An Improvement on the Standard Linear Uncertainty Quantification Using a Least-Squares Method

Abstract Linear uncertainty analysis based on a first order Taylor series expansion, described in ASME PTC (Performance Test Code) 19.1 “Test Uncertainty” and the ISO Guide for the “Expression of Uncertainty in Measurement,” has been the most widely technique used both in industry and academia. A co...
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Autor*in:	Cho, Heejin [verfasserIn] Luck, Rogelio Stevens, James W.

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2015

Schlagwörter:	Uncertainty Sensitivity analysis Linear regression Covariance

Anmerkung:	© Cho et al. 2015

Übergeordnetes Werk:	Enthalten in: Journal of Uncertainty Analysis and Applications - Berlin : SpringerOpen, 2013, 3(2015), 1 vom: 02. Dez.
Übergeordnetes Werk:	volume:3 ; year:2015 ; number:1 ; day:02 ; month:12

Links:	Volltext

DOI / URN:	10.1186/s40467-015-0041-9

Katalog-ID:	SPR036488542

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520			\|a Abstract Linear uncertainty analysis based on a first order Taylor series expansion, described in ASME PTC (Performance Test Code) 19.1 “Test Uncertainty” and the ISO Guide for the “Expression of Uncertainty in Measurement,” has been the most widely technique used both in industry and academia. A common approach in linear uncertainty analysis is to use local derivative information as a measure of the sensitivity needed to calculate the uncertainty percentage contribution (UPC) and uncertainty magnification factors (UMF) due to each independent variable in the measurement/process being examined. The derivative information is typically obtained by either taking the symbolic partial derivative of an analytical expression or the numerical derivative based on central difference techniques. This paper demonstrates that linear multivariable regression is better suited to obtain sensitivity coefficients that are representative of the behavior of the data reduction equations over the region of interest. A main advantage of the proposed approach is the possibility of extending the range, within a fixed tolerance level, for which the linear approximation technique is valid. Three practical examples are presented in this paper to demonstrate the effectiveness of the proposed least-squares method.
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allfields	10.1186/s40467-015-0041-9 doi (DE-627)SPR036488542 (SPR)s40467-015-0041-9-e DE-627 ger DE-627 rakwb eng Cho, Heejin verfasserin (orcid)0000-0003-2789-510X aut An Improvement on the Standard Linear Uncertainty Quantification Using a Least-Squares Method 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Cho et al. 2015 Abstract Linear uncertainty analysis based on a first order Taylor series expansion, described in ASME PTC (Performance Test Code) 19.1 “Test Uncertainty” and the ISO Guide for the “Expression of Uncertainty in Measurement,” has been the most widely technique used both in industry and academia. A common approach in linear uncertainty analysis is to use local derivative information as a measure of the sensitivity needed to calculate the uncertainty percentage contribution (UPC) and uncertainty magnification factors (UMF) due to each independent variable in the measurement/process being examined. The derivative information is typically obtained by either taking the symbolic partial derivative of an analytical expression or the numerical derivative based on central difference techniques. This paper demonstrates that linear multivariable regression is better suited to obtain sensitivity coefficients that are representative of the behavior of the data reduction equations over the region of interest. A main advantage of the proposed approach is the possibility of extending the range, within a fixed tolerance level, for which the linear approximation technique is valid. Three practical examples are presented in this paper to demonstrate the effectiveness of the proposed least-squares method. Uncertainty (dpeaa)DE-He213 Sensitivity analysis (dpeaa)DE-He213 Linear regression (dpeaa)DE-He213 Covariance (dpeaa)DE-He213 Luck, Rogelio aut Stevens, James W. aut Enthalten in Journal of Uncertainty Analysis and Applications Berlin : SpringerOpen, 2013 3(2015), 1 vom: 02. Dez. (DE-627)745007392 (DE-600)2713511-1 2195-5468 nnns volume:3 year:2015 number:1 day:02 month:12 https://dx.doi.org/10.1186/s40467-015-0041-9 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 3 2015 1 02 12
spelling	10.1186/s40467-015-0041-9 doi (DE-627)SPR036488542 (SPR)s40467-015-0041-9-e DE-627 ger DE-627 rakwb eng Cho, Heejin verfasserin (orcid)0000-0003-2789-510X aut An Improvement on the Standard Linear Uncertainty Quantification Using a Least-Squares Method 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Cho et al. 2015 Abstract Linear uncertainty analysis based on a first order Taylor series expansion, described in ASME PTC (Performance Test Code) 19.1 “Test Uncertainty” and the ISO Guide for the “Expression of Uncertainty in Measurement,” has been the most widely technique used both in industry and academia. A common approach in linear uncertainty analysis is to use local derivative information as a measure of the sensitivity needed to calculate the uncertainty percentage contribution (UPC) and uncertainty magnification factors (UMF) due to each independent variable in the measurement/process being examined. The derivative information is typically obtained by either taking the symbolic partial derivative of an analytical expression or the numerical derivative based on central difference techniques. This paper demonstrates that linear multivariable regression is better suited to obtain sensitivity coefficients that are representative of the behavior of the data reduction equations over the region of interest. A main advantage of the proposed approach is the possibility of extending the range, within a fixed tolerance level, for which the linear approximation technique is valid. Three practical examples are presented in this paper to demonstrate the effectiveness of the proposed least-squares method. Uncertainty (dpeaa)DE-He213 Sensitivity analysis (dpeaa)DE-He213 Linear regression (dpeaa)DE-He213 Covariance (dpeaa)DE-He213 Luck, Rogelio aut Stevens, James W. aut Enthalten in Journal of Uncertainty Analysis and Applications Berlin : SpringerOpen, 2013 3(2015), 1 vom: 02. Dez. (DE-627)745007392 (DE-600)2713511-1 2195-5468 nnns volume:3 year:2015 number:1 day:02 month:12 https://dx.doi.org/10.1186/s40467-015-0041-9 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 3 2015 1 02 12
allfields_unstemmed	10.1186/s40467-015-0041-9 doi (DE-627)SPR036488542 (SPR)s40467-015-0041-9-e DE-627 ger DE-627 rakwb eng Cho, Heejin verfasserin (orcid)0000-0003-2789-510X aut An Improvement on the Standard Linear Uncertainty Quantification Using a Least-Squares Method 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Cho et al. 2015 Abstract Linear uncertainty analysis based on a first order Taylor series expansion, described in ASME PTC (Performance Test Code) 19.1 “Test Uncertainty” and the ISO Guide for the “Expression of Uncertainty in Measurement,” has been the most widely technique used both in industry and academia. A common approach in linear uncertainty analysis is to use local derivative information as a measure of the sensitivity needed to calculate the uncertainty percentage contribution (UPC) and uncertainty magnification factors (UMF) due to each independent variable in the measurement/process being examined. The derivative information is typically obtained by either taking the symbolic partial derivative of an analytical expression or the numerical derivative based on central difference techniques. This paper demonstrates that linear multivariable regression is better suited to obtain sensitivity coefficients that are representative of the behavior of the data reduction equations over the region of interest. A main advantage of the proposed approach is the possibility of extending the range, within a fixed tolerance level, for which the linear approximation technique is valid. Three practical examples are presented in this paper to demonstrate the effectiveness of the proposed least-squares method. Uncertainty (dpeaa)DE-He213 Sensitivity analysis (dpeaa)DE-He213 Linear regression (dpeaa)DE-He213 Covariance (dpeaa)DE-He213 Luck, Rogelio aut Stevens, James W. aut Enthalten in Journal of Uncertainty Analysis and Applications Berlin : SpringerOpen, 2013 3(2015), 1 vom: 02. Dez. (DE-627)745007392 (DE-600)2713511-1 2195-5468 nnns volume:3 year:2015 number:1 day:02 month:12 https://dx.doi.org/10.1186/s40467-015-0041-9 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 3 2015 1 02 12
allfieldsGer	10.1186/s40467-015-0041-9 doi (DE-627)SPR036488542 (SPR)s40467-015-0041-9-e DE-627 ger DE-627 rakwb eng Cho, Heejin verfasserin (orcid)0000-0003-2789-510X aut An Improvement on the Standard Linear Uncertainty Quantification Using a Least-Squares Method 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Cho et al. 2015 Abstract Linear uncertainty analysis based on a first order Taylor series expansion, described in ASME PTC (Performance Test Code) 19.1 “Test Uncertainty” and the ISO Guide for the “Expression of Uncertainty in Measurement,” has been the most widely technique used both in industry and academia. A common approach in linear uncertainty analysis is to use local derivative information as a measure of the sensitivity needed to calculate the uncertainty percentage contribution (UPC) and uncertainty magnification factors (UMF) due to each independent variable in the measurement/process being examined. The derivative information is typically obtained by either taking the symbolic partial derivative of an analytical expression or the numerical derivative based on central difference techniques. This paper demonstrates that linear multivariable regression is better suited to obtain sensitivity coefficients that are representative of the behavior of the data reduction equations over the region of interest. A main advantage of the proposed approach is the possibility of extending the range, within a fixed tolerance level, for which the linear approximation technique is valid. Three practical examples are presented in this paper to demonstrate the effectiveness of the proposed least-squares method. Uncertainty (dpeaa)DE-He213 Sensitivity analysis (dpeaa)DE-He213 Linear regression (dpeaa)DE-He213 Covariance (dpeaa)DE-He213 Luck, Rogelio aut Stevens, James W. aut Enthalten in Journal of Uncertainty Analysis and Applications Berlin : SpringerOpen, 2013 3(2015), 1 vom: 02. Dez. (DE-627)745007392 (DE-600)2713511-1 2195-5468 nnns volume:3 year:2015 number:1 day:02 month:12 https://dx.doi.org/10.1186/s40467-015-0041-9 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 3 2015 1 02 12
allfieldsSound	10.1186/s40467-015-0041-9 doi (DE-627)SPR036488542 (SPR)s40467-015-0041-9-e DE-627 ger DE-627 rakwb eng Cho, Heejin verfasserin (orcid)0000-0003-2789-510X aut An Improvement on the Standard Linear Uncertainty Quantification Using a Least-Squares Method 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Cho et al. 2015 Abstract Linear uncertainty analysis based on a first order Taylor series expansion, described in ASME PTC (Performance Test Code) 19.1 “Test Uncertainty” and the ISO Guide for the “Expression of Uncertainty in Measurement,” has been the most widely technique used both in industry and academia. A common approach in linear uncertainty analysis is to use local derivative information as a measure of the sensitivity needed to calculate the uncertainty percentage contribution (UPC) and uncertainty magnification factors (UMF) due to each independent variable in the measurement/process being examined. The derivative information is typically obtained by either taking the symbolic partial derivative of an analytical expression or the numerical derivative based on central difference techniques. This paper demonstrates that linear multivariable regression is better suited to obtain sensitivity coefficients that are representative of the behavior of the data reduction equations over the region of interest. A main advantage of the proposed approach is the possibility of extending the range, within a fixed tolerance level, for which the linear approximation technique is valid. Three practical examples are presented in this paper to demonstrate the effectiveness of the proposed least-squares method. Uncertainty (dpeaa)DE-He213 Sensitivity analysis (dpeaa)DE-He213 Linear regression (dpeaa)DE-He213 Covariance (dpeaa)DE-He213 Luck, Rogelio aut Stevens, James W. aut Enthalten in Journal of Uncertainty Analysis and Applications Berlin : SpringerOpen, 2013 3(2015), 1 vom: 02. Dez. (DE-627)745007392 (DE-600)2713511-1 2195-5468 nnns volume:3 year:2015 number:1 day:02 month:12 https://dx.doi.org/10.1186/s40467-015-0041-9 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 3 2015 1 02 12
language	English
source	Enthalten in Journal of Uncertainty Analysis and Applications 3(2015), 1 vom: 02. Dez. volume:3 year:2015 number:1 day:02 month:12
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author	Cho, Heejin
spellingShingle	Cho, Heejin misc Uncertainty misc Sensitivity analysis misc Linear regression misc Covariance An Improvement on the Standard Linear Uncertainty Quantification Using a Least-Squares Method
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topic_title	An Improvement on the Standard Linear Uncertainty Quantification Using a Least-Squares Method Uncertainty (dpeaa)DE-He213 Sensitivity analysis (dpeaa)DE-He213 Linear regression (dpeaa)DE-He213 Covariance (dpeaa)DE-He213
topic	misc Uncertainty misc Sensitivity analysis misc Linear regression misc Covariance
topic_unstemmed	misc Uncertainty misc Sensitivity analysis misc Linear regression misc Covariance
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title	An Improvement on the Standard Linear Uncertainty Quantification Using a Least-Squares Method
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title_full	An Improvement on the Standard Linear Uncertainty Quantification Using a Least-Squares Method
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title_sort	improvement on the standard linear uncertainty quantification using a least-squares method
title_auth	An Improvement on the Standard Linear Uncertainty Quantification Using a Least-Squares Method
abstract	Abstract Linear uncertainty analysis based on a first order Taylor series expansion, described in ASME PTC (Performance Test Code) 19.1 “Test Uncertainty” and the ISO Guide for the “Expression of Uncertainty in Measurement,” has been the most widely technique used both in industry and academia. A common approach in linear uncertainty analysis is to use local derivative information as a measure of the sensitivity needed to calculate the uncertainty percentage contribution (UPC) and uncertainty magnification factors (UMF) due to each independent variable in the measurement/process being examined. The derivative information is typically obtained by either taking the symbolic partial derivative of an analytical expression or the numerical derivative based on central difference techniques. This paper demonstrates that linear multivariable regression is better suited to obtain sensitivity coefficients that are representative of the behavior of the data reduction equations over the region of interest. A main advantage of the proposed approach is the possibility of extending the range, within a fixed tolerance level, for which the linear approximation technique is valid. Three practical examples are presented in this paper to demonstrate the effectiveness of the proposed least-squares method. © Cho et al. 2015
abstractGer	Abstract Linear uncertainty analysis based on a first order Taylor series expansion, described in ASME PTC (Performance Test Code) 19.1 “Test Uncertainty” and the ISO Guide for the “Expression of Uncertainty in Measurement,” has been the most widely technique used both in industry and academia. A common approach in linear uncertainty analysis is to use local derivative information as a measure of the sensitivity needed to calculate the uncertainty percentage contribution (UPC) and uncertainty magnification factors (UMF) due to each independent variable in the measurement/process being examined. The derivative information is typically obtained by either taking the symbolic partial derivative of an analytical expression or the numerical derivative based on central difference techniques. This paper demonstrates that linear multivariable regression is better suited to obtain sensitivity coefficients that are representative of the behavior of the data reduction equations over the region of interest. A main advantage of the proposed approach is the possibility of extending the range, within a fixed tolerance level, for which the linear approximation technique is valid. Three practical examples are presented in this paper to demonstrate the effectiveness of the proposed least-squares method. © Cho et al. 2015
abstract_unstemmed	Abstract Linear uncertainty analysis based on a first order Taylor series expansion, described in ASME PTC (Performance Test Code) 19.1 “Test Uncertainty” and the ISO Guide for the “Expression of Uncertainty in Measurement,” has been the most widely technique used both in industry and academia. A common approach in linear uncertainty analysis is to use local derivative information as a measure of the sensitivity needed to calculate the uncertainty percentage contribution (UPC) and uncertainty magnification factors (UMF) due to each independent variable in the measurement/process being examined. The derivative information is typically obtained by either taking the symbolic partial derivative of an analytical expression or the numerical derivative based on central difference techniques. This paper demonstrates that linear multivariable regression is better suited to obtain sensitivity coefficients that are representative of the behavior of the data reduction equations over the region of interest. A main advantage of the proposed approach is the possibility of extending the range, within a fixed tolerance level, for which the linear approximation technique is valid. Three practical examples are presented in this paper to demonstrate the effectiveness of the proposed least-squares method. © Cho et al. 2015
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title_short	An Improvement on the Standard Linear Uncertainty Quantification Using a Least-Squares Method
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