Large-scale nuclear radiation field reconstruction simulation method and system under limited sparse detection data and medium

Abstract

The invention discloses a large-scale nuclear radiation field reconstruction simulation method and system under limited sparse detection data, and the method specifically comprises the steps: determining target space geometry and material information, and carrying out the discretization of the information into grids; inputting a nuclear radiation field detection point position and dose data, and constructing a dose vector and a measurement matrix; constructing a nuclear radiation field reconstruction sensing matrix; sparse reconstruction of radioactive source items; calculating nuclear radiation field distribution; and the dose distribution result of the radiation field is visualized in a different color distinguishing mode and is output to a display. Complete nuclear radiation field distribution information can be effectively obtained under limited sparse detection data, environment information can be considered, storage space and calculation amount required by simulation are greatly reduced, and the method is suitable for parallel calculation, so that nuclear radiation field reconstruction quality and efficiency are improved, cost and safety risks are reduced, and the method is suitable for popularization and application. And an effective scheme is provided for solving the problem of large-scale nuclear radiation field reconstruction simulation under limited sparse detection data.

Description

Technical Field

[0001] The present invention relates to radiation protection, and in particular to a large-scale nuclear radiation field reconstruction simulation method and system under limited sparse detection data. Background Art

[0002] During the utilization of nuclear energy, nuclear radiation fields are inevitably present, and the hazards of nuclear radiation to human health cannot be ignored. Understanding nuclear radiation field information is crucial for ensuring the safety of personnel and the environment. Nuclear radiation fields at nuclear facilities are large, highly radioactive, and sometimes even difficult to reach and measure, with no early detection points deployed, and unknown radioactive source terms. The available nuclear radiation field data is often limited and sparse, making it difficult to obtain complete information on the distribution of large-scale nuclear radiation fields. Therefore, it is crucial to develop a simulation method for reconstructing large-scale nuclear radiation fields using limited and sparse detection data.

[0003] Currently, methods for simulating nuclear radiation fields can be categorized into two main approaches: forward calculation and inverse reconstruction. Forward calculation involves directly calculating the radiation field information based on known radioactive source information. Common methods include the Monte Carlo method, the point kernel method, and the discrete ordinate method. Inverse reconstruction, on the other hand, involves inverting the complete radiation field information, including the source information, based on local information acquired by the detector, when the radioactive source information is unknown. Common methods include interpolation and machine learning. These methods fail to fully utilize environmental information and often require a large number of detection point data points to obtain high-quality radiation field reconstruction results. Furthermore, existing research primarily focuses on small-scale, simple scenarios. However, for large-scale reconstruction problems, the computational matrix size and computational complexity of the simulation process increase dramatically, leading to a significant increase in memory requirements and computational time, making the simulation difficult to perform.

[0004] In summary, making full use of environmental information and developing a large-scale nuclear radiation field reconstruction simulation method suitable for limited and sparse detection data is of great significance for ensuring the safety of relevant practitioners, the public and the environment. Summary of the Invention

[0005] The purpose of the present invention is to provide a large-scale nuclear radiation field reconstruction simulation method and system under limited sparse detection data, so as to improve the quality and efficiency of large-scale nuclear radiation field reconstruction simulation under limited sparse detection data.

[0006] The purpose of the present invention is achieved through the following technical solutions:

[0007] A large-scale nuclear radiation field reconstruction simulation method based on limited sparse detection data, the specific steps are as follows:

[0008] Step 1: Determine the target space geometry and material information and discretize it into a grid;

[0009] Step 2: Input the position and dose data of m nuclear radiation field detection points to construct the dose vector Y and measurement matrix Φ;

[0010] Step 3: Simplify the cluster transport process and rewrite it into a matrix form to construct the nuclear radiation field reconstruction sensing matrix A;

[0011] Step 4: Construct a sparse reconstruction simulation model of the radioactive source term by combining the dose vector Y and the sensor matrix A, and use the sparse reconstruction simulation method to calculate the sparse reconstruction simulation model of the radioactive source term to obtain the radioactive source term S;

[0012] Step 5: Calculate the nuclear radiation field distribution and obtain the dose value at each grid center point;

[0013] Step 6: Map the dose value to RGB color space and visualize the radiation field distribution.

[0014] Furthermore, the step 1 first obtains a three-dimensional model of the target space B, and discretizes the three-dimensional model into n grids; traverses each grid area, and records the material number corresponding to each grid as grid material identification.

[0015] Furthermore, the construction of the measurement matrix in step 2 is as follows: according to the number of grids n in the target space, a matrix Φ with an initial value of zero is generated. n×n ; Get the index of the target space grid where the m detection points are located, and generate paired indexes with the same row and column indexes based on the index values, and find the diagonal elements corresponding to Φ; set the found diagonal elements to 1 to obtain the measurement matrix Φ.

[0016] Furthermore, the step 3 specifically includes:

[0017] Step 3.1: With m detection points as the center, construct the neighborhood space of m detection points according to the set range;

[0018] Step 3.2: Construct a neighborhood space LB centered on one of the detection points P, and discretize LB into a grid. The volume of the i-th grid is V i , point P is located at the center of the i-th grid;

[0019] Step 3.3: Simplify the group transport process and rewrite it into a matrix calculation form to obtain the average dose contribution matrix D of each initial energy group per unit intensity in the neighborhood space LB grid:

[0020] D=C(A -1 -V diag M) -1 A -1 F

[0021] Among them, the matrix composed of the initial flux density of each energy group in the entire LB grid is F, the direct contribution matrix of each energy group in the grid when it is unit intensity is A, the group scattering matrix is ​​M, the flux dose conversion factor matrix is ​​C, and the diagonal matrix composed of each grid volume is V diag ;

[0022] Let the matrix W = C(A -1 -V diag M) -1 A -1 , extract the LB grid's contribution to the group dose at point P, i.e., the i-th row data of the g-th group in D

[0023]

[0024] in, is the data of the i-th row of the g-th group of matrix W, F g is the flux density of the gth group in F;

[0025] Step 3.4: The grouped direct dose contribution F of any j-th grid in the target space B to each grid in LB is j As the initial group flux density in the LB grid, that is, F = F j , calculate the contribution of the group dose of grid j in B to the detection point P The calculation is as follows:

[0026]

[0027] Among them, the superscript g represents the gth group data;

[0028] Dividing the γ photon energy into G groups, the complete sparse basis matrix Ψ is expressed as follows:

[0029]

[0030] Step 3.5: Equivalently transform the nuclear radiation field into a spatially superimposed signal, introduce the compressed sensing theory from the field of signal processing, and calculate the sensing matrix A:

[0031] A=ΦΨ

[0032] The relationship between the sensing matrix A and the radioactive source term S is:

[0033] Y=AS

[0034] Y and A are both known, and S is an unknown vector.

[0035] Furthermore, the radioactive source term sparse reconstruction simulation model in step 4 is:

[0036]

[0037] Where λ is the regularization coefficient.

[0038] Furthermore, the sparse reconstruction simulation model of the distress radioactive source term specifically includes:

[0039] (1) Input detection data Y and sensor matrix A, reconstruction error threshold td, minimum coefficient filtering threshold e, clipping ratio a∈(0,1), define column index set bestJ=J={0,1,…,n-1}, intermediate variables X, Xt, bestX, the initial final solution S is set to zero vector, and the length of J is recorded as L;

[0040] (2) Use non-negative Lasso regression to solve AX=Y and obtain the non-negative solution X n ; Calculate the residual r = Y-AX n , define the current cost c as the 1-norm of r, let bestX=X n , bestJ = J;

[0041] (3) If L≤2, execute step (11) to end the calculation; otherwise, the algorithm enters step (4);

[0042] (4) Record the cost oldC = c, and calculate the new length based on the length L of J and the trimming ratio a The remaining length is k2 = L - k1;

[0043] (5) Select the k1 elements with the largest coefficients in bestX from J to form the optimal set bJ, and the rest to form the suboptimal set wJ; select the columns corresponding to bJ from A to form the matrix A b , and solve A by non-negative Lasso regression b X=Y, and we get the new solution X b , let X t =X b , update r = Y - AX b ,

[0044] (6) If k2≤1 or c≤oldC, let J=bJ and execute step (10); otherwise, execute step (7) to screen the suboptimal set;

[0045] (7) Select the columns corresponding to wJ from A to form the matrix A w , solve A by non-negative Lasso regression w X=Y, and we get the new solution X w ; from X w Select the number k of effective coefficients greater than the threshold e t , remember k n =min(max(1,k t ),k2-1);

[0046] (8) According to X w The largest k n The index of the value, extract the corresponding elements from wJ to form a new set wJt; let J be the union of bJ and wJt; select the column corresponding to J from A to form the matrix A J , solve A using non-negative Lasso regression J X=Y, and we get the new solution X J , let X t =X J , and update r = YA J X J ,

[0047] (9) If c>td, execute step (11) to end the calculation; otherwise, execute step (10);

[0048] (10) Let bestX = X t , bestJ=J, return to step (3) and enter the next round of iteration;

[0049] (11) Use the value in bestJ as the index to find the element set S corresponding to S t , let S t =bestX, divided by S t Except that the rest of the elements in S are 0, output the final solution S.

[0050] Furthermore, the step 5 of calculating the nuclear radiation field distribution specifically includes:

[0051] Step 5.1: The center point of the i-th grid in the target space B is b i , with b i Construct a neighborhood space B with a spatial range of LB for the geometric center i ; Discretization B i , b i Located in B i The kth grid in ;

[0052] Step 5.2: Get B i The dose contribution matrix W of each initial energy group per unit intensity in the grid i , and extract W i The kth row of data constitutes the neighborhood space B i Each grid pair b i Cluster dose contribution vector of points

[0053] Step 5.3: Calculate the effect of the radioactive source term S on B i The direct flux density of the regional grid is divided into groups. The direct flux density of each grid and energy group constitutes the vector Fi , then b i Dosage value at point

[0054] Step 5.4: Repeat steps 5.1 to 5.3 until all grid centers in B are traversed and the dose value at each center point is obtained, completing the calculation of the nuclear radiation field distribution D. t =ΨS, calculate the columns in Ψ corresponding to the non-zero data in S.

[0055] Furthermore, the visual display of step 6 specifically includes:

[0056] Step 6.1: Arrange the dose values ​​at the centers of all grids in the target space B from small to large and divide them into four equal parts: minimum value d1, lower quartile d2, median dm, upper quartile d3, and maximum value d4;

[0057] Step 6.2: Map the dose value at the center of the grid B to the RGB intervals of blue, green, and red as follows: For any dose value D i , if D i belongs to the interval [d1,d2], then D i The RGB value of the corresponding color is If D i belongs to the interval (d2,dm], then D i The RGB value of the corresponding color is If D i belongs to the interval (dm,d3], then D i The RGB value of the corresponding color is If D i belongs to the interval (d3,d4], then D i The RGB value of the corresponding color is

[0058] Step 6.3: Output the colored center points of the B grid to the display, and use linear interpolation to transition the colors of adjacent points to complete the visualization of the radiation field dose distribution.

[0059] A computer device / equipment / system includes a memory, a processor, and a computer program stored in the memory. The processor executes the computer program to implement the steps of a large-scale nuclear radiation field reconstruction simulation method under limited sparse detection data.

[0060] A computer-readable storage medium stores a computer program / instruction, which, when executed by a processor, implements the steps of a large-scale nuclear radiation field reconstruction simulation method under limited sparse detection data.

[0061] The beneficial effects of the present invention are:

[0062] 1. The present invention can realize nuclear radiation field reconstruction under limited and sparse detection data. Only a small amount of detection point data is needed to reconstruct the nuclear radiation field distribution information and present it in a visual manner, reducing costs and safety risks.

[0063] 2. The present invention utilizes cluster transport simulation calculations in the reconstruction model construction process, fully considering environmental information, and can greatly improve the quality of nuclear radiation field reconstruction;

[0064] 3. In the calculation of the present invention, the reconstruction results of the detection points and radioactive source terms are sparse, which can greatly reduce the storage space and calculation amount required for simulation. At the same time, most of the matrix construction processes are independent processes, which are suitable for parallel computing, thereby improving computing efficiency. It is very suitable for solving the problem of large-scale nuclear radiation field reconstruction under limited sparse detection data. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 is a flow chart of the simulation method of the present invention;

[0066] Figure 2 Information about radiation sources and shielding objects in the simulation scene;

[0067] Figure 3 Relative error distribution maps of radiation field reconstruction for different air positions in the target space. DETAILED DESCRIPTION

[0068] The present invention will be further described below with reference to the accompanying drawings.

[0069] The present invention provides a large-scale nuclear radiation field reconstruction simulation method and system under limited sparse detection data. The software of the present invention is written in C++ on the platform of Visual Studio 2022. Its main functions are: reading the input file containing large-scale nuclear radiation field sparse data, constructing the sensor matrix using compressed sensing theory, solving the sparse solution of the radioactive source term using the limited sparse detection data and the sensor matrix, and performing nuclear radiation field distribution calculation, finally achieving high-quality reconstruction and visualization of the complete nuclear radiation field distribution information. Figure 1 , the method specifically comprises the following steps:

[0070] Step 1: Determine the target space geometry and material information and discretize it into a grid;

[0071] (1) Obtain a three-dimensional model of the target space B and discretize the three-dimensional model into a cubic grid with n number of discrete grids.

[0072] (2) Establish a material information database in advance, with each material corresponding to a number.

[0073] (3) Traverse each grid area and record the material number corresponding to each grid as grid material identification.

[0074] Step 2: Input the nuclear radiation field detection point position and dose data to construct the dose vector and measurement matrix;

[0075] (1) Input the position and dose data of m detection points in the target space B to form a dose vector Y.

[0076] (2) Construct the measurement matrix Φ: According to the number of grids n in the target space, the matrix Φ is generated. n×n , initially Φ n×n = 0; take the index of the target space grid where the m detection points are located to form a set T, and traverse each element in T: for the i-th element T in T i , generate pairs of indexes with the same row and column indexes (T i ,T i ), and find the corresponding diagonal element Φ(T i ,T i ), then let Φ(T i ,T i )=1, and traverse all elements of T according to the above steps to obtain the final measurement matrix Φ.

[0077] Step 3: Construction of nuclear radiation field reconstruction sensing matrix;

[0078] (1) Discretization of the detection point neighborhood space: With each detection point as the center, construct m cuboid neighborhood spaces and discretize them uniformly. If the neighborhood space is divided into 3×3×3 grids with a grid volume of V, then the detection point P is located at the center of the 12th grid in its neighborhood space.

[0079] (2) Group transport simulation calculation: G photons are divided into G energy groups according to their energy range, and the group transport process is simulated for the neighborhood space of m detection points. For a certain detection point P, its neighborhood space is LB, and the matrix composed of the initial flux density of each energy group in the LB grid is denoted as F. When each energy group in the LB grid has unit intensity, the direct penetration contribution matrix between each grid is A, the group scattering matrix is ​​M, and the flux dose conversion factor matrix is ​​C. After the scene is determined, A, B, and C are all fixed values.

[0080] The dose contribution matrix W between each grid under the unit intensity of each initial energy group in the neighborhood space LB of the detection point P is calculated as follows:

[0081] W=C(A -1 -V diag M) -1 A -1

[0082] Finally, the average dose D in each grid of LB can be calculated by the following formula:

[0083] D=WF

[0084] In fact, we only need to care about the contribution of each grid in LB to the group dose at point P, that is, the data of the i-th row of the g-th group in D therefore, The calculation can be simplified as follows:

[0085]

[0086] Where, is the data of the i-th row of the g-th group of matrix W, F g is the flux density of the gth group in F.

[0087] (3) Sparse basis matrix construction: Select the target space B to be reconstructed, discretize B into grids, and the number of grids is n. The contribution of the jth grid in B to the clustered direct dose of each grid in the LB area is F j As the initial group flux density in the LB grid, that is, F = F j , the contribution of the grouped dose of the j grid area to the P point can be calculated:

[0088]

[0089] Then the complete sparse basis matrix Ψ is expressed as follows:

[0090]

[0091] (4) Sensing matrix construction: Let S be the intensity of the radiation source of different energy groups in the grid of the target space B, that is, the sparse vector to be solved; the detection point position and dose are known, and the measurement matrix Φ is known, then:

[0092] Y=ΦΨS=AS

[0093] A=ΦΨ

[0094] Where Y is the vector of dose values ​​at different detection points, A is the sensing matrix, and A corresponds to m rows of data in Ψ:

[0095]

[0096] In the above process, both Y and A are known, and only S is the unknown vector. Since A is an m×nG matrix, where m is the number of detection points and m << nG, Y = AS is an underdetermined problem, and a sparse reconstruction method needs to be used to solve for S. Also, because the number of detection points m is limited and is finitely sparse relative to the number of discretized grid points n in the target space, in actual calculations, Ψ does not need to be calculated in its entirety. Only the data corresponding to the m detection points' rows need to be calculated, that is, directly calculate the sensing matrix A, which greatly saves calculation time and resources.

[0097] Step 4: Sparse reconstruction of the radioactive source term;

[0098] (1) Using the sparse detection data vector Y and the established sensing matrix A, establish a sparse reconstruction model for the radioactive source term; the radioactive source term region is often sparse relative to the target space. In addition, due to factors such as detection data noise and calculation errors, it is difficult to ensure that Y = AS holds strictly. Therefore, a simulation model for sparse reconstruction of the radioactive source term is constructed by combining the L2 norm and the L1 norm. The L2 norm is used to make the reconstruction result AS approach Y as much as possible, and the L1 norm is used to compress the solution S so that most of the coefficients of S are 0. The equivalent model corresponding to the above simulation objective can be expressed as follows:

[0099]

[0100] where λ is the regularization coefficient.

[0101] (2) Sparse reconstruction simulation method: Solving the above model requires matching a suitable simulation method. The specific process is as follows:

[0102] ① Initialization: Input the detection data Y and the sensing matrix A m×n , the reconstruction error threshold td, the minimum coefficient filtering threshold e, the clipping ratio a ∈ (0, 1), define the column index set bestJ = J = {0, 1,..., n - 1}, intermediate variables X, Xt, bestX, and set the initial final solution S as the zero vector. The length of J is denoted as L.

[0103] ② Use non - negative Lasso regression to solve AX = Y to obtain the non - negative solution X n , X n The magnitude of the coefficients in X reflects the importance of the column vectors in A corresponding to those position indices; calculate the residual r = Y - AX n , and define the current cost c as the 1 - norm of r, that is Let bestX = X n , bestJ = J.

[0104] ③ If L ≤ 2, it means that the current J does not need to be further clipped. Execute step End the calculation; otherwise, the algorithm enters step ④ of the primary and secondary set division stage.

[0105] ④ Primary and secondary set division: record the last iteration error oldC = c. Calculate the new length based on J length L and trimming ratio a That is, after rounding down the product of a and L, the maximum value compared with 1, the remaining length is k2=L-k1.

[0106] ⑤ Select the k1 elements with the largest coefficients in bestX from J to form the optimal set bJ, and the rest to form the suboptimal set wJ. Select the columns corresponding to bJ from A to form the matrix A b , and solve A by non-negative Lasso regression b X=Y, and we get the new solution X b , let X t =X b , update r = Y - AX b ,

[0107] ⑥If k2≤1 or c≤oldC, it means that bJ obtained after pruning J will obtain a better solution. Let J=bJ and execute step ⑩; otherwise, it means that J is over-pruned and some important elements are divided into wJ. It is necessary to add more important elements from wJ to bJ. Therefore, execute the backtracking mechanism of step ⑦ to screen the suboptimal set.

[0108] ⑦ Suboptimal set screening: Select the columns corresponding to wJ from A to form matrix A w , solve A by non-negative Lasso regression w X=Y, and we get the new solution X w From X w Select the number k of effective coefficients greater than the threshold e t , remember k n =min(max(1,k t ),k2-1).

[0109] ⑧According to X w The largest k n The index of the value, extract the corresponding elements from wJ, and form a new set wJt; merge wJt with bJ, and update the current J set to J = bJ ∪ wJt. Select the column corresponding to J from A to form the matrix A J , solve A using non-negative Lasso regression J X=Y, and we get the new solution X J , let X t =X J , and update r = YA J X J ,

[0110] ⑨ Cost judgment: If c>td, it means that the cost c has mutated and J cannot be further trimmed, so execute step End the calculation; otherwise, it means that the pruned J makes the cost c change within the allowable threshold range, and the current solution can be accepted.

[0111] ⑩ Let bestX = X t , bestJ=J, return to step ③ and enter the next round of iteration.

[0112] Use the value in bestJ as the index to find the element set S corresponding to S t , let S t =bestX, divided by S t Except that the rest of the elements in S are 0, output the final solution S.

[0113] Step 5: Calculation of nuclear radiation field distribution;

[0114] After solving the radioactive source term S, the entire radiation field dose distribution D t The calculation is as follows:

[0115] D t =ΨS

[0116] At this point, we only need to calculate the columns in Ψ corresponding to the non-zero data in S. The specific steps are as follows:

[0117] (1) First, the center of each grid in the target space B is used as the calculation point of the nuclear radiation field. For the i-th grid of B, its center point b i As the center, according to the size of space LB, construct a neighborhood space B i ;

[0118] (2) B i The region is discretized, b i Located in B i In the kth grid;

[0119] (2) Get B i The dose contribution matrix W of each initial energy group per unit intensity in the grid i , and extract W i The kth row of data constitutes the neighborhood space B i Each grid pair b i Cluster dose contribution vector of points

[0120] (3) Calculate the source term s for B i The direct flux density of the regional grid is divided into groups. The direct flux density of each grid and energy group constitutes the vector F i , then b iDosage value at point

[0121] (4) Repeat the above process to traverse all grid centers in B, calculate the dose value at each center point, and complete the nuclear radiation field distribution calculation.

[0122] The above process demonstrates that the entire Ψ matrix does not need to be constructed. This is because, during the A matrix construction phase, the number of detection points is often limited. Therefore, only the row data corresponding to m detection points need to be constructed directly, directly building the A matrix. During the radiation field distribution calculation phase, since most S values ​​are zero, only the column data corresponding to the non-zero data need to be constructed, significantly reducing the computational effort. Furthermore, the matrix construction process described above is largely independent, making it well-suited for parallel computing, thereby improving computational efficiency and making it suitable for large-scale nuclear radiation field reconstruction.

[0123] Step 6: The radiation field dose distribution is visualized and displayed on a monitor;

[0124] (1) Arrange the dose values ​​at the center of the grid of the entire target space B from small to large and divide them into four equal parts: minimum value d1, lower quartile d2, median dm, upper quartile d3, and maximum value d4;

[0125] (2) Map the dose value at the center of the grid B to the RGB intervals of blue, green, and red. The mapping method is as follows: For any dose value D i , if D i belongs to the interval [d1,d2], then D i The RGB value of the corresponding color is If D i belongs to the interval (d2,dm], then D i The RGB value of the corresponding color is If D i belongs to the interval (dm,d3], then D i The RGB value of the corresponding color is If D i belongs to the interval (d3,d4], then D i The RGB value of the corresponding color is

[0126] 3) The colored center points of the B grid are output to the display, and the color transition of adjacent points is performed using linear interpolation to complete the visualization of the radiation field dose distribution.

[0127] The method of the present invention can not only effectively obtain complete radiation field dose distribution information under limited and sparse detection data, but also make full use of environmental information, save the storage space and computing power required for simulation, and is suitable for parallel computing, thereby improving the quality and efficiency of large-scale nuclear radiation field reconstruction simulation under limited and sparse detection data.

[0128] Example:

[0129] The distribution information of radiation sources and shielding objects in the simulation scene is as follows: Figure 2 As shown in the figure, the target space is a 400 cm × 100 cm × 400 cm cuboid, uniformly discretized into a 20 × 5 × 20 grid space with a step size of 20 cm. There are three isotropic photon sources in the target space, each uniformly distributed within a 20 cm × 20 cm × 20 cm grid. Point source 1 has a geometric center at (-90 cm, 0 cm, 70 cm), with an energy uniformly distributed between 1 and 1.5 MeV and a radioactivity of 4e+10 Bq. Point source 2 has a geometric center at (-70 cm, 0 cm, -90 cm), with an energy uniformly distributed between 0.6 and 0.7 MeV and a radioactivity of 2e+10 Bq. Point source 3 has a geometric center at (50 cm, 20 cm, -30 cm), with an energy uniformly distributed between 2 and 3 MeV and a radioactivity of 4e+10 Bq. The shield consists of 12 rectangular concrete columns with dimensions of 40cm×100cm×20cm, and the remaining space is air.

[0130] The grids in the entire target space are numbered in ascending order according to the coordinates of the center of each grid, z, y, and x axis. When the radioactive source term is known, the radiation dose distribution data calculated by the Monte Carlo method is used as a reference to verify the effectiveness of the method proposed in this invention. When performing radiation field reconstruction, the radiation source information is unknown. The Monte Carlo dose data of 80 air positions are randomly selected in the target space for radiation field reconstruction. The reconstruction results are compared with the Monte Carlo method results. The relative error distribution diagram of different air positions is shown in the figure below. Figure 3 As shown. Figure 3 As can be seen, in the above simulation scenario, the radiation field reconstruction results of the proposed method are within 30% of the Monte Carlo method results, and the relative error in most areas is within 10%, indicating that the reconstructed radiation field is highly consistent with the radiation field distribution calculated by the Monte Carlo method, verifying the effectiveness of the proposed method.

[0131] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A large-scale nuclear radiation field reconstruction simulation method based on limited and sparse detection data, characterized by: The specific steps are as follows: Step 1: Determine the target space geometry and material information and discretize it into a grid; Step 2: Input the position and dose data of m nuclear radiation field detection points to construct the dose vector Y and measurement matrix Φ; Step 3: Simplify the cluster transport process and rewrite it into a matrix form to construct the nuclear radiation field reconstruction sensing matrix A; Step 4: Construct a sparse reconstruction simulation model of the radioactive source term by combining the dose vector Y and the sensor matrix A, and use the sparse reconstruction simulation method to calculate the sparse reconstruction simulation model of the radioactive source term to obtain the radioactive source term S; Step 5: Calculate the nuclear radiation field distribution and obtain the dose value at each grid center point; Step 6: Map the dose value to RGB color space to visualize the nuclear radiation field distribution.

2. The large-scale nuclear radiation field reconstruction simulation method under limited sparse detection data according to claim 1 is characterized by: The step 1 first obtains a three-dimensional model of the target space B and discretizes the three-dimensional model into n grids; traverses each grid area and records the material number corresponding to each grid as grid material identification.

3. The large-scale nuclear radiation field reconstruction simulation method under limited sparse detection data according to claim 1 is characterized by: The construction of the measurement matrix in step 2 is as follows: according to the number of grids n in the target space, a matrix Φ with an initial value of zero is generated. n×n ; Get the index of the target space grid where the m detection points are located, and generate paired indexes with the same row and column indexes based on the index values, and find the diagonal elements corresponding to Φ; set the found diagonal elements to 1 to obtain the measurement matrix Φ.

4. The large-scale nuclear radiation field reconstruction simulation method with limited sparse detection data according to claim 1 is characterized by: The step 3 specifically includes: Step 3.1: With m detection points as the center, construct the neighborhood space of m detection points according to the set range; Step 3.2: Construct a neighborhood space LB centered on one of the detection points P, and discretize LB into a grid. The volume of the i-th grid is V i , point P is located at the center of the i-th grid; Step 3.3: Simplify the group transport process and rewrite it into a matrix calculation form to obtain the average dose contribution matrix D of each initial energy group per unit intensity in the neighborhood space LB grid: D=C(A -1 -V diag M) -1 A -1 F Among them, the matrix composed of the initial flux density of each energy group in the entire LB grid is F, the direct contribution matrix of each energy group in the grid when it is unit intensity is A, the group scattering matrix is ​​M, the flux dose conversion factor matrix is ​​C, and the diagonal matrix composed of each grid volume is V diag ; Let matrix W = C(A -1 -V diag M) -1 A -1 , extract the LB grid's contribution to the group dose at point P, i.e., the i-th row data of the g-th group in D in, is the data of the i-th row of the g-th group of matrix W, F g is the flux density of the gth group in F; Step 3.4: The grouped direct dose contribution F of any j-th grid in the target space B to each grid in LB is j As the initial group flux density in the LB grid, that is, F = F j , calculate the contribution of the group dose of grid j in B to the detection point P The calculation is as follows: Among them, the superscript g represents the gth group data; Dividing the γ photon energy into G groups, the complete sparse basis matrix Ψ is expressed as follows: Step 3.5: Equivalently transform the nuclear radiation field into a spatially superimposed signal, introduce the compressed sensing theory from the field of signal processing, and calculate the sensing matrix A: A=ΦΨ The relationship between the sensing matrix A and the radioactive source term S is: Y=AS Y and A are both known, and S is an unknown vector.

5. The large-scale nuclear radiation field reconstruction simulation method under limited sparse detection data according to claim 1 is characterized by: The simulation model for the sparse reconstruction of radioactive source terms in step 4 is: Where λ is the regularization coefficient.

6. The large-scale nuclear radiation field reconstruction simulation method with limited sparse detection data according to claim 5 is characterized by: The sparse reconstruction simulation model of the distress radioactive source term specifically includes: (1) Input detection data Y and sensor matrix A, reconstruction error threshold td, minimum coefficient filtering threshold e, clipping ratio a∈(0,1), define column index set bestJ=J={0,1,…,n-1}, intermediate variables X, Xt, bestX, the initial final solution S is set to zero vector, and the length of J is recorded as L; (2) Use non-negative Lasso regression to solve AX=Y and obtain the non-negative solution X n ; Calculate the residual r = Y-AX n , define the current cost c as the 1-norm of r, let bestX=X n , bestJ = J; (3) If L≤2, execute step (11) to end the calculation; otherwise, the algorithm enters step (4); (4) Record the cost oldC = c, and calculate the new length based on the length L of J and the trimming ratio a The remaining length is k2 = L - k1; (5) Select the k1 elements with the largest coefficients in bestX from J to form the optimal set bJ, and the rest to form the suboptimal set wJ; select the columns corresponding to bJ from A to form the matrix A b , and solve A by non-negative Lasso regression b X=Y, and we get the new solution X b , let X t =X b , update r = Y - AX b , (6) If k2≤1 or c≤oldC, let J=bJ and execute step (10); otherwise, execute step (7) to screen the suboptimal set; (7) Select the columns corresponding to wJ from A to form the matrix A w , solve A by non-negative Lasso regression w X=Y, and we get the new solution X w ; from X w Select the number k of effective coefficients greater than the threshold e t , remember k n =min(max(1,k t ),k2-1); (8) According to X w The largest k n The index of the value, extract the corresponding elements from wJ to form a new set wJt; let J be the union of bJ and wJt; select the column corresponding to J from A to form the matrix A J , solve A using non-negative Lasso regression J X=Y, and we get the new solution X J , let X t =X J , and update r = YA J X J , (9) If c>td, execute step (11) to end the calculation; otherwise, execute step (10); (10) Let bestX = X t , bestJ=J, return to step (3) and enter the next round of iteration; (11) Use the value in bestJ as the index to find the element set S corresponding to S t , let S t =bestX, divided by S t Except that the rest of the elements in S are 0, output the final solution S.

7. The large-scale nuclear radiation field reconstruction simulation method with limited sparse detection data according to claim 1 is characterized by: The step 5 of calculating the nuclear radiation field distribution specifically includes: Step 5.1: The center point of the i-th grid in the target space B is b i , with b i Construct a neighborhood space B with a spatial range of LB for the geometric center i ; Discretization B i , b i Located in B i The kth grid in ; Step 5.2: Get B i The dose contribution matrix W of each initial energy group per unit intensity in the grid i , and extract W i The kth row of data constitutes the neighborhood space B i Each grid pair b i Cluster dose contribution vector of points Step 5.3: Calculate the effect of the radioactive source term S on B i The direct flux density of the regional grid is divided into groups. The direct flux density of each grid and energy group constitutes the vector F i , then b i Dosage value at point Step 5.4: Repeat steps 5.1 to 5.3 until all grid centers in B are traversed and the dose value at each center point is obtained, completing the calculation of the nuclear radiation field distribution D. t =ΨS, calculate the columns in Ψ corresponding to the non-zero data in S.

8. The large-scale nuclear radiation field reconstruction simulation method with limited sparse detection data according to claim 1 is characterized by: The step 6 of visual display specifically includes: Step 6.1: Arrange the dose values ​​at the centers of all grids in the target space B from small to large and divide them into four equal parts: minimum value d1, lower quartile d2, median dm, upper quartile d3, and maximum value d4; Step 6.2: Map the dose value at the center of the grid B to the RGB intervals of blue, green, and red as follows: For any dose value D i , if D i belongs to the interval [d1,d2], then D i The RGB value of the corresponding color is If D i belongs to the interval (d2,dm], then D i The RGB value of the corresponding color is If D i belongs to the interval (dm,d3], then D i The RGB value of the corresponding color is If D i belongs to the interval (d3,d4], then D i The RGB value of the corresponding color is Step 6.3: Output the colored center points of the B grid to the display, and use linear interpolation to transition the colors of adjacent points to complete the visualization of the radiation field dose distribution.

9. A computer device / apparatus / system comprising a memory, a processor, and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 8.

10. A computer-readable storage medium having a computer program / instruction stored thereon, characterized in that: When the computer program / instructions are executed by a processor, the steps of the method according to any one of claims 1 to 8 are implemented.

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