Neutron source energy spectrum unfolding method based on compressed sensing and GA-PSO algorithm

Abstract

The invention discloses a neutron source energy spectrum unfolding method based on compressed sensing and a GA-PSO algorithm. The neutron source energy spectrum unfolding method is suitable for neutron energy spectrum measurement through a multi-sphere neutron spectrometer. According to the method, firstly, a sparse dictionary is constructed by using discrete cosine transform in a compressed sensing method, sparse reconstruction is performed by using an orthogonal matching pursuit algorithm, so that an initialized particle swarm is obtained, and the problem of low quality of an initial population in a traditional method is solved; and then a genetic algorithm and a particle swarm optimization algorithm are combined, a particle swarm is optimized through crossover, variation and a dynamic inertia weight strategy, and high-precision expansion of the neutron energy spectrum is realized. Experimental results show that the spectrum unfolding precision and the operation efficiency of the method are obviously superior to those of a single CS or GA-PSO method, the root-mean-square error is reduced to 0.055, and the operation time is shortened from several hours to about 8 seconds. The method is suitable for energy spectrum analysis of the neutron source, and an efficient and accurate spectrum unfolding scheme is provided for the fields of nuclear physics, radiation protection and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of neutron energy spectrum decomposition algorithms, and in particular to a neutron source energy spectrum decomposition method based on compressed sensing and a GA-PSO algorithm. Background Art

[0002] Neutron energy spectra, which describe the statistical characteristics of neutron energy distribution, are of great significance to fields such as nuclear physics, nuclear engineering, radiation protection, and astrophysics. Neutron energy spectra not only deepen our understanding of the interaction between neutrons and matter, but also provide essential insights for nuclear reactor design, radiation therapy, and space radiation environment assessment.

[0003] The multi-sphere neutron spectrometer, proposed by Bramblet in the 1960s, uses polyethylene moderator spheres of varying thickness to measure neutron energy spectra. Multi-sphere spectrometers have a wide energy measurement range, from thermal neutrons to 20 MeV, and are therefore often used as a method for neutron energy spectrum measurement. However, this measurement method cannot directly obtain the neutron energy spectrum; it requires the use of the detection system's response function and experimental counts in conjunction with appropriate spectrum decomposition algorithms.

[0004] Existing spectral decomposition algorithms include least squares, maximum entropy, genetic algorithms (GA), particle swarm optimization (PSO), artificial neural networks, and compressed sensing (CS). Among these existing spectral decomposition methods, compressed sensing is fast but not very accurate, while genetic algorithms and particle swarm optimization have strong global search capabilities but are slow.

[0005] Therefore, the present invention proposes a neutron source spectrum decomposition method based on compressed sensing and GA-PSO algorithm. The method of the present invention uses the results of compressed sensing as the initialization particle swarm of GA-PSO to accelerate the convergence speed of the algorithm. The method of the present invention can effectively improve the accuracy of the energy spectrum and increase the running calculation speed. Summary of the Invention

[0006] The present invention aims to provide a neutron source energy spectrum decomposition method based on compressed sensing and GA-PSO algorithm. The root mean square error of the neutron energy spectrum obtained by the decomposition method is smaller than that of the existing decomposition methods, and the accuracy and running speed of the energy spectrum obtained by the decomposition are improved compared with the existing methods.

[0007] In order to achieve the above object, the present invention provides the following technical solutions:

[0008] A neutron source energy spectrum decomposition method based on compressed sensing and GA-PSO algorithm, which uses multi-sphere neutron spectrometer measurement to perform energy spectrum expansion. The method includes constructing a sparse dictionary using discrete cosine transform in the compressed sensing method, performing sparse reconstruction using orthogonal matching pursuit algorithm, thereby obtaining an initialization particle group, and using GA-PSO algorithm to perform neutron energy spectrum expansion on the initialized particle group.

[0009] The energy spectrum measurement relationship of the multi-sphere neutron spectrometer can be expressed by the first-kind Fredholm integral equation:

[0010]

[0011] Where N i is the neutron count measured by the i-th detector; E max 、E min are the upper and lower limits of the neutron energy spectrum to be determined; R i (E) is the neutron response function of the i-th moderator sphere; Φ(E) is the neutron energy spectrum; after converting this formula into discrete form and writing it into a matrix form, it is:

[0012] N±ε=RΦ

[0013] In the compressed sensing method, discrete cosine transform is used to construct a sparse dictionary, and the orthogonal matching pursuit algorithm is used for sparse reconstruction. The process of obtaining the initial particle swarm is as follows:

[0014] When the neutron spectrum to be solved satisfies the sparsity condition, the equation N±ε=RΦ has a unique solution. However, the neutron spectrum is almost non-sparse. The linear combination is used to represent Φ as shown below:

[0015] Φ=Ψs

[0016] Where Ψ is the sparse basis matrix, which ensures that the signal projected from the original signal into a certain domain is sparse; s is the sparse coefficient; the above formula can be written as:

[0017] N±ε=RΨs=As

[0018] Where A = RΨ, which can be equivalently expressed as a compressed sensing model for neutron spectrum decomposition:

[0019]

[0020] In the formula, ||·||0 represents norm, which represents the number of non-zero entries;

[0021] The discrete cosine transform is used as a sparse dictionary, and the FOCUSS algorithm is used to sparsely represent the signal. The orthogonal matching pursuit algorithm is used in the sparse reconstruction process. The input parameters of the algorithm are the observation value y, the perception matrix A, and the sparsity k. The specific steps of the algorithm are as follows:

[0022] S1, initialization: difference r0 = y; index set Iteration number i = 1;

[0023] S2. Find the residual r i-1 and a column a in matrix A j The subscript λ corresponding to the maximum inner product is

[0024] S3. Update index set Λ i =Λ i-1 ∪{λ i},

[0025] S4. Use the least squares method to obtain the i-th order approximation

[0026] S5. Update residual i=i+1;

[0027] S6. Determine whether the iteration is finished. If i ≥ k, stop the iteration; otherwise, repeat steps S2-S5.

[0028] The process of neutron spectrum expansion of the initialized particle swarm using the GA-PSO algorithm is as follows:

[0029] First, the initialized particle swarm randomly generates 4D individuals, i.e., the population size. These individuals are regarded as chromosomes in GA and particles in PSO. These individuals are sorted in descending order of fitness, and the top 2D individuals with high fitness are input into the real-coded GA. During the GA stage, these individuals are created into 2D new individuals through crossover and mutation operations. The new 2D individuals created by the real-coded GA are combined with the remaining 2D particles and adjusted and updated through the PSO method.

[0030] The adjustment process in the PSO method includes selecting the global optimal particle and the local optimal particle, as well as the final speed and position update;

[0031] The dynamic inertia weight in the PSO method is updated as a linear decreasing weight strategy, which is expressed as follows:

[0032]

[0033] Where, T max is the maximum number of iterations; ω max is the maximum inertia weight; ω min is the minimum inertia weight; t is the current number of iterations. By adjusting ω, we can balance the global search and local search capabilities;

[0034] The velocity and position of each of the 4D particles are updated according to the following formula:

[0035] v ij (t+1)=w·v ij (t)+c1·r1·(pbest i (t)-Φ ij (t))+c2·r2·(gbest(t)-Φ ij (t))

[0036] Φ ij (t+1)=v ij (t+1)+Φ ij (t)

[0037] Where c1 and c2 are learning factors; r1 and r2 are random numbers between 0 and 1; pbest is the local optimal particle; gbest is the global optimal particle; Φ ij is the neutron injection to be determined.

[0038] Furthermore, in the linear decreasing weight strategy of the dynamic inertia weight update in the PSO method, setting ω max =0.9,ω min =0.4 can better balance the global search and local search capabilities of the algorithm.

[0039] Furthermore, in the GA stage, individuals are created into 2D new individuals through crossover and mutation operations. The operation is as follows: by randomly selecting a crossover point, the gene fragments of the two parent individuals are recombined to generate two new offspring individuals, and the crossover probability is set to 100%.

[0040] A neutron source energy spectrum decomposition method based on compressed sensing and GA-PSO algorithm is applied to 241 Neutron spectrum expansion of the Am-Be neutron source.

[0041] The principle and beneficial effects of this technical solution:

[0042] 1. In the first stage of the method of the present invention, the compressed sensing (CS) method is used to obtain the initialized particle swarm. Since CS is a signal recovery method based on sparsity, it can effectively reduce the amount of sampling data required, thereby speeding up the signal processing. At the same time, the sparse reconstruction process adopts the orthogonal matching pursuit (OMP) algorithm. The OMP algorithm can effectively utilize parallel computing, which means that multiple computing tasks can be performed simultaneously, thereby significantly improving computing efficiency.

[0043] 2. Neutron spectrum decomposition is an underdetermined equation solution problem, which is consistent with the fact that the CS method can efficiently obtain effective signal information at a low sampling rate. Therefore, the method of the present invention uses the results of the CS method as the initial particles of the GA-PSO method, which can to a certain extent solve the problem of the slow running speed of the GA-PSO method and improve the running speed and accuracy of the algorithm.

[0044] 3. The compressed sensing method used in the present invention can reconstruct the signal with fewer sampling points, thereby obtaining high-quality reconstruction results on a smaller data set. Using the CS result as the initial population of GA-PSO can help the algorithm start searching from a better starting point, which helps to accelerate convergence to the optimal solution because the initial population already contains better solution candidates, which can effectively reduce the overall calculation time. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 Schematic diagram of the CS combined with GA-PSO method of the present invention;

[0046] Figure 2 This is a simulation diagram of a multi-sphere spectrometer obtained by simulation during the implementation of the present invention;

[0047] Figure 3 is the neutron response function obtained by simulation during the implementation of the present invention;

[0048] Figure 4 The CS spectrum analysis method is used in the implementation process of the present invention. 241 Comparison chart of Am-Be neutron spectrum results and ISO international standard spectrum;

[0049] Figure 5 The GA-PSO spectrum analysis method is used in the implementation of the present invention. 241 Comparison chart of Am-Be neutron spectrum results and ISO international standard spectrum;

[0050] Figure 6 In the implementation process of this invention, CS combined with GA-PSO method is used to carry out 241 Comparison of Am-Be neutron spectrum results with ISO international standard spectrum. DETAILED DESCRIPTION

[0051] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments:

[0052] Neutron spectrum expansion principle

[0053] The multi-sphere neutron spectrometer is a detection system composed of multiple thermal neutron detectors, which are located at the center of the moderator sphere. Neutrons of different energies will experience different degrees of slowing down in moderator spheres of different diameters, thus producing different responses in the center of the moderator sphere. When neutrons are slowed down into thermal neutrons by polyethylene shells of different sizes, these thermal neutrons will interact with the thermal neutrons in the sensitive volume of the detector. 3 He reacts as follows:

[0054] n+ 3 He→p+ 3 T+0.765MeV

[0055] Therefore, by measuring these different response data combined with the measured count rate, an inversion algorithm is used to recover the energy spectrum of the neutron source.

[0056] The energy spectrum measurement relationship of the multi-sphere neutron spectrometer can be expressed by the first-kind Fredholm integral equation:

[0057]

[0058] Where N i is the neutron count measured by the i-th detector; E max 、E min are the upper and lower limits of the neutron energy spectrum to be determined; R i (E) is the neutron response function of the ith moderator sphere; Φ(E) is the neutron energy spectrum. Convert the above formula into discrete form:

[0059]

[0060] Where R ij is the response of the i-th detector to the incident neutron of the j-th energy group, which can be obtained by Geant4 simulation calculation; Φ j is the neutron flux of the jth energy group; m is the number of detectors used, and n is the number of energy groups. Since the number of m is much smaller than the number of n, this problem is mathematically underdetermined and cannot be solved directly. Therefore, it is necessary to combine the spectral solution algorithm to solve it. This formula is usually written in matrix form:

[0061] N±ε=RΦ

[0062] Spectral decomposition algorithm:

[0063] 1. Compressed Sensing Method

[0064] Compressed sensing (CS) methods state that as long as a signal is compressible or sparse in a certain transform domain, the resulting high-dimensional signal can be projected onto a low-dimensional space using a measurement matrix unrelated to the transform basis. Optimization methods can then be used to reconstruct the original signal with high probability from these small number of projections. Neutron spectrum deconvolution, on the other hand, reconstructs the energy spectrum across a wide energy range using a small number of detector response counts, making it a well-suited problem for CS.

[0065] According to compressed sensing theory, when the neutron spectrum to be solved satisfies the sparsity condition, the equation N±ε=RΦ has a unique solution. However, the neutron spectrum is almost never sparse. If Φ is represented by a linear combination, it can be expressed as follows:

[0066] Φ=Ψs

[0067] Where Ψ is the sparse basis matrix, which ensures that the signal projected from the original signal into a certain domain is sparse; s is the sparse coefficient. Since s is sparse, the above problem is solved. The above formula can be written as:

[0068] N±ε=RΨs=As

[0069] Where A=RΨ, the formula can be equivalently written as:

[0070]

[0071] This formula is the compressed sensing model of neutron spectrum decomposition. In the formula, ||·||0 represents Norm, representing the number of non-zero entries.

[0072] The present invention adopts discrete cosine transform as a sparse dictionary and uses the FOCUSS algorithm to sparsely represent the signal. The sparse reconstruction process adopts the orthogonal matching pursuit (OMP) algorithm. This is a classic greedy algorithm. Greedy algorithms reconstruct sparse signals based on the problem of minimizing the l_0 norm. The core idea of ​​the OMP algorithm is to reconstruct the signal through atoms in the perception matrix. It first selects appropriate atoms from the perception matrix, then combines these atoms into a support set, and finally uses the support set to estimate the signal. Therefore, the OMP algorithm can be divided into two key steps: atom selection and signal estimation. In the atom selection stage, the OMP algorithm uses the inner product matching criterion to identify the atom that best matches the current signal residual. Once the best matching atom is found, its index is added to the support set. Then, in the signal estimation stage, the OMP algorithm uses the least squares method to estimate the value of the signal to gradually reduce the signal residual until the preset sparsity or error requirements are reached. The input parameters of the algorithm are the observation value y, the perception matrix A, and the sparsity k. The specific steps of the algorithm are as follows:

[0073] 1. Initialization: difference r0 = y; index set Iteration number i = 1;

[0074] 2. Find the residual r i-1 and a column a in matrix A j The subscript λ corresponding to the maximum inner product is

[0075] 3. Update index set Λ i =Λ i-1 ∪{λ i},

[0076] 4. Use the least squares method to obtain the i-order approximation

[0077] 5. Update residual i=i+1;

[0078] 6. Determine whether the iteration is over. If i ≥ k, stop the iteration; otherwise, repeat steps 2-5.

[0079] 2. CS combined with GA-PSO method

[0080] like Figure 1 The figure shows a schematic diagram of the CS combined with GA-PSO method of the present invention. When solving a D-dimensional problem, 4D individuals, i.e., the population size, are first randomly generated. These individuals are regarded as chromosomes in GA and as particles in PSO. These individuals are sorted in descending order according to fitness, and then the first 2D individuals with high fitness are input into the real-number-encoded GA. In the GA stage, these individuals are created into 2D new individuals through crossover and mutation operations. A random single-point crossover operation is used in the method of the present invention, which randomly selects a crossover point and recombines the gene fragments of the two parent individuals to generate two new offspring individuals, with the crossover probability set to 100%. The new 2D individuals created by the real-number-encoded GA are combined with the remaining 2D particles and adjusted and updated through the PSO method.

[0081] The adjustment process in the PSO method includes selecting the global optimal particle and the local optimal particle, and finally updating the speed and position. The speed and position of each of the 4D particles are updated according to the following formula:

[0082] v ij (t+1)=w·v ij (t)+c1·r1·(pbest i (t)-Φ ij (t))+c2·r2·(gbest(t)-Φ ij (t))

[0083] Φ ij (t+1)=v ij (t+1)+Φ ij (t)

[0084] Where c1 and c2 are learning factors; r1 and r2 are random numbers between 0 and 1; pbest is the local optimal particle; gbest is the global optimal particle; Φ ij is the neutron injection to be determined.

[0085] The dynamic inertia weight update in the PSO method adopts a linear decreasing weight strategy, which is expressed as follows:

[0086]

[0087] Where, T max is the maximum number of iterations; ω max is the maximum inertia weight; ω min is the minimum inertia weight; t is the current iteration number. By adjusting ω, we can balance the global search and local search capabilities. When ω is large, the particle swarm tends to global search; when ω is small, the particle swarm tends to local search. After consulting the literature and multiple parameter tuning, ω max =0.9,ω min =0.4 can better balance the global search and local search capabilities of the algorithm.

[0088] The implementation process is as follows:

[0089] In order to verify the advantages of the method of the present invention, experiments were designed to use the CS method, GA-PSO method and the CS combined with GA-PSO method of the present invention to 241 Energy spectrum expansion with Am-Be neutron source

[0090] 241 Am-Be neutron sources are often used as radioactive neutron sources in laboratories due to their long lifespan, stable neutron radiation, and portability. The moderating material used in the multi-sphere neutron spectrometer is 8 polyethylene spheres of different sizes, namely 4, 5, 6, 7, 8, 9, 10, and 12 inches. The detector used is SP9 3 And proportional counter. 241 The response function of the Am-Be neutron source is obtained by Geant4 simulation. Geant4 simulation builds a multi-sphere spectrometer neutron experiment simulation platform that is highly consistent with the real experimental environment. The multi-sphere spectrometer simulation diagram is shown in the figure. Figure 2 shown.

[0091] like Figure 3The figure shows the neutron response function obtained from the simulation. The neutron moderation process is affected by the size of the polyethylene sphere, resulting in a unique response for each sphere. For smaller spheres, low-energy neutrons may still have sufficient velocity to reach the center of the sphere and be detected after moderation, while high-energy neutrons are more likely to escape into the surrounding environment. In contrast, larger spheres may cause low-energy neutrons to be absorbed after moderation, making it more difficult for them to reach the center of the sphere. High-energy neutrons, however, still have a high probability of reaching the center of the sphere and being detected after moderation. Therefore, as the size of the polyethylene sphere increases, the response characteristics of each sphere gradually shift from being more active at low energies to being more active at high energies.

[0092] Because both laboratory environmental scattering and inter-sphere scattering affect the polyethylene sphere counts, the Geant4 simulation fully accounts for environmental scattering from the four walls, floor, ceiling, air, and the inter-sphere spheres. Neutrons change energy when they scatter from matter. We can distinguish between direct neutrons and scattered neutrons by analyzing the energy difference upon entry into the polyethylene sphere. Table 1 shows the composition of neutrons detected in the polyethylene sphere, including direct neutrons from the neutron source and neutrons scattered from matter in the laboratory environment. When a neutron is detected by the polyethylene sphere after being scattered by multiple objects, the last object before entering the sphere is used to determine the source of the scattering. After obtaining the scattering count for each object, we divide it by the total number of scattered neutrons to determine the scattering contribution of each object. The data shows that floor scattering is the primary source of laboratory environmental scattering, with a far greater impact than wall and ceiling scattering.

[0093] Table 1 Neutron fraction detected in polyethylene spheres

[0094]

[0095] Table 2 shows the air scattering coefficient at a distance of 40 cm from the neutron source to the center of the polyethylene sphere. When air is present, the neutrons emitted from the neutron source detected by the polyethylene sphere can be divided into three categories: direct neutrons, which are detected by the polyethylene sphere without scattering from the air; inwardly scattered neutrons, which are detected by the polyethylene sphere after scattering from the air; and outwardly scattered neutrons, which are direct neutrons that deviate from the polyethylene sphere after scattering from the air. As Table 2 shows, the air scattering coefficient for most polyethylene spheres is greater than 0, indicating that inwardly scattered air is the primary factor affecting polyethylene sphere counts.

[0096] Table 240cm air scattering rate

[0097]

[0098] Table 3 shows the normalized count values ​​for polyethylene spheres with and without inter-sphere scattering. The data shows that inter-sphere scattering causes the greatest counting error for 4-inch spheres, followed by 5-inch and 12-inch spheres. Therefore, inter-sphere scattering can cause significant errors in the measurement of smaller and larger polyethylene spheres. When calculating the neutron energy spectrum, if the effects of scattering can be subtracted from the simulated scattering results, the accuracy of the neutron spectrum will be improved.

[0099] Table 3 Normalized values ​​with and without interspherical scattering

[0100]

[0101] In order to ensure the accuracy of the experimental measurement, all neutron counts of the 8 polyethylene balls need to be collected synchronously and realistically. 241 In the Am-Be neutron source experiment, polyethylene spheres are arranged around the neutron source to form geometric symmetry. 241 An Am-Be neutron source was placed on a central cylindrical platform, while eight polyethylene spheres were placed 40 cm from the center. All polyethylene spheres shared the same distance and height from the central neutron source. This spatial symmetry generally ensured that all polyethylene spheres were exposed to the same neutron radiation, thus ensuring measurement consistency. The entire experimental measurement lasted 50 seconds, and the neutron counts at the 4-, 5-, 6-, 7-, 8-, 9-, 10-, and 12-inch polyethylene sphere positions were 534, 1077, 1161, 1717, 1768, 2367, 1959, and 662, respectively. Neutron count rates were calculated for each polyethylene sphere based on the real-time neutron counting data. After subtracting for scatter, the corrected counts for the polyethylene spheres were 404, 841, 933, 1410, 1469, 2002, 1718, and 588, respectively.

[0102] The following is the method of CS, GA-PSO and CS combined with GA-PSO. 241 The decomposition results of the energy spectrum expansion using an Am-Be neutron source.

[0103] like Figure 4 The following is the expansion using the CS spectrum solution method. 241Comparison chart of the Am-Be neutron energy spectrum results with the ISO international standard spectrum. As can be seen from the figure, the curve of the entire energy spectrum is offset compared to the standard spectrum, and the obtained neutron energy spectrum is not very accurate. The main reason may be that the information in the sparse domain is incomplete. We only selected the signs and order of the first five elements of the reference spectrum in the sparse domain to reconstruct the spectrum. The first few important features of the neutron energy spectrum can generally cover the overall trend of the spectrum, ignoring the less significant parts. This usually provides enough physical information to recover the neutron source characteristics while avoiding the introduction of too much complexity. The CS method models the signal through sparse representation. In the low-energy region, the energy of the energy spectrum is usually more concentrated. Through sparse representation, CS can recover the true characteristics of the signal from a limited number of elements and better capture the energy distribution in the low-energy region during the reconstruction process.

[0104] like Figure 5 The figure shows the GA-PSO spectrum solution method. 241 Comparison chart of the Am-Be neutron energy spectrum results with the ISO international standard spectrum. As can be seen from the figure, the resulting energy spectrum curves align with the standard spectrum, with high accuracy in the mid- and high-energy regions, but lower accuracy in the low-energy region. This is because neutron energy spectra in the low-energy region typically have complex structures and characteristics, potentially containing multiple local optima or nonlinear relationships. Genetic algorithms and particle swarm optimization algorithms can struggle to effectively conduct global searches when faced with complex search spaces, especially in the low-energy region, where they are more likely to fall into local optima and fail to find a global optimal solution or a superior local solution. Furthermore, this method takes a long time to run, up to several hours.

[0105] like Figure 6 The CS combined with GA-PSO method of the present invention is shown. 241 Comparison chart of Am-Be neutron spectrum results and ISO international standard spectrum. Figure 4 As can be seen, the neutron spectrum obtained by the CS method can more accurately reconstruct the spectrum data at the low energy end. Therefore, when CS is combined with the GA-PSO method, it can also better fit and reconstruct low-energy data at the low energy end. As can be seen from the figure, the addition of CS, using its results as the initial population for the GA-PSO spectrum solution, accelerates iterative convergence, thereby reducing the runtime from approximately 4 hours to approximately 8 seconds.

[0106] In order to more accurately evaluate the accuracy of the spectrum interpretation results, the root mean square error is used to measure the deviation between the spectrum interpretation results and the standard energy spectrum. The value of RMSE is the sum of the squares of the errors between the spectrum interpretation value and the standard value divided by the number of spectrum points N, and then taking the square root. The calculation formula is as follows:

[0107]

[0108] Calculations show that the RMSE of the neutron spectrum obtained using only the CS method is 0.162, the RMSE of the neutron spectrum obtained using the GA-PSO method is 0.056, and the RMSE of the neutron spectrum obtained using the CS combined with the GA-PSO method is 0.055. Clearly, the addition of the GA-PSO method improves the performance of the compressed sensing method and significantly improves the accuracy of the spectrum interpretation. Furthermore, the addition of the CS method to the GA-PSO method significantly increases the algorithm's speed.

[0109] In summary, using only the CS method for spectrum interpretation results in biased results and low accuracy. Using only the GA-PSO method for neutron spectrum interpretation results in low efficiency. However, the neutron spectrum obtained using the CS combined with the GA-PSO method of the present invention has the smallest root mean square error (RMS) of 0.055. Compared to the CS method, the interpretation accuracy is improved by approximately 11%, and the GA-PSO method's runtime is reduced from approximately 4 hours to approximately 8 seconds.

[0110] The above is only an embodiment of the present invention, and common knowledge such as the specific technical solutions or characteristics in the solution is not described in detail here. For those skilled in the art, without departing from the technical solution of the present invention, several variations and improvements can be made, which should also be regarded as the scope of protection of the present invention, and these will not affect the effect of the implementation of the present invention and the practicality of the patent. The scope of protection required by this application shall be based on the content of its claims, and the specific implementation methods and other records in the description can be used to interpret the content of the claims.

Claims

1. A neutron source energy spectrum decomposition method based on compressed sensing and GA-PSO algorithm, characterized by: The method uses a multi-ball neutron spectrometer to perform energy spectrum expansion, including constructing a sparse dictionary using discrete cosine transform in a compressed sensing method, and performing sparse reconstruction using an orthogonal matching pursuit algorithm to obtain an initialized particle group, and then using a GA-PSO algorithm to perform neutron energy spectrum expansion on the initialized particle group; The energy spectrum measurement relationship of the multi-sphere neutron spectrometer can be expressed by the first-kind Fredholm integral equation: Where N i is the neutron count measured by the i-th detector; E max 、E min are the upper and lower limits of the neutron energy spectrum to be determined; R i (E) is the neutron response function of the i-th moderator sphere; Φ(E) is the neutron energy spectrum; after converting this formula into discrete form and writing it into a matrix form, it is: N±ε=RΦ In the compressed sensing method, a sparse dictionary is constructed using discrete cosine transform, and an orthogonal matching pursuit algorithm is used for sparse reconstruction. The process of obtaining the initial particle swarm is as follows: When the neutron spectrum to be solved satisfies the sparsity condition, the equation N±ε=RΦ has a unique solution. However, the neutron spectrum is almost non-sparse. The linear combination is used to represent Φ as shown below: Φ=Ψs Where Ψ is a sparse basis matrix, which ensures that the signal projected from the original signal into a certain domain is sparse; s is the sparse coefficient; The above formula can be written as: N±ε=RΨs=As Where A = RΨ, which can be equivalently expressed as a compressed sensing model for neutron spectrum decomposition: Where ||·||0 represents the l0 norm, which represents the number of non-zero items; The discrete cosine transform is used as a sparse dictionary, and the FOCUSS algorithm is used to sparsely represent the signal. The orthogonal matching pursuit algorithm is used in the sparse reconstruction process. The input parameters of the algorithm are the observation value y, the perception matrix A, and the sparsity k. The specific steps of the algorithm are as follows: S1, initialization: difference r0 = y; index set Iteration number i = 1; S2. Find the residual r i-1 and a column a in matrix A j The subscript λ corresponding to the maximum inner product is S3. Update index set Λ i =Λ i-1 ∪{λ i }, S4. Use the least squares method to obtain the i-th order approximation S5. Update residual S6. Determine whether the iteration is finished. If i ≥ k, stop the iteration; otherwise, repeat steps S2-S5. The process of using the GA-PSO algorithm to expand the neutron energy spectrum of the initialized particle swarm is as follows: First, the initialized particle swarm randomly generates 4D individuals, i.e., the population size. These individuals are regarded as chromosomes in GA and particles in PSO. These individuals are sorted in descending order of fitness, and the top 2D individuals with high fitness are input into the real-coded GA. During the GA stage, these individuals are created into 2D new individuals through crossover and mutation operations. The new 2D individuals created by the real-coded GA are combined with the remaining 2D particles and adjusted and updated through the PSO method. The adjustment process in the PSO method includes selecting the global optimal particle and the local optimal particle, as well as the final speed and position update; The dynamic inertia weight in the PSO method is updated as a linear decreasing weight strategy, which is expressed as follows: Where, T max is the maximum number of iterations; ω max is the maximum inertia weight; ω min is the minimum inertia weight; t is the current number of iterations. By adjusting ω, we can balance the global search and local search capabilities; The velocity and position of each of the 4D particles are updated according to the following formula: v ij (t+1)=w·v ij (t)+c1·r1·(pbest i (t)-Φ ij (t))+c2·r2·(gbest(t)-Φ ij (t)) Φ ij (t+1)=v ij (t+1)+Φ ij (t) Where c1 and c2 are learning factors; r1 and r2 are random numbers between 0 and 1; pbest is the local optimal particle; gbest is the global optimal particle; Φ ij is the neutron injection to be determined.

2. The neutron source energy spectrum decomposition method based on compressed sensing and GA-PSO algorithm according to claim 1, characterized in that: In the linear decreasing weight strategy of dynamic inertia weight update in the PSO method, set ω max =0.9,ω min =0.4 can better balance the global search and local search capabilities of the algorithm.

3. The neutron source energy spectrum decomposition method based on compressed sensing and GA-PSO algorithm according to claim 1, characterized in that: In the GA stage, through crossover and mutation operations, individuals are created into 2D new individuals by randomly selecting a crossover point and recombining the gene fragments of the two parent individuals to generate two new offspring individuals. The crossover probability is set to 100%.

4. The neutron source energy spectrum decomposition method based on compressed sensing and GA-PSO algorithm according to claim 1, characterized in that: This method is applied to 241 Neutron spectrum expansion of the Am-Be neutron source.

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