CN116070533B - Neutron energy spectrum determination method - Google Patents
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Abstract
The embodiment of the application discloses a method for determining neutron energy spectrum. The determining method comprises the following steps: step S10, constructing a generalized neural network, wherein the input of the generalized neural network is the reaction rate of an activation detector, and the output of the generalized neural network is neutron energy spectrum; step S20, placing a plurality of activation detectors with known reaction cross sections in a region to be detected of a target reactor, and obtaining a reaction rate measured value of each activation detector; step S30, inputting the measured value of the reaction rate of each activation detector into a generalized neural network, and outputting a reconstructed spectrum by the generalized neural network; and S40, determining neutron energy spectrum of the region to be detected according to the reconstructed spectrum, the reaction cross section of each activation detector and the measured value of the reaction rate. Compared with the traditional iterative method spectrum decomposition, the method does not need to rely on an initial spectrum, can perform more accurate spectrum decomposition calculation under the condition of no initial spectrum, and has more accurate result compared with the general fission spectrum serving as the initial spectrum.
Description
Technical Field
The embodiment of the application relates to the technical field of neutron energy spectrum of reactors, in particular to a method for determining neutron energy spectrum.
Background
Neutron energy spectrum is one of the important parameters in reactor design, physical analysis, and various experimental studies, and it is critical for reactor critical state and burnup analysis to measure neutron energy spectrum accurately and rapidly. Accurate measurement of neutron energy spectrum has been a difficult problem due to the complexity of the neutron energy spectrum of the reactor and the harshness of the measurement environment.
Currently, the neutron spectrum measurement means mainly include a time-of-flight method, an organic scintillator measurement method, a multi-sphere spectrometer method, a detection foil activation method and the like. Except the time-of-flight method, all the other three measurement methods can not directly measure and acquire neutron energy spectrum, but need to solve according to the measured value of the detection system to acquire neutron energy spectrum, namely, perform spectrum solving calculation.
However, current solution spectrum methods, such as iterative methods, least squares methods, mostly rely on the initial spectrum, and if the initial spectrum shape does not conform to the shape of the real spectrum, then the correct solution result cannot be obtained. In practice, it is difficult to obtain reliable initial spectrum information, and particularly for a novel reactor, it is difficult to solve the spectrum because an accurate initial spectrum cannot be obtained.
Disclosure of Invention
According to one aspect of the application, a method of determining neutron energy spectrum is provided. The determining method comprises the following steps: step S10, constructing a generalized neural network, wherein the input of the generalized neural network is the reaction rate of an activation detector, and the output of the generalized neural network is neutron energy spectrum; step S20, placing a plurality of activation detectors with known reaction cross sections in a region to be detected of a target reactor, and obtaining a reaction rate measured value of each activation detector; step S30, inputting the measured value of the reaction rate of each activation detector into a generalized neural network, and outputting a reconstructed spectrum by the generalized neural network; and S40, determining neutron energy spectrum of the region to be detected according to the reconstructed spectrum, the reaction cross section of each activation detector and the measured value of the reaction rate.
The determining method in the embodiment of the application combines a generalized neural network algorithm and an iterative algorithm to realize the spectrum solving calculation of neutron energy spectrum. Compared with the traditional iterative method spectrum decomposition, the method has the advantages that the original spectrum is not required to be relied on, the reconstructed spectrum is obtained by using the generalized neural network algorithm and is used as one of input files of the iterative algorithm, more accurate spectrum decomposition calculation is carried out under the condition that the original spectrum is not available, and compared with the general fission spectrum which is used as the original spectrum, the result is more accurate.
Drawings
Other objects and advantages of the present application will become apparent from the following description of embodiments of the present application, which is to be read in connection with the accompanying drawings, and may assist in a comprehensive understanding of the present application.
FIG. 1 is a flow chart of a method of determining neutron spectrum according to one embodiment of the application.
Fig. 2 is a schematic flow diagram of constructing a generalized neural network according to one embodiment of the present application.
FIG. 3 is a schematic flow chart of extracting neutron spectrum data according to one embodiment of the application.
FIG. 4 is a schematic flow chart of a process for producing a reaction cross-section according to one embodiment of the application.
Fig. 5 is a schematic structural view of a generalized neural network according to an embodiment of the present application.
FIG. 6 is a flow chart of an iterative method for determining neutron energy spectrum according to one embodiment of the application.
It should be noted that the drawings are not necessarily to scale, but are merely shown in a schematic manner that does not affect the reader's understanding.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the technical solutions of the present application will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present application. It will be apparent that the described embodiments are one embodiment, but not all embodiments, of the present application. All other embodiments, which can be made by a person skilled in the art without creative efforts, based on the described embodiments of the present application fall within the protection scope of the present application.
It is to be noted that unless otherwise defined, technical or scientific terms used herein should be taken in a general sense as understood by one of ordinary skill in the art to which the present application belongs. If, throughout, reference is made to "first," "second," etc., the description of "first," "second," etc., is used merely for distinguishing between similar objects and not for understanding as indicating or implying a relative importance, order, or implicitly indicating the number of technical features indicated, it being understood that the data of "first," "second," etc., may be interchanged where appropriate. If "and/or" is present throughout, it is meant to include three side-by-side schemes, for example, "A and/or B" including the A scheme, or the B scheme, or the scheme where A and B are satisfied simultaneously. Furthermore, for ease of description, spatially relative terms, such as "above," "below," "top," "bottom," and the like, may be used herein merely to describe the spatial positional relationship of one device or feature to another device or feature as illustrated in the figures, and should be understood to encompass different orientations in use or operation in addition to the orientation depicted in the figures.
When the traditional iterative algorithm is used for spectrum decomposition, the initial spectrum is required to be relied on, and the reliable initial spectrum which is more consistent with the actual is difficult to obtain in practice, especially for some novel reactors. And when a universal fissile spectrum is used as an initial spectrum, inaccurate results obtained by spectrum calculation are easy to cause. Therefore, the embodiment of the application provides a neutron spectrum decomposition method, which uses a generalized neural network algorithm to obtain a reconstructed spectrum as one of input files of an iterative algorithm, and can also perform more accurate spectrum decomposition calculation under the condition of no initial spectrum, and compared with the general fission spectrum as the initial spectrum, the result is more accurate.
FIG. 1 shows a flow diagram of a method of determining neutron energy spectrum according to one embodiment of the application. As shown in fig. 1, the determination method in the present embodiment specifically includes steps S10 to S40.
Step S10, a generalized neural network is constructed, the input of the generalized neural network is the reaction rate of the activation detector, and the output is neutron energy spectrum.
And step S20, placing a plurality of activation detectors with known reaction cross sections in the region to be detected of the target reactor, and obtaining the measured value of the reaction rate of each activation detector.
Step S30, the measured value of the reaction rate of each activation detector is input into a generalized neural network, and the generalized neural network outputs a reconstructed spectrum.
And S40, determining neutron energy spectrum of the region to be detected according to the reconstructed spectrum, the reaction cross section of each activation detector and the measured value of the reaction rate.
Compared with the traditional iterative method spectrum decomposition, the method for determining the neutron spectrum can obtain the accurate neutron spectrum without depending on the initial spectrum. The method is wider in application range and suitable for determining neutron energy spectrum at each position of the novel reactor of various reactor types enveloped by the early database. For the work of needing to perform a large amount of spectrum decomposition, the method can save a large amount of time for accurately calculating the initial spectrum in the earlier stage.
In some embodiments, as shown in fig. 2, step S10 includes: step S11, a neutron spectrum data set is established; and S13, constructing a generalized neural network, and training and verifying the generalized neural network by using the neutron spectrum data set. In order to obtain a relatively accurate generalized neural network, the embodiment establishes a data set containing a large amount of neutron spectrum data, and trains and verifies the generalized neural network by using the data set, so that the generalized neural network is optimized, and a relatively accurate prediction result can be output.
Specifically, in step S11, a reactor having a similarity with the target reactor greater than a threshold is first selected, and the reactor is simulated to obtain a plurality of neutron spectrums of a region in the reactor that matches with the region to be measured; then, selecting a plurality of standard neutron spectrums from a standard neutron spectrum database; finally, a plurality of neutron spectra and a plurality of standard neutron spectra are established as neutron spectrum datasets. It should be noted that, the threshold value of the similarity may be set according to the actual situation, and the embodiment of the present application is not limited.
In this embodiment, a reactor similar to the target reactor is first selected, and modeling is performed on the reactor to simulate neutron energy spectra at different positions of the reactor, so that neutron energy spectrum data which is more consistent with the target reactor is obtained to train and verify the generalized neural network, and a more accurate generalized neural network is obtained, so that the shortage of the number of true spectrums in a training sample is avoided. In addition, in the embodiment, a plurality of standard neutron energy spectrums are selected from the standard neutron energy spectrum database and added into the data set, so that the diversity of the neutron energy spectrums in the data set can be increased.
In some embodiments, the neutron spectrum at different locations of the reactor may be simulated using a monte carlo procedure. Because the neutron energy spectrum difference at different areas of the reactor core is large, different areas need to be distinguished, and neutron energy spectrum data sets are established for the different areas, so that the neutron energy spectrum data sets can be matched with the areas to be detected.
Specifically, when the reactor is simulated, the region in the reactor, which is matched with the region to be detected in the target reactor, is divided into N grids, and the neutron spectrum energy interval corresponding to each grid is divided into M energy groups, so that M multiplied by N neutron energy spectrums are obtained. Neutron spectrum data is obtained by the method, and the statistical error is within 5%.
Further, since the neutron spectrum data amount obtained by modeling is larger, in order to reduce the time for extracting the neutron spectrum data from the generalized neural network, the step S10 further includes: step S12, an extraction program is compiled to extract neutron spectrum data. Specifically, a Mesh2data program may be programmed using MATLAB to extract the above-described mxn neutron spectrum data.
Referring to fig. 3, a neutron spectrum data file is first read, and in this embodiment, the neutron spectrum data file is a merwtan file output by a monte carlo program. Then, the number of divisions of the three-dimensional mesh and the number of energy interval segments (i.e., the number of energy clusters) are identified. In this embodiment, the number of divisions of the three-dimensional mesh is N, and the number of energy section divisions is M. And then reading the data row by row, writing the coordinates (namely, the coordinates of X, Y, Z axes) of the three-dimensional grid, the energy group and neutron flux information in each row of data into a data array until the end of the file is reached, and deriving the data array into an Excel file.
In some embodiments, the standard neutron spectrum data is internationally disclosed neutron spectrum data, and L standard neutron spectrums are selected from the standard neutron spectrum data, wherein the selected standard neutron spectrums have the same energy group structure as the neutron energy spectrum of the similar pile type. Specifically, L standard neutron spectrums can be selected from a standard neutron spectrum database disclosed by an international atomic energy organization (IAEA), for example, L standard neutron spectrums in an IAEA 318 th report can be selected and added into an established neutron spectrum data set to obtain a neutron spectrum data set containing m×n+l neutron spectrums.
Further, M multiplied by N+L neutron energy spectrums in the neutron energy spectrum data set are used as training samples and test samples of the generalized neural network, and the generalized neural network is trained and verified, so that the structure of the generalized neural network is optimized.
In some embodiments, in constructing the generalized neural network, the reactivity of the activation detector is first calculated from the neutron spectrum dataset and the reaction cross section of the activation detector. And then, taking the reaction rate and neutron spectrum data set of the activation detector as a training sample and a testing sample, taking a Gaussian function as a radial basis function of the generalized neural network, training and testing the generalized neural network, and optimizing the generalized neural network. When the generalized neural network is trained, the input value of the generalized neural network is the reaction rate of n activation detectors, and the output value of the generalized neural network is the neutron energy spectrum with the energy group m in the neutron energy spectrum data set.
Wherein, when calculating the input value of the generalized neural network (i.e. the reaction rate of the activation detector), the reaction section of the used activation detector can be produced by the NJOY program. Specifically, referring to fig. 4, in step S101, resonance reconstruction is performed using interpolation based on resonance parameters provided in the ECDF core database, reconstructing an energy-based point section. In step S102, doppler broadening is performed on the point section and the point section is thinned. In step S103, a neutron thermalization treatment is performed on the point cross section. In step S104, data processing is performed on the unresolved resonance region, and a self-screen dot cross section in the unresolved resonance region is calculated. Finally, in step S105, a group average reaction cross section, a self-shielded multi-group cross section, a KERMA coefficient, and the like are generated.
A generalized neural network (GRNN) is a feedforward neural network based on a nonlinear regression theory, and is structurally composed of an input layer, a pattern layer, a summation layer, and an output layer, as shown in fig. 5. GRNN is suitable for small sample, high precision prediction. According to the embodiment of the application, the relation between neutron energy spectrum and the reaction rate of the activation detector is trained through a generalized neural network algorithm, a reconstructed spectrum is generated and is used as an initial spectrum for iterative decomposition, the accuracy is similar to a theoretical spectrum, and the neural network model is superior to the theoretical spectrum.
In this embodiment, when the generalized neural network is constructed, first, input and output of the generalized neural network are determined, and the hidden layer and output layer forward neural network is constructed. The input is the reaction rate of n activation detectors, and the output is the neutron energy spectrum with the energy group of m. Since the change of the diffusion length of the radial basis function has a great influence on the GRNN, the embodiment optimizes the diffusion length through training and verification, so that the spectrum resolution result has higher accuracy.
In some embodiments, when training and testing the generalized neural network, the input values are first normalized by maximum segmentation, so as to eliminate errors caused by dimension. And then training and testing the generalized neural network by using the normalized input value and using a 4 k-time cross validation method to determine the optimal value of the diffusion length of the generalized neural network, so as to obtain the optimized generalized neural network and improve the accuracy of the reconstructed spectrum.
When the generalized neural network is trained and tested by a 4 k-time cross validation method to determine the optimal value of the diffusion length of the generalized neural network, three-fourths of the data in the neutron spectrum data set and the response rate of the corresponding activation detector are used as training samples to train the generalized neural network. And then, taking the neutron spectrum data set and the residual data in the response rate of the corresponding activation detector as test samples, and testing the generalized neural network to evaluate the performance of the trained neural network. Wherein, the diffusion length takes the value in 0.01 increment in the range of 0 to 2, the generalized neural network is trained and tested for multiple times in a circulating way, and the optimal value of the diffusion length is determined.
Specifically, the neutron spectrum data set and the response rate of the corresponding activation detector are taken as samples, the sample data are divided into 4k parts, 3k parts of the sample data are selected in turn as training samples to train, the remaining k parts are taken as test samples to test to evaluate the performance, and the diffusion length is optimized from 0 to 2 in 0.01 increments. Each group of training samples corresponds to different test samples and diffusion lengths, so that the generalized neural network is circularly trained and verified.
In this embodiment, in order to evaluate the performance for GRNN, after training the generalized neural network, the response rate of the activation probe in the test sample is input into the trained generalized neural network to obtain the output value. Then, the mean square error between the output value and the expected value is compared. Wherein the expected value is neutron spectrum in the test sample. And selecting a diffusion length value corresponding to the minimum mean square error as an optimal value, and constructing and obtaining the generalized neural network. In embodiments of the present application, the trained GRNN shows high efficiency and generalization capability when performing a mesospectral analysis.
Further, after the GRNN is constructed, the measured values of the reaction rates of the plurality of activated detectors in the region to be measured can be input into the GRNN, and the reconstructed spectrum output by the GRNN can be used as an initial spectrum of an iterative spectrum decomposition process. The reconstructed spectrum is neutron energy spectrum calculated and output by the generalized neural network according to the measured value of the reaction rate. In this embodiment, the activation detector used may be an activation detection foil.
As shown in fig. 6, in the present embodiment, an iterative solution spectroscopy may be utilized to determine neutron energy spectrum. Specifically, step S40 includes the following steps S42 to S47.
Step S42, dividing the neutron spectrum energy interval of the region to be measured into m energy groups, and setting the reconstructed spectrum as the initial neutron spectrumThe reaction cross section sigma of the ith activation probe from the reconstructed spectrum i (E) Calculating the calculated value of the reactivity of the ith activation detector at the jth energy group after the kth iteration +.>
Specifically, if the measurement is performed using n activation probes whose reaction cross sections are known, the following n sets of linear equations (1) independent of each other can be obtained.
Wherein i=1, 2, … n, n is the number of activated detectors for measuring the area to be measured; j=1, 2, …m, m is the number of divided energy intervals (i.e., the number of energy clusters); k represents the iteration number, and K is more than or equal to 0;the neutron energy spectrum of the j energy group after the K iteration.
In some embodiments, when the divided energy intervals are small, the average reaction cross-section at the jth energy group may be used with the ith activation detectorInstead of the reaction cross section sigma i (E) Calculating the calculated value of the reaction rate +.>At this time, the calculated reaction rate value may be calculated using the following formula (2)>
Step S43, calculating a value according to the reaction rateCalculating the total reaction rate calculation value of the ith activation detector after the kth iteration +.>Specifically, the total reaction rate may be calculated using the following formula (3).
Step S44, calculating a value according to the total reaction rateIth activation probeThe measured value A of the reaction rate obtained by measuring the measuring instrument i Calculating correction factor of the jth energy group at the kth iteration->
Specifically, in step S44, a value is first calculated from the total reaction rateThe reaction rate measured value A measured by the ith activation detector i Calculating a measured value A of the reaction rate i Calculated value of reaction rate after the K-th iteration +.>Ratio of (2)The ratio can be calculated using the following equation (4).
Then, according to the calculated value of the reaction rateAnd total reaction Rate->Calculating the weight of the ith activation detector in the jth energy group after the kth iteration +.>Wherein the weight function formula (5) is as follows.
According to the weightSum ratio->Calculating correction factor of jth energy group at the time of Kth iteration>The correction factor can be expressed by the following formula (6).
Step S45, correcting the neutron energy spectrum after the K iteration according to the correction factor to obtain the K+1st corrected neutron energy spectrumThe k+1st modified neutron spectrum can be calculated using the following equation (7).
And step S47, stopping iteration until reaching a convergence standard for ending the iteration, and obtaining a neutron energy spectrum of the region to be detected.
As shown in FIG. 6, in some embodiments, step S40 further includes step S46, i.e., after obtaining the K+1st modified neutron spectrum, the K-th modified neutron spectrum is usedCalculated value of the reaction rate->Correction of the mean reaction cross section of the ith activation probe at the kth iteration +.>Obtaining the average reaction cross section +.1 at the K+1th iteration>
It should be noted that, in the conventional iterative method spectrum resolving process, the average reaction section of each activation detector in the j-th energy group is a constant value. However, in fact, after each iteration, the average reaction cross section corresponding to the neutron spectrum after adjustment also changes, so this embodiment corrects the average reaction cross section by using the following formula (8), and the corrected average reaction cross section of the k+1st iteration is used for the correction iteration of the k+1st neutron spectrum.
In some embodiments, step S40 further includes step S41 of setting at least one convergence criterion. Meanwhile, in step S47, when one of the convergence criteria is satisfied, the iteration may be stopped, and a final neutron spectrum may be obtained.
Specifically, the convergence criterion includes at least one of: the standard deviation of the calculated reaction rate and the measured reaction rate is controlled, the convergence speed is controlled, and the maximum iteration number is controlled.
In some embodiments, the standard deviation of the calculated reaction rate from the measured reaction rate is controlled, i.e., the standard deviation Q of the calculated reaction rate from the measured reaction rate is controlled K Less than or equal to the deviation threshold epsilon Q . Wherein the deviation threshold epsilon Q To the convergence criterion preset in step S41, Q K Is represented by the following formula (9).
Due to Q K The decrease in value slows down as the number of iterations increases, ε Q The value of (2) is determined according to the number of the selective activation detectors, the measurement accuracy of the reaction rate and the uncertainty of the reaction cross section.
In some embodiments of the present application, in some embodiments,the convergence speed can be controlled to be smaller than the speed threshold epsilon D . The convergence rate may be represented by a difference between differential spectrums of two adjacent iterations of each energy group, as shown in equation (10).
In the speed threshold epsilon D Is a convergence criterion preset in step S41. Stopping iteration when the formula (10) is established, and obtaining neutron energy spectrum of the region to be detected as
In some embodiments, the maximum number of iterations K may be controlled max Maximum number of iterations K max The convergence criterion set in advance in step S41. When the maximum number of iterations K is exceeded max And when the neutron energy spectrum obtained in the last iteration is the neutron energy spectrum of the region to be detected.
It should be noted that in some embodiments, the iteration may be stopped when any of the above three convergence criteria are met. In addition, the convergence criterion can be flexibly selected according to the reaction rate, the energy group number, the reconstruction spectrum and other factors of the activation detector.
It should also be noted that, in the embodiments of the present application, the features of the embodiments of the present application and the features of the embodiments of the present application may be combined with each other to obtain new embodiments without conflict.
The present application is not limited to the above embodiments, but the scope of the application is defined by the claims.
Claims (13)
1. A method of determining neutron energy spectrum, comprising:
s10, constructing a generalized neural network, wherein the input of the generalized neural network is the reaction rate of an activation detector, and the output of the generalized neural network is neutron energy spectrum;
step S20, placing a plurality of activation detectors with known reaction cross sections in a region to be detected of a target reactor, and obtaining a reaction rate measured value of each activation detector;
step S30, inputting the measured value of the reaction rate of each activation detector into the generalized neural network, and outputting a reconstructed spectrum by the generalized neural network;
step S40, determining neutron energy spectrum of the region to be detected according to the reconstruction spectrum, the reaction cross section of each activation detector and the reaction rate measurement value;
wherein, the step S40 includes:
step S42, dividing the neutron spectrum energy interval of the region to be measured into m energy groups, and setting the reconstructed spectrum as an initial neutron spectrumFrom the reconstructed spectrum and the reaction cross section sigma of the ith activation detector i (E) Calculating the calculated value of the reactivity of the ith activation detector at the jth energy group after the kth iteration +.>
Step S43, calculating a value according to the reaction rateCalculating the calculated total reaction rate of the ith activation detector after the kth iteration +.>
Step S44, calculating a value according to the total reaction rateThe reaction rate measured value A measured by the ith activation detector i Calculating correction factor of the jth energy group at the kth iteration->
Step S45, correcting the neutron energy spectrum after the K iteration according to the correction factor to obtain the K+1st corrected neutron energy spectrum
Step S47, stopping iteration until reaching a convergence standard for ending the iteration, and obtaining a neutron energy spectrum of the region to be detected;
wherein i=1, 2, … n, n is the number of activation detectors for measuring the region to be measured; j=1, 2, … m, m being the number of divided energy groups; k represents the number of iterations, and K is 0 or more.
2. The method according to claim 1, wherein the step S10 includes:
step S11, a neutron spectrum data set is established;
and S13, constructing a generalized neural network, and training and verifying the generalized neural network by using the neutron spectrum data set.
3. The method according to claim 2, wherein the step S11 includes:
selecting a reactor with similarity to the target reactor being greater than a threshold value, and simulating the reactor to obtain a plurality of neutron energy spectrums of a region matched with the region to be detected in the reactor;
selecting a plurality of standard neutron spectrums from a standard neutron spectrum database;
the plurality of neutron energy spectra and a plurality of standard neutron spectra are established as the neutron energy spectrum dataset.
4. The method for determining a neutron spectrum according to claim 3, wherein when the reactor is simulated, the region of the reactor matched with the region to be measured is divided into N grids, and the neutron spectrum energy interval corresponding to each grid is divided into M energy groups to obtain M×N neutron energy spectrums.
5. The method according to claim 2, wherein the step S13 includes:
calculating the reaction rate of the activation detector according to the neutron spectrum data set and the reaction section of the activation detector;
taking the reaction rate of the activation detector and the neutron spectrum data set as training samples and test samples, taking a Gaussian function as a radial basis function of the generalized neural network, training and testing the generalized neural network, and optimizing the generalized neural network;
the input value of the generalized neural network is the reaction rate of n activation detectors, and the output value of the generalized neural network is the neutron energy spectrum with the energy group of m in the neutron energy spectrum data set.
6. The method of determining of claim 5, wherein the training and testing the generalized neural network comprises:
performing maximum segmentation normalization standardization on the input value;
training and testing the generalized neural network by using a 4 k-time cross validation method, and determining an optimal value of the diffusion length of the generalized neural network to obtain the optimized generalized neural network.
7. The method of determining of claim 6, wherein training and testing the generalized neural network with a 4 k-fold cross-validation method to determine an optimal value for a diffusion length of the generalized neural network comprises:
training the generalized neural network by taking three-fourths of the neutron spectrum data set and the corresponding response rate of the activation detector as training samples;
taking the neutron spectrum data set and the residual data in the corresponding reaction rate of the activation detector as test samples, and testing the generalized neural network;
and taking the value of the diffusion length in 0.01 increment in the range of 0 to 2, circularly training and testing the generalized neural network for multiple times, and determining the optimal value of the diffusion length.
8. The method according to claim 7, wherein after training the generalized neural network, the response rate of the activation detector in the test sample is input into the trained generalized neural network to obtain an output value;
comparing the mean square error between the output value and an expected value; wherein the expected value is neutron spectrum in the test sample;
and selecting a diffusion length value corresponding to the minimum mean square error as the optimal value, and constructing the generalized neural network.
9. The method of determining according to claim 1, wherein the i-th activation detector is used to determine the average reaction cross-section at the j-th energy groupInstead of the reaction cross section sigma i (E) Calculating the calculated value of the reaction rate +.>
10. The method according to claim 9, wherein the step S40 further includes:
after obtaining the K+1st corrected neutron spectrum, the method comprises the following steps of correcting the neutron spectrum according to the KCalculated reaction rateCorrecting the ith activation detector at the kth iterationThe mean reaction cross section at the time of substitution +.>Obtaining the average reaction cross section +.1 at the K+1th iteration>
11. The method according to claim 1, wherein the step S44 includes:
calculated from the total reaction rateThe reaction rate measured value A measured by the ith activation detector i Calculating the measured value A of the reaction rate i Calculated value of reaction rate after the K-th iteration +.>Ratio of->
Calculated from the reaction rateAnd total reaction Rate->Calculating the weight of the ith activation detector in the jth energy group after the kth iteration +.>
According to the weightAnd said ratio->Calculating correction factor of jth energy group at the time of Kth iteration>
12. The method for determining according to claim 1, wherein,
the step S40 further includes: step S41, setting at least one convergence criterion;
in step S47, when one of the convergence criteria is satisfied, the iteration is stopped.
13. The method of determining according to claim 12, wherein the convergence criterion comprises at least one of:
standard deviation Q of the calculated reaction rate value from the measured reaction rate value K Less than or equal to the deviation threshold;
the convergence speed is less than the speed threshold;
exceeding the maximum number of iterations K max 。
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