1、Designation: E 944 02Standard Guide forApplication of Neutron Spectrum Adjustment Methods inReactor Surveillance, E 706 (IIA)1This standard is issued under the fixed designation E 944; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision
2、, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This guide covers the analysis and interpretation of thephysics dosimetry for Light Water Reactor (LWR)
3、 surveillanceprograms. The main purpose is the application of adjustmentmethods to determine best estimates of neutron damage expo-sure parameters and their uncertainties.1.2 This guide is also applicable to irradiation damagestudies in research reactors.1.3 This standard does not purport to address
4、 all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:E 170 Terminology
5、Relating to Radiation Measurementsand Dosimetry2E 262 Test Method for Determining Thermal Neutron Re-action and Fluence Rates by Radioactivation Techniques2E 263 Test Method for Measuring Fast-Neutron ReactionRates by Radioactivation of Iron2E 264 Test Method for Measuring Fast-Neutron ReactionRates
6、 by Radioactivation of Nickel2E 265 Test Method for Measuring Reaction Rates andFast-Neutron Fluences by Radioactivation of Sulfur-322E 266 Test Method for Measuring Fast-Neutron ReactionRates by Radioactivation of Aluminum2E 343 Test Method for Measuring Reaction Rates by Analy-sis of Molybdenum-99
7、 Radioactivity from Fission Dosim-eters2E 393 Test Method for Measuring Reaction Rates by Analy-sis of Barium-140 from Fission Dosimeters2E 481 Test Method for Measuring Neutron Fluence Rate byRadioactivation of Cobalt and Silver2E 482 Guide for Application of Neutron Transport Methodsfor Reactor Ve
8、ssel Surveillance, E 706(IID)2,3E 523 Test Method for Measuring Fast-Neutron ReactionRates by Radioactivation of Copper2E 526 Test Method for Measuring Fast-Neutron ReactionRates by Radioactivation of Titanium2E 693 Practice for Characterizing Neutron Exposures inIron and Low Alloy Steels in Terms o
9、f Displacements PerAtom (DPA), E 706(ID)2,3E 704 Test Method for Measuring Reaction Rates by Ra-dioactivation of Uranium-2382E 705 Test Method for Measuring Reaction Rates by Ra-dioactivation of Neptunium-2372E 706 Master Matrix for Light-Water Reactor PressureVessel Surveillance Standards2E 844 Gui
10、de for Sensor Set Design and Irradiation forReactor Surveillance, E 706(IIC)2,3E 853 Practice for Analysis and Interpretation of Light-Water Reactor Surveillance Results, E 706(IA)2,3E 854 Test Method for Application and Analysis of SolidState Track Recorder (SSTR) Monitors for Reactor Sur-veillance
11、, E 706(IIIB)2,3E 910 Test Method for Application and Analysis of HeliumAccumulation Fluence Monitors for Reactor Vessel Sur-veillance, E706(IIIC)2,3E 1005 Test Method for Application and Analysis of Radio-metric Monitors for Reactor Vessel Surveillance,E 706(IIIA)2E 1018 Guide for Application of AS
12、TM Evaluated CrossSection Data File, E706(IIB)2,3E 2005 Guide for the Benchmark Testing of Reactor Do-simetry in Standard and Reference Neutron Field, E706(IIE-I)2E 2006 Guide for the Benchmark Testing of LWR Calcula-tions E706 (IIE-2)2,32.2 Nuclear Regulatory Commission Documents:4NUREG/CR-1861 PCA
13、 Experiments and Blind TestNUREG/CR-2222 Theory and Practice of General Adjust-ment and Model Fitting Procedures1This guide is under the jurisdiction of ASTM Committee E10 on NuclearTechnology and Applicationsand is the direct responsibility of SubcommitteeE10.05on Nuclear Radiation Metrology. A bri
14、ef overview of Guide E 944 appears inMaster Matrix E 706 in 5.3.1(IIA).Current edition approved June 10, 2002. Published September 2002. Originallypublished as E 944 83. Last previous edition E944 96.2Annual Book of ASTM Standards, Vol 12.02.3The unnumbered references in parentheses refer to Section
15、 5 as well as Figs. 1and 2 of Matrix E 706.4Available from Superintendents of Documents, U. S. Government PrintingOffice, Washington, DC 20402.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.NUREG/CR-3318 LWR Pressure Vessel Surveill
16、ance Do-simetry Improvement Program: PCA Experiments, BlindTest, and Physics-Dosimetry Support for the PSF Experi-mentNUREG/CR-3319 LWR Power Reactor SurveillancePhysics-Dosimetry Data Base CompendiumNUREG/CR-5049 Pressure Vessel Fluence Analysis andNeutron Dosimetry2.3 Electric Power Research Insti
17、tute:5EPRI NP-2188 Development and Demonstration of an Ad-vanced Methodology for LWR Dosimetry Applications2.4 Government Document:4NBSIR 853151 Compendium of Benchmark NeutronFields for Reactor Dosimetry3. Significance and Use3.1 Adjustment methods provide a means for combining theresults of neutro
18、n transport calculations with neutron dosimetrymeasurements in order to obtain optimal estimates for neutrondamage exposure parameters with assigned uncertainties. Theinclusion of measurements reduces the uncertainties for theseparameter values and provides a test for the consistencybetween measurem
19、ents and calculations and between differentmeasurements (see 3.3.3). This does not, however, imply thatthe standards for measurements and calculations of the inputdata can be lowered; the results of any adjustment procedurecan be only as reliable as are the input data.3.2 Input Data and Definitions:
20、3.2.1 The symbols introduced in this section will be usedthroughout the guide.3.2.2 Dosimetry measurements are given as a set of reactionrates (or equivalent) denoted by the following symbols:ai, i 5 1,2, . (1)These data are, at present, obtained primarily from radio-metric dosimeters, but other typ
21、es of sensors may be included(see 4.1).3.2.3 The neutron spectrum at the dosimeter location, flu-ence or fluence rate F(E) as a function of neutron energy E,isobtained by appropriate neutronics calculations (neutron trans-port using the methods of discrete ordinates or Monte Carlo,see Guide E 482).
22、The results of the calculation are customarilygiven in the form of k group fluences or fluence rates.Fj5*EjEj11F E!dE,j 5 1,2, . k (2)where:Ejand Ej+1are the lower and upper bounds for the j-th energygroup, respectively.3.2.4 The reaction cross sections of the dosimetry sensorsare obtained from an e
23、valuated cross section file. The crosssection for the i-th reaction as a function of energy E will bedenoted by the following:siE!,i 5 1,2, . (3)Used in connection with the group fluences, Eq 2, are thecalculated group-averaged cross sections sij. These values aredefined through the following equati
24、on:sij5*EjEj11FE!siE!dE/Fji5 1,2, . . n;j5 1,2, . k (4)3.2.5 Uncertainty information in the form of variances andcovariances must be provided for all input data. Appropriatecorrections must be made if the uncertainties are due to biasproducing effects (for example, effects of photo reactions).3.3 Su
25、mmary of the Procedures:3.3.1 An adjustment algorithm modifies the set of input dataas defined in 3.2 in the following manner (adjusted quantitiesare indicated by a tilde, for example, i):i5 ai1Dai(5)FE! 5FE! 1DFE! (6)or for group fluence ratesFj5Fj1DFj(7)siE! 5siE! 1DsiE!, (8)or for group-averaged
26、cross sectionssij5sij1Dsij(9)The adjusted quantities must satisfy the following condi-tions:i5*0FE!siE!dE,i 5 1,2, . n (10)or in the form of group fluence ratesi5(j 5 1ksijFj,i 5 1,2, . n (11)Since the number of equations in Eq 11 is much smaller thanthe number of adjustments, there exists no unique
27、 solution tothe problem unless it is further restricted. The mathematicalalgorithm in current adjustment codes are intended to make theadjustments as small as possible relative to the uncertainties ofthe corresponding input data. The more recent codes likeSTAYSL, FERRET, LEPRICON, and LSL-M2 (see Ta
28、ble1)are based explicitly on the statistical principles such as“Maximum Likelihood Principle” or “Bayes Theorem,” whichare generalizations of the well-known least squares principle.Using variances and correlations of the input fluence, dosim-etry, and cross section data (see 4.1.1, 4.2.2, and 4.3.3)
29、, eventhe older codes, notably SAND-II and CRYSTAL BALL, canbe interpreted as application of the least squares principlealthough the statistical assumptions are not spelled out explic-itly (see Table 1). A detailed discussion of the mathematicalderivations can be found in NUREG/CR-2222 and EPRINP-21
30、88.3.3.1.1 An important problem in reactor surveillance is thedetermination of neutron fluence inside the pressure vessel wallat locations which are not accessible to dosimetry. Estimatesfor exposure parameter values at these locations can beobtained from adjustment codes which adjust fluences simul
31、-taneously at more than one location when the cross correlationsbetween fluences at different locations are given. LEPRICON5Available from the Electric Power Research Institute, P. O. Box 10412, PaloAlto, CA 94303.E944022has provisions for the estimation of cross correlations forfluences and simulta
32、neous adjustment. LSL-M2 also allowssimultaneous adjustment, but cross correlations must be given.3.3.2 The adjusted data i, etc., are, for any specific algo-rithm, unique functions of the input variables. Thus, uncertain-ties (variances and covariances) for the adjusted parameterscan, in principle,
33、 be calculated by propagation the uncertaintiesfor the input data. Linearization may be used before calculatingthe uncertainties of the output data if the adjusted data arenonlinear functions of the input data.3.3.2.1 The algorithms of the adjustment codes tend todecrease the variances of the adjust
34、ed data compared to thecorresponding input values. The linear least squares adjustmentcodes yield estimates for the output data with minimumvariances, that is, the “best” unbiased estimates. This is theprimary reason for using these adjustment procedures.3.3.3 Properly designed adjustment methods pr
35、ovide meansto detect inconsistencies in the input data which manifestthemselves through adjustments that are larger than the corre-sponding uncertainties or through large values of chi-square, orboth. Any detection of inconsistencies should be documented,and output data obtained from inconsistent in
36、put should not beused. All input data should be carefully reviewed wheneverinconsistencies are found, and efforts should be made toresolve the inconsistencies as stated below.3.3.3.1 Input data should be carefully investigated for evi-dence of gross errors or biases if large adjustments arerequired.
37、 Note that the erroneous data may not be the ones thatrequired the largest adjustment; thus, it is necessary to reviewall input data. Data of dubious validity may be eliminated ifproper corrections cannot be determined. Any elimination ofdata must be documented and reasons stated which areindependen
38、t of the adjustment procedure. Inconsistent datamay also be omitted if they contribute little to the output underinvestigation.3.3.3.2 Inconsistencies may also be caused by input vari-ances which are too small. The assignment of uncertainties tothe input data should, therefore, be reviewed to determ
39、inewhether the assumed precision and bias for the experimentaland calculational data may be unrealistic. If so, variances maybe increased, but reasons for doing so should be documented.Note that in statistically based adjustment methods, listed inTable 1 the output uncertainties are determined only
40、by theinput uncertainties and are not affected by inconsistencies inthe input data (see NUREG/CR-2222). Note also that too largeadjustments may yield unreliable data because the limits of thelinearization are exceeded even if these adjustments are con-sistent with the input uncertainties.3.3.4 Using
41、 the adjusted fluence spectrum, estimates ofdamage exposure parameter values can be calculated. Theseparameters are weighted integrals over the neutron fluencep 5*oFE!wE!dE (12)or for group fluencesp 5(j 5 1kFjwj(13)with given weight (response) functions w (E)orwj, respec-tively. The response functi
42、on for dpa of iron is listed in PracticeE 693. Fluence greater than 1.0 MeV or fluence greater than0.1 MeV is represented as w (E)=1forE above the limit andw (E)=0forE below.3.3.4.1 Finding best estimates of damage exposure param-eters and their uncertainties is the primary objective in the useof ad
43、justment procedures for reactor surveillance. If calculatedTABLE 1 Available Unfolding CodesProgram Solution MethodCode AvailableFromRefer-encesCommentsSAND-II semi-iterative RSIC Prog. No. CCC-112, CCC-619, PSR-3451 contains trial spectra library. No output uncertainties in theoriginal code, but mo
44、dified Monte Carlo code provides outputuncertainties (12, 22)SPECTRA statistical, linear estimation RSIC Prog. No. CCC-1082, 3 minimizes deviation in magnitude, no output uncertainties.IUNFLD/UNFOLDstatistical, linear estimation 5 constrained weighted linear least squares code using B-splinebasic fu
45、nctions. No output uncertainties.WINDOWS statistical, linear estimation, linearprogrammingRSIC Prog. No. PSR-136, 1616 minimizes shape deviation, determines upper and lower boundsfor integral parameter and contribution of foils to bounds andestimates. No statistical output uncertainty.RADAK,SENSAKst
46、atistical, linear estimation 7, 8 RADAK is a general adjustment code not restricted to spectrumadjustment.STAYSL statistical linear estimation RSIC Prog. No. PSR-1139 permits use of full or partial correlation uncertainty data foractivation and cross section data.NEUPAC(J1) statistical, linear estim
47、ation RSIC Prog. No. PSR-17710, 11 permits use of full covariance data and includes routine ofsensitivity analysis.FERRET statistical, least squares with log normala priori distributionsRSIC Prog. No. PSR-14512, 22 flexible input options allow the inclusion of both differential andintegral measureme
48、nts. Cross sections and multiple spectra maybe simultaneously adjusted. FERRET is a general adjustmentcode not restricted to spectrum adjustments.LEPRICON statistical, generalized linear leastsquares with normal a priori and aposteriori distributionsRSIC Prog. No. PSR-27714, 15, 18 simultaneous adju
49、stment of absolute spectra at up to twodosimetry locations and one pressure vessel location. Combinesintegral and differential data with built-in uncertainties. Providesreduced adjusted pressure vessel group fluence covariancesusing built-in sensitivity database.LSL-M2 statistical, least squares, with log normala priori and a posteriori distributionsRSIC Prog. No. PSR-23319 simultaneous adjustment of several spectra. Providescovariances for adjusted integral parameters. Dosimetry cross-section file included.E944023according to Eq 12 or Eq 13, unbiased minimum
