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Title: Verification of unfold error estimates in the unfold operator code

Abstract

Spectral unfolding is an inverse mathematical operation that attempts to obtain spectral source information from a set of response functions and data measurements. Several unfold algorithms have appeared over the past 30 years; among them is the unfold operator (UFO) code written at Sandia National Laboratories. In addition to an unfolded spectrum, the UFO code also estimates the unfold uncertainty (error) induced by estimated random uncertainties in the data. In UFO the unfold uncertainty is obtained from the error matrix. This built-in estimate has now been compared to error estimates obtained by running the code in a Monte Carlo fashion with prescribed data distributions (Gaussian deviates). In the test problem studied, data were simulated from an arbitrarily chosen blackbody spectrum (10 keV) and a set of overlapping response functions. The data were assumed to have an imprecision of 5{percent} (standard deviation). One hundred random data sets were generated. The built-in estimate of unfold uncertainty agreed with the Monte Carlo estimate to within the statistical resolution of this relatively small sample size (95{percent} confidence level). A possible 10{percent} bias between the two methods was unresolved. The Monte Carlo technique is also useful in underdetermined problems, for which the error matrix methodmore » does not apply. UFO has been applied to the diagnosis of low energy x rays emitted by Z-pinch and ion-beam driven hohlraums. {copyright} {ital 1997 American Institute of Physics.}« less

Authors:
;  [1]
  1. Sandia National Laboratories, Albuquerque, New Mexico 87185 (United States)
Publication Date:
Research Org.:
Sandia National Laboratories (SNL), Albuquerque, NM, and Livermore, CA (United States)
OSTI Identifier:
451908
Report Number(s):
CONF-960543-
Journal ID: RSINAK; ISSN 0034-6748; TRN: 97:006265
DOE Contract Number:  
AC04-94AL85000
Resource Type:
Journal Article
Journal Name:
Review of Scientific Instruments
Additional Journal Information:
Journal Volume: 68; Journal Issue: 1; Conference: 11. annual high-temperature plasma diagnostics conference, Monterey, CA (United States), 12-16 May 1996; Other Information: PBD: Jan 1997
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION; PLASMA DIAGNOSTICS; ERRORS; RESPONSE FUNCTIONS; LINEAR Z PINCH DEVICES; BLACKBODY RADIATION; VERIFICATION; ALGORITHMS; MONTE CARLO METHOD; KEV RANGE 01-10; COMPUTER CODES; X RADIATION; Z pinch; Monte Carlo methods; matrix algebra; error analysis

Citation Formats

Fehl, D L, and Biggs, F. Verification of unfold error estimates in the unfold operator code. United States: N. p., 1997. Web. doi:10.1063/1.1147713.
Fehl, D L, & Biggs, F. Verification of unfold error estimates in the unfold operator code. United States. https://doi.org/10.1063/1.1147713
Fehl, D L, and Biggs, F. 1997. "Verification of unfold error estimates in the unfold operator code". United States. https://doi.org/10.1063/1.1147713.
@article{osti_451908,
title = {Verification of unfold error estimates in the unfold operator code},
author = {Fehl, D L and Biggs, F},
abstractNote = {Spectral unfolding is an inverse mathematical operation that attempts to obtain spectral source information from a set of response functions and data measurements. Several unfold algorithms have appeared over the past 30 years; among them is the unfold operator (UFO) code written at Sandia National Laboratories. In addition to an unfolded spectrum, the UFO code also estimates the unfold uncertainty (error) induced by estimated random uncertainties in the data. In UFO the unfold uncertainty is obtained from the error matrix. This built-in estimate has now been compared to error estimates obtained by running the code in a Monte Carlo fashion with prescribed data distributions (Gaussian deviates). In the test problem studied, data were simulated from an arbitrarily chosen blackbody spectrum (10 keV) and a set of overlapping response functions. The data were assumed to have an imprecision of 5{percent} (standard deviation). One hundred random data sets were generated. The built-in estimate of unfold uncertainty agreed with the Monte Carlo estimate to within the statistical resolution of this relatively small sample size (95{percent} confidence level). A possible 10{percent} bias between the two methods was unresolved. The Monte Carlo technique is also useful in underdetermined problems, for which the error matrix method does not apply. UFO has been applied to the diagnosis of low energy x rays emitted by Z-pinch and ion-beam driven hohlraums. {copyright} {ital 1997 American Institute of Physics.}},
doi = {10.1063/1.1147713},
url = {https://www.osti.gov/biblio/451908}, journal = {Review of Scientific Instruments},
number = 1,
volume = 68,
place = {United States},
year = {Wed Jan 01 00:00:00 EST 1997},
month = {Wed Jan 01 00:00:00 EST 1997}
}