Neutron energy spectrum unfolding method
By constructing a neutron energy spectrum interpretation method and combining the MLEM and GOLD algorithms, and dynamically adjusting the weighting coefficients, the accuracy problem of neutron energy spectrum analysis in fast response neutron spectrometers is solved, achieving high precision and environmental adaptability in neutron energy spectrum measurement, which is applicable to fields such as reactor safety monitoring and radiation protection.
Patent Information
- Application Number
- CN202511686996.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-17
- Publication Date
- 2026-02-27
AI Technical Summary
In the existing technology, fast response neutron spectrometers lack systematic research methods for neutron energy spectrum analysis. Traditional spectral analysis packages cannot be adapted to their unique structure, and nuclear data such as neutron reaction cross sections are not updated in a timely manner, affecting the accuracy of response matrix calculation and resulting in inaccurate neutron energy spectrum measurements.
A neutron energy spectrum decomposition method is constructed. This method obtains the energy response matrix based on the detector, performs iterative calculations using the MLEM and GOLD algorithms, dynamically adjusts the weighting coefficients, constructs the energy response matrix using Geant4 Monte Carlo simulation, and integrates the MLEM and GOLD algorithms into a hybrid iterative decomposition algorithm to accurately obtain the energy spectrum components.
It significantly improves the accuracy of neutron energy spectrum measurement and the calculation precision of the response matrix, adapts to complex reactor environments, meets the real-time monitoring requirements of fast response neutron spectrometers, and has high spectral resolution accuracy and a wide range of applications.
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Figure CN121578359A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of neutron energy spectrum measurement technology, and more specifically, to a method for interpreting neutron energy spectra. Background Technology
[0002] Neutron energy spectrum measurement is a key part of reactor physics research, and it is of great significance for neutron shielding design, evaluation of material radiation resistance performance, and improvement of reactor safety control.
[0003] However, the neutron field environment inside a reactor is extremely complex, characterized by a wide energy spectrum distribution, high flux density, strong gamma background, and confined space with high temperatures, posing significant challenges to measurement instruments and methods. Traditional threshold-activated detector methods suffer from a measurement blind zone in the critical energy range of 1 keV to 0.5 MeV due to the limited energy threshold distribution of selectable activation materials, making it difficult to meet the requirements for accurate full-spectrum measurements. Although some progress has been made in detection hardware such as fast-response neutron spectrometers based on semiconductor detectors, a systematic research method for neutron energy spectrum analysis remains lacking, which has become a major factor restricting the acquisition of accurate neutron energy spectra. Currently used spectrum interpretation packages for generating detector response functions and performing energy spectrum inversion have significant limitations: they can only simulate a limited number of standard detector models and are difficult to adapt to the unique structure of fast-response spectrometers. The lack of timely updates to key nuclear data such as the neutron reaction cross section affects the accuracy of the fast-response spectrometer response matrix calculation. Furthermore, the built-in spectrum interpretation algorithms are relatively fixed and cannot flexibly adapt to the unique characteristics of the energy spectrum measured by fast-response spectrometers. Summary of the Invention
[0004] The technical problem to be solved by the present invention is to provide a neutron energy spectrum interpretation method in view of the above-mentioned technical defects of the prior art.
[0005] The technical solution adopted by this invention to solve its technical problem is: to construct a neutron energy spectrum interpretation method, including the following steps: S1. Obtain the energy response matrix corresponding to the detector by performing an energy spectrum detection process based on the detector; S2. For each neutron energy range in the energy response matrix, obtain the corresponding first energy spectrum component and second energy spectrum component based on the first preset spectral resolution algorithm and the second preset spectral resolution algorithm, respectively. S3. Obtain the first weight coefficient corresponding to the first preset spectral decomposition algorithm and the second weight coefficient corresponding to the second preset spectral decomposition algorithm respectively, so as to obtain the final energy spectrum component corresponding to each neutron energy range in the energy response matrix according to the first weight coefficient, the second weight coefficient, the first energy spectrum component and the second energy spectrum component, so as to complete the spectral decomposition.
[0006] Preferably, in one embodiment of the neutron energy spectrum descaling method of the present invention, in step S1, obtaining the energy response matrix corresponding to the detector based on the energy spectrum detection process of the detector includes: During the detection process of the detector, the energy response matrix is obtained based on Geant4 Monte Carlo simulation.
[0007] Preferably, in one embodiment of the neutron energy spectrum decomposition method of the present invention, in step S2, for each neutron energy range in the energy response matrix, the corresponding first energy spectrum component and second energy spectrum component are obtained based on a first preset decomposition algorithm and a second preset decomposition algorithm, respectively; including: Iterative formulas based on the MLEM algorithm To obtain the first energy spectrum component; in, and These represent the components of the neutron energy spectrum in the j-th neutron energy range after the k-th and k+1-th iterations based on the MLEM algorithm, respectively. is the normalization factor, representing the detector's overall sensitivity to neutrons in the j-th energy range; The count is the experimentally measured count of the coincidence signal between the α particle and the T nucleus within the i-th energy range; This represents the predicted count within the i-th energy interval calculated based on the current energy spectrum estimate; elements of the energy response matrix. Indicates energy as The probability that a neutron will generate a count in the i-th energy range of the detector, where m is the total number of energy ranges of the detector; Iterative formulas are constructed based on the GOLD algorithm. To obtain the second energy spectrum component; in, and These represent the components of the neutron energy spectrum in the j-th neutron energy range after the k-th and k+1-th iterations based on the GOLD algorithm, respectively. It is a regularization function; It is the dynamic regularization coefficient for the k-th iteration; This is a correction item.
[0008] Preferably, in one embodiment of the neutron energy spectrum decomposition method of the present invention, in step S2, the regularization function satisfies the following formula: ; in, denoted as , represents the difference in neutron flux between the j-th neutron energy range and the previous neutron energy range.
[0009] Preferably, in one embodiment of the neutron energy spectrum decomposition method of the present invention, in step S3, obtaining the final energy spectrum component corresponding to each neutron energy interval in the energy response matrix based on the first weighting coefficient, the second weighting coefficient, the first energy spectrum component, and the second energy spectrum component includes: based on the formula Obtain the final energy spectrum components corresponding to each neutron energy range; in, Let be the final component of the neutron energy spectrum in the j-th neutron energy range. The first weighting coefficient, This is the second weighting coefficient.
[0010] Preferably, in one embodiment of the neutron energy spectrum interpretation method of the present invention, the method further includes: Based on the current energy spectrum solution, the gradient at each neutron energy range is calculated, and then the first weighting coefficient is dynamically adjusted according to the following formula. ; in, and These are the preset boundaries of the weighting factors. and This represents the extreme value of the gradient in the current solution. Let be the gradient of the current energy spectrum solution at the j-th neutron energy region.
[0011] Preferably, in one embodiment of the neutron energy spectrum interpretation method of the present invention, the method further includes: During the process of obtaining the final energy spectrum components corresponding to each neutron energy range, it is determined whether the spectrum resolution process meets the preset convergence condition, so that the spectrum resolution is completed when the spectrum resolution process meets the preset convergence condition.
[0012] Preferably, in one embodiment of the neutron energy spectrum decomposition method of the present invention, the step of determining whether the decomposition process satisfies the preset convergence condition includes: during the iteration process, based on the formula... Obtaining weighted residuals and in the weighted residual Less than the weighted residual convergence threshold When the spectral resolution process satisfies a preset convergence condition, it is determined that the spectral resolution process meets the preset convergence condition; wherein .
[0013] Preferably, in one embodiment of the neutron energy spectrum interpretation method of the present invention, the step of determining whether the interpretation process satisfies the preset convergence condition includes: based on the formula Obtain the relative rate of change of the energy spectrum solution obtained from two consecutive iterations. And in the relative change rate of the energy spectrum solution Below the predetermined threshold The spectral resolution process is determined to satisfy the preset convergence condition, where .
[0014] Preferably, in one embodiment of the neutron energy spectrum interpretation method of the present invention, the method further includes: In satisfying At that time, based on the formula To obtain the stability of the regularization term, and in At that time, the spectral interpretation is completed; or In satisfying At that time, based on the formula To obtain the stability of the regularization term, and in At that time, the spectral interpretation is completed; or In satisfying At that time, based on the formula Obtain the degree of agreement between the predicted counts calculated from the current energy spectrum solution and the measured counts, and in At that time, the spectral interpretation was completed; among which ,in, It is the tolerance coefficient. It's about freedom. It is the Tao, This represents the number of energy regions.
[0015] The neutron energy spectrum interpretation method of the present invention has the following beneficial effects: it effectively improves the accuracy of energy calculation during the energy spectrum measurement process. Attached Figure Description
[0016] The present invention will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings: Figure 1 This is a flowchart of an embodiment of a neutron energy spectrum interpretation method according to the present invention; Figure 2 This is a schematic diagram of the fitting of the peak position and the incident neutron energy according to an embodiment of the present invention; Figure 3 This is a function for distinguishing neutrons of different energies according to an embodiment of the present invention. Detailed Implementation
[0017] To provide a clearer understanding of the technical features, objectives, and effects of the present invention, specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.
[0018] like Figure 1 The figure shows an embodiment of a neutron energy spectrum interpretation method according to the present invention. Figure 1In an embodiment of the neutron energy spectrum descaling method of the present invention, the method specifically includes the following steps: S1, obtaining the energy response matrix corresponding to the detector through an energy spectrum detection process based on the detector; S2, for each neutron energy interval in the energy response matrix, obtaining the corresponding first energy spectrum component and second energy spectrum component based on a first preset descaling algorithm and a second preset descaling algorithm, respectively; S3, obtaining the first weighting coefficient corresponding to the first preset descaling algorithm and the second weighting coefficient corresponding to the second preset descaling algorithm, respectively, so as to obtain the final energy spectrum component corresponding to each neutron energy interval in the energy response matrix according to the first weighting coefficient, the second weighting coefficient, the first energy spectrum component and the second energy spectrum component, so as to complete the descaling.
[0019] Specifically, the steps based on the embodiments of the present invention aim to overcome the shortcomings of existing general-purpose spectral interpretation programs that cannot adapt to the unique structure of fast response neutron spectrometers, have insufficient response matrix accuracy, and have mismatched spectral interpretation algorithms.
[0020] Based on step S1, during the detector detection process, an energy response function covering the energy range from thermal neutrons to fast neutrons is calculated and generated using a specific method based on the physical structure model of the fast response spectrometer, forming a response matrix. This is achieved using a silicon carbide (SiC) semiconductor detector and... The following is a detailed explanation using a fast-response neutron spectrometer constructed from a converter. Silicon carbide (SiC) semiconductor detectors and... The detection principle of the fast-response neutron spectrometer composed of a converter is based on Nuclear reaction. Incident neutron and In the layer After the nuclear reaction, the resulting alpha particles and T nuclei enter the SiC detectors on both sides, and their deposition energies are recorded separately. During the energy recording process, the corresponding energy response matrix can be obtained. In a specific embodiment, the incident neutron energy spectrum... energy spectrum as measured experimentally The quantitative relationship between them is described by the following formula: ;in, express Reaction cross section; It is the absolute detection efficiency; It is the energy response function, a key parameter that represents the incident energy. The energy of the single-energy neutron pair measured in the energy spectrum is The degree of contribution of the channel. In actual numerical calculations, the continuous integral equations need to be discretized. A series of discrete monoenergetic neutron points are simulated using Monte Carlo simulation. Each energy point is obtained upon impact. Corresponding energy response function All discrete energy The response functions are arranged in columns to form the system's energy response matrix.
[0021] In one embodiment, in step S1, obtaining the energy response matrix corresponding to the detector based on the energy spectrum detection process of the detector includes: obtaining the energy response matrix based on Geant4 Monte Carlo simulation calculation during the detector detection process.
[0022] Specifically, the response matrix can be obtained based on Geant4 Monte Carlo simulation. The process is as follows: to accurately simulate the detector response, a detailed geometric model is first established in Geant4 based on the actual physical structure of the SiC sandwich spectrometer. The model precisely includes the sensitive volume of the SiC detector, The spatial relationships of key components such as the neutron conversion layer, electrodes, and packaging shell are carefully considered to ensure accurate reproduction of experimental conditions. In the sandwich structure, the energy signals generated by alpha particles and T nuclei are summed to form a "sum peak". The energy of this sum peak... With the energy of the incident neutron A linear relationship exists: ; By simulating different monoenergetic neutron incidences, the linear relationship between the peak position and neutron energy was verified, such as... Figure 2 As shown, this confirms the feasibility of calculating neutron energy using peaks. By simulating the incidence of monoenergetic neutrons and recording the resulting pulse height distribution, the resolution function for each energy point can be obtained, as shown in the figure. Figure 3 As shown. By simulating the incidence of a series of discrete monoenergetic neutrons in the range from thermal neutrons to fast neutrons, recording and normalizing the resulting pulse height distribution, the resolution function corresponding to each energy point can be obtained, and then integrated into the complete energy response matrix corresponding to the detector.
[0023] Based on step S2, after obtaining the energy response matrix, spectral analysis is performed on each neutron energy range using different spectral analysis algorithms to obtain the corresponding energy spectrum components. In other words, each neutron energy range can have its corresponding first and second energy spectrum components obtained using a first preset spectral analysis algorithm and a second preset spectral analysis algorithm, respectively.
[0024] In one embodiment, in step S2, obtaining the corresponding first energy spectrum component and second energy spectrum component for each neutron energy range in the energy response matrix based on a first preset spectral resolution algorithm and a second preset spectral resolution algorithm, respectively, includes: Iterative formulas based on the MLEM algorithm To obtain the first energy spectrum component; in, and These represent the components of the neutron energy spectrum in the j-th neutron energy range after the k-th and k+1-th iterations based on the MLEM algorithm, respectively. is the normalization factor, representing the detector's overall sensitivity to neutrons in the j-th energy range; The count is the experimentally measured count of the coincidence signal between the α particle and the T nucleus within the i-th energy range; This represents the predicted count within the i-th energy interval calculated based on the current energy spectrum estimate, and the elements of the energy response matrix. Indicates energy as The probability that a neutron will generate a count in the i-th energy range of the detector, where m is the total number of energy ranges of the detector; Iterative formulas based on the GOLD algorithm: To obtain the second energy spectrum component; in, and These represent the components of the neutron energy spectrum in the j-th neutron energy range after the k-th and k+1-th iterations based on the GOLD algorithm, respectively. It is a regularization function; It is the dynamic regularization coefficient for the k-th iteration; This is a correction item.
[0025] Specifically, it can be understood that the first and second preset spectral resolution algorithms correspond to the MLEM algorithm and the GOLD algorithm, respectively. Iterative formulas are then constructed based on the MLEM and GOLD algorithms to determine the components of the neutron energy spectrum in the corresponding neutron energy ranges. The iterative formula corresponding to the MLEM algorithm uses ratios... By comparing the measured counts with the predicted counts, the current energy spectrum estimate can be corrected in a targeted manner, gradually approaching the true solution.
[0026] In one embodiment, in step S2, the regularization function satisfies the following formula: ; in, It is the difference in neutron flux between the j-th neutron energy range and the previous neutron energy range.
[0027] Specifically, in the iterative formula constructed based on the GOLD algorithm, This is the regularization function. Considering the continuity of the neutron energy spectrum, a quadratic smoothing regularization term is used. To constrain the physical rationality of the energy spectrum solution. It is the dynamic regularization coefficient for the k-th iteration.
[0028] Based on step S3, different weighting coefficients are set for different spectral decomposition algorithms. For example, corresponding first weighting coefficients and second weighting coefficients are set for the first preset spectral decomposition algorithm and the second preset spectral decomposition algorithm, respectively. The final energy spectrum components are calculated based on the spectral components obtained by the spectral decomposition algorithm and the weighting coefficients, thus completing the spectral decomposition process.
[0029] In one embodiment, in step S3, obtaining the final energy spectrum component corresponding to each neutron energy range in the energy response matrix based on the first weighting coefficient, the second weighting coefficient, the first energy spectrum component, and the second energy spectrum component includes: based on the formula: Obtain the final energy spectrum components corresponding to each neutron energy range; in, Let be the final component of the neutron energy spectrum in the j-th neutron energy range. The first weighting coefficient, This is the second weighting coefficient.
[0030] Specifically, in each iteration, for each neutron energy range , Its energy spectrum components The updated value is calculated by the MLEM algorithm and the GOLD algorithm based on the weight factor. The above formula is obtained by linear combination, where and The results were obtained based on the MLEM algorithm and the GOLD algorithm, respectively.
[0031] In one embodiment, the neutron energy spectrum decomposition method of the present invention further includes: calculating the gradient at each neutron energy range based on the current energy spectrum solution, and then dynamically adjusting the first weighting coefficient according to the following formula; ; in, and These are the preset boundaries of the weighting factors. and This represents the extreme value of the gradient in the current solution. Let be the gradient of the current energy spectrum solution at the j-th neutron energy region.
[0032] Specifically, in each iteration, based on the current energy spectrum solution... Calculate the gradient at point j for each energy group. The weights are then adjusted based on the dynamics of the listing process. and This is a preset boundary for the weighting factors. In one embodiment, it can be set... , This avoids extreme situations where a single algorithm dominates. and The extreme value of the gradient in the current solution is determined in each iteration based on the current energy spectrum solution. Instead of fixing the extreme value to the initial iteration, recalculate the gradient. Define the gradient as the first-order gradient. The gradient directly reflects the variation range of adjacent energy bands and is sensitive to abrupt changes such as spikes and steps. For the first neutron energy region (j=1) and the last neutron energy region (j=n), due to the lack of adjacent energy regions, directly calculating the gradient will produce boundary errors. Different boundary processing strategies are adopted for different scenarios: In the scenario where the energy spectrum naturally decays to 0, it is assumed that the energy spectrum of the energy region outside the boundary is 0, i.e. , In scenarios where the energy spectrum changes gently at the boundary, it is assumed that the energy spectrum outside the boundary is symmetrical to that inside the boundary, i.e. , .
[0033] In one embodiment, the neutron energy spectrum decomposition method of the present invention further includes: during the process of obtaining the final energy spectrum components corresponding to each neutron energy range, determining whether the decomposition process meets a preset convergence condition, so as to complete the decomposition when the decomposition process meets the preset convergence condition. Specifically, in order to enable the algorithm to automatically terminate under appropriate conditions and avoid underfitting or overfitting, it is necessary to preset the optimal iteration judgment condition in the iteration process. The iteration process is monitored and judged based on the judgment condition.
[0034] In one embodiment, determining whether the spectral resolution process satisfies a preset convergence condition includes: during the iteration process, based on the formula... Obtaining weighted residuals and in the weighted residual Less than the weighted residual convergence threshold When the spectral resolution process satisfies a preset convergence condition, it is determined that the spectral resolution process meets the preset convergence condition; wherein Specifically, the convergence criterion is used to assess whether the iterative process itself tends to stabilize, mainly through the relative rate of change criterion of the energy spectrum solution and the weighted residual convergence criterion. In the hybrid algorithm described above, different energy regions are dominated by the MLEM and GOLD algorithms with different weights. The weighted residual criterion reflects this difference, making the convergence judgment consistent with the core idea of the algorithm. In the specific iterative process, the weighted residual can be obtained through the above process. In the high-statistic region, the MLEM algorithm is dominant, using high weights to amplify the convergence requirements in these regions, ensuring that iteration stops once the peak's position and shape are determined. In the low-statistic region, the GOLD algorithm is dominant, using low weights to relax the convergence requirements, avoiding excessive iteration and computational waste. In this method, the threshold for the weighted residuals can be set to... .
[0035] In one embodiment, determining whether the spectral resolution process satisfies a preset convergence condition includes: based on the formula Obtain the relative rate of change of the energy spectrum solution obtained from two consecutive iterations. And in the relative change rate of the energy spectrum solution Below the predetermined threshold The spectral resolution process is determined to satisfy the preset convergence condition, where Specifically, when the relative rate of change of the energy spectrum solutions obtained in two consecutive iterations is lower than a predetermined threshold, it indicates that the algorithm has found a relatively stable solution, and further iterations will have very limited effect on improving the solution. Therefore, the solution process is considered to have converged. This is the energy spectrum convergence threshold. After iteration, the convergence accuracy should not exceed the inherent statistical fluctuations of the data; therefore, the convergence threshold is set as... Set as ,in, This represents the measured count within the i-th energy range.
[0036] In one embodiment, to ensure that the converged solution is physically correct, a prediction count fit criterion and a regularization term stability criterion are introduced as criteria to prevent overfitting and underfitting. That is, while satisfying... At that time, based on the formula To obtain the stability of the regularization term, and in When the spectral interpretation is completed; or when the condition is met... At that time, based on the formula To obtain the stability of the regularization term, and in When the spectral interpretation is completed; or when the condition is met... At that time, based on the formula Obtain the degree of agreement between the predicted counts calculated from the current energy spectrum solution and the measured counts, and in At that time, the spectral interpretation was completed; among which ,in, It is the tolerance coefficient. It's about freedom. It is the Tao, This represents the number of energy regions.
[0037] in, The predictive count agreement criterion is used to evaluate the degree of agreement between predicted counts calculated based on the current energy spectrum solution and measured counts, and a threshold is set based on the properties of the chi-square distribution. , This is the tolerance coefficient, typically ranging from 1.0 to 3.0. In the low-statistic region dominated by the GOLD algorithm, to prevent non-physical oscillations in the solution, the regularization term needs to be monitored. The stability of the regularization term is determined by setting a threshold based on the benchmark of the regularization term change. The range of values is to In one specific embodiment, it is The above process balances computational reliability and efficiency to obtain the optimal iteration point. Furthermore, to prevent the algorithm from getting stuck in an infinite loop due to extreme cases, a maximum number of iterations is set. As a safety measure. When The iteration is forcibly stopped, and the current optimal solution is output.
[0038] Based on the above process, the pulse height spectrum data obtained from actual measurement can be input into the response matrix, the energy spectrum inversion calculation can be performed by applying a hybrid iterative algorithm, and the inversion results can be optimized by monitoring the optimal iteration judgment conditions, and finally the neutron energy spectrum can be output.
[0039] Based on specific embodiments of the present invention, a SiC detector and... were constructed through Geant4 Monte Carlo simulation. 6 The physical structure model of the LiF converter fully reproduces the spatial configuration of the detector's sensitive volume, neutron conversion layer, and encapsulation structure. By systematically simulating the incident processes of different monoenergetic neutrons, an energy response function covering the thermal to fast neutron energy range was obtained to verify the linear relationship between peak position and incident neutron energy. This effectively improves the accuracy of energy calculations and significantly enhances the overall precision of the response matrix, providing a reliable foundation for subsequent energy spectrum analysis.
[0040] In a specific embodiment of this invention, a hybrid iterative spectral resolution algorithm is constructed by integrating the characteristics of the Maximum Likelihood Expectation-Maximization (MLEM) algorithm and the Gradient Optimization (GOLD) algorithm. This algorithm can dynamically adjust the weight distribution of the two algorithms according to the statistical characteristics of different regions of the energy spectrum: in continuous energy regions with high fluence rates and small statistical fluctuations, the weight of the MLEM algorithm is increased to effectively extract sharp spectral line features and fine structure; in high-energy tails or low-energy ends with significant statistical fluctuations, the weight of the GOLD algorithm is increased to suppress non-physical oscillations by introducing a prior physical model, ensuring the stability of the spectral resolution results. The algorithm also has adaptive optimization capabilities, dynamically adjusting the weight factors according to the gradient of the current energy spectrum solution to control the iterative process. Simultaneously, a multi-dimensional judgment system is established, including the relative rate of change of the energy spectrum solution, the weighted residual convergence criterion, the predictive count consistency, and the stability of the regularization term, effectively preventing overfitting and underfitting. A maximum number of iterations is set as a safety mechanism to avoid infinite loops in extreme cases, significantly improving computational efficiency while ensuring spectral resolution accuracy.
[0041] Furthermore, based on specific embodiments of the present invention, it is also possible to effectively address the complex environment within a reactor, characterized by a wide energy spectrum distribution, high flux density, and strong gamma background. The nanosecond-level rapid time response characteristics meet real-time monitoring requirements. It eliminates the dependence on specific spectral interpretation packages. It significantly improves the energy spectrum resolution capability of fast-response neutron spectrometers, while possessing significant advantages such as high spectral accuracy, strong environmental adaptability, high computational efficiency, and wide application range. This provides a crucial technological breakthrough for the development of neutron energy spectrum measurement technology and has broad application prospects in reactor safety monitoring, radiation protection, materials science, and other fields.
[0042] It is understood that the above embodiments only illustrate preferred embodiments of the present invention, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can freely combine the above technical features without departing from the concept of the present invention, and can also make several modifications and improvements, all of which fall within the protection scope of the present invention. Therefore, all equivalent transformations and modifications made with respect to the scope of the claims of the present invention should fall within the scope of the claims of the present invention.
Claims
1. A method of neutron spectrum unfolding, characterized in that, The method comprises the following steps: S1, acquiring an energy response matrix corresponding to a detector based on a spectrum detection process of the detector; S2, acquiring a first spectrum component and a second spectrum component corresponding to each neutron energy interval in the energy response matrix based on a first preset spectrum decomposition algorithm and a second preset spectrum decomposition algorithm respectively; S3, acquiring a first weight coefficient corresponding to the first preset spectrum decomposition algorithm and a second weight coefficient corresponding to the second preset spectrum decomposition algorithm respectively, so as to acquire a final spectrum component corresponding to each neutron energy interval in the energy response matrix according to the first weight coefficient, the second weight coefficient, the first spectrum component and the second spectrum component, so as to complete spectrum decomposition.
2. The method of claim 1, wherein, In the step S1, the energy response matrix corresponding to the detector is acquired based on the spectrum detection process of the detector; comprising: In the detector detection process, the energy response matrix is acquired based on Geant4 Monte Carlo simulation calculation.
3. The method of claim 1, wherein, In the step S2, the first spectrum component and the second spectrum component corresponding to each neutron energy interval in the energy response matrix are acquired based on the first preset spectrum decomposition algorithm and the second preset spectrum decomposition algorithm respectively; comprising: An iterative formula is constructed based on the MLEM algorithm to obtain the first spectral component; where, and denote the components of the neutron energy spectrum in the jth neutron energy bin after the kth and k+1th iteration based on the MLEM algorithm, respectively; is a normalization factor, which represents the total sensitivity of the detector to neutrons in the jth energy bin; is the experimentally measured counts of the coincidence signals of the alpha particles and the T nuclei in the ith energy bin; denotes the predicted counts in the ith energy bin based on the current energy spectrum estimation; the energy response matrix element denotes the probability that a neutron with energy produces one count in the ith energy bin of the detector, and m is the total number of energy bins of the detector; An iterative formula is constructed based on the GOLD algorithm to obtain the second spectral component; wherein, and denote the components of the neutron energy spectrum in the jth neutron energy bin after the kth and k+1th iteration, respectively, based on the GOLD algorithm; is a regularization function; is the dynamic regularization coefficient of the kth iteration; is a correction term.
4. The method of claim 3, wherein, In the step S2, the regularization function satisfies the following formula: ; wherein, is the difference between the neutron fluence rate of the jth neutron energy bin and the previous neutron energy bin.
5. The method of claim 4, wherein, In the step S3, the final spectrum component corresponding to each neutron energy interval in the energy response matrix is acquired according to the first weight coefficient, the second weight coefficient, the first spectrum component and the second spectrum component, comprising: The final spectrum component corresponding to each neutron energy interval is acquired based on the formula wherein, is a final component of the neutron spectrum on the jth neutron energy interval, is the first weight coefficient, is the second weight coefficient.
6. The method of claim 5, wherein, The method further comprises: The gradient at each neutron energy interval is calculated based on the current spectrum decomposition, and then the first weight coefficient is dynamically adjusted according to the formula ; wherein, and are preset bounds for the weight factors, and are extrema of the gradient in the current solution, is the gradient of the current energy spectrum solution at the jth neutron energy bin.
7. The method of claim 5, wherein, The method further comprises: In the process of acquiring the final spectrum component corresponding to each neutron energy interval, it is judged whether the spectrum decomposition process satisfies a preset convergence condition, so that the spectrum decomposition is completed when the spectrum decomposition process satisfies the preset convergence condition.
8. The method of claim 7, wherein, The judging whether the solution spectrum process meets the preset convergence condition comprises: judging whether the weighted residual error meets the preset convergence condition based on a formula obtaining a weighted residual error , and judging that the solution spectrum process meets the preset convergence condition when the weighted residual error is less than a weighted residual error convergence threshold value ; wherein .
9. The method of claim 8, wherein, The determination of whether the spectral resolution process meets the preset convergence condition includes: based on the formula Obtain the relative rate of change of the energy spectrum solution obtained from two consecutive iterations. And in the relative change rate of the energy spectrum solution Below the predetermined threshold The spectral resolution process is determined to satisfy the preset convergence condition, where .
10. The method of claim 8, wherein, The method further comprises: When the condition is met, the stability of the regularization term is obtained based on the formula and the solution spectrum is completed when is met; or When the condition is met, the stability of the regularization term is obtained based on the formula and when the condition is met, the solution spectrum is completed. When the condition is met , the formula is used to obtain the degree of agreement between the predicted counts and the measured counts of the current energy spectrum solution, and when , the spectrum is solved; wherein , wherein is the tolerance coefficient, is the degree of freedom, is the channel number, is the number of energy regions.