are limited.
Disclosure of Invention
In order to solve the defects in the prior art, the invention aims to provide a feedback type radiation shielding analysis method, a system, a terminal and a medium, wherein the method has the characteristics of nuclear reaction section feedback and database self-adaption and can overcome the limitation problem of deep penetration shielding calculation capacity caused by inconsistency of a plurality of groups of section libraries and a continuous energy section library.
The technical purpose of the invention is realized by the following technical scheme:
in a first aspect, a feedback radiation shielding analysis method is provided, which includes the following steps:
acquiring a forward solution of forward transport and an accompanying solution of accompanying transport of a radiation region by a determinism method based on an initial multi-group section library;
determining a required variance reduction parameter calculated by an MC method according to a forward solution and a concomitant solution of a radiation area;
counting and analyzing the forward transport count of the MC method to generate nuclear reaction macroscopic cross sections of the materials in each space area, feeding the nuclear reaction macroscopic cross sections back to the initial multi-group cross section library, and forming an updated multi-group cross section library in the same format;
and carrying out forward transport and accompanying transport calculation again according to the updated multi-group section library until the difference between the continuous section library used by the MC method and the multi-group section library used by the determinism method is reduced by iterative updating for many times, and outputting a radiation field space distribution result obtained by forward transport calculation of the MC method.
Further, the solving equation of the forward transport is specifically as follows:
wherein H represents a neutron forward transport operator;
represents the neutron fluence rate;
representing a neutron state phase space; q represents the external neutron source intensity;
representing a spatial gradient operator;
a unit vector representing a neutron motion direction after a collision;
representing a spatial location; e represents the neutron energy after impact;
represents the total cross-section of the neutron interaction with the medium;
a scattering cross-section representing the interaction of neutrons with the medium;
representing pre-impact neutron energy;
a unit vector representing the direction of neutron motion before impact.
Further, the accompanying solution acquisition process accompanying transportation specifically includes: and solving and acquiring by a deterministic method based on the initial multi-group section library and the forward solution of the radiation area.
Further, the solution equation for the accompanying transport is specifically:
wherein the content of the first and second substances,
representing a neutron companion transport operator;
representing the neutron fluence rate;
representing a neutron state phase space;
representing the incidental neutron source intensity;
representing a spatial gradient operator;
a unit vector representing a neutron motion direction after a collision;
representing a spatial location; e represents the neutron energy after impact;
represents the total cross-section of the neutron interaction with the medium;
a scattering cross-section representing the interaction of neutrons with the medium;
representing pre-impact neutron energy;
a unit vector representing the direction of neutron motion before impact.
Further, the determinism method is a discrete ordinate method SNSpherical harmonic method RNThe characteristic line method MOC, the penetration probability method TPM, the collision probability method CPM and the finite element method.
Further, the variance reduction parameters required for the calculation by the MC method include a source bias parameter and a weight window parameter.
Further, the nuclear reaction macroscopic cross section comprises a total cross section, an absorption cross section and a scattering cross section, and the calculation formulas of the total cross section, the absorption cross section and the scattering cross section are specifically as follows:
wherein the content of the first and second substances,
represents a nuclear reaction cross section;
representing the nuclear reaction section types including a total section, an absorption section and a scattering section; d represents the space region; g represents a neutron n energy group number;
for summation coincidence, the index i represents the ith neutron history, the index j represents the jth track in the history, and the jth free flight;
represents the weight of the ith neutron j trajectory;
represents the energy of the ith neutron j trajectory;
representing the track length of the ith neutron j track;
for an illustrative function, the value of a neutron in the space D is 1 when the energy group number is g, otherwise, the value is 0.
In a second aspect, a feedback radiation shielded analysis system is provided, comprising:
the solution calculation module is used for obtaining a forward solution of forward transport and an accompanying solution of accompanying transport of the radiation region by a determinism method based on the initial multi-group section library;
the parameter determining module is used for determining a variance reducing parameter required by calculation of the MC method according to the forward solution and the concomitant solution of the radiation area;
the iteration updating module is used for counting and analyzing the counting in the forward transport of the MC method, generating a nuclear reaction macroscopic cross section of the material in each space region, feeding the nuclear reaction macroscopic cross section back to the initial multi-group cross section library and then forming an updated multi-group cross section library in the same format;
and the updating calculation module is used for carrying out forward transport and accompanying transport calculation again according to the updated multi-group section library until the continuous section library used by the MC method and the multi-group section library used by the determinism method are subjected to iterative updating for multiple times, and then the radiation field space distribution result obtained by forward transport calculation of the MC method is output.
In a third aspect, there is provided a computer terminal comprising a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement a method of feedback radiation shielding analysis as set forth in any one of the first aspect.
In a fourth aspect, there is provided a computer readable medium having a computer program stored thereon, wherein the computer program is executed by a processor to implement a method for feedback radiation shielding analysis according to any of the first aspect.
Compared with the prior art, the invention has the following beneficial effects:
1. the feedback type radiation shielding analysis method provided by the invention can avoid the problems of rough calculation results caused by independently using a determinism method and no counting or technical non-convergence in the deep penetration problem caused by independently using an MC method;
2. the method can break through the limitation that the shielding calculation result is not converged due to inconsistency of the multi-group database and the continuous energy database;
3. the invention can realize the self-adaptive calculation of deep penetration shielding analysis;
4. the invention can effectively meet the requirements of large-scale, deep penetration and high-precision radiation shielding analysis in scientific research and engineering.
Drawings
The accompanying drawings, which are included to provide a further understanding of the embodiments of the invention and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the invention and together with the description serve to explain the principles of the invention. In the drawings:
FIG. 1 is a flow chart in an embodiment of the invention;
fig. 2 is a block diagram of a system in an embodiment of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to examples and accompanying drawings, and the exemplary embodiments and descriptions thereof are only used for explaining the present invention and are not meant to limit the present invention.
Example 1: a feedback radiation shielding analysis method, as shown in fig. 1, comprising the steps of:
s1: acquiring a forward solution of forward transport and an accompanying solution of accompanying transport of a radiation region by a determinism method based on an initial multi-group section library;
s2: determining a required variance reducing parameter by combining a variance reducing parameter making program with a forward solution and an adjoint solution of a radiation area; the variance reduction parameters required by the MC method calculation comprise a source bias parameter and a weight window parameter;
s3: counting and analyzing the forward transport count of the MC method to generate nuclear reaction macroscopic cross sections of the materials in each space area, feeding the nuclear reaction macroscopic cross sections back to the initial multi-group cross section library, and forming an updated multi-group cross section library in the same format; accurately obtaining the nuclear reaction macroscopic cross section of each material after simulation of a certain sample number source particles;
s4: and (4) carrying out forward transport and accompanying transport calculation again according to the updated multi-group section library until the iteration is updated for N-1 (N is a natural number, and N is more than or equal to 1) times, so that the difference between the continuous section library used by the MC method and the multi-group section library used by the determinism method is reduced, and outputting a radiation field space distribution result obtained by the forward transport calculation of the MC method after the Nth iteration is finished.
The forward transport solution equation specifically comprises:
wherein H represents a neutron forward transport operator;
represents the neutron fluence rate;
representing a neutron state phase space; q represents the external neutron source intensity;
representing a spatial gradient operator;
a unit vector representing a neutron motion direction after a collision;
representing a spatial location; e represents the neutron energy after impact;
represents the total cross-section of the neutron interaction with the medium;
representing the scattering cross section of a neutron interacting with the medium.
In addition, the adjoint solution acquisition of adjoint transportation is solved by a determinism method based on the initial multi-group section library and the forward solution of the radiation area.
The solution equation accompanying the transport is specifically:
wherein the content of the first and second substances,
representing a neutron companion transport operator;
representing the neutron fluence rate;
indicating the accompanying neutron source intensity.
In the present embodiment, the determinism method is the discrete ordinate method SNSpherical harmonic method RNThe characteristic line method MOC, the penetration probability method TPM, the collision probability method CPM and the finite element method.
The nuclear reaction macroscopic cross section comprises a total cross section, an absorption cross section and a scattering cross section, and the calculation formulas of the total cross section, the absorption cross section and the scattering cross section are as follows:
wherein the content of the first and second substances,
represents a nuclear reaction cross section;
represents a nuclear reaction cross sectionTypes including total cross-section, absorption cross-section, scattering cross-section; d represents the space region; g represents a neutron n energy group number;
for summation coincidence, the index i represents the ith neutron history, the index j represents the jth track in the history, and the jth free flight;
represents the weight of the ith neutron j trajectory;
represents the energy of the ith neutron j trajectory;
representing the track length of the ith neutron j track;
for an illustrative function, the value of a neutron in the space D is 1 when the energy group number is g, otherwise, the value is 0.
Example 2: a feedback radiation shielding analysis system, as shown in fig. 2, includes a solution calculation module, a parameter determination module, an iterative update module, and an update calculation module.
The solving and calculating module is used for obtaining a forward solution of forward transport and an accompanying solution of accompanying transport of a radiation region by a determinism method based on an initial multi-group section library; the parameter determining module is used for determining a variance reducing parameter required by calculation of the MC method according to the forward solution and the concomitant solution of the radiation area; the iteration updating module is used for counting and analyzing the counting in the forward transport of the MC method, generating a nuclear reaction macroscopic cross section of the material in each space region, feeding the nuclear reaction macroscopic cross section back to the initial multi-group cross section library and then forming an updated multi-group cross section library in the same format; and the updating calculation module is used for carrying out forward transport and accompanying transport calculation again according to the updated multi-group section library until the continuous section library used by the MC method and the multi-group section library used by the determinism method are subjected to iterative updating for multiple times, and then the radiation field space distribution result obtained by forward transport calculation of the MC method is output.
The working principle is as follows: the invention provides a feedback type radiation shielding analysis method combining a determinism method and a Monte Carlo (MC) method, which solves a forward solution and an accompanying solution of a concerned radiation area through the determinism method, establishes a forward transport calculation model parameter for the MC method, further iteratively updates a multi-group section library used by the determinism method through the MC method, establishes a new MC method forward transport calculation model parameter by using the updated multi-group section library, and finally obtains a calculation result through continuous energy MC forward transport calculation.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may 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, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The above embodiments are provided to further explain the objects, technical solutions and advantages of the present invention in detail, it should be understood that the above embodiments are merely exemplary embodiments of the present invention and are not intended to limit the scope of the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (10)
1. A feedback type radiation shielding analysis method is characterized by comprising the following steps:
acquiring a forward solution of forward transport and an accompanying solution of accompanying transport of a radiation region by a determinism method based on an initial multi-group section library;
determining a required variance reduction parameter calculated by an MC method according to a forward solution and a concomitant solution of a radiation area;
counting and analyzing the forward transport count of the MC method to generate nuclear reaction macroscopic cross sections of the materials in each space area, feeding the nuclear reaction macroscopic cross sections back to the initial multi-group cross section library, and forming an updated multi-group cross section library in the same format;
and carrying out forward transport and accompanying transport calculation again according to the updated multi-group section library until the difference between the continuous section library used by the MC method and the multi-group section library used by the determinism method is reduced by iterative updating for many times, and outputting a radiation field space distribution result obtained by forward transport calculation of the MC method.
2. The method of claim 1, wherein the forward transport solution equation is specifically:
wherein H represents a neutron forward transport operator;
represents the neutron fluence rate;
representing a neutron state phase space; q represents the external neutron source intensity;
representing a spatial gradient operator;
a unit vector representing a neutron motion direction after a collision;
representing a spatial location; e represents the neutron energy after impact;
represents the total cross-section of the neutron interaction with the medium;
a scattering cross-section representing the interaction of neutrons with the medium;
representing pre-impact neutron energy;
a unit vector representing the direction of neutron motion before impact.
3. The method of claim 1, wherein the acquisition of the solution accompanying the transport is specifically: and solving and acquiring by a deterministic method based on the initial multi-group section library and the forward solution of the radiation area.
4. The method of claim 1, wherein the equation for solving for the adjoint transport is specifically:
wherein the content of the first and second substances,
representing a neutron companion transport operator;
representing the neutron fluence rate;
representing a neutron state phase space;
representing the incidental neutron source intensity;
representing a spatial gradient operator;
a unit vector representing a neutron motion direction after a collision;
representing a spatial location; e represents the neutron energy after impact;
represents the total cross-section of the neutron interaction with the medium;
a scattering cross-section representing the interaction of neutrons with the medium;
representing pre-impact neutron energy;
a unit vector representing the direction of neutron motion before impact.
5. A method according to any of claims 1-4, characterized in that the determinism is the discrete ordinate method SNSpherical harmonic method RNThe characteristic line method MOC, the penetration probability method TPM, the collision probability method CPM and the finite element method.
6. The method of any of claims 1-4, wherein the variance reduction parameters required for the MC method to calculate comprise source bias parameters and weight window parameters.
7. The method according to any one of claims 1 to 4, wherein the nuclear reaction macroscopic cross section includes a total cross section, an absorption cross section and a scattering cross section, and the calculation formula of the total cross section, the absorption cross section and the scattering cross section is specifically as follows:
wherein the content of the first and second substances,
represents a nuclear reaction cross section;
representing the nuclear reaction section types including a total section, an absorption section and a scattering section; d represents the space region; g represents a neutron n energy group number;
for summation coincidence, the index i represents the ith neutron history, the index j represents the jth track in the history, and the jth free flight;
represents the weight of the ith neutron j trajectory;
represents the energy of the ith neutron j trajectory;
representing the track length of the ith neutron j track;
for an illustrative function, the value of a neutron in the space D is 1 when the energy group number is g, otherwise, the value is 0.
8. A feedback radiation shielded analysis system, comprising:
the solution calculation module is used for obtaining a forward solution of forward transport and an accompanying solution of accompanying transport of the radiation region by a determinism method based on the initial multi-group section library;
the parameter determining module is used for determining a variance reducing parameter required by calculation of the MC method according to the forward solution and the concomitant solution of the radiation area;
the iteration updating module is used for counting and analyzing the counting in the forward transport of the MC method, generating a nuclear reaction macroscopic cross section of the material in each space region, feeding the nuclear reaction macroscopic cross section back to the initial multi-group cross section library and then forming an updated multi-group cross section library in the same format;
and the updating calculation module is used for carrying out forward transport and accompanying transport calculation again according to the updated multi-group section library until the continuous section library used by the MC method and the multi-group section library used by the determinism method are subjected to iterative updating for multiple times, and then the radiation field space distribution result obtained by forward transport calculation of the MC method is output.
9. A computer terminal comprising a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement a method of feedback radiation shielding analysis according to any of claims 1 to 7.
10. A computer-readable medium, on which a computer program is stored which, when being executed by a processor, is adapted to carry out a method of feedback radiation shielding analysis according to any one of claims 1 to 7.
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