CN106991511B - Strong backward thrust method and system for point source, line source and surface source combined composite radiation source of nuclear power plant - Google Patents
Strong backward thrust method and system for point source, line source and surface source combined composite radiation source of nuclear power plant Download PDFInfo
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Abstract
The invention discloses a composite radiation source strength backward-pushing method and a composite radiation source strength backward-pushing system for point source and line source and surface source combination of a nuclear power plant, wherein in the method, dosage rates of a plurality of positions are obtained through a detector, normalized radiation source strength is dispersed in space, an optical distance is calculated by using a ray tracing method, and the calculation of equation coefficient is carried out by combining information such as materials, accumulation factors and the like, so that the source strength is reversely pushed; calculating the dose rate of the detector position, calculating key parameters such as standard deviation, slope, intercept and the like by carrying out linear regression analysis on the measured value and the calculated value, and further calculating a quality factor to measure the acceptability degree of each calculation result; and simultaneously, a weighted iteration method is provided, the error introduced by the detector with larger uncertainty is reduced, and the steps are repeated for multiple times in an iteration mode until the quality factor reaches a preset value, so that expected radiation source intensity information is obtained.
Description
Technical Field
The invention relates to a method and a system for calculating the intensity of a radiation source in a nuclear power plant, in particular to a method and a system for strongly backward pushing a composite radiation source combined by a point source, a line source and a surface source of the nuclear power plant.
Background
The radioactivity of a nuclear power plant comes from the active area of the fuel assemblies in the pressure vessel and the radiation source consists mainly of fission products, actinides and corrosion activation products. In the system operation, the radiation sources flow along with the coolant through a main loop system (including a pressure vessel, a main pump, a pressure stabilizer, a main pipeline and the like), a chemical vessel control system and the like, and the radiation sources are distributed on the surfaces of the coolant and related equipment. The radioactive source is strong in radioactivity, the dosage of daily activities of workers in normal operation of a nuclear power plant accounts for about 20% of the total annual dosage, the dosage of the workers accounts for 80% of the total annual dosage during overhaul of the nuclear power plant, and the exposure dosage is reduced mainly by shortening the stay time of the workers in a radiation area during overhaul of the nuclear power plant.
The radiation sources in the nuclear power plant are widely distributed, and particularly after long-time use and overhaul, the radiation intensity of the radiation sources at each position is more and more difficult to deduce according to engineering experience, so that when a lot of data are calculated, particularly in the calculation according to the radiation source intensity, because accurate basic information is difficult to obtain, the accuracy and the practicability are greatly influenced, and meanwhile, under the condition that the domestic current protection facilities and means are not complete, the irradiation risk of workers is greatly increased.
In the prior art, when the intensity of a radiation source needs to be calculated, a source item analysis method is generally adopted, firstly, generation items (such as inflow items, decay generation items and the like) and disappearance items (such as filtering items, leakage items and the like) of the radioactive substance are determined according to the generation and disappearance ways of the radioactive substance, physical models of the items are determined, then a nuclear concentration balance equation (set) is established for the radioactive substance according to the items, and finally the equation (set) is solved in a simultaneous manner The accuracy and the like are all problematic, and a new radiation source intensity acquisition way needs to be improved or proposed.
Due to the reasons, the inventor conducts intensive research on the existing method for calculating the source intensity information, according to experience, part of radioactive assemblies in a nuclear power plant can be simplified into a point source or a group of point sources, a line source or a group of line sources, and a plane source or a group of plane sources, for example, a thermal valve can be simplified into a point source, a pipeline can be simplified into a point source or a plurality of point sources, a line source, and some pipelines can be simplified into a cylindrical plane source, discretization treatment can be conducted on the plane source and the line sources, and then source intensity information is obtained by performing source intensity back-pushing according to information after discretization treatment, so that the composite radiation source intensity back-pushing method and the composite radiation source intensity back-pushing system for the combination of the point source and the plane source of the nuclear power plant, which can solve the problems, are designed.
Disclosure of Invention
In order to overcome the problems, the inventor of the invention carries out intensive research and designs a composite radiation source strong backward-pushing method and a system for point source, line source and surface source combination in a nuclear power plant, and the method and the system can obtain source strong data of the point source, the line source and the surface source in a complex geometric space structure in the nuclear power plant under the condition of fully ensuring the radiation safety of a human body; in the method, a detector is placed at a preset position in a nuclear power plant, and a detector with a shield is also placed at the position, so that the average energy of gamma rays emitted by a radiation source is obtained; in addition, a plurality of detectors for monitoring radiation values of the nuclear power plant are arranged in the nuclear power plant to obtain the dose rates of partial acquisition points, the normalized radiation source intensity is dispersed in space by using a point nuclear integration and weighted least square method combined mode, the passing distance of gamma rays emitted by each point source, line source and surface source in the space is judged by using a ray tracing method, the optical distance is calculated, the calculation of the coefficients of an equation set is carried out by combining information such as materials, accumulation factors and the like, and the source intensity is reversely deduced; then, a calculated value of the dose rate at the position of the detector is obtained, linear regression analysis processing is carried out on the measured value and the calculated value, key parameters such as standard deviation, slope, intercept and the like are obtained, and further a quality factor capable of representing physical meaning is obtained, and the quality factor can measure the acceptability of each calculation result; meanwhile, a weighted iteration method is provided, the error introduced by a detector with larger uncertainty is reduced, the steps are repeated for multiple times in an iteration mode until the quality factor meets the preset condition, and further the expected radiation source intensity and the uncertainty of the radiation field result are obtained, so that the method is completed.
Specifically, the present invention aims to provide the following:
(1) a composite radiation source strong backward pushing method of a point source, a line source and a surface source combination in a nuclear power plant is characterized by comprising the following steps:
step one, detecting dose rate D in a nuclear power plant by using a detector1,D2,D3…Di，
Step two, establishing an overdetermined equation set containing the radiation source intensity as shown in the following formula (one) according to the detected dose rate information,
Wherein the coefficient matrix a of the over-determined equation seti,jObtained by the following formulae (II) and (III),
(II)
In formula (iii), when the radiation source is a point source, p is 0, M is 1, and N is 1; when the radiation source is a line source, p is 1, and N is 1; when the radiation source is a plane source, p is 1;
step three, calculating the overdetermined equation set in the step two by a least square method to obtain the intensity information of the radiation source, wherein the intensity of the radiation source is represented by the following formula (IV)
Sj,0＝(aj,i·ai,j)-1·aj,i·Di(IV)
Wherein D isiIndicating the dose rate detected by the ith detector; j represents the number of radiation sources; m represents the maximum value which can be reached by the number of radiation sources; sjRepresents the intensity of the jth radiation source; sj,0Representing the intensity of the jth radiation source for which the initial calculation was not iterated; a isi,jRepresenting a coefficient matrix which is the dose response coefficient of the jth radiation source to the ith detector; BD (E, L (. mu. (E), r)0→rp) Indicating an accumulation factor, E and L (. mu. (E), r)0→rp) A function of (a); l (. mu.E, r)0→rp) Denotes an optical distance, is μ (E) and r0→rpA function of (a); μ (E) represents a cross-sectional/linear attenuation coefficient; r is0→rpRepresenting the distance of the radiation source to the detection point; c (E) represents a flux-dose conversion factor, which is a function of E; e represents energy, which is the average energy of gamma rays emitted by a radiation source in a nuclear power plant;
representing discrete source intensities; m and N respectively represent discrete labels on two coordinate axes after the surface source is dispersed on a two-dimensional coordinate;
preferably, after step three, the method further comprises the step of,
step four, calculating the dose rate D at the position of the detector according to the intensity information of the radiation source obtained in the step three1′,D2′,D3′…Di′；
And step five, performing linear fitting on the dose rate information detected by the detector and the dose rate information at the position of the detector obtained by calculation to obtain a linear equation of the relationship between the dose rate information and the dose rate information after fitting, and further obtain fitting parameters, wherein the fitting parameters comprise: average uncertainty, goodness-of-fit and corresponding weight matrix;
step six, iterating the new weight matrix obtained in the step five to the overdetermined equation set in the step two to obtain a weighted overdetermined equation, and further repeating the step two, the step three and the step four until the expected radiation source intensity information is obtained;
wherein D isi' denotes the calculated dose rate at the ith detector position.
(2) The composite radiation of the point source and the surface source combination of the nuclear power plant according to the above (1)The strong backward pushing method of the radiation source is characterized in that when the radiation source is a surface source, the discrete source is strong
Obtained by the following formula (V):
wherein S isU(M) and SV(N) respectively representing a source intensity weight factor on a U coordinate axis and a source intensity weight factor on a V coordinate axis after the surface source is dispersed on a two-dimensional coordinate;
preferably, when the surface source is a cylindrical surface source, SU(M) and SV(N) is obtained by the following formulae (six) and (seven), respectively:
Wherein eta is2,1、η2,2、η3,1And η3,2All represent cosine distribution constants, Z represents the height of the cylindrical surface source,
representing the angle of the cylindrical surface source;
preferably, when the surface source is a spherical source, SU(M) and SV(N) is obtained by the following formulae (eight) and (nine), respectively:
Wherein eta is2,1、η2,2、η3,1And η3,2All represent cosine distribution constants, theta represents the horizontal angle of the spherical source,
represents the vertical angle of the spherical source;
preferably, when the surface source is a rectangular surface source, SU(M) and SV(N) is obtained by the following formulas (ten) and (eleven), respectively:
Wherein eta is2,1、η2,2、η3,1And η3,2All represent cosine distribution constants, Z represents the length of the rectangular surface source, and y represents the width of the rectangular surface source;
preferably, when the surface source is a disk surface source, SU(M) and SV(N) is obtained by the following formulae (twelve) and (thirteen), respectively:
Wherein eta is1,1、η1,2、η3,1And η3,2Are all indicative of the cosine distribution constant,
representing the angle of the disk-shaped source and R the radius of the disk-shaped source.
(3) The method for strongly backward estimating the composite radiation source of the point source, the line source and the surface source combination in the nuclear power plant according to the above (1), is characterized in that the method for calculating the average energy E of the gamma rays emitted by the radiation source in the nuclear power plant comprises the following substeps:
substep 1, selecting a preset position in a nuclear power plant, wherein the preset position is at a distance t from a radiation source, placing a detector at the preset position, and collecting the dose rate I detected by the detector0，
Substep 2, retrieving the detector, covering a shielding layer on the outside of the detector, placing the detector at the preset position, and collecting the dose rate I detected by the detector;
or, the detector is taken back, a shielding body is placed at a preset position, then the detector is placed in the shielding body, and the dosage rate I detected by the detector is collected;
substep 3, I and I obtained according to substeps 1 and 20The mass attenuation coefficient μ of the clad or shield is calculated by the following formula (fourteen),
I/I0＝BDe-μt(fourteen)
And a substep 4 of obtaining the average energy E of the gamma rays emitted by the radiation source according to the calculation result of the substep 3.
(4) The method for strongly backward pushing the composite radiation source of the nuclear power plant point source/line source/surface source combination is characterized in that the method for calculating the optical distance L comprises the following substeps,
a sub-step a of tracking the passing process of the gamma ray from the radiation source to the detection point, recording the sequence of the gamma ray passing through the radiation region,
and a substep b, respectively calculating the distance of each radiation area, and finally calculating the total optical distance L by combining the linear attenuation coefficient of the material of each radiation area.
(5) The method for strongly backward pushing the composite radiation source of the point source and the surface source combination in the nuclear power plant according to the above (1), is characterized in that the overdetermined equation set in the second step is processed by using a least square method, and the process of obtaining the intensity information of the radiation source comprises the following substeps:
substep 3-1. solving the overdetermined system of equations
Expressed in matrix form as AX ═ b;
substep 3-2, solving the normal equation A of the matrixTAX＝ATb, i.e. X ═ ATA)-1ATb；
Substep 3-3, solving equation by trigonometric decomposition of symmetric matrix, and recording G ═ ATA, wherein G is a symmetric matrix;
substeps 3-4, solving for G ═ LDL by trigonometric decompositionTWherein L is a small triangular matrix and D is a diagonal matrix;
substeps 3-5, solving the lower triangular matrix equation system LY1＝ATb；
Substeps 3-6, solving the diagonal matrix equation set: DY (DY)2＝Y1；
And substeps 3-7, solving an upper triangular matrix equation set: l isTX＝Y2。
(6) The method for strongly backward pushing the composite radiation source of the combination of the point source, the line source and the surface source of the nuclear power plant according to the above (2), is characterized in that in the fifth step, linear fitting is performed by the following formula (fifteen),
Wherein, the estimated dose rate is represented; which is indicative of the slope of the estimate,
the estimated intercept is represented as a function of,
n represents the maximum number of detectors i can reach,
representing the calculated average value of the dose rate at the detector position,
representing the average value of the dose rate detected by the detector.
(7) The method for strongly backward pushing the composite radiation source of the combination of the point source, the line source and the surface source of the nuclear power plant according to the above item (6), is characterized in that in the fifth step, a weight function is obtained according to the uncertainty, and then a weight matrix W is obtained through the weight function, wherein the weight matrix W is obtained through the following formula (sixteen),
Where f represents the uncertainty of the fit,
the mean fit uncertainty is represented as a function of,
fia fit uncertainty representing an ith detector position; (ii) a
Representing a weight function.
(8) The method for strongly backward pushing the composite radiation source of the point source and the surface source combination in the nuclear power plant according to the item (6),
in step six, when SiIf the quality factor M is greater than 0, stopping the weighting iteration when the quality factor M reaches the maximum value, and outputting the intensity information of the radiation source, wherein the output intensity information of the radiation source is the expected intensity information of the radiation source;
wherein, each time step six is executed, a quality factor M is correspondingly obtained, and the quality factor M is obtained by the following formula (seventeen),
Wherein R is2The goodness of fit is expressed,
(9) a composite radiation source strong backward pushing system of a point source and line source and surface source combination of a nuclear power plant is used for executing the composite radiation source strong backward pushing method of the point source and line source and surface source combination of the nuclear power plant as claimed in claims 1 to 8.
(10) The composite radiation source strong backward-thrust system of the nuclear power plant point source line source and surface source combination according to the above (9), characterized in that the system comprises a detector, a gamma ray average energy calculation module and a radiation source intensity calculation module;
the detector is provided with a plurality of detectors, including a preset position detector and a nuclear power plant radiation value monitoring detector,
the preset position detector is arranged at a preset position with a determined distance from a radiation source in a radiation area of a nuclear power plant, and a detachable shielding layer is optionally coated outside the preset position detector;
the preset position detector is used for transmitting the detected radiation rate information to the gamma ray average energy calculating module,
the nuclear power plant radiation value monitoring detectors are distributed in a radiation area of the nuclear power plant and used for transmitting respectively detected dose rate information in the nuclear power plant to the radiation source intensity calculating module,
the gamma ray average energy calculating module is used for calculating the average energy E of gamma rays,
the radiation source intensity calculating module is used for calculating the intensity of the radiation source in the nuclear power plant.
The invention has the advantages that:
(1) according to the composite radiation source strong backward pushing method for the point source, the line source and the surface source combination of the nuclear power plant, provided by the invention, source strength data of the point source and the surface source under a complex geometric space structure in the nuclear power plant can be obtained under the condition of fully guaranteeing the radiation safety of a human body;
(2) according to the composite radiation source intensity backward-pushing method for the point source, the line source and the surface source combination of the nuclear power plant, provided by the invention, through repeated iterative computation, the finally obtained source intensity information of the point source, the line source and the surface source is ensured to be more close to a true value, and the method has a very high engineering application value.
Drawings
Fig. 1 shows an overall workflow diagram according to a preferred embodiment of the present invention.
Detailed Description
The invention is explained in more detail below with reference to the figures and examples. The features and advantages of the present invention will become more apparent from the description.
The word "exemplary" is used exclusively herein to mean "serving as an example, embodiment, or illustration. Any embodiment described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other embodiments.
The invention provides a strong backward pushing method of a composite radiation source of a point source, a line source and a surface source combination of a nuclear power plant, which comprises the following steps:
step one, receiving dose rate information D detected by a detector in a power plant1,D2,D3…DiIn the present invention, a plurality of detectors may be placed in a power plant, or a detector already existing in the nuclear power plant may be directly utilized, the detector already existing in the nuclear power plant is a nuclear power plant radiation value monitoring detector, or the two methods may be used in combination, where the position of the detector is required to be: there is no shield between the radiation source and the location, and the dose rate in the present invention is the irradiation dose rate. In the invention, the number of detectors is greater than the number of radiation sources in the nuclear power plant.
Step two, establishing an overdetermined equation set containing the intensity of the radiation source according to the detected dose rate information, wherein the overdetermined equation set is a formula (one) as follows,
Step three, calculating the overdetermined equation set in the step two by a least square method to obtain the intensity information of the radiation source, wherein the intensity of the radiation source is represented by the following formula (IV)
Sj,0＝(aj,i·ai,j)-1·aj,i·Di(IV)
Coefficient matrix a of the overdetermined system of equationsi,jIs obtained by the following formulas (two) and (three) after dispersing the surface source on the radiation space coordinate,
(II)
in formula (iii), when the radiation source is a point source, p is 0, M is 1, and N is 1; when the radiation source is a line source, p is 1, and N is 1; when the radiation source is a plane source, p is 1;
in the invention, because a plurality of areas needing to measure and calculate the intensity of the radiation source exist in one nuclear power plant, a plurality of radiation sources needing to be measured and calculated exist, in different areas or aiming at different radiation sources, the radiation sources can be simulated into point sources, line sources or plane sources, and can be measured and calculated by the formula (III), when the radiation sources are point sources, p is 0, M is 1, and N is 1; when the radiation source is a line source, p is 1, and N is 1; when the radiation source is a planar source, p is 1. When the radiation source is a point source, the radiation source may not be discretely treated, i.e.
After the third step, the intensity information of the radiation source can be obtained, but the intensity information may not be accurate enough, so the calculation is continued through the following steps to obtain the intensity information of the radiation source closer to the true value;
step four, calculating the dose rate D at the position of the detector according to the intensity information of the radiation source obtained in the step three1′,D2′,D3′…Di′；
And step five, performing linear fitting on the dose rate information detected by the detector and the dose rate information at the position of the detector obtained by calculation to obtain a linear equation of the relationship between the dose rate information and the dose rate information after fitting, and further obtain fitting parameters, wherein the fitting parameters comprise: average uncertainty, goodness-of-fit and corresponding weight matrix; the weight matrix in the present invention can be an internal weight matrix or an external weight matrix, and the obtaining method is consistent, except that the uncertainty of the external weight matrix is not calculated by the system, but is the error range of the detector input by the operator means.
Step six, iterating the weight matrix obtained in the step five to the overdetermined equation set in the step two to obtain a weighted overdetermined equation, and further repeating the step two, the step three and the step four until expected radiation source intensity information is obtained;
in the invention, D represents the dosage rate detected by a detector; diIndicating the dose rate detected by the ith detector; i represents the number of detectors; j represents the number of radiation sources, and m represents the maximum value which can be reached by the number of radiation sources; s represents the intensity of the radiation source; sjRepresents the intensity of the jth radiation source; sj,0Representing the intensity of the jth radiation source for which the initial calculation was not iterated; a isi,jThe representing coefficient matrix is the dose response coefficient of the jth radiation source to the ith detector, namely, the representing point source to detector response coefficient also represents the response coefficient of the discrete surface source to the detector in the invention; BD (E, L (. mu. (E), r)0→rp) Indicating an accumulation factor, E and L (. mu. (E), r)0→rp) A function of (a); l (. mu.E, r)0→rp) Denotes an optical distance, is μ (E) and r0→rpI.e. the optical distance is a function of the energy and the actual distance; μ (E) represents a linear attenuation coefficient; r is0→rpRepresenting the distance of the radiation source to the detection point; c (E) represents a flux-dose conversion factor, which is a function of E; e represents energy, which is the average energy of gamma rays emitted by a radiation source in a nuclear power plant; di' represents the calculated dose rate at the ith detector position;
representing discrete source intensities; m and N respectively represent discrete labels on two coordinate axes after the surface source is dispersed on the two-dimensional coordinates. Wherein the detection points represent the position of the detector, more precisely the position on the detector at which the radiation information is received.
Discrete source intensities as described in the present invention
Obtained by the following formula (V):
wherein S isU(M) and SV(N) respectively representing a source intensity weight factor on a U coordinate axis and a source intensity weight factor on a V coordinate axis after the surface source is dispersed on a two-dimensional coordinate;
preferably, when the surface source is a cylindrical surface source, SU(M) and SV(N) is obtained by the following formulae (six) and (seven), respectively:
Wherein eta is2,1、η2,2、η3,1And η3,2All represent cosine distribution constants, the default value of the cosine distribution constants is zero and can be set according to actual conditions, Z represents the height of the cylindrical surface source,
representing the angle of the cylindrical surface source; that is to say that the first and second electrodes,
preferably, when the surface source is a spherical source, SU(M) and SV(N) is obtained by the following formulae (eight) and (nine), respectively:
Wherein eta is2,1、η2,2、η3,1And η3,2All represent cosine distribution constants, the default value of the cosine distribution constants is zero, the cosine distribution constants can be set according to actual conditions, theta represents the horizontal angle of the spherical source,
represents the vertical angle of the spherical source; i.e. when eta2,1When equal to 0, SU(M)＝cosθM-cosθM+1，
When eta2,1When not equal to 0: sUThe value of (M) is:
when eta2,1When equal to 0
When eta2,1When not equal to 0:
preferably, when the surface source is a rectangular surface source, SU(M) and SV(N) is obtained by the following formulas (ten) and (eleven), respectively:
Wherein eta is2,1、η2,2、η3,1And η3,2The method comprises the following steps that cosine distribution constants are represented, default values of the cosine distribution constants are zero and can be set according to actual conditions, Z represents the length of a rectangular surface source, and y represents the width of the rectangular surface source; namely, it is
Preferably, when the surface source is a disk surface source, SU(M) and SV(N) is obtained by the following formulae (twelve) and (thirteen), respectively:
Wherein eta is1,1、η1,2、η3,1And η3,2All represent cosine distribution constants, the default value of the cosine distribution constant is zero, and the cosine distribution constant can be set according to actual conditions,
representing the angle of the disk-shaped source, and R representing the radius of the disk-shaped source, i.e.
When eta1,1When equal to 0
When eta2,1When not equal to 0: sU(M) has a value of
The accumulation factor described in the present invention is a term commonly used in the art, and can be explained and calculated with reference to the ordinary meaning in the art, and the general formula of the calculation is given as follows:
wherein KxThe fitting formula of (a) is as follows:
K(E,x)＝cxa+d[tanh(x/Xk-2)-tanh(-2)]/[1-tanh(-2)]；
where E is photon energy, MeV;xdistance from source point to calculated point, mfp; b is the accumulation factor at one mean free path; a, c, d, XkFor the empirical parameters, when the accumulation factor coefficient is selected, a logarithmic difference mode can be selected, that is:
a(Ea)＝{a(E1)·[log(E2)-log(Ea)]+a(E2)·[log(Ea)-log(E1)]}/[log(E2)-log(E1)]
in a preferred embodiment, the method for calculating the mean energy E of gamma rays emitted by a radiation source in a nuclear power plant comprises the following sub-steps:
substep 1, inside the nuclear power plantSelecting a preset position, wherein the preset position is at a distance t from the radiation source, placing a detector at the preset position, and collecting the dose rate I detected by the detector0，
Substep 2, retrieving the detector, covering a shielding layer on the outside of the detector, placing the detector at the preset position, and collecting the dose rate I detected by the detector;
or, the detector is taken back, a shielding body is placed at a preset position, then the detector is placed in the shielding body, and the dosage rate I detected by the detector is collected;
substep 3, I and I obtained according to substeps 1 and 20The mass attenuation coefficient μ of the clad or shield is calculated by the following formula (fourteen),
I/I0＝BDe-μt(fourteen)
And a substep 4, obtaining the average energy E of the gamma rays emitted by the radiation source by looking up a table according to the calculation result of the substep 3. The table of the lookup table may be a material section table, which is presented at pages 16-67 of ANSI/ANS 6.4.3, "Gamma-ray attenuation Coefficients and Buildup factory for Engineering Materials", American Nuclear Society, 1991. In the invention, all the used radiation energy is calculated by using the average energy, and if the energy difference of different areas in the nuclear power plant is large, the area can be considered to be independently measured, namely the average energy is independently measured, and the radiation source intensity is independently measured.
In a preferred embodiment, the method for calculating the optical distance L comprises the sub-steps of a tracking the course of the gamma rays passing from the radiation source to the detection point, and recording the sequence of the gamma rays passing through the radiation zone, i.e. calculating the distance r from the radiation source to the detection point by ray tracing0→rpWherein r is0Indicating the position of the radiation source, indicating the position r of the detection spotp. And a substep b, respectively calculating the distance of each radiation area, and finally calculating the total optical distance L by combining the linear attenuation coefficient of the material of each radiation area.
Specifically, when the traveling distance of the gamma ray is calculated, the space is described by a combined geometric method, and the spaces of different media are divided into different regions. And respectively calculating the distance Di between the intersection point of the gamma ray and each basic body and the inlet and the distance Do between the intersection point of the gamma ray and each basic body and the outlet. All the basic body numbers plus and minus are found in each area, with "+" and "-", which may include the following six steps,
(1) starting point r of each line0Determination of the region number Istart:
if there is no "-" element in a region, then all "+" elements in that region must satisfy the starting point r0In all "+" basis volumes, then the starting area of the ray can be considered to be that area; if there are "-" elements in the region, then all "+" elements in the region must satisfy the starting point r0In all "+" basis bodies, and all "-" basis bodies must satisfy the starting point r not containing the ray0Then the starting region of the ray is considered to be that region.
(2) End point r of each linepDetermination of the region number Ipend:
similarly, if there is no "-" element in a region, then all "+" elements in that region must meet the end point rpIn all "+" elementary volumes, then the ending area of the ray can be considered to be that area; if there are "-" elements in the zone, then all "+" elements in the zone must meet the end point rpIn all "+" basic bodies and all "-" basic bodies must satisfy the end point r not containing the raypThen the termination region of the ray is considered to be that region.
(3) Starting point r of each line0Determining the area outlet distance Zo corresponding to the area number:
if there is no "-" basic body in the gamma-ray starting region number, the smallest of the distances Do of taking out the basic bodies of all "+" in the starting region is the outlet distance of the gamma-ray starting region. If there are "-" basic bodies in the gamma-ray starting region, the minimum distance Do is taken out of all "+" basic bodies in the starting region, and then the minimum distance Di is taken out of all "-" basic bodies in the starting region, and the maximum value of the distances is taken as the outlet distance of the gamma-ray starting region.
(4) Determination of the number IP of each region through which the ray passes:
under the condition that the end point is not in the outermost zone, if no basic body exists in the zone number, firstly, judging adjacent sub-zones, and for all the plus basic bodies, when the inlet distance of the basic body is less than or equal to the inlet distance of the zone and less than the outlet distance of the basic body (Di < ═ Zin < Do), the zone is an adjacent zone of the previous zone, and solving a corresponding zone number IP; if the gamma ray area number has "-" basic bodies, the inlet distance of the basic bodies is less than or equal to the inlet distance of the area and less than the outlet distance (Di < ═ Zin < Do) of the basic bodies for all "+" basic bodies, and when the inlet distance of the basic bodies is greater than the inlet distance of the area or the outlet distance of the basic bodies is less than or equal to the inlet distance (Di > Zin or Do < ═ Zin) of the area for all "-" basic bodies, the area is the adjacent area of the previous area, and the corresponding area number IP is calculated.
(5) Determination of the entrance distance Zi and exit distance Zo of each zone traversed by the ray:
if there is no "-" basic body in the adjacent area, the outlet distance of the area is the minimum of the outlet distances Do of all "+" basic bodies, and the inlet distance of the area is the outlet distance of the previous area; if there is "-" basic body in the adjacent area, the smallest distance Do between the take-out ports of all "+" basic bodies is first determined, the smallest distance Di between the take-in ports of all "-" basic bodies is then determined, the largest value of the two distances is taken as the outlet distance of the area, and the inlet distance of the area is the outlet distance of the previous area.
(6) In the case that the end point is in the area of the outermost layer, firstly, finding all base body numbers aa of the outermost layer, and when the "+" base body in the area contains the base body aa and the "-" base body does not contain the area of the base body aa, finding whether the "-" base body exists, wherein the inlet distance of the "-" base body in the area is larger than the inlet distance (Di (k, minus (i, m)) > Zi (k, n)) of the area, if the "-" base body exists, taking the outlet distance of the area as the minimum of the inlet distances Di of all the "-" base bodies, and if the "-" base body does not contain the base body aa, taking the outlet distance of the area as.
Track to rpThe area IPend where the point is located and the ray exit distance is equal to the ray length. Thereby obtaining the traveling path of the gamma ray.
And then calculating the times of the ray passing through the area and the distance of each passing:
if the number of the passing area of the ray is not 0, the passing distance of the gamma ray in the area is equal to the distance of the inlet of the area minus the distance of the outlet of the area, and the passing times of the gamma ray is added with 1; if the passing area number of the gamma ray is 0, stopping tracking.
Gamma section mu is obtained by utilizing gamma mass attenuation coefficient and material of regional mediumn；
Through the above-mentioned process of recording the passing process of gamma ray passing through the area, the optical distance of each area is respectively calculated and then summed, namely:
where N denotes the number of radiation areas, which is mainly determined by the environment inside the building.
In a preferred embodiment, the process of processing the over-determined equation set in step two by using the least square method and obtaining the radiation source intensity information comprises the following sub-steps:
substep 3-1. solving the overdetermined system of equations
Expressed in matrix form as AX ═ b;
substep 3-2, solving the normal equation A of the matrixTAX＝ATb, i.e. X ═ ATA)-1ATb；
Substep 3-3, solving equation by trigonometric decomposition of symmetric matrix, and recording G ═ ATA, wherein G is a symmetric matrix;
substeps 3-4, solving for G ═ LDL by trigonometric decompositionTWherein L is a small triangular matrix and D is a diagonal matrix;
substeps 3-5, solving the lower triangular matrix equation system LY1＝ATb；
Substeps 3-6, solving the diagonal matrix equation set: DY (DY)2＝Y1；
And substeps 3-7, solving an upper triangular matrix equation set: l isTX＝Y2。
Wherein X is (A)TA)-1ATb and
correspondingly, the calculated value of the intensity of the radiation source is obtained through the substep 3-1 to the substep 3-7, and the least square method is a general overdetermined equation solving method in the field.
In a preferred embodiment, in step five, a linear fit is performed by the following equation (fifteen),
Wherein, the estimated dose rate is represented; which is indicative of the slope of the estimate,
the estimated intercept is represented as a function of,
n represents the maximum number of detectors i can reach,
representing the calculated average value of the dose rate at the detector position,
representing the average value of the dose rate detected by the detector.
In a preferred embodiment, after the linear fitting, the average uncertainty, the goodness of fit, the quality factor, the weighting function and the corresponding weight matrix of the linear fitting are obtained, respectively, and the quality factor represents the reliability of the current iteration calculation. In the fifth step, a weight function is obtained according to the uncertainty, and a weight matrix W is obtained through the weight function, wherein the weight matrix W is obtained through the formula (sixteen),
Where f denotes the fit uncertainty, fiA fit uncertainty representing an ith detector position; the mean fit uncertainty is represented as a function of,
representing a weight function.
In a preferred embodiment, in step six, the judgment condition for obtaining the expected radiation source intensity information is when Si> 0, and the quality factor M reaches a maximum value, i.e. when SiAnd when the quality factor M reaches the maximum value, stopping the weighting iteration and outputting the radiation source intensity information, wherein the radiation source intensity information is the expected radiation source intensity finally obtained and is the radiation source intensity closest to the true value.
The invention aims to obtain the intensity of the radiation source closest to the true value, the reliability of the intensity of the radiation source obtained in the step three is low, and the error between the intensity of the radiation source and the true value is large, so in order to improve the accuracy of the value, namely to obtain the intensity of the radiation source closest to the true value, the invention provides the weighted iteration process from the step four to the step six, and finally sets the condition of iteration termination, so as to reduce the workload as much as possible under the condition of ensuring the accurate result, shorten the operation time and improve the efficiency of data acquisition. According to the weighted iteration method and the judgment standard of iteration termination. In addition, the intensity of the radiation source obtained by the method is more accurate than that obtained by a source item analysis method, is closer to a real value, and can ensure that the obtained value and the real value are within an order of magnitude. In a preferred embodiment, each time step six is executed, a figure of merit M is obtained accordingly, which is obtained by the following formula (seventeen),
Wherein R is2The goodness of fit is expressed,
in a preferred embodiment, the system of over-determined equations
In the form of a matrix, see the formula (eighteen)
Wherein the error introduced by each detector is represented; considering the physical implications, the error caused at each detection point can be considered to be caused by the radiation source, and the above equation is simplified to the following equation (nineteen),
it can be further found that the coefficient matrix ai,jEquivalent to the dose response coefficient of the jth radiation source to the ith detector, wherein the dose response coefficient of the detectors is calculated using a point-kernel integration technique, which is a calculation method conventional in the art.
According to the composite radiation source strong backward pushing system of the point source and surface source combination of the nuclear power plant, which is provided by the invention, the system is used for executing the composite radiation source strong backward pushing method of the point source and surface source combination of the nuclear power plant.
Preferably, the system comprises a detector, a gamma ray average energy calculation module and a radiation source intensity calculation module;
the detector is provided with a plurality of detectors, including a preset position detector and a nuclear power plant radiation value monitoring detector,
the preset position detector is arranged at a preset position with a determined distance from a radiation source in a radiation area of a nuclear power plant, and a detachable shielding layer is optionally coated outside the preset position detector; the distance of the predetermined position from the radiation source may appear as a known quantity in a subsequent calculation;
the preset position detector is used for transmitting the detected radiation dose rate information to the gamma ray average energy calculating module for calculating the average gamma ray energy;
the nuclear power plant radiation value monitoring detectors are distributed in the radiation area of the nuclear power plant, are respectively positioned at the key positions in the invention, and are used for transmitting the respectively detected dose rate information in the nuclear power plant to the radiation source intensity calculation module,
the gamma ray average energy calculating module is used for calculating the average energy E of gamma rays,
the radiation source intensity calculating module is used for calculating the intensity of the radiation source in the nuclear power plant.
Experimental example:
an NB281 room in a nuclear island of a unit of a nuclear power station No. 1 of a Bay great bay is taken as an experimental object, the room is a place for placing a radioactive wastewater collecting barrel in a nuclear island control area, the wastewater collecting barrel is a cylindrical container, and the intensity of an internal radioactive liquid source is 0.7586E +10MeV/cm3S (or 4.2898E + 14/s). Simplifying the upper half part of the cylindrical container into 2 point sources, the middle part into 1 cylindrical surface source and the lower half part into 2 line sources, arranging a detector at the middle part of the wastewater collection barrel every 50cm, totally five detectors, wherein the detection values obtained by each detector are respectively 2.032mSv/hr, 0.685mSv/hr, 0.255mSv/hr, 0.1446mSv/hr and 0.0929mSv/hr, namely D in the invention1,D2,D3,D4,D5，The average energy obtained by the average energy obtaining method and the system provided by the invention is 1.3MeV, the source strength reverse pushing method and the system provided by the invention are adopted, the source strengths of 2 points obtained respectively are 7.0856E +13MeV/s and 7.1763E +13MeV/s, the source strengths of 2 line sources are 2.6677E +12MeV/(cm.s) (or 7.1228E +13MeV/s) and 2.7132E +12MeV/(cm.s) (or 7.2441E +13MeV/s), and the source strengths of 1 surface source are 2.9225E +10 MeV/(cm.s) (or 7.2441E +13MeV/s)2S) (alternatively 7.3413E +13 MeV/s).
From the final result, the sum of the obtained intensities of the five radiation sources is basically consistent with the true value of the radiation intensity of the radiation source, so that the method and the system provided by the invention can obtain the radiation source intensity information close to the true value.
The present invention has been described above in connection with preferred embodiments, but these embodiments are merely exemplary and merely illustrative. On the basis of the above, the invention can be subjected to various substitutions and modifications, and the substitutions and the modifications are all within the protection scope of the invention.
Claims (15)
1. A composite radiation source strong backward pushing method of a point source, a line source and a surface source combination in a nuclear power plant is characterized by comprising the following steps:
step one, detecting dose rate D in a nuclear power plant by using a detector1,D2,D3…Di；
Step two, establishing an overdetermined equation set containing the radiation source intensity as shown in the following formula (one) according to the detected dose rate information,
wherein the coefficient matrix a of the over-determined equation seti,jObtained by the following formulae (II) and (III),
in formula (iii), when the radiation source is a point source, p is 0, M is 1, and N is 1; when the radiation source is a line source, p is 1, and N is 1; when the radiation source is a plane source, p is 1;
step three, processing the overdetermined equation set in the step two by a least square method to obtain the intensity information of the radiation source shown in the following formula (four),
Sj,0＝(aj,i·ai,j)-1·aj,i·Di(IV);
wherein D isiIndicating the dose rate detected by the ith detector; j represents the number of radiation sources; m represents the maximum value which can be reached by the number of radiation sources; sjRepresents the intensity of the jth radiation source; sj,0Representing the intensity of the jth radiation source for which the initial calculation was not iterated; a isi,jRepresenting a coefficient matrix which is the dose response coefficient of the jth radiation source to the ith detector; BD (E, L (. mu. (E), r)0→rp) Indicating an accumulation factor, E and L (. mu. (E), r)0→rp) A function of (a); l (. mu.E, r)0→rp) Denotes an optical distance, is μ (E) and r0→rpA function of (a); μ (E) represents a cross-sectional/linear attenuation coefficient; r is0→rpRepresenting the distance of the radiation source to the detection point; c (E) represents a flux-dose conversion factor, which is a function of E; e represents energy, which is the average energy of gamma rays emitted by a radiation source in a nuclear power plant;
representing discrete source intensities; m and N respectively represent discrete labels on two coordinate axes after the surface source is dispersed on the two-dimensional coordinates.
2. The method for strong backward thrust of a composite radiation source of a nuclear power plant point source-surface source combination according to claim 1, further comprising, after step three, the steps of,
step four, obtaining the compound according to the step threeCalculating the dose rate, D 'at the detector location from the radiation source intensity information of'1,D′2,D′3…D′i；
And step five, performing linear fitting on the dose rate information detected by the detector and the dose rate information at the position of the detector obtained by calculation to obtain a linear equation of the relationship between the dose rate information and the dose rate information after fitting, and further obtain fitting parameters, wherein the fitting parameters comprise: average uncertainty, goodness-of-fit and corresponding weight matrix;
step six, iterating the weight matrix obtained in the step five to the overdetermined equation set in the step two to obtain a weighted overdetermined equation, and further repeating the step two, the step three and the step four until expected radiation source intensity information is obtained;
wherein, D'iRepresenting the calculated dose rate at the i-th detector position.
3. The method for strongly backward pushing the combined composite radiation source of the point source and the surface source of the nuclear power plant as claimed in claim 1, wherein when the radiation source is a surface source, the discrete source intensity is strong
Obtained by the following formula (V):
wherein S isU(M) and SVAnd (N) respectively representing the source intensity weight factor on the U coordinate axis and the source intensity weight factor on the V coordinate axis after the surface source is dispersed on the two-dimensional coordinate.
4. The method for strongly backward pushing the composite radiation source of the nuclear power plant point source and surface source combination according to claim 3, wherein S is a cylindrical surface source when the surface source is a cylindrical surface sourceU(M) and SV(N) is obtained by the following formulae (six) and (seven), respectively:
wherein eta is2,1、η2,2、η3,1And η3,2All represent cosine distribution constants, Z represents the height of the cylindrical surface source,
representing the angle of the cylindrical surface source.
5. The method for strongly backward pushing the composite radiation source of the nuclear power plant point source and surface source combination according to claim 3, wherein S is a spherical source when the surface source is a spherical sourceU(M) and SV(N) is obtained by the following formulae (eight) and (nine), respectively:
wherein eta is2,1、η2,2、η3,1And η3,2All represent cosine distribution constants, theta represents the horizontal angle of the spherical source,
representing the vertical angle of the spherical source.
6. The method for strongly backward pushing the composite radiation source of the nuclear power plant point source and surface source combination according to claim 3, wherein S is a rectangular surface source when the surface source is a rectangular surface sourceU(M) and SV(N) is obtained by the following formulas (ten) and (eleven), respectively:
wherein eta is2,1、η2,2、η3,1And η3,2All represent cosine distribution constants, Z represents the length of the rectangular surface source, and y represents the width of the rectangular surface source.
7. The method for strongly backward pushing the combined composite radiation source of the nuclear power plant point source and surface source combination as claimed in claim 3, wherein S is the disk surface source when the surface source is the disk surface sourceU(M) and SV(N) is obtained by the following formulae (twelve) and (thirteen), respectively:
wherein eta is1,1、η1,2、η3,1And η3,2Are all indicative of the cosine distribution constant,
representing the angle of the disk-shaped source and R the radius of the disk-shaped source.
8. The method for strongly backward estimating the composite radiation source of the point source and the surface source combination in the nuclear power plant as claimed in claim 1, wherein the method for calculating the average energy E of the gamma rays emitted by the radiation source in the nuclear power plant comprises the following sub-steps:
substep 1, selecting a preset position in a nuclear power plant, wherein the preset position is at a distance t from a radiation source, placing a detector at the preset position, and collecting the dose rate I detected by the detector0，
Substep 2, retrieving the detector, covering a shielding layer on the outside of the detector, placing the detector at the preset position, and collecting the dose rate I detected by the detector;
or, the detector is taken back, a shielding body is placed at a preset position, then the detector is placed in the shielding body, and the dosage rate I detected by the detector is collected;
substep 3, I and I obtained according to substeps 1 and 20The mass attenuation coefficient μ of the clad or shield is calculated by the following formula (fourteen),
I/I0＝BD(E,L(μ(E),r0→rp)e-μt
(fourteen)
And a substep 4 of obtaining the average energy E of the gamma rays emitted by the radiation source according to the calculation result of the substep 3.
9. The method of claim 1, wherein the method of calculating the optical distance L comprises the sub-steps of,
a sub-step a of tracking the passing process of the gamma ray from the radiation source to the detection point, recording the sequence of the gamma ray passing through the radiation region,
and a substep b, respectively calculating the distance of each radiation area, and finally calculating the total optical distance L by combining the linear attenuation coefficient of the material of each radiation area.
10. The method for strongly backward pushing the composite radiation source of the point source and the surface source combination in the nuclear power plant according to claim 1, wherein the overdetermined equation set in the second step is processed by using a least square method, and the process of obtaining the intensity information of the radiation source comprises the following sub-steps:
substep 3-1. solving the overdetermined system of equations
Expressed in matrix form as AX ═ b;
substep 3-2, solving the normal equation A of the matrixTAX＝ATb, i.e. X ═ ATA)-1ATb；
Substep 3-3, solving equation by trigonometric decomposition of symmetric matrix, and recording G ═ ATA, wherein G is a symmetric matrix;
substeps 3-4, solving for G ═ LDL by trigonometric decompositionTWherein L is a small triangular matrix and D is a diagonal matrix;
substeps 3-5, solving the lower triangular matrix equation system LY1＝ATb；
Substeps 3-6, solving the diagonal matrix equation set: DY (DY)2＝Y1；
And substeps 3-7, solving an upper triangular matrix equation set: l isTX＝Y2。
11. The method for strongly backward pushing a composite radiation source of a nuclear power plant point source and surface source combination is characterized in that in the fifth step, a linear fitting is carried out by the following formula (fifteen),
wherein the content of the first and second substances,
represents the estimated dose rate;
which is indicative of the slope of the estimate,
the estimated intercept is represented as a function of,
n represents the maximum number of detectors i can reach,
representing the calculated average value of the dose rate at the detector position,
representing the average value of the dose rate detected by the detector.
12. The method for strongly backward pushing a composite radiation source of a nuclear power plant point source and surface source combination is characterized in that in the fifth step, after linear fitting, a weight function is obtained according to uncertainty, and then a weight matrix W is obtained through the weight function, wherein the weight matrix W is obtained through the following formula (sixteen),
where f represents the uncertainty of the fit,
the mean fit uncertainty is represented as a function of,
fia fit uncertainty representing an ith detector position;
representing a weight function.
13. The method of claim 11, wherein the method comprises a step of generating a composite radiation source by a nuclear power plant point source and surface source combination,
in step six, i represents the number of detectors; j represents the number of radiation sources; s represents the intensity of the radiation source; sjRepresents the intensity of the jth radiation source; when S isj> 0 and a quality factor MArticle (A)Stopping the weighted iteration when the maximum value is reached, and outputting the intensity information of the radiation source, wherein the output intensity information of the radiation source is the expected intensity information of the radiation source;
wherein, each time step six is executed, a quality factor M is obtained correspondinglyArticle (A)Said quality factor MArticle (A)Obtained by the following formula (seventeen),
wherein R is2The goodness of fit is expressed,
14. a system for strongly backward pushing a composite radiation source of a point source and surface source combination of a nuclear power plant, which is used for executing the method for strongly backward pushing the composite radiation source of the point source and surface source combination of the nuclear power plant according to claims 1 to 13.
15. The system of claim 14, comprising a detector, a gamma ray mean energy calculation module, and a radiation source intensity calculation module;
the detector is provided with a plurality of detectors, including a preset position detector and a nuclear power plant radiation value monitoring detector,
the preset position detector is arranged at a preset position with a determined distance from a radiation source in a radiation area of a nuclear power plant, and a detachable shielding layer is optionally coated outside the preset position detector;
the preset position detector is used for transmitting the detected radiation rate information to the gamma ray average energy calculating module,
the nuclear power plant radiation value monitoring detectors are distributed in a radiation area of the nuclear power plant and used for transmitting respectively detected dose rate information in the nuclear power plant to the radiation source intensity calculating module,
the gamma ray average energy calculating module is used for calculating the average energy E of gamma rays,
the radiation source intensity calculating module is used for calculating the intensity of the radiation source in the nuclear power plant.
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