[精品論文]The Radioactive Source Distribution Calculation and Gauging Nonlinear Correction of Multi-point Source Nuclear Gauge Based on the Numeric Analys

精品論文the radioactive source distribution calculation and gauging nonlinear correction of multi-point source nuclear gauge based on the numeric analysis method5cheng xiaolong, zhao xiuliang(school of nuclear science and technology,university of south china,hunan hengyang 421001)abstract: the nuclear material level gauge with approximate linear scale is realized by the numerical analysis method. in this paper, according to the real project design a theoretical calculation model,10using the multipoint combination source and single detector measurement scheme. referencing the line-source design method, calculate the multipoint combination source activity which satisfy themeasurement range and accuracy requirement, and through the excel and matlab software complete thedata calculation and dispose, drawing out the count rate - material level diagram. according to the nonlinear measurement, use the equivalent point source method, compensating the bottom source15activity and residual analysis method , revise the gauging nonlinear separately. finally complete the theoretical design of multipoint source nuclear material level gauge with the total source activity of633mci, measurement range 80cm, 5mm measurement precision and response time 14-33s.through the protective calculation, do the comprehensive analysis for the three ways, confirm the residual analysis as the best design scheme.20keywords: nuclear gauge; multi-point source; two-point standardization; nonlinear correction;numeric analysis; linear output; shielding calculationrd 30introductionthe nuclear material level gauge based on -ray technology has been widely used in the25real engineering. the fundamental is that the material will absorb the passing ray, the ray intensity will change accompany the material level, the nuclear instrumentation will transfer the ray intensity into electrical signal or other kinds of signals for displaying and controlling. thecollocation method of radioactive source and detection can use point source and point detector、point source and rod detector、rod source and point detector、rod source and rod detector etc ways30based on different gauging targets. because of the limit of source activity and measurement accuracy the point source cannot been applied on the project of wide measurement range、thick wall and the material with high ray absorption strength, but the line-like source is the mostsuitable. the biggest advantage is that not only can satisfy the measurement demand but also realize the linear scale, only need one point or two points demarcation in the actual projects. the35lb serial line-like nuclear gauges produced by berthold company are one of the most popular productions, there are many theoretic research about source distribution of the line-like source in our country1-15.the newest patent cn102735312a public one technology about 60co rod-likesource16.but the existing line-like source distribution functions are so complicate that cannotguide the real production due to the theoretic calculations and research results, which is40bottle-neck that limit the development of line-like source technology.this paper propose one method of calculating the multipoint source activity distribution that can realize the approximate linear output based on the line-like source theory, do nonlinearanalysis with the software of excel and matlab，and correct the nonlinearity.foundations: national military supporting project(jppt-115-5-882)brief author introduction:xiao-long cheng, (1987-),man,xingtai hebei province, master of nuclear technology and applications.correspondance author: zhao xiuliang, (1968-),man,professor,nuclear electronics. e-mail: zhaoxiul163.com- 16 -1the radioactive source design of multipoint source nuclear gauge45due to the defects of the line-like source manufacture craft, multipoint source nuclear gauge is the best way to realize high accuracy measurement on the target with large size and complex construction instead of line-like source. the multipoint source activity distribution function could learn from the much more mature line-like source calculation function. the following text illustrate the multipoint source calculation process base on one actual project.501.1 the establish of theoretical calculation model and relevant parameters setthe following figure 1 show the relevant parameters and coordinate system:fig. 1 nuclear gauge system schematic diagram55container size is 100cm*100cm*100cm, wall is carbon steel material with thick of 5cm,the material density in the container is 7.83g/cm3;the inner temperature is from 200c to 1200c;the inner pressure is from -0.05mpa to 0.1mpa. the measurement technology indexes: measurement range from 0 to 90cm,measurement accuracy less than 5mm, the material level gauging up dead zone less than 5mm,down dead zone less than 5mm,response time from 10 to 60 seconds.601 is the -ray mass-absorption coefficient of the container wall material, according to thechart17 60co source has the mass-absorption coefficient of 0.0531cm2/g under the iron medium,2 as the inner material mass-absorption coefficient has the similar property, so the value is0.053cm2/g. l is the horizontal distance between source and detector, l=125cm；d is the horizontal distance between the detector and the left inner wall, d=105cm.651.2 the calculation of multipoint source activity distributionas the figure 2 lay the top point source and material top limit the same horizon line, divide the measurement rang into 10 sections each one has the length of 8cm,there are 11 point sources at the left side. depend on the line-like source theory set the line-like source distribution function as s(x) ,the point source activity is s(x) on the coordinate point x. when the material level at the70height of h, detector receive the ray sent from the point sources under and up the material level.setting the detector effective cross section as s the detection efficiency is , and the radioactive sent out the average number of -ray is in each decay, then the following formula is about count per second with the material level:hl75n(h) = q（ ds(y) b1 e( 1 t1 ( y )hdx + s(y) b1b 2 e( 1 t1 ( x ) +2 t 2 ( x )dx）(1)04 ( l2+ y 2 )hld4 ( l2+ x 2 )q = 3.7e7s , b1 and b2 are the exposure accumulation factors when the wide -ray through the container wall and inner material respectively, which could be checked as thefollowing formula17:11b = a e 1r + (1 a)e 2 r(2)80t1 ( x)andt 2 ( x) are the real thicknesses when the ray through the container wall and innermaterial respectively.a1 is related to the source style and inner material kind and ray activity,can be checked in related references, the following calculation with the 60co source:1b = 23.123e( 0.057210.05317.8t（1 x）) 22.123e( 0.019790.0537.8t（1 x）)2b = 23.123e(0.057210.0537.83t（2 x）) 22.123e(0.019790.0537.83t（2 x）)85although formula(1) cannot get the serious linear output, the value of2 d always much bigand2 d5 in this measurement target, so the inner material will absorb the ray from thesource under the material level strongly, the first part is far more large than the second part in the formula(1), besides, its possible to choose one suitable s(x) help the first part realize the serious linearity, the count rate and the material level can realize the approximate linearity. setting the90s(x) as the following formula:s( x) = s0 e1t1 ( x ) ( l2 + x 2 )b1(3)2d l2 + x 2add thet1 ( x) =,formula(1) become the following form:ln(h) =s0 l h + s04d4hhl b2 ed 2 t2 ( x ) dx(4)s0 is one constant can be sure by the total source activity and measurement accuracy.95compare with the first part in formula(4) the second part is a small value, so n(h) can be seen as linear function, and the nonlinear error can satisfy the production process requirements.e 1t1 ( x )theb1is the weaken multiple of wide -ray when the penetrable thickness is1t ( x) = 2dl2 + x 2l,which could be checked in references17,while in this paper the value is100calculated by formula(2).1.3 the total source activity of the multipoint sourcesetting the error of material measurement as e and the instrument response time is t, the error created by radioactive source is only caused by the radioactive statistical fluctuation, settingthe limit error as:emax= 3 =3nn(5)is the standard error and n is the particle number emitted in time t. in order to make sure the105emax less than e,3 e , while thenn = ntso n 9e 2t,n is the counting rate, if use thelimit value :n = 9e 2t(6)as the figure2 the 11 point sources have equidistant distribution with the total source activity a:11 ai = ai =1(7)110in order to make sure the measurement accuracy requirement the total source activity must big enough, set all of the point sources as one single point source, install at the a1 position, take the ray as narrow beam then:3.7e7 a s e 1 2 d / cos 114 l 2= n =9e 2 t(8)1151 is the elevation of a1 toward detector, t is secondary instrument response time, after the calculation the total source activity is 633mci.1.4 calculation resultscalculate each point source activity with the formula(3),add the detector the calculation model of counting rate-level is:nn (h) = s (i) b b e( 1 t1 ( x )+ 2 t2 ( x )l2 + x 2(9)i =0124 ()120s(i) is the point source activity in the i point and x is the point source coordinate. the followingcalculation set the relevant parameters as these: 60co as the source nai(ti) scintillation crystaldetector as the detector,s = 3cm * 3cm 、detection efficiency = 30% 、the 60co source=2.the table1 figure2、3 are the calculation results:table 1 the relevant parameters of 60co multipoint sourcespoint source numbersource coordinates(cm)source activity（mci）material level coordinates（cm）counting rate s-115.955.055433.31215.485.2313861.06325.005.56211274.04434.526.09291664.78544.056.85372028.21653.577.89452361.59763.109.29532664.17872.6211.16612936.81982.1413.63693181.581091.6716.91773401.0211101.1921.25853578.93total source activity（mci）108.92125fig.2 60co source counting rate-material level curve130fig.3 the point source activity distribution of the multipoint source1351401.5 theoretical analysis of the output characteristicsthe material level gauging system composed by nonlinear distribution multipoint source has not reach the serious linearity scale. because of the instrument is adopted two points demarcate, take the detector counting rate correspond with the material lower limit and up limit as the instrument zero point and full point, the middle is demarcated by linearity. this method will cause the error between instrument display and the real material level, so this nonlinearity distribution multipoint sources cannot used in the high accuracy gauging projects, need nonlinearity correction.2nonlinearity correctionthere are three nonlinearity correction methods: compensating the point source activity;doing software compensation with the residual theory; calculating the source distribution with thelinearity equation theory. the following figure4 is the flow chart of nonlinearity correction.n(hl)=khl +n(h0)nl 1 nl = nl nl +1hl 1 hlhl hl +1ia i = w a 0145fig.4 the flow chart used for realizing the counting rate-level1501552.1do nonlinearity compensation by improve source activityfigure 2 shows that with the increase of material level h, the increasing rate of counting rate decreases. according to the references8-15,the contribution that bottom point source made to the counting rate of detector increases in exponent along with the material level decreases, therefore by compensating the bottom source activity, better linearity output can be acquired. the detailedmethod is: based on the original data, utilizing the excel calculation function and letting the point source multipliy a series of decreasing number from the bottom to the top, and then adjusting locally according to the new graph, better linearity output can be attained after several trials. theresults are showed in table 2、figure 5and figure 6.table 2 the relevant parameters of 60co multipoint sources after correctionpoint source numbersource coordinates(cm)source activity（mci）material level coordinates（cm）counting rate s-115.955.055429.94215.485.2213854.34325.006.11211307.04434.527.31291779.25544.058.90372263.58653.5711.04452754.40763.1013.93533247.78872.6217.84613741.36982.1423.16694234.261091.6730.41774727.6311101.1942.48855222.28total source activity（mci）171.45160165170fig.5 60co source counting rate-material level curve after correctionfig.6 the point source activity distribution of the multipoint sourceit can be seen from the corrected charts that the nuclear gauge has achieved much higher linearity with r2=0.9996.in order to realize 5mm measurement accuracy in the full measuring range from 5 to 85cm, the following table 3 is the related data calculated by the fitting function y = 60.392 x + 60.712 .table 3 the counting rate on different levels based on formulamaterial level cmcounting rate s-1material level cmcounting rate s-15.0362.6782.05012.865.5392.8782.55043.056.0423.0683.05073.256.5453.2683.55103.447.0483.4684.05133.647.5513.6584.55163.848.0543.8585.05194.03175in theory, only if the counting change value reaches the 3 times absolute deviationcausedby radioactive statistical fluctuation should the counting number changes as the distinguish level change, otherwise the accurate material level cannot be measured . as to the requirement of 5 mm180measurement accuracy, it can be seen from the former table when the material level changes from84.5cm to 85cm, the counting rate difference is 31 while the absolute error is about 73. it can by increasing the radioactive source activity and measurement time reach the accuracy requirement. due to this calculation model, when the source activity is enlarged by 3.7 times into 633mci, the measurement time is 14s, as well as the counting difference is about 1550 and the absolute error is about 516,which have achieved the degree for distinguishing accurately.2.2utilize the residual do software nonlinearity compensationanalysing the figure 2 with matlab, the residual distribution curve can be as the following figure 7:5000cps & level4000y = 41*x + 4.1e+002cps300020001000data 1 linear00 10 20 30 40 50 60 70 80 903002001000-100-200-300residualslinear: norm of residuals = 384.3953level(cm)1850 10 20 30 40 50 60 70 80 90fig.7 residual distribution curveanalysing the residual curve and cubic polynomial fitting can get the figure 8:2001000y = - 0.00054*x3 - 0.13*x2 + 16*x - 2.6e+002data 1 cubic-100-200-300420102030405060708090 residualscubic: norm of residuals = 7.77150-2-40102030405060708090190fig.8 the residual fitting curve graphsetting the counting rate-material level spline function isy1 =f1 ( x)based on the3theoretical calculation; the fitting linear function isy2 =f2 ( x)through the least square method;the residual spline function isy3 = f3 ( x) .the residual function is formed by the subtraction195between theoretical calculation and curve fitting linear18: yis the specific steps:= y1 y2 ,y2 = y1 y3.following(1) calculating the theoretic spline function parameters;y1 based on the calculation model and setting(2) fittingy1 to get the linearity functiony2 with the least square method;200(3) doing residual analysis to get the functiony3 through matlab;(4) doing two points calibration: taking two different material level randomlyx1 and x2(generally taking the measurement lower limit and upper limit), through the functiony1 =f1 ( x)to get the valuef1 ( x1 )andf1 ( x2 ) respectively; then calcula