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ASTM E944-13e1
Standard Guide for Application of Neutron Spectrum Adjustment Methods in Reactor Surveillance (Includes all amendments And changes 10/28/2019).
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STANDARD published on 1.1.2013
The information about the standard:
Designation standards: ASTM E944-13e1
Note: WITHDRAWN
Publication date standards: 1.1.2013
SKU: NS-682176
The number of pages: 8
Approximate weight : 24 g (0.05 lbs)
Country: American technical standard
Category: Technical standards ASTM
The category - similar standards:
Annotation of standard text ASTM E944-13e1 :
Keywords:
dosimetry, exposure parameters, irradiation damage, least squares, neutron, reactor surveillance, spectrum adjustment ,, ICS Number Code 27.120.20 (Nuclear power plants. Safety)
Additional information
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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/CR-5049) 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 3.2 Input Data and Definitions : 3.2.1 The symbols introduced in this section will be used throughout the guide. 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: Used in connection with the group fluences, Eq 2, are the calculated group-averaged cross sections σ3.2.5 Uncertainty information in the form of variances and covariances must be provided for all input data. Appropriate corrections must be made if the uncertainties are due to bias producing effects (for example, effects of photo reactions). 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, ãi): or for group fluence rates or for group-averaged 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 LSL-M2 (see Table 1) are based explicitly on the statistical principles such as “Maximum Likelihood Principle” or “Bayes Theorem,” which are generalizations of the well-known 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 SAND-II 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/CR-2222 and EPRI NP-2188. Program
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Solution Method |
Code Available |
Refer- |
Comments |
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SAND-II |
semi-iterative |
RSICC Prog. No. CCC-112, CCC-619, PSR-345 |
1A |
contains trial spectra library. No output uncertainties in the original code, but modified Monte Carlo code provides output uncertainties ( |
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SPECTRA |
statistical, linear estimation |
RSICC Prog. No. CCC-108 |
minimizes deviation in magnitude, no output uncertainties. |
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IUNFLD/ |
statistical, linear estimation |
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7 |
constrained weighted linear least squares code using B-spline basic functions. No output uncertainties. |
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WINDOWS |
statistical, linear estimation, linear programming |
RSICC Prog. No. PSR-136, 161 |
8 |
minimizes shape deviation, determines upper and lower bounds for integral parameter and contribution of foils to bounds and estimates. No statistical output uncertainty. |
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RADAK, |
statistical, linear estimation |
RSICC Prog. No. PSR-122 |
RADAK is a general adjustment code not restricted to spectrum adjustment. |
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STAY'SL |
statistical linear estimation |
RSICC Prog. No. PSR-113 |
13 |
permits use of full or partial correlation uncertainty data for activation and cross section data. |
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NEUPAC(J1) |
statistical, linear estimation |
RSICC Prog. No. PSR-177 |
permits use of full covariance data and includes routine of sensitivity analysis. |
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FERRET |
statistical, least squares with log normal a priori distributions |
RSICC Prog. No. PSR-145 |
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. |
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LEPRICON |
statistical, generalized linear least squares with normal a priori and a posteriori distributions |
RSICC Prog. No. PSR-277 |
simultaneous adjustment of absolute spectra at up to two dosimetry locations and one pressure vessel location. Combines integral and differential data with built-in uncertainties. Provides reduced adjusted pressure vessel group fluence covariances using built-in sensitivity database. |
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LSL-M2 |
statistical, least squares, with log normal a priori and a posteriori distributions |
RSICC Prog. No. |
19 |
simultaneous adjustment of several spectra. Provides covariances for adjusted integral parameters. Dosimetry cross-section file included. |
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UMG |
Statistical, maximum entropy with output uncertatinties |
RSICC Prog. No. |
Two components. MAXED is a maximum entropy code. GRAVEL ( |
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NMF-90 |
Statistical, least squares |
IAEA NDS |
Several components, STAY'NL, X333, and MIEKE. Distributed by IAEA as part of the REAL-84 interlaboratory exercise on spectrum adjustment (25). |
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GMA |
Statistical, general least squares |
RSICC Prog. No. |
26 |
Simultaneous evaluation with differential and integral data, primarily used for cross-section 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. LSL-M2 also allows
simultaneous adjustment, but cross correlations must be given.
3.3.2 The adjusted data ãi, 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 chi-square, or both. (See NUREG/CR-3318 and NUREG/CR-3319.) 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 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
or for group fluences
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 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, wj, 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.
1.1 This guide covers the analysis and interpretation of the physics dosimetry for Light Water Reactor (LWR) surveillance programs. The main purpose is the application of adjustment methods to determine best estimates of neutron damage exposure parameters and their uncertainties.
1.2 This guide is also applicable to irradiation damage studies in research reactors.
1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.
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