阅读说明：本技术 体素衰减效率加权平均的sgs断层效率刻度方法 (SGS fault efficiency calibration method for voxel attenuation efficiency weighted average ) 是由 郑洪龙 庹先国 石睿 李怀良 李志刚 何艾静 母襄樊 王叶蔺 刘威 于 2018-09-07 设计创作，主要内容包括：本发明公开了一种解决已有方法通用性差、工作量大、准确度低问题的体素衰减效率加权平均的SGS断层效率刻度方法。该方法首先通过建立空间点源效率函数确定SGS断层体素的无衰减效率,然后计算体素发射的γ射线进入探测器过程中在不同断层里的衰减长度,结合各断层的线衰减系数确定体素的衰减效率,最后对断层中所有体素的衰减效率进行加权平均,实现断层的衰减效率刻度。采用该方法在探测系统不变的情况下,对探测区域内的任意核废物桶位置、断层个数和体素个数,可快速实现断层衰减效率刻度,使刻度实现过程通用化、简单快捷化,避免了蒙特卡罗方法计算量巨大的局限,同时相比传统方法提高了效率刻度准确度。(The invention discloses an SGS fault efficiency calibration method for weighted average of voxel attenuation efficiency, which solves the problems of poor universality, large workload and low accuracy of the existing method. The method comprises the steps of firstly determining the non-attenuation efficiency of SGS fault voxels by establishing a space point source efficiency function, then calculating the attenuation lengths of gamma rays emitted by the voxels in different faults in the process of entering a detector, determining the attenuation efficiency of the voxels by combining the line attenuation coefficients of all the faults, and finally performing weighted average on the attenuation efficiencies of all the voxels in the faults to realize the attenuation efficiency scale of the faults. By adopting the method, under the condition that a detection system is not changed, the fault attenuation efficiency scale can be quickly realized for any nuclear waste barrel position, fault number and voxel number in a detection area, so that the scale realization process is generalized, simple and rapid, the limitation of huge calculation amount of a Monte Carlo method is avoided, and meanwhile, the efficiency scale accuracy is improved compared with the traditional method.)

1. The SGS fault efficiency calibration method for the voxel attenuation efficiency weighted average is characterized by comprising the following steps of:

1) establishing a point source space efficiency function of a detector system;

selecting a standard experimental point source with a wider gamma ray emission energy E range, placing the point source in a system detection area space, and carrying out experimental measurement on the detection efficiency of a plurality of equally spaced scattered point positions (x, y, z) in the area; and carrying out multivariate nonlinear regression fitting on the obtained detection efficiency of the gamma rays with different energies at different spatial positions by adopting a point source spatial efficiency function model, wherein the function model is as follows:

in the formula,. epsilon. (x, y, z, E, a)_i) For the space efficiency of the point source, (x, y, z) is the coordinate position of the point source under a rectangular space coordinate system, E is the energy of the point source for emitting gamma rays, and a_i(i ═ 1,2, …,9) as parameters;

2) calculating the attenuation length between voxel gamma ray layers;

dividing a nuclear waste barrel into N layers longitudinally at equal intervals, wherein each fault is evenly divided into K voxels; when the detector is at the ith layer position, gamma rays emitted by the kth voxel in the jth fault enter the detector, and the attenuation distance of each fault is T_kj；

The kth voxel in the jth fault is projected onto the ith fault, and the length from the projection point to the center of the end face of the detector is L₁The length from the center of the ith fault to the center of the end face of the detector is L₂，L₁And L₂Has an included angle theta, L₁Is divided into an outer barrel part L₃And a barrel inner part L₄(i.e., L)₁＝L₃+L₄) The radius of the barrel is R, and the length from the voxel point to the center of the end face of the detector is L₅，L₅And L₁Is at an included angle of

Total attenuation length L in the bucket during gamma photons emitted from kth voxel center point enter the detector₆The calculation is as follows:

L₂＝y₀-y_H

from the trigonometric relation:

L₄＝L₁-L₃

according to the obtained included angle

until the gamma ray exits the nuclear waste bin, the attenuation length through the jth fault is:

when j < i, starting from the jth fault where the kth voxel is, the attenuation lengths are sequentially as follows:

until the gamma ray exits the nuclear waste bin, the attenuation length through the jth fault is:

3) calculating the attenuation coefficient of gamma rays;

transmitting each fault of the nuclear waste barrel through gamma rays of multiple energy E emitted by an external transmission source to obtain the gamma ray attenuation coefficient of each fault medium, and the line attenuation coefficient of the jth layer of sample medium:

in the formula I₀(E) Intensity of incident gamma rays of energy E, I_j(E) Intensity of gamma ray after penetration of fault, mu_j(E) The gamma ray attenuation coefficient of the j-th layer medium of the waste barrel, and d is the diameter of the nuclear waste barrel. According to the calculated linear attenuation coefficient mu of different energies E_j(E) Establishing mu_j(E) Relation to gamma ray energy E: mu.s_j(E)＝f(E)；

4) A scale of attenuation efficiency;

calculating the non-attenuation efficiency epsilon of the center point of each voxel by adopting the point source space efficiency function in the step 1)_ijk(E) Epsilon (x, y, z, E); the attenuation efficiency calculation of the fault is realized by carrying out weighted average on the attenuation efficiency of K voxels in the fault, and the detection efficiency of the detector on the sample on the j layer at the i layer position is as follows:

in the formula, epsilon_ijk(E) Efficiency of unattenuated detection of kth voxel center in jth layer sample for detector at i-layer position, μ_j(E) Is the line attenuation coefficient, T, of the sample at layer j_kjAt each sample layer during entry of gamma photons emitted for the kth voxel center point into the detectorThe decay length.

2. A voxel attenuation efficiency weighted average SGS tomographic efficiency calibration method according to claim 1, characterized in that: the attenuation effect of different faults is considered by the voxel attenuation efficiency; in the step 4), calculating the attenuation efficiency of the voxel, and considering the attenuation effect of different faults; the specific measures are as follows: calculating attenuation lengths of rays in different faults through the step 2), calculating a line attenuation coefficient of each fault through the step 3), and calculating an attenuation factor in a single fault according to a gamma ray attenuation law, wherein the total attenuation factor is a product of the attenuation factors of each fault; therefore, the calculation of the voxel attenuation efficiency is realized.

3. A voxel attenuation efficiency weighted average SGS tomographic efficiency calibration method according to claim 1, characterized in that: carrying out weighted average on the attenuation efficiency of all voxels in each fault to realize the attenuation efficiency calculation of the fault; a single fault is divided into K voxels, the attenuation efficiencies of the K voxels in the fault are weighted and averaged, the weighting coefficient of the attenuation efficiency of each voxel is 1/K, namely the attenuation efficiencies of the K voxels are averaged, and the attenuation efficiency of the fault is calculated.

Technical Field

The invention relates to an SGS fault efficiency calibration method based on voxel attenuation efficiency weighted average in a nuclear waste bucket layered gamma scanning analysis process.

Background

It is well known that: in the gamma nondestructive detection analysis of the nuclear waste bin, qualitative and quantitative analysis of radionuclide in the nuclear waste bin can be quickly realized by a layered gamma scanning (SGS) technology. The method comprises the steps of detecting a 200L nuclear waste barrel by adopting an SGS technology, longitudinally dividing the whole nuclear waste barrel into a plurality of layers, then rotating each fault at a constant speed to realize equivalent and uniform distribution of a sample medium and radioactive nuclides of each fault, and realizing radioactive nuclide identification and activity calculation in the nuclear waste barrel through transmission measurement and emission measurement.

In the transmission measurement, each fault of the nuclear waste barrel is transmitted by multi-energy gamma rays emitted by an external transmission source, and the gamma ray attenuation coefficient of each fault medium is obtained, wherein the line attenuation coefficient is calculated as follows:

in the formula I₀(E) Intensity of incident gamma rays of energy E, I_i(E) Intensity of gamma ray after penetration of fault, mu_i(E) The gamma ray attenuation coefficient of the ith layer of the waste barrel medium, and d is the diameter of the nuclear waste barrel.

In emission measurement, a transmission source is closed, the radioactive nuclide in the nuclear waste barrel fault is measured, the radioactive nuclide species and the characteristic peak count are obtained, and the attenuation efficiency is calculated by combining the attenuation coefficient of the line obtained by transmission measurement, so that the activity of the radioactive nuclide in the fault is obtained:

F_i(E)＝exp(-μ_i·R)

ε_i(E)＝ε₀(E)·F_i(E)

in the formula, F_i(E) For the attenuation factor, R is the radius of the barrel, ε₀(E) For efficiency of detection without attenuation, e_i(E) For attenuation efficiency, n_i(E) Is characteristic peak count, f (E) is emissivity branch ratio, t is measurement time, A_i(E) Is the activity of the fault radionuclide.

And (3) combining transmission measurement and emission measurement to finish SGS scanning analysis of all faults of the nuclear waste bucket, summing the activity of each layer, and calculating the radioactivity of the whole nuclear waste bucket:

wherein A (E) is the activity of the nuclear waste bucket, and I is the total number of layers.

The traditional SGS method adopts the fault central point source efficiency epsilon₀(E) And an attenuation factor F with the barrel radius R as the attenuation length_i(E) And calculating the central attenuation efficiency epsilon of the layer of sample_i(E) Without considering the decay efficiency at all positions of the fault, which is not in accordance with the equivalent uniform distribution of radionuclides. Meanwhile, in emission measurement, when a detector detects a current layer sample, gamma photons emitted by an adjacent multilayer sample enter the detector, and the problem of interlayer crosstalk correction is not considered in the conventional method, so that the detection precision of the current SGS method is low and the error is large. At present, the efficiency calibration by a shell source method provided by researchers still needs to manufacture an experimental line source, and meanwhile, the method is limited to be only suitable for the situation that all sample media in the whole barrel are the sameIn the case of different densities of the sample media for each layer, this cannot be calculated.

According to the actual SGS detection of the nuclear waste barrel, the sample medium and the radionuclide of each fault are equivalently and uniformly distributed, but the sample medium and the radionuclide distribution among the faults are different, and meanwhile, the interlayer crosstalk effect must be considered, and the activity is calculated as follows:

in the formula, epsilon_ij(E) Attenuation efficiency of the detector at the i-layer position for the j-th layer sample, N is the number of layers of the nuclear waste bucket, A_j(E) Activity of sample at layer j, n_i(E) Counts the detector's full energy peak at the ith position, and A (E) counts the activity of the entire nuclear waste bucket.

For attenuation efficiency epsilon_ij(E) The calibration is the key for obtaining the activity of the nuclide, the density range of the fault medium in the bucket is large, the energy of the gamma ray emitted by the nuclide is wide, and the Monte Carlo method is a feasible method in theory, but the workload of simulation work is huge, the time cost is too high, once the relative position of a detection part or the bucket of a detection system is changed, the calibration of the attenuation efficiency is needed to be done again, and the practicability of the method is limited.

Disclosure of Invention

The invention aims to provide a nuclear waste barrel SGS fault efficiency calibration method which is strong in universality, small in workload, simple, convenient and fast and high in accuracy.

The technical scheme adopted by the invention for solving the technical problems is as follows: the SGS fault efficiency calibration method for the voxel attenuation efficiency weighted average comprises the following steps:

1) establishing a point source space efficiency function of a detector system;

selecting a standard experimental point source with a wider gamma ray emission energy E range, placing the point source in a system detection area space, and carrying out experimental measurement on the detection efficiency of a plurality of equally spaced scattered point positions (x, y, z) in the area; and carrying out multivariate nonlinear regression fitting on the obtained detection efficiency of the gamma rays with different energies at different spatial positions by adopting a point source spatial efficiency function model, wherein the function model is as follows:

in the formula,. epsilon. (x, y, z, E, a)_i) For the space efficiency of the point source, (x, y, z) is the coordinate position of the point source under a rectangular space coordinate system, E is the energy of the point source for emitting gamma rays, and a_i(i ═ 1,2, …,9) as parameters;

2) calculating the attenuation length between voxel gamma ray layers;

dividing a nuclear waste barrel into N layers longitudinally at equal intervals, wherein each fault is evenly divided into K voxels; when the detector is at the ith layer position, gamma rays emitted by the kth voxel in the jth fault enter the detector, and the attenuation distance of each fault is T_kj；

The kth voxel in the jth fault is projected onto the ith fault, and the length from the projection point to the center of the end face of the detector is L₁The length from the center of the ith fault to the center of the end face of the detector is L₂，L₁And L₂Has an included angle theta, L₁Is divided into an outer barrel part L₃And a barrel inner part L₄(i.e., L)₁＝L₃+L₄) The radius of the barrel is R, and the length from the voxel point to the center of the end face of the detector is L₅，L₅And L₁Is at an included angle of

The total length of the attenuation of the voxel point by the medium in the barrel is L₆(ii) a The voxel position coordinates are (x, y, z), and the current layer center position coordinates are (0, y)₀0) and the central coordinates of the end face of the detector are (0, y)_H,0)；

Total attenuation length L in the bucket during gamma photons emitted from kth voxel center point enter the detector₆The calculation is as follows:

L₂＝y₀-y_H

from the trigonometric relation:

obtaining:

L₄＝L₁-L₃

according to the obtained included angle

And the total attenuation length L of the medium₆Determining the position of the fault at which the gamma ray emitted by the kth voxel is specifically attenuated; let each fault be h, when j>When the number i is larger, the attenuation lengths are sequentially as follows from the jth fault in which the kth voxel is positioned:

until the gamma ray exits the nuclear waste bin, the attenuation length through the jth fault is:

when j < i, starting from the jth fault where the kth voxel is, the attenuation lengths are sequentially as follows:

until the gamma ray exits the nuclear waste bin, the attenuation length through the jth fault is:

3) calculating the attenuation coefficient of gamma rays;

transmitting each fault of the nuclear waste barrel through gamma rays of multiple energy E emitted by an external transmission source to obtain the gamma ray attenuation coefficient of each fault medium, and the line attenuation coefficient of the jth layer of sample medium:

in the formula I₀(E) Intensity of incident gamma rays of energy E, I_j(E) Intensity of gamma ray after penetration of fault, mu_j(E) The gamma ray attenuation coefficient of the j-th layer medium of the waste barrel, and d is the diameter of the nuclear waste barrel. According toCalculating the obtained linear attenuation coefficient mu of different energies E_j(E) Establishing mu_j(E) Relation to gamma ray energy E: mu.s_j(E)＝f(E)；

4) A scale of attenuation efficiency;

calculating the non-attenuation efficiency epsilon of the center point of a single voxel by adopting the point source space efficiency function in the step 1)_ijk(E) Epsilon (x, y, z, E); adopting the step 2) to calculate the attenuation length T of the gamma ray emitted by a single voxel in each fault in the process of entering the detector_kj(ii) a Calculating the line attenuation coefficient mu of the gamma ray emitted by a single voxel in the sample of the j layer by adopting the step 3)_j(E)。

According to the law of gamma ray attenuation, exp (-mu)_j(E)T_kj) Is the attenuation factor of a single voxel gamma ray in a single slice. Considering the attenuation effect of different faults, according to the gamma ray attenuation law, the total attenuation factor is the product of the attenuation factors of the faults, namely

Voxel attenuation efficiency thus the attenuation efficiency epsilon of a detector for a single voxel, taking into account the attenuation effects of the various faults_ijkk(E) Can be calculated from the following relation:

dividing a single fault into K voxels, carrying out weighted average on the attenuation efficiency of the K voxels in the fault, wherein the weighting coefficient of the attenuation efficiency of each voxel is 1/K, namely, the average value of the attenuation efficiency of the K voxels is obtained, and the attenuation efficiency of the fault is calculated; therefore, the detection efficiency of the detector for the sample on the j-th layer at the i-layer position is as follows:

in the formula, epsilon_ijk(E) Efficiency of unattenuated detection of kth voxel center in jth layer sample for detector at i-layer position, μ_j(E) Line attenuation for sample of layer jCoefficient, T_kjThe attenuation length of the gamma photon emitted for the kth voxel center point at each sample layer during its entry into the detector.

For a fixed detection system, the point source space efficiency function obtained by fitting is unique, and when the linear distance between the nuclear waste barrel and the detection system, the volume of the barrel, the number of faults and the number of voxels are changed, the established point source space efficiency function can determine the voxel non-attenuation efficiency, so that the method has universality.

In step 4), the voxel attenuation efficiency is calculated, taking into account the attenuation effects of different faults. (ii) a The specific measures are as follows: calculating the attenuation lengths of rays in different faults through the step 2), calculating the line attenuation coefficient of each fault through the step 3), and calculating the attenuation factor in a single fault according to the gamma ray attenuation law, wherein the total attenuation factor is the product of the attenuation factors of the faults (namely the attenuation effects of the different faults are considered), thereby realizing the calculation of the voxel attenuation efficiency.

And carrying out weighted average on the attenuation efficiency of all voxels in one fault, and realizing the attenuation efficiency calculation of the fault. The single fault is divided into K voxels, and the attenuation efficiency of the single voxel is epsilon_ijkk(E) The attenuation efficiency epsilon of the fault is realized by carrying out weighted average on the attenuation efficiency of K voxels in the fault, and the weighting coefficient of the attenuation efficiency of each voxel is 1/K, namely the average value of the attenuation efficiency of K voxels is obtained_ij(E) Is calculated as_ij(E) The calculation method of (2) is as follows:

the invention has the beneficial effects that: the SGS fault efficiency calibration method based on voxel attenuation efficiency weighted average can improve the accuracy of efficiency calibration, and meanwhile, the method has universality and is simple, convenient and quick. Firstly, uniformly dividing a fault sample into a plurality of tiny voxels (K voxels), wherein the weighting coefficient of the attenuation efficiency of each voxel is 1/K, and the method is fully close to the theoretical assumption of uniform distribution of radioactive nuclides; the attenuation effect of gamma rays emitted by each fine voxel in different faults is considered, so that the attenuation efficiency calculation of the detector on different fault samples is accurately realized, an activity calculation equation set capable of eliminating interlayer crosstalk is finally established, and the accuracy of efficiency calibration is improved. The method combines the center point efficiency of each voxel with the attenuation factor of each fault to realize the calculation of the attenuation efficiency of the fault, is not influenced by the linear distance between a barrel and a detection system, the medium in the barrel, the number of the faults, the number of the voxels and other factors, and has universality, simplicity and convenience. Compared with the traditional method, the method provided by the invention is more in line with the actual detection process, the calibration accuracy is higher, the limitation of huge calculation amount of the Monte Carlo method is avoided, and the method has high actual use value and wide application prospect.

Secondly, the SGS fault efficiency calibration method for weighted average of voxel attenuation efficiency has the advantages that a point source space efficiency function obtained by fitting is unique for a fixed detection system, and when the linear distance between a nuclear waste barrel and the detection system, the volume of the barrel, the number of faults and the number of voxels change, the established point source space efficiency function can determine the voxel non-attenuation efficiency and has universality.

Drawings

FIG. 1 is a schematic diagram of a nuclear waste bucket SGS test;

FIG. 2 is a schematic diagram of experimental measurement of the spatial efficiency of a point source;

FIG. 3 is a schematic view of voxel division of a single slice sample;

FIG. 4 is a schematic of a total attenuation length calculation;

FIG. 5 is a schematic of the decay length calculation for different faults.

The following are marked in the figure: 1-nuclear waste bucket, 2-collimator, 3-transmission source, 4-detector, 5-voxel.

Detailed Description

The invention is further illustrated with reference to the following figures and examples.

As shown in fig. 1 to 5, the SGS fault efficiency calibration method based on voxel attenuation efficiency weighted average according to the present invention includes the following steps:

1) establishing a point source space efficiency function of a detector system;

selecting a standard experimental point source with a wider gamma ray emission energy E range, placing the point source in a system detection area space, and carrying out experimental measurement on the detection efficiency of a plurality of equally spaced scattered point positions (x, y, z) in the area; and carrying out multivariate nonlinear regression fitting on the obtained detection efficiency of the gamma rays with different energies at different spatial positions by adopting a point source spatial efficiency function model, wherein the function model is as follows:

in the formula,. epsilon. (x, y, z, E, a)_i) For the space efficiency of the point source, (x, y, z) is the coordinate position of the point source under a rectangular space coordinate system, E is the energy of the point source for emitting gamma rays, and a_i(i ═ 1,2, …,9) as parameters;

2) calculating the attenuation length between voxel gamma ray layers;

dividing a nuclear waste barrel into N layers longitudinally at equal intervals, wherein each fault is evenly divided into K voxels; when the detector is at the ith layer position, gamma rays emitted by the kth voxel in the jth fault enter the detector, and the attenuation distance of each fault is T_kj；

The kth voxel in the jth fault is projected onto the ith fault, and the length from the projection point to the center of the end face of the detector is L₁The length from the center of the ith fault to the center of the end face of the detector is L₂，L₁And L₂Has an included angle theta, L₁Is divided into an outer barrel part L₃And a barrel inner part L₄(i.e., L)₁＝L₃+L₄) The radius of the barrel is R, and the length from the voxel point to the center of the end face of the detector is L₅，L₅And L₁Is at an included angle of

The total length of the attenuation of the voxel point by the medium in the barrel is L₆(ii) a The voxel position coordinates are (x, y, z), and the current layer center position coordinates are (0, y)₀0) and the central coordinates of the end face of the detector are (0, y)_H,0)；

From kth voxel central pointTotal attenuation length L in the barrel during entry of emitted gamma photons into the detector₆The calculation is as follows:

L₂＝y₀-y_H

from the trigonometric relation:

obtaining:

L₄＝L₁-L₃

according to the obtained included angle

And the total attenuation length L of the medium₆Determining the position of the fault at which the gamma ray emitted by the kth voxel is specifically attenuated; let each fault be h, when j>When the number i is larger, the attenuation lengths are sequentially as follows from the jth fault in which the kth voxel is positioned:

until the gamma ray exits the nuclear waste bin, the attenuation length through the jth fault is:

when j < i, starting from the jth fault where the kth voxel is, the attenuation lengths are sequentially as follows:

until the gamma ray exits the nuclear waste bin, the attenuation length through the jth fault is:

3) calculating the attenuation coefficient of gamma rays;

transmitting each fault of the nuclear waste barrel through gamma rays of multiple energy E emitted by an external transmission source to obtain the gamma ray attenuation coefficient of each fault medium, and the line attenuation coefficient of the jth layer of sample medium:

in the formula I₀(E) Intensity of incident gamma rays of energy E, I_j(E) Intensity of gamma ray after penetration of fault, mu_j(E) The gamma ray attenuation coefficient of the j layer medium of the waste barrel, and d is the diameter of the nuclear waste barrel; according to the calculated linear attenuation coefficient mu of different energies E_j(E) Establishing mu_j(E) Relation to gamma ray energy E: mu.s_j(E)＝f(E)；

4) A scale of attenuation efficiency;

calculating the non-attenuation efficiency epsilon of the center point of each voxel by adopting the point source space efficiency function in the step 1)_ijk(E) Epsilon (x, y, z, E); the attenuation efficiency calculation of the fault is realized by carrying out weighted average on the attenuation efficiency of K voxels in the fault, and the detection efficiency of the detector on the sample on the j layer at the i layer position is as follows:

in the formula, epsilon_ijk(E) Efficiency of unattenuated detection of kth voxel center in jth layer sample for detector at i-layer position, μ_j(E) Is the line attenuation coefficient, T, of the sample at layer j_kjThe attenuation length of the gamma photon emitted for the kth voxel center point at each sample layer during its entry into the detector.

Specifically, for a fixed detection system, a point source space efficiency function obtained through fitting is unique, when the linear distance between a nuclear waste barrel and the detection system, the volume of the barrel, the number of faults and the number of voxels are changed, the established point source space efficiency function can determine the voxel non-attenuation efficiency, and the method has universality. The attenuation effect of different faults is considered by the voxel attenuation efficiency; and carrying out weighted average on the attenuation efficiency of all voxels in one fault, and realizing the attenuation efficiency calculation of the fault.

The function parameters were obtained by fitting the experimental data in step 1) and the function model was obtained as follows:

calculating the voxel gamma ray interlayer attenuation length T in the step 2)_kj；

Calculating the gamma ray attenuation in step 3)Coefficient of reduction

Step 1) of adopting a point source space efficiency function in step 4), and T obtained in step 2 and step 3_kj、

Finally, calculating the attenuation-free efficiency of the center point of each voxel.