Neutron spectrum unfolding method based on perturbation theory

Abstract

The invention belongs to the technical field of neutron spectrum measurement, and provides a neutron spectrum unfolding method based on a perturbation theory, which does not need a user to provide preset spectrum or neutron field information, divides the number of neutron energy groups to be the same as the number of equivalent detectors of a detection system, and converts an inverse problem into a process of solving a suitable equation. And a neutron energy spectrum is solved by adopting a Monte-Carlo random sampling mode. The solving result of the method can be directly applied or further used as a preset spectrum of other'multi-group 'neutron spectrum unfolding methods for correction iteration, and the accuracy, stability and universality of neutron spectrum unfolding are effectively improved.

Description

Technical Field

[0001] The invention belongs to the technical field of neutron spectrum measurement, and in particular relates to a neutron spectrum analysis method based on perturbation theory. Background Art

[0002] Neutron spectrum measurement is an important part of neutron detection physics, mainly used to obtain neutron flux (rate) distribution information of different neutron energies. Neutron spectrum measurement plays an important role in the basic and applied research of neutron nuclear physics and the research of neutron radiation dose and shielding design. It is widely used in the design and operation of nuclear reactor devices, radiation measurement in space, laboratory neutron ray measurement and environmental assessment, boron neutron capture therapy, nuclear weapons security inspection and identification and other fields.

[0003] At present, the main measurement methods of neutron energy spectrum include time-of-flight method, recoil proton method, nuclear reaction method, multi-foil activation plate method, Bonner multi-sphere neutron spectrometer method, quasi-multi-sphere neutron spectrometer method, single-sphere multi-detector neutron spectrometer method, etc. Except for the time-of-flight method, the other measurement methods cannot directly measure and obtain the neutron energy spectrum. It is necessary to infer the real neutron energy spectrum of the measurement point through the measurement data combined with the neutron energy spectrum interpretation method.

[0004] In the classic neutron spectrum analysis model, the neutron spectrum With the jth detector count M j The energy response function R j (E) is connected and satisfies the Fredholm homogeneous integral equation:

[0005]

[0006] In practical applications, the neutron energy E is usually approximated into n discrete energy groups E i , the neutron energy spectrum function that changes continuously with the neutron energy E The corresponding distribution is approximated as a discrete distribution with respect to discrete energy groups Detector count M j Through experimental measurement, we can obtain that the response function is approximately discretized into R ij The neutron spectrum analysis process is transformed into the solution process of the following discrete Fredholm homogeneous equations:

[0007]

[0008] A large number of decomposition methods have been developed to address the "inverse problem" of neutron energy spectrum decomposition. These mainly include the least squares method, maximum entropy algorithm, Bayesian algorithm, regularization algorithm based on iterative correction of preset neutron energy spectrum, the undetermined parameter method and Monte Carlo algorithm based on prior neutron field information, and genetic intelligence algorithm and artificial neural network algorithm for global optimization solution.

[0009] Existing neutron energy spectrum decomposition methods are mainly based on a single decomposition algorithm, relying on preset spectra or neutron field information, and there is still much room for improvement in the accuracy, universality, and solution speed of the decomposition. Summary of the invention

[0010] The purpose of the present invention is to overcome the deficiencies in the prior art and provide a neutron spectrum analysis method based on perturbation theory. The method does not require the user to provide preset spectrum or neutron field information. The number of neutron energy groups is divided into the same number as the number of equivalent detectors in the detection system, thereby converting the "inverse problem" into a process of solving well-posed equations. Based on perturbation theory, the neutron energy spectrum is solved by Monte-Carlo random sampling.

[0011] The purpose of the present invention is achieved through the following technical measures.

[0012] The present invention provides a neutron spectrum analysis method based on perturbation theory, comprising the following steps:

[0013] (1) Determine the number of neutron energy groups

[0014] The number of neutron energy groups should be the same as the number of equivalent detectors m in the neutron spectrum detection system: in the Bonner multi-sphere neutron spectrum detection system, the number of neutron energy groups is the same as the number of Bonner spheres; in the single-sphere neutron spectrum measurement system, the number of neutron energy groups is the same as the number of layers; in the activated sheet neutron spectrum detection system, the number of neutron energy groups is the same as the number of activated sheets;

[0015] (2) Classification of neutron energy groups

[0016] Neutron energy groups are divided logarithmically in a wide energy range of 0.025eV to 20MeV. The logarithmic division includes equal-width and non-equal-width division. In applications related to unknown neutron fields or non-neutron radiation dose measurement, equal-width neutron energy group division is used. In applications related to predicted neutron fields or neutron radiation dose measurement, non-equal-width neutron energy group division is used.

[0017] In the application of neutron energy spectrum measurement with predicted neutron field, neutron energy groups are divided according to the following principles: the energy groups in the energy range of interest are densely divided, and the number of energy groups is large; the energy groups in the energy range of non-interest are sparsely divided, and the number of energy groups is small;

[0018] In the application of neutron radiation dose measurement, neutron energy groups are divided according to the following principles:

[0019] In thermal neutrons ~ 10 -2 There is at least one energy group in the range of MeV; -2 There are at least two energy groups in the range of MeV to 1MeV; at least one energy group in the range of 1MeV to 10MeV; at least one energy group in the range of 10MeV to 20MeV; and at least one energy group in the range of 10MeV to 20MeV. -2 Set energy limits at MeV, 1MeV, 10MeV energy points or nearby points;

[0020] (3) Import the neutron energy response matrix R'

[0021] Import the initial partitioned energy groups and the initial energy response matrix R. If the number of initial energy groups is n and the number of equivalent detectors in the system is m, then the dimension of R is n×m. The number of energy groups of the neutron energy response matrix R' in the same group is the same as the number of equivalent detectors, and the dimension is m×m. The n initial energy groups of the m equivalent detectors need to be merged into m new energy groups.

[0022] Energy group merging principle: For each equivalent detector, the total neutron response in each energy interval of the new energy response curve is equal to the total neutron response in the energy interval of the original energy response curve;

[0023] The upper limit of the new energy interval i is determined by dividing the neutron energy groups in step (2): The lower bound is In a wide energy range, the upper bound of the new energy interval i-1 is and the lower bound of the new energy interval i Overlap, that is, satisfy

[0024] Assume that the upper bound of the original energy group covered by the new energy interval i is The lower bound is We need to find the upper bounds and the lower bound The energy group sequence ind corresponding to the initial energy group, that is, the hth initial energy boundary is ind(h), which satisfies at the same time The upper bound of the original energy interval i-1 and the lower bound of the original energy interval i Overlap, that is, satisfy

[0025] Neutron energy response R of new energy interval i i ' can be divided into three parts: the front part R' i，before The energy range is The equivalent response function is R ind(h-1) , the equivalent neutron energy is Middle part R' i，middle The energy range is The equivalent response function is the equivalent energy response function of the energy group between ind(h) and ind(h-1), that is, the sum of the response and energy products corresponding to each energy group in the initial energy group interval covered; the latter part R′ i，after The energy group range is The equivalent response function is R ind(h) , the equivalent neutron energy is

[0026]

[0027] R′ i =R′ i，before +R′ i，middle +R′ i，after ,i=1,2,3,…,m

[0028]

[0029] (4) Inverse analysis of neutron spectrum

[0030] A set of readings M of the equivalent detector of the measuring device, i.e., an m-dimensional vector, is taken as input, and the m-group neutron energy spectrum is directly obtained by deforming the response matrix using the direct method as shown in the following formula:

[0031]

[0032] The m-group neutron spectrum to be solved There are two situations:

[0033] Case 1: Energy spectrum in the solution result If each element of the vector is non-negative and conforms to the physical meaning, it is accepted as the neutron energy spectrum result;

[0034] Case 2: Energy spectrum in the solution result At least one of the vector elements is negative, which does not conform to physical meaning and the result cannot be accepted;

[0035] When situation 2 occurs, the results need to be divided and processed again, and a perturbation threshold is set. This threshold is a negative number and is the critical value for determining whether to use perturbation theory.

[0036] Case 2-a, energy spectrum There are negative elements in the vector, but the values ​​are close to 0, that is, greater than the perturbation threshold;

[0037] Case 2-b, energy spectrum The elements in the vector are negative, and there is at least one element that is not close to 0, that is, less than the perturbation threshold;

[0038] In case 2-a, the perturbation theory is used to solve the problem, that is, in is a non-negative vector, take The corresponding non-negative elements in the vector, and the negative elements close to 0 are set to 0, M0 is the corresponding equivalent detector reading, ε M is the added random disturbance term, and satisfies the following formula:

[0039]

[0040] ε M Assume a Gaussian random distribution with a mean of 0 and a standard deviation of σ, and set the random disturbance term ε M Perform Monte-Carlo random sampling. If situation 1 does not occur within the set sampling number range, the random perturbation term ε can be increased according to the set step size. M Until we find the value of σ Until every element is non-negative;

[0041] In case 2-b, random perturbation is required for the response function. It can be expressed as:

[0042]

[0043] For the random disturbance term ε R Perform Monte-Carlo random sampling if If the result is case 1, then accept it directly. This is case 2-a in the result of case 2. Use the corresponding method of case 2-a to continue searching. If none of them meet the requirement, re-sampling is required until the For case 1, if case 1 does not occur within the set sampling number range, the random disturbance term ε can be increased according to the set step size R The standard deviation σ value is Until every element in is non-negative. If a suitable solution cannot be found within the set maximum variance range of the perturbation, the neutron energy group division can be fine-tuned by setting the step size until a suitable solution is found.

[0044] The neutron spectrum analysis method based on perturbation theory of the present invention does not require the user to provide preset spectrum or neutron field information. The solution result can be directly applied, or further used as the preset spectrum of other "multi-group" neutron spectrum analysis methods (such as least squares method, maximum entropy algorithm, Bayesian algorithm, regularization algorithm and other spectrum analysis algorithms, and genetic algorithm based on initial neutron spectrum population, etc.) for correction iteration, thereby improving the accuracy, stability and versatility of neutron spectrum analysis. At the same time, it provides a new development direction for the research of neutron spectrum analysis technology, and has a positive and important contribution to the research of neutron spectrum measurement. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 The figure is an overall flow chart of the neutron spectrum solving method of the present invention.

[0046] Figure 2 This is a curve showing the relationship between the ambient dose equivalent value per unit neutron injection of ICRP-74 and the neutron energy.

[0047] Figure 3-9 This is a diagram showing the effect of the 7 neutron energy response function groups before and after they are merged in the 7-ball Bonner multi-ball neutron energy spectrum detection system.

[0048] Fig.10 In order to use the method of the present invention 241 Comparison diagram of Am-Be neutron spectrum decomposition results and theoretical neutron spectrum. DETAILED DESCRIPTION

[0049] The technical solution of the present invention will be described in detail below in conjunction with the accompanying drawings and specific algorithm formulas. Obviously, the described embodiments are partial embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the patent of the present invention.

[0050] like Figure 1 As shown, an embodiment of the present invention provides a neutron spectrum analysis method based on perturbation theory, comprising the following steps:

[0051] (1) Determine the number of neutron energy groups.

[0052] The number of neutron energy groups should be the same as the number of equivalent detectors m in the neutron spectrum detection system. For example, in the Bonner multi-sphere neutron spectrum detection system, the number of neutron energy groups is the same as the number of Bonner spheres; in the single-sphere neutron spectrum measurement system, the number of neutron energy groups is the same as the number of layers; in the activated sheet neutron spectrum detection system, the number of neutron energy groups is the same as the number of activated sheets. Different from the traditional "few channel spectrum solution" method, "same channel" or "same group" is the basis for this method to use "well-posed equations" to solve.

[0053] (2) Classification of neutron energy groups

[0054] In the field of neutron radiation protection and detection, the neutron energy range is usually 0.025eV to 20MeV, spanning 9 orders of magnitude. If m energy groups (m is generally 5 to 10) are required to cover the entire range, the energy groups are generally not divided linearly, otherwise the energy resolution of slow neutrons and medium-energy neutrons in the neutron energy spectrum relative to fast neutrons will become very poor, unless it is known that the neutron field to be measured is a fast neutron energy spectrum, and the distribution of slow neutrons and medium-energy neutrons in the entire energy range is not of interest, but this is not usually the case. The division of energy groups can be logarithmic. Set the energy upper limit E of a certain energy zone upper The logarithm of the energy lower bound E of this energy range lower The logarithmic difference is called the Le width ΔlnE of the energy range. The equal Le width division method makes the energy resolution of the neutron energy spectrum the same in the entire energy range, and the weight distribution of neutrons of different energies is relatively uniform. If there is a certain understanding of the neutron field to be measured, the energy range of interest can be divided more densely, and the energy range of non-interest can be divided more sparsely.

[0055] ΔlnE=lnE upper -lnE lower

[0056] If applied to the calculation of neutron ambient dose equivalent rate based on neutron energy spectrum, the ambient dose equivalent conversion factors of neutrons with different energies are different (for details, see the dose equivalent conversion factors of neutrons with different energies calculated by tissue equivalent materials in the ICRP-74 report of the International Commission on Radiological Protection in 1996, see Figure 2 ), especially when the neutron energy is from 10 -2 When the conversion factor is between MeV and 1MeV, the difference is as large as dozens of times. The same energy resolution will lead to inaccurate calculation of the neutron ambient dose equivalent rate in the full energy range. If the dose equivalent rates of neutrons of different energies are normalized, and the dose equivalent contribution of neutrons with an energy of 1MeV is taken as 1, then the thermal neutrons ~ 10 -2 Neutrons with energy of MeV contribute approximately 0.03, neutrons with energy of 0.1MeV contribute approximately 0.26, neutrons with energy of 1MeV to 10MeV contribute approximately 1.07, and neutrons with energy of 20MeV contribute approximately 1.28. -2 There is at least one energy group distributed in the range of MeV, and within 10 -2 Energy limits are set at or near MeV energy points; -2 At least two energy groups are distributed in the range of MeV to 1MeV, and an energy limit is set at or near the 1MeV energy point; at least one energy group is distributed in the range of 1MeV to 10MeV, and an energy limit is set at or near the 10MeV energy point; at least one energy group is distributed in the energy range of 10MeV to 20MeV.

[0057] (3) Import the neutron energy response matrix R'

[0058] Import the initial partitioned energy groups and the initial energy response matrix R. If the number of initial energy groups is n and the number of equivalent detectors in the system is m, then the dimension of R is n×m. The number of energy groups of the neutron energy response matrix R' in the same group is the same as the number of equivalent detectors, and the dimension is m×m. The n initial energy groups of the m equivalent detectors need to be merged into m new energy groups.

[0059] Energy group merging principle: For each equivalent detector, the total neutron response in each energy interval of the new energy response curve is equal to the total neutron response in the energy interval of the original energy response curve;

[0060] The upper limit of the new energy interval i is determined by dividing the neutron energy groups in step (2): The lower bound is In a wide energy range, the upper bound of the new energy interval i-1 is and the lower bound of the new energy interval i Overlap, that is, satisfy

[0061] Assume that the upper bound of the original energy group covered by the new energy interval i is The lower bound is We need to find the upper bounds and lower bound The energy group sequence ind corresponding to the initial energy group, that is, the hth initial energy boundary is ind(h), which satisfies at the same time The upper bound of the original energy interval i-1 and the lower bound of the original energy interval i Overlap, that is, satisfy

[0062] Neutron energy response R of new energy interval i i ' can be divided into three parts: the front part R' i，before The energy range is The equivalent response function is R ind(h-1) , the equivalent neutron energy is Middle part R' i，middle The energy range is The equivalent response function is the equivalent energy response function of the energy group between ind(h) and ind(h-1), that is, the sum of the response and energy products corresponding to each energy group in the initial energy group interval covered; the latter part R′ i，after The energy group range is The equivalent response function is R ind(h) , the equivalent neutron energy is

[0063]

[0064] R′ i =R′ i，before +R′ i，middle +R′ i，after ,i=1,2,3,…,m

[0065]

[0066] (4) Inverse analysis of neutron spectrum

[0067] Taking a set of readings M (m-dimensional vector) of the equivalent detector of the measuring device as input, the direct method is used to deform the response matrix to directly obtain the m-group neutron energy spectrum as shown in the following formula:

[0068]

[0069] The m-group neutron spectrum to be solved There are two situations:

[0070] Case 1: If the energy spectrum in the solution is If each element of the vector is non-negative and conforms to physical meaning, it is accepted as the neutron energy spectrum result.

[0071] Case 2: If the energy spectrum in the solution is At least one of the elements of the vector is negative, which does not conform to the physical meaning, because the neutron flux in each energy group cannot be negative, and the result is unacceptable.

[0072] When the second case occurs, the results need to be divided and processed again. Set the perturbation threshold, which is a negative value and is the critical value for deciding whether to use the perturbation theory.

[0073] Case 2-a, although the energy spectrum There are negative elements in the vector, but the values ​​are close to 0, that is, greater than the perturbation threshold; Case 2-b, the energy spectrum The elements in the vector are negative, and there is at least one element that is not close to 0, that is, less than the perturbation threshold.

[0074] In case 2-a, the perturbation theory can be used to solve the problem, that is, in is a non-negative vector, take The corresponding non-negative elements in the vector are set to 0, and the negative elements close to 0 are set to 0. M0 is the corresponding equivalent detector reading, ε M is the added random disturbance term, and satisfies the following formula:

[0075]

[0076] ε M It is set to a Gaussian random distribution with a mean of 0 and a standard deviation of σ, where the value of the standard deviation σ can be changed in equal steps. M Perform Monte-Carlo random sampling. If situation 1 does not occur within the set sampling number range, the random perturbation term ε can be increased according to the set step size. M Until we find the value of σ Until every element is non-negative;

[0077] In case 2-b, random perturbation is required for the response function. It can be expressed as:

[0078]

[0079] For the random disturbance term ε R Perform Monte-Carlo random sampling if For case 1, directly accept, if This is case 2-a in case 2. Use the method in case 2-a to continue searching. If none of them meet the requirement, re-sampling is required until the For case 1, if case 1 does not occur within the set sampling number range, the random disturbance term ε can be increased according to the set step size R The standard deviation σ value is Until every element in is non-negative.

[0080] (5) Judgment and screening of spectrum interpretation results.

[0081] Case 1: Without using perturbation theory, a physically meaningful neutron energy spectrum is directly given. This result is the only solution and can be directly accepted without any identification.

[0082] Case 2: It is necessary to apply perturbation theory and adopt the Monte-Carlo random sampling method. The solution is usually not unique, and the neutron energy spectrum solution needs to be screened. The principle of screening is based on the continuity of the neutron energy spectrum distribution. Unless the number of energy groups is very small and the division is very sparse, for the case where the number of energy groups is greater than 3, the energy spectrum distribution should not show an obvious peak-trough-peak shape in any continuous three energy regions.

[0083] (6) Changes and cycles of perturbations with step length

[0084] Without perturbation, directly solving the problem of case 1 is less likely. Usually, perturbation needs to be added. The quantitative measure of perturbation is mainly the perturbation term ε of the detector reading. M and the response matrix perturbation term ε R, both perturbation terms are Gaussian random distributions with a mean of 0; if the expected neutron energy spectrum result is not found within the set total number of sampling times, it is necessary to gradually increase the perturbation term and continue random sampling. By determining the step size and gradually increasing the perturbation term, the expected neutron energy spectrum result can be finally obtained.

[0085] Implementation effect description, Figure 3-9 The initial response functions of 53 energy groups in the neutron spectrum detection system of 7 equivalent detectors are compared with the "same group" neutron energy response functions after group processing.

[0086] Fig.10 The neutron spectrum analysis method based on perturbation theory is used to solve 241 The Am-Be neutron spectrum and the reference neutron spectrum obtained from the measurement data of the difference between the shadow cone and the shadowless cone in the IAEA table 4.IX (PTB) report. The detector readings were obtained by calculating the reference neutron spectrum and the 53-group initial neutron response function using the Fredholm equations, and the detector readings were input into the 7-group neutron spectrum obtained by this neutron spectrum solution method. The results showed that the agreement was very good.

[0087] The contents not described in detail in this specification belong to the prior art known to those skilled in the art.

[0088] The method described above is only a preferred specific implementation method of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

Claims

1. A neutron spectrum analysis method based on perturbation theory, characterized in that The method comprises the following steps: (1) Determine the number of neutron energy groups The number of neutron energy groups should be the same as the number of equivalent detectors m in the neutron spectrum detection system: in the Bonner multi-sphere neutron spectrum detection system, the number of neutron energy groups is the same as the number of Bonner spheres; in the single-sphere neutron spectrum measurement system, the number of neutron energy groups is the same as the number of layers; in the activated sheet neutron spectrum detection system, the number of neutron energy groups is the same as the number of activated sheets; (2) Classification of neutron energy groups Neutron energy groups are divided logarithmically in a wide energy range of 0.025eV to 20MeV. The logarithmic division includes equal-width and non-equal-width division. In applications related to unknown neutron fields or non-neutron radiation dose measurement, equal-width neutron energy group division is used. In applications related to predicted neutron fields or neutron radiation dose measurement, non-equal-width neutron energy group division is used. In the application of neutron energy spectrum measurement in the predicted neutron field, the neutron energy groups are divided according to the following principles: the energy groups in the energy range of interest are densely divided, and the number of energy groups is large; the energy groups in the energy range of non-interest are sparsely divided, and the number of energy groups is small; In the application of neutron radiation dose measurement, neutron energy groups are divided according to the following principles: In thermal neutrons ~ 10 -2 There is at least one energy group in the range of MeV; -2 There are at least two energy groups in the range of MeV to 1MeV; at least one energy group in the range of 1MeV to 10MeV; at least one energy group in the range of 10MeV to 20MeV; and at least one energy group in the range of 10MeV to 20MeV. -2 Set energy limits at MeV, 1MeV, 10MeV energy points or nearby points; (3) Import the neutron energy response matrix R' Import the initial partitioned energy groups and the initial energy response matrix R. If the number of initial energy groups is n and the number of equivalent detectors in the system is m, then the dimension of R is n×m. The number of energy groups of the neutron energy response matrix R' in the same group is the same as the number of equivalent detectors, and the dimension is m×m. The n initial energy groups of the m equivalent detectors need to be merged into m new energy groups. Energy group merging principle: For each equivalent detector, the total neutron response in each energy interval of the new energy response curve is equal to the total neutron response in the energy interval of the original energy response curve; The upper limit of the new energy interval i is determined by dividing the neutron energy groups in step (2): The lower bound is In a wide energy range, the upper bound of the new energy interval i-1 is and the lower bound of the new energy interval i Overlap, that is, satisfy Assume that the upper bound of the original energy group covered by the new energy interval i is The lower bound is We need to find the upper bounds and the lower bound The energy group sequence ind corresponding to the initial energy group, that is, the hth initial energy boundary is ind(h), which satisfies at the same time The upper bound of the original energy interval i-1 and the lower bound of the original energy interval i Overlap, that is, satisfy Neutron energy response R of new energy interval i i ' is divided into three parts: the front part R' i，before The energy range is The equivalent response function is R ind(h-1) , the equivalent neutron energy is Middle part R' i , middle The energy range is The equivalent response function is the equivalent energy response function of the energy group between ind(h) and ind(h-1), that is, the sum of the response and energy products corresponding to each energy group in the initial energy group interval covered; the latter part R′ i，after The energy group range is The equivalent response function is R ind(h) , the equivalent neutron energy is R′ i =R′ i，before +R′ i，middle +R′ i，after ,i=1,2,3,…,m (4) Inverse analysis of neutron spectrum A set of readings M of the equivalent detector of the measuring device, i.e., an m-dimensional vector, is taken as input, and the m-group neutron energy spectrum is directly obtained by deforming the response matrix using the direct method as shown in the following formula: The m-group neutron spectrum to be solved There are two situations: Case 1: Energy spectrum in the solution result If each element of the vector is non-negative and conforms to the physical meaning, it is accepted as the neutron energy spectrum result; Case 2: Energy spectrum in the solution result At least one of the vector elements is negative, which does not conform to physical meaning and the result cannot be accepted; When situation 2 occurs, the results need to be divided and processed again, and a perturbation threshold is set. This threshold is a negative number and is the critical value for determining whether to use perturbation theory. Case 2-a, energy spectrum There are negative elements in the vector, but the values ​​are close to 0, that is, greater than the perturbation threshold; Case 2-b, energy spectrum The elements in the vector are negative, and there is at least one element that is not close to 0, that is, less than the perturbation threshold; In case 2-a, the perturbation theory is used to solve the problem, that is, in is a non-negative vector, take The corresponding non-negative elements in the vector, and the negative elements close to 0 are set to 0, M0 is the corresponding equivalent detector reading, ε M is the added random disturbance term, and satisfies the following formula: ε M Assume a Gaussian random distribution with a mean of 0 and a standard deviation of σ, and set the random disturbance term ε M Perform Monte-Carlo random sampling. If situation 1 does not occur within the set sampling number range, the random perturbation term ε can be increased according to the set step size. M Until we find the value of σ Until every element is a non-negative number; In case 2-b, random perturbation is required for the response function. It can be expressed as: For the random disturbance term ε R Perform Monte-Carlo random sampling if If the result is case 1, then accept it directly. This is case 2-a in the result of case 2. Use the corresponding method of case 2-a to continue searching. If none of them meet the requirement, re-sample until the For case 1, if case 1 does not occur within the set sampling number range, the random disturbance term ε can be increased according to the set step size R The standard deviation σ value is Until every element in is non-negative.

2. The neutron spectrum analysis method based on perturbation theory according to claim 1 is characterized in that This method requires judging and screening the spectrum analysis results: Case 1: A neutron energy spectrum with physical significance is directly given. This result is the only solution and is directly accepted without identification. Case 2: It is necessary to apply perturbation theory and adopt the Monte-Carlo random sampling method. The solution is not unique and the neutron energy spectrum solution needs to be screened. The screening principle is based on the continuity of the neutron energy spectrum distribution. For the case where the number of energy groups is greater than 3, the energy spectrum distribution should not show obvious peak-trough-peak shapes in any continuous three energy zones.

3. The neutron spectrum analysis method based on perturbation theory according to claim 1 is characterized in that The method involves perturbations with varying step sizes and loops: A quantitative measure of the perturbation is the perturbation term ε in the detector reading M and the response matrix perturbation term ε R , both perturbation terms are Gaussian random distributions with a mean of 0; if the expected neutron energy spectrum result is not found within the set total number of sampling times, it is necessary to gradually increase the perturbation term and continue random sampling. By determining the step size and gradually increasing the perturbation term, the expected neutron energy spectrum result can be finally obtained.

4. The neutron spectrum analysis method based on perturbation theory according to claim 1 is characterized in that The method includes forward merging of neutron energy groups, thereby transforming the inverse solution process of the few-path spectrum into the process of solving the well-posed equation.

5. The neutron spectrum analysis method based on perturbation theory according to claim 1 is characterized in that The results of this method can be used as the preset neutron spectrum for other multi-group neutron spectrum decomposition methods after decomposition.

6. The neutron spectrum analysis method based on perturbation theory according to claim 1, characterized in that: If a suitable solution cannot be found within the maximum variance range of the perturbation set by the user, the neutron energy group division is fine-tuned by setting the step size until a suitable solution is found.

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