A fast method for obtaining prompt nuclear radiation environmental parameters based on interpolation

Abstract

To address the problem of existing methods for obtaining prompt nuclear radiation environmental parameters, which cannot balance calculation accuracy with solution time, the present invention provides a method for rapidly obtaining prompt nuclear radiation environmental parameters based on interpolation. Based on the Monte Carlo method, the present invention pre-calculates a two-dimensional data table for interpolation. The prompt nuclear radiation environmental parameters at the target point are obtained by interpolation from both the distance and source height directions. The average of the two is taken as the final prompt nuclear radiation environmental parameter result at the target point to be measured. This method maintains high calculation accuracy while effectively reducing calculation time, thereby rapidly providing prompt nuclear radiation environmental parameters at a certain height above the ground under arbitrary distance and arbitrary source height conditions.

Description

Technical Field

[0001] The invention belongs to the technical field of numerical simulation calculation of nuclear radiation environment, and particularly relates to a method for quickly acquiring prompt nuclear radiation environment parameters based on interpolation. Background Art

[0002] The prompt component of early nuclear radiation originates from the large number of neutrons and gamma rays released by the radiation source in a very short period of time. These rays can propagate great distances in the atmosphere, interacting with the atmosphere to form a strong nuclear radiation dose field. Prompt nuclear radiation environmental parameters primarily include prompt neutron fluence, prompt neutron tissue dose, neutron secondary gamma fluence, neutron secondary gamma tissue dose, prompt gamma fluence, and prompt gamma tissue dose. Accurately and rapidly determining how prompt nuclear radiation environmental parameters at a given height above the ground vary with the horizontal distance from the measurement point to the projection of the radiation source (hereinafter referred to as distance) and the height of the radiation source (hereinafter referred to as source height) is crucial for studying the patterns of early nuclear radiation and its effects on personnel.

[0003] Traditional methods for obtaining prompt nuclear radiation environment parameters mainly include empirical / semi-empirical formulas, deterministic methods, and Monte Carlo methods. The empirical / semi-empirical formula method combines theoretical analysis and experimental data to obtain parameterized formulas for solution. Its calculation speed is fast, but its scope of application is limited and the calculation results are not accurate. In some cases, they may deviate significantly from the actual results. The deterministic method uses various direct numerical methods to solve the Boltzmann transport equation. Its calculation speed is fast, but its processing ability for complex geometry is insufficient, and the solution accuracy in complex systems is often not high. The Monte Carlo (MC) method describes the physical process of particle transport based on random sampling and probability statistics. It can handle complex geometric conditions and achieve accurate solutions to physical problems, but the solution time is generally long. It is not applicable in application scenarios where radiation environment parameters need to be given immediately. Summary of the Invention

[0004] The purpose of the present invention is to solve the problem that the existing method for obtaining prompt nuclear radiation environmental parameters cannot balance the accuracy of calculation results and the calculation solution time, and to provide a method for quickly obtaining prompt nuclear radiation environmental parameters based on interpolation.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is:

[0006] A method for rapidly acquiring prompt nuclear radiation environmental parameters based on interpolation is characterized in that it comprises the following steps:

[0007] Step 1) Establish a prompt nuclear radiation transport model;

[0008] Step 2) Using the Monte Carlo method, calculate n×m nodes (d i ,h j )(i=0,1,…,n-1;j=0,1,…,m-1) the prompt nuclear radiation environment parameter value P(h i ,d j ), and generate a two-dimensional data table, where m≥8, n≥8, and both are positive integers;

[0009] Step 3) Determine the target scene parameters to be measured: target distance interpolation point d tar (d0≤d tar ≤d n-1 ) and the target source high interpolation point h tar (h0≤h tar ≤h m-1 );

[0010] Step 4) Find the target distance interpolation point d tar Two-dimensional data table d i The left boundary d in the sequence left and right boundary d right , and obtain the corresponding one-dimensional source high data node sequence value P(d left ,h j ) and P(d right ,h j );

[0011] Step 5), respectively with P(d left ,h j ) and P(d right ,h j ) as the interpolation node sequence, interpolation calculation of the target source high interpolation point h on the left and right boundary sequences tar The approximate value of the nuclear radiation environment parameter P(d left ,h tar ) and P(d right ,h tar );

[0012] Step 6) Interpolate the result P(d) with the left and right boundaries left ,h tar ) and P(d right ,h tar ) is the data point, and the interpolation calculation target distance interpolation point d tar The prompt nuclear radiation environment parameter value P1(d tar ,h tar );

[0013] Step 7) Find the target source high interpolation point htar In the two-dimensional data table h j The lower boundary h in the sequence down and the upper boundary h up , and obtain the corresponding one-dimensional distance data node sequence P(d i ,h down ) and P(d i ,h up );

[0014] Step 8), respectively with P(d i ,h down ) and P(d i ,h up ) as the interpolation node sequence, interpolation calculation upper and lower boundary sequence target distance interpolation point d tar The approximate value of the nuclear radiation environment parameter P(d tar ,h down ) and P(d tar ,h up );

[0015] Step 9), upper and lower boundary interpolation results P(d tar ,h down ) and P(d tar ,h up ) is the data point, and the interpolation calculation target source high interpolation point h tar The prompt nuclear radiation environment parameter value P2(d tar ,h tar );

[0016] Step 10) Take the interpolation result P1(d tar ,h tar ) and the interpolation result P2(d tar ,h tar ) as the target distance interpolation point d tar and the target source high interpolation point h tar The prompt nuclear radiation environment parameter value of the target scene to be measured is P(d tar ,h tar )=(P1+P2) / 2.

[0017] Furthermore, in step 4) and step 7), the target distance interpolation point d is found by using the binary search method. tar Two-dimensional data table d i The left boundary d in the sequence left and right boundary d right and the target source high interpolation point h tar In the two-dimensional data table h j The lower boundary h in the sequencedown and the upper boundary h up .

[0018] Furthermore, in step 6) and step 9), a linear interpolation method is used for interpolation calculation.

[0019] Furthermore, in step 5) and step 8), the Lagrange interpolation method is used for interpolation calculation.

[0020] Furthermore, in step 5), step 6), step 8) and step 9), the interpolation calculation is specifically as follows:

[0021] ① Take the logarithm with base 10 of the nuclear radiation environment parameter value used as the interpolation data point;

[0022] ②Perform interpolation calculation;

[0023] ③ The interpolation result is used as an exponential and an exponential operation with a base of 10 is performed to convert it into the prompt nuclear radiation environmental parameter value of the corresponding interpolation point.

[0024] Furthermore, when the Lagrange interpolation method is used for interpolation calculation in step 5) and step 8), at least 4 interpolation nodes are selected; when the interpolation point is located in the node interval and the number of nodes before and after it is greater than 4, 8 interpolation nodes are selected; when the interpolation point is close to either end of the node interval and the number of nodes on one side is less than 4, 4 to 7 interpolation nodes are selected; when the interpolation node is located outside the node interval, the interpolation nodes selected are the 4 nodes close to the interpolation point in the node interval.

[0025] Furthermore, in step 2), the selection of n×m nodes on the two-dimensional rectangular domain is non-uniform, the selection of nodes near the radiation source is dense, and the selection of nodes far away from the radiation source is sparse.

[0026] Compared with the prior art, the present invention has the following beneficial technical effects:

[0027] 1. The interpolation-based rapid acquisition method for prompt nuclear radiation environmental parameters proposed in the present invention can effectively reduce the calculation time while maintaining high calculation accuracy, thereby quickly giving the prompt nuclear radiation environmental parameters at a certain height above the ground under any distance and any source height conditions.

[0028] 2. The proposed interpolation-based method for rapidly acquiring prompt nuclear radiation environmental parameters uses Monte Carlo methods to pre-calculate a two-dimensional data table for interpolation. The interpolation results have similar accuracy to Monte Carlo methods. This method also boasts a very short calculation time and can instantly acquire high-precision prompt nuclear radiation environmental parameters at multiple detection locations.

[0029] 3. The interpolation-based rapid acquisition method for prompt nuclear radiation environmental parameters proposed in the present invention interpolates the prompt nuclear radiation environmental parameters at the target point from the two directions of distance and source height, and takes the average of the two as the final calculation result. This avoids the large deviation between the interpolation result and the true value caused by excessive data changes between nodes in a certain direction, effectively reducing the error of the interpolation result. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 This is a flow chart of an embodiment of a method for rapidly acquiring prompt nuclear radiation environment parameters based on interpolation according to the present invention;

[0031] Figure 2 Schematic diagram of the non-uniform atmosphere-soil model used in an embodiment of the present invention;

[0032] Figure 3 is the boundary node sequence selected in the embodiment of the present invention; wherein (a) is the boundary node sequence selected at a target distance of about 1200m; (b) is the boundary node sequence selected at a target source height of 1120m above and below;

[0033] Figure 4 Schematic diagram of the binary Lagrangian-linear interpolation averaging method in an embodiment of the present invention. DETAILED DESCRIPTION

[0034] To make the objectives, advantages, and features of the present invention more apparent, the following describes in further detail a method for rapidly acquiring prompt nuclear radiation environment parameters based on interpolation, in conjunction with the accompanying drawings and specific examples. Those skilled in the art should understand that these embodiments are merely intended to illustrate the technical principles of the present invention and are not intended to limit the scope of protection of the present invention.

[0035] like Figure 1 As shown, the method for quickly acquiring prompt nuclear radiation environment parameters based on interpolation proposed by the present invention specifically includes the following steps:

[0036] Step 1) Establish a prompt nuclear radiation transport model;

[0037] Step 2) Using the Monte Carlo method, by adjusting the detector distance d and the radiation source height h, calculate n×m nodes (d i ,h j )(i=0,1,…,n-1;j=0,1,…,m-1) the prompt nuclear radiation environment parameter value P(h i ,d j ), and generate a two-dimensional data table, where m≥8, n≥8, and both are positive integers;

[0038] The selection of n×m nodes on the two-dimensional rectangular domain is non-uniform. Due to the existence of the scattering enhancement effect near the radiation source, the changes in the prompt radiation environment parameters deviate from the exponential decay law. The selection of nodes needs to be denser, and the selection of nodes farther away from the radiation source can be sparser.

[0039] Step 3) Determine the target scene parameters to be measured: target distance interpolation point d tar (d0≤d tar ≤d n-1 ) and the target source high interpolation point h tar (h0≤h tar ≤h m-1 );

[0040] Step 4) Use the bisection method to find the target distance interpolation point d tar Two-dimensional data table d i The left boundary d in the sequence left and right boundary d right , and obtain the corresponding one-dimensional source high data node sequence value P(d left ,h j ) and P(d right ,h j );

[0041] Step 5), respectively with P(d left ,h j ) and P(d right ,h j ) as the interpolation node sequence, and use the Lagrange interpolation method to calculate the target source high interpolation point h on the left and right boundary sequences. tar The approximate value of the nuclear radiation environment parameter P(d left ,h tar ) and P(d right ,h tar );

[0042] Step 6) Interpolate the result P(d) with the left and right boundaries left ,h tar ) and P(d right ,h tar ) is the data point, and the linear interpolation method is used to calculate the target distance interpolation point d tar The prompt nuclear radiation environment parameter value P1(d tar ,h tar );

[0043] Step 7) Use the bisection method to find the target source high interpolation point h tar In the two-dimensional data table h j The lower boundary h in the sequence down and the upper boundary hup , and obtain the corresponding one-dimensional distance data node sequence P(d i ,h down ) and P(d i ,h up );

[0044] Step 8), respectively with P(d i ,h down ) and P(d i ,h up ) as the interpolation node sequence, and use the Lagrange interpolation method to calculate the target distance interpolation point d on the upper and lower boundary sequences tar The approximate value of the nuclear radiation environment parameter P(d tar ,h down ) and P(d tar ,h up );

[0045] Step 9), upper and lower boundary interpolation results P(d tar ,h down ) and P(d tar ,h up ) is the data point, and the target source high interpolation point h is calculated using the linear interpolation method. tar The prompt nuclear radiation environment parameter value P2(d tar ,h tar );

[0046] Step 10) Take the interpolation result P1(d tar ,h tar ) and the interpolation result P2(d tar ,h tar ) as the target distance interpolation point d tar and the target source high interpolation point h tar The prompt nuclear radiation environment parameter value of the target scene to be measured is P(d tar ,h tar )=(P1+P2) / 2.

[0047] In the interpolation calculation process in step 5), step 6), step 8), and step 9), it is necessary to first take the base 10 logarithm of the nuclear radiation environment parameter value used as the interpolation data point, and then use the corresponding interpolation method to perform interpolation. The obtained interpolation result is used as an exponential to perform an exponential operation with base 10 to convert it into the prompt nuclear radiation environment parameter value of the corresponding interpolation point, thereby avoiding the negative value that is inconsistent with physical laws when the direct interpolation result is obtained.

[0048] To avoid the Runge effect, the Lagrange interpolation method in steps 5) and 8) automatically selects eight nodes from the given interpolation nodes for interpolation, with the specified interpolation point located in the middle of these nodes. If the interpolation point is near one end of the interval where the node resides, fewer than eight nodes are selected. If the interpolation point is outside the interval where the node resides, only four nodes at the end of the interval are used for interpolation.

[0049] Taking the two-dimensional data table of prompt gamma tissue dose as an example, the binary Lagrangian-linear interpolation average method (hereinafter referred to as the interpolation method) is used to give the interpolation results of the target distance and target source height. The specific steps include:

[0050] Step 1) Construct a uniform atmosphere-soil model for atmospheric transport of prompt γ radiation, such as Figure 2 Specifically, the atmosphere is an air layer 5000m thick with a density of 1.225g / cm 3 The soil is 2m thick concrete with a density of 2.31g / cm 3 .

[0051] Step 2) Use the Monte Carlo method to calculate a two-dimensional data table showing the prompt gamma tissue dose at 1 m above the ground as a function of source height and distance. Nineteen nodes were set within a 2000 m source height range, and 14 nodes were set within a 4000 m distance range. See Table 1 for details.

[0052] Table 1 Prompt γ tissue dose two-dimensional data table

[0053]

[0054]

[0055] Step 3) Set the radiation environment to be calculated as: prompt γ tissue dose at a target distance of 1200m and a target source height of 1120m.

[0056] Step 4) Use the dichotomy method to take the left and right boundaries of the target distance 1200m in the two-dimensional data table distance interval as 1000m and 1500m respectively.

[0057] Step 5) Select the left and right boundaries of 1000m and 1500m as the interpolation node sequence. First, take the base 10 logarithm of the node sequence. Then use the 8-node Lagrange interpolation method to interpolate the point 1120m above the target source and use the interpolation result as the exponential operation with base 10. The prompt γ tissue dose at (1000m, 1120m) is approximately 0.388Gy, and the prompt γ tissue dose at (1500m, 1120m) is approximately 0.070Gy. Figure 3 As shown in (a).

[0058] Step 6) Take the values at (1000 m, 1120 m) and (1500 m, 1120 m) as data points. First, take the base 10 logarithm of the data points. Then, use the linear interpolation method to interpolate the points at a target distance of 1200 m and use the interpolation result as the exponential operation with base 10. Finally, the prompt γ tissue dose at the target point (1200 m, 1120 m) after interpolation in the distance direction is approximately 0.196 Gy.

[0059] Step 7) Use the binary method to take the target source height of 1120m and the upper and lower boundaries of the source height interval in the two-dimensional data table as 1100m and 1200m respectively.

[0060] Step 8) Select the upper and lower boundaries of the source height of 1100m and 1200m as the interpolation node sequence. First, take the logarithm of the node sequence with base 10. Then use the 8-node Lagrange interpolation method to interpolate the points at a target distance of 1200m and use the interpolation result as the exponential operation with base 10 to obtain the approximate prompt γ tissue dose of 0.213Gy at (1200m, 1100m) and the approximate prompt γ tissue dose of 0.154Gy at (1200m, 1200m). Figure 3 (b) shown.

[0061] Step 9) Take the values at (1200 m, 1100 m) and (1200 m, 1200 m) as data points. First, take the base 10 logarithm of the data points. Then, use the linear interpolation method to interpolate the points at the target source height of 1120 m and use the interpolation result as the exponential operation with base 10. Finally, the prompt γ tissue dose at the target point (1200 m, 1120 m) after interpolation from the source height direction is approximately 0.199 Gy.

[0062] Step 10) Take the average value of the interpolation results in the two directions as the final prompt γ tissue dose value at the point (1200m, 1120m), which is 0.198Gy. Figure 4 shown.

[0063] For comparison, the prompt gamma tissue doses at a source height of 875 m were calculated using the binary Lagrangian-linear interpolation averaging method and the Monte Carlo method at distances of 80 m, 150 m, 300 m, 500 m, 700 m, 900 m, 1300 m, 1700 m, 2400 m, 2800 m, 3100 m, and 3800 m, respectively, at a height of 1 m above the ground. The results and relative deviations are shown in Table 2. Considering the inherent statistical error of the Monte Carlo (MC) calculation method, the results of the two calculations can be considered consistent.

[0064] Table 2 Prompt γ tissue dose and relative deviation

[0065]

[0066] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the present invention.

Claims

1. A method for rapidly acquiring prompt nuclear radiation environment parameters based on interpolation, characterized in that: The following steps are involved: Step 1) Establish a prompt nuclear radiation transport model; Step 2) Using the Monte Carlo method, calculate n×m nodes (d i ,h j ) of the prompt nuclear radiation environment parameter value P(h i ,d j ) and generate a two-dimensional data table, where i = 0, 1, ..., n-1; j = 0, 1, ..., m-1; m ≥ 8, n ≥ 8, and they are all positive integers; Step 3) Determine the target scene parameters to be measured: target distance interpolation point d tar The interpolation point h with the target source tar ; where d0≤d tar ≤d n-1 ,h0≤h tar ≤h m-1 ; Step 4) Find the target distance interpolation point d tar Two-dimensional data table d i The left boundary d in the sequence left and right boundary d right , and obtain the corresponding one-dimensional source high data node sequence value P(d left ,h j ) and P(d right ,h j ); Step 5), respectively with P(d left ,h j ) and P(d right ,h j ) as the interpolation node sequence, interpolation calculation of the target source high interpolation point h on the left and right boundary sequences tar The approximate value of the nuclear radiation environment parameter P(d left ,h tar ) and P(d right ,h tar ); Step 6) Interpolate the result P(d) with the left and right boundaries left ,h tar ) and P(d right ,h tar ) is the data point, and the interpolation calculation target distance interpolation point d tar The prompt nuclear radiation environment parameter value P1(d tar ,h tar ); Step 7) Find the target source high interpolation point h tar In the two-dimensional data table h j The lower boundary h in the sequence down and the upper boundary h up , and obtain the corresponding one-dimensional distance data node sequence P(d i ,h down ) and P(d i ,h up ); Step 8), respectively with P(d i ,h down ) and P(d i ,h up ) as the interpolation node sequence, interpolation calculation upper and lower boundary sequence target distance interpolation point d tar The approximate value of the nuclear radiation environment parameter P(d tar ,h down ) and P(d tar ,h up ); Step 9), upper and lower boundary interpolation results P(d tar ,h down ) and P(d tar ,h up ) is the data point, and the interpolation calculation target source high interpolation point h tar The prompt nuclear radiation environment parameter value P2(d tar ,h tar ); Step 10) Take the interpolation result P1(d tar ,h tar ) and the interpolation result P2(d tar ,h tar ) as the target distance interpolation point d tar and the target source high interpolation point h tar The prompt nuclear radiation environment parameter value of the target scene to be measured is P(d tar ,h tar )=(P1+P2) / 2.

2. The method for rapidly acquiring prompt nuclear radiation environmental parameters based on interpolation according to claim 1, characterized in that: In both step 4) and step 7), the binary search method is used to find the target distance interpolation point d tar Two-dimensional data table d i The left boundary d in the sequence left and right boundary d right , and the target source high interpolation point h tar In the two-dimensional data table h j The lower boundary h in the sequence down and the upper boundary h up .

3. The method for rapidly acquiring prompt nuclear radiation environmental parameters based on interpolation according to claim 2, characterized in that: In step 6) and step 9), the linear interpolation method is used for interpolation calculation.

4. The method for rapidly acquiring prompt nuclear radiation environmental parameters based on interpolation according to claim 3, characterized in that: In step 5) and step 8), the Lagrange interpolation method is used for interpolation calculation.

5. The method for rapidly acquiring prompt nuclear radiation environmental parameters based on interpolation according to any one of claims 1 to 4, characterized in that: In step 5), step 6), step 8) and step 9), the interpolation calculation process is: ① Take the logarithm with base 10 of the nuclear radiation environment parameter value used as the interpolation data point; ②Perform interpolation calculation; ③ The interpolation result is used as an exponential and an exponential operation with a base of 10 is performed to convert it into the prompt nuclear radiation environmental parameter value of the corresponding interpolation point.

6. The method for rapidly acquiring prompt nuclear radiation environmental parameters based on interpolation according to claim 4, characterized in that: When the Lagrange interpolation method is used for interpolation calculation in step 5) and step 8), at least 4 interpolation nodes are selected, and the determination rule is: When the interpolation point is in the node interval and the number of nodes before and after it is greater than 4, 8 interpolation nodes are selected; when the interpolation point is close to either end of the node interval and the number of nodes on one side is less than 4, 4 to 7 interpolation nodes are selected; when the interpolation node is outside the node interval, the interpolation nodes selected are the 4 nodes close to the interpolation point in the node interval.

Images