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Significance and Use
3.1 Adjustment methods provide a means for combining the results of neutron transport calculations with neutron dosimetry measurements (see Test Method E1005 and NUREG/CR5049) in order to obtain optimal estimates for neutron damage exposure parameters with assigned uncertainties. The inclusion of measurements reduces the uncertainties for these parameter values and provides a test for the consistency between measurements and calculations and between different measurements (see 3.3.3). This does not, however, imply that the standards for measurements and calculations of the input data can be lowered; the results of any adjustment procedure can be only as reliable as are the input data.
3.2 Input Data and Definitions :
3.2.2 Dosimetry measurements are given as a set of reaction rates (or equivalent) denoted by the following symbols:
These data are, at present, obtained primarily from radiometric dosimeters, but other types of sensors may be included (see 4.1).
3.2.3 The neutron spectrum (see Terminology E170) at the dosimeter location, fluence or fluence rate Φ(E) as a function of neutron energy E , is obtained by appropriate neutronics calculations (neutron transport using the methods of discrete ordinates or Monte Carlo, see Guide E482). The results of the calculation are customarily given in the form of multigroup fluences or fluence rates.
where:
E_{j} and E_{j}_{+1 } are the lower and upper bounds for the jth energy group, respectively, and k is the total number of groups.
3.2.4 The reaction cross sections of the dosimetry sensors are obtained from an evaluated cross section file. The cross section for the ith reaction as a function of energy E will be denoted by the following:
Used in connection with the group fluences, Eq 2, are the calculated groupaveraged cross sections σ_{ij}. These values are defined through the following equation:
3.3 Summary of the Procedures:
3.3.1 An adjustment algorithm modifies the set of input data as defined in 3.2 in the following manner (adjusted quantities are indicated by a tilde, for example, ã_{i}):
or for groupaveraged cross sections
The adjusted quantities must satisfy the following conditions:
or in the form of group fluence rates
Since the number of equations in Eq 11 is much smaller than the number of adjustments, there exists no unique solution to the problem unless it is further restricted. The mathematical algorithm in current adjustment codes are intended to make the adjustments as small as possible relative to the uncertainties of the corresponding input data. Codes like STAY'SL, FERRET, LEPRICON, and LSLM2 (see Table 1) are based explicitly on the statistical principles such as “Maximum Likelihood Principle” or “Bayes Theorem,” which are generalizations of the wellknown least squares principle. Using variances and correlations of the input fluence, dosimetry, and cross section data (see 4.1.1, 4.2.2, and 4.3.3), even the older codes, notably SANDII and CRYSTAL BALL, can be interpreted as application of the least squares principle although the statistical assumptions are not spelled out explicitly (see Table 1). A detailed discussion of the mathematical derivations can be found in NUREG/CR2222 and EPRI NP2188.
Program  Solution Method  Code Available  Refer  Comments 
SANDII  semiiterative  RSICC Prog. No. CCC112, CCC619, PSR345  1^{A}  contains trial spectra library. No output uncertainties in the original code, but modified Monte Carlo code provides output uncertainties (2, 3, 4) 





SPECTRA  statistical, linear estimation  RSICC Prog. No. CCC108  minimizes deviation in magnitude, no output uncertainties.  





IUNFLD/  statistical, linear estimation 
 constrained weighted linear least squares code using Bspline basic functions. No output uncertainties.  





WINDOWS  statistical, linear estimation, linear programming  RSICC Prog. No. PSR136, 161  minimizes shape deviation, determines upper and lower bounds for integral parameter and contribution of foils to bounds and estimates. No statistical output uncertainty.  





RADAK,  statistical, linear estimation  RSICC Prog. No. PSR122  RADAK is a general adjustment code not restricted to spectrum adjustment.  





STAY'SL  statistical linear estimation  RSICC Prog. No. PSR113  permits use of full or partial correlation uncertainty data for activation and cross section data.  





NEUPAC(J1)  statistical, linear estimation  RSICC Prog. No. PSR177  permits use of full covariance data and includes routine of sensitivity analysis.  





FERRET  statistical, least squares with log normal a priori distributions  RSICC Prog. No. PSR145  flexible input options allow the inclusion of both differential and integral measurements. Cross sections and multiple spectra may be simultaneously adjusted. FERRET is a general adjustment code not restricted to spectrum adjustments.  





LEPRICON  statistical, generalized linear least squares with normal a priori and a posteriori distributions  RSICC Prog. No. PSR277  simultaneous adjustment of absolute spectra at up to two dosimetry locations and one pressure vessel location. Combines integral and differential data with builtin uncertainties. Provides reduced adjusted pressure vessel group fluence covariances using builtin sensitivity database.  





LSLM2  statistical, least squares, with log normal a priori and a posteriori distributions  RSICC Prog. No.  simultaneous adjustment of several spectra. Provides covariances for adjusted integral parameters. Dosimetry crosssection file included.  





UMG  Statistical, maximum entropy with output uncertatinties  RSICC Prog. No.  Two components. MAXED is a maximum entropy code. GRAVEL (22) is an iterative code.  





NMF90  Statistical, least squares  IAEA NDS  Several components, STAY'NL, X333, and MIEKE. Distributed by IAEA as part of the REAL84 interlaboratory exercise on spectrum adjustment (25).  





GMA  Statistical, general least squares  RSICC Prog. No.  Simultaneous evaluation with differential and integral data, primarily used for crosssection evaluation but extensible to spectrum adjustments. 
3.3.1.1 An important problem in reactor surveillance is the determination of neutron fluence inside the pressure vessel wall at locations which are not accessible to dosimetry. Estimates for exposure parameter values at these locations can be obtained from adjustment codes which adjust fluences simultaneously at more than one location when the cross correlations between fluences at different locations are given. LEPRICON has provisions for the estimation of cross correlations for fluences and simultaneous adjustment. LSLM2 also allows simultaneous adjustment, but cross correlations must be given.
3.3.2 The adjusted data ã_{i}, etc., are, for any specific algorithm, unique functions of the input variables. Thus, uncertainties (variances and covariances) for the adjusted parameters can, in principle, be calculated by propagation the uncertainties for the input data. Linearization may be used before calculating the uncertainties of the output data if the adjusted data are nonlinear functions of the input data.
3.3.2.1 The algorithms of the adjustment codes tend to decrease the variances of the adjusted data compared to the corresponding input values. The linear least squares adjustment codes yield estimates for the output data with minimum variances, that is, the “best” unbiased estimates. This is the primary reason for using these adjustment procedures.
3.3.3 Properly designed adjustment methods provide means to detect inconsistencies in the input data which manifest themselves through adjustments that are larger than the corresponding uncertainties or through large values of chisquare, or both. (See NUREG/CR3318 and NUREG/CR3319.) Any detection of inconsistencies should be documented, and output data obtained from inconsistent input should not be used. All input data should be carefully reviewed whenever inconsistencies are found, and efforts should be made to resolve the inconsistencies as stated below.
3.3.3.1 Input data should be carefully investigated for evidence of gross errors or biases if large adjustments are required. Note that the erroneous data may not be the ones that required the largest adjustment; thus, it is necessary to review all input data. Data of dubious validity may be eliminated if proper corrections cannot be determined. Any elimination of data must be documented and reasons stated which are independent of the adjustment procedure. Inconsistent data may also be omitted if they contribute little to the output under investigation.
3.3.3.2 Inconsistencies may also be caused by input variances which are too small. The assignment of uncertainties to the input data should, therefore, be reviewed to determine whether the assumed precision and bias for the experimental and calculational data may be unrealistic. If so, variances may be increased, but reasons for doing so should be documented. Note that in statistically based adjustment methods, listed in Table 1 the output uncertainties are determined only by the input uncertainties and are not affected by inconsistencies in the input data (see NUREG/CR2222). Note also that too large adjustments may yield unreliable data because the limits of the linearization are exceeded even if these adjustments are consistent with the input uncertainties.
3.3.4 Using the adjusted fluence spectrum, estimates of damage exposure parameter values can be calculated. These parameters are weighted integrals over the neutron fluence
with given weight (response) functions w(E) or w_{ j}, respectively. The response function for dpa of iron is listed in Practice E693. Fluence greater than 1.0 MeV or fluence greater than 0.1 MeV is represented as w(E) = 1 for E above the limit and w(E) = 0 for E below.
3.3.4.1 Finding best estimates of damage exposure parameters and their uncertainties is the primary objective in the use of adjustment procedures for reactor surveillance. If calculated according to Eq 12 or Eq 13, unbiased minimum variance estimates for the parameter p result, provided the adjusted fluence Φ˜ is an unbiased minimum variance estimate. The variance of p can be calculated in a straightforward manner from the variances and covariances of the adjusted fluence spectrum. Uncertainties of the response functions, w_{j}, if any, should not be considered in the calculation of the output variances when a standard response function, such as the dpa for iron in Practice E693, is used. The calculation of damage exposure parameters and their variances should ideally be part of the adjustment code.
1. Scope
2. Referenced Documents (purchase separately) The documents listed below are referenced within the subject standard but are not provided as part of the standard.
ASTM Standards
E170 Terminology Relating to Radiation Measurements and Dosimetry
E262 Test Method for Determining Thermal Neutron Reaction Rates and Thermal Neutron Fluence Rates by Radioactivation Techniques
E263 Test Method for Measuring FastNeutron Reaction Rates by Radioactivation of Iron
E264 Test Method for Measuring FastNeutron Reaction Rates by Radioactivation of Nickel
E265 Test Method for Measuring Reaction Rates and FastNeutron Fluences by Radioactivation of Sulfur32
E266 Test Method for Measuring FastNeutron Reaction Rates by Radioactivation of Aluminum
E393 Test Method for Measuring Reaction Rates by Analysis of Barium140 From Fission Dosimeters
E481 Test Method for Measuring Neutron Fluence Rates by Radioactivation of Cobalt and Silver
E482 Guide for Application of Neutron Transport Methods for Reactor Vessel Surveillance, E706 (IID)
E523 Test Method for Measuring FastNeutron Reaction Rates by Radioactivation of Copper
E526 Test Method for Measuring FastNeutron Reaction Rates by Radioactivation of Titanium
E693 Practice for Characterizing Neutron Exposures in Iron and Low Alloy Steels in Terms of Displacements Per Atom (DPA), E 706(ID)
E704 Test Method for Measuring Reaction Rates by Radioactivation of Uranium238
E705 Test Method for Measuring Reaction Rates by Radioactivation of Neptunium237
E706 Master Matrix for LightWater Reactor Pressure Vessel Surveillance Standards, E 706(0)
E844 Guide for Sensor Set Design and Irradiation for Reactor Surveillance, E 706 (IIC)
E853 Practice for Analysis and Interpretation of LightWater Reactor Surveillance Results, E706(IA)
E854 Test Method for Application and Analysis of Solid State Track Recorder (SSTR) Monitors for Reactor Surveillance, E706(IIIB)
E910 Test Method for Application and Analysis of Helium Accumulation Fluence Monitors for Reactor Vessel Surveillance, E706 (IIIC)
E1005 Test Method for Application and Analysis of Radiometric Monitors for Reactor Vessel Surveillance, E 706 (IIIA)
E1018 Guide for Application of ASTM Evaluated Cross Section Data File, Matrix E706 (IIB)
E2005 Guide for Benchmark Testing of Reactor Dosimetry in Standard and Reference Neutron Fields
E2006 Guide for Benchmark Testing of Light Water Reactor Calculations
Nuclear Regulatory Commission Documents
NUREG/CR5049 Pressure Vessel Fluence Analysis and Neutron DosimetryElectric Power Research Institute
EPRI NP2188 Development and Demonstration of an Advanced Methodology for LWR Dosimetry ApplicationsGovernment Document
NBSIR 85–3151 Compendium of Benchmark Neutron Fields for Reactor DosimetryICS Code
ICS Number Code 27.120.20 (Nuclear power plants. Safety)
UNSPSC Code
UNSPSC Code 46171600(Surveillance and detection equipment); 26142100(Nuclear reactor equipment)
DOI: 10.1520/E094413
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Citation Format
ASTM E94413, Standard Guide for Application of Neutron Spectrum Adjustment Methods in Reactor Surveillance, E 706 (IIA), ASTM International, West Conshohocken, PA, 2013, www.astm.org
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