Summary of Experimental Uncertainty Assessment Methodology With Example

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1 Summa of Epemenal ncean Aemen Mehodolog Wh Eample F. Sen, M. Mue, M-L. M enna,, and W.E. Echnge 5//00 1

2 Table of Conen A hlooph Temnolog ncean opagaon Equaon A fo Sngle Te A fo Mulple Te Eample Recommendaon fo Implemenaon

3 Inoducon efnon Epemen Eo nceane The mo updae andad fo uncean aemen mehodolog: AIAA S Th lecue: umma of he AIAA andad wh eample fo he meauemen of den and vco

4 Te degn phlooph EFINE ROSE OF TEST AN RESLTS NCERTAINTY REQIREMENTS SELECT NCERTAINTY METHO ESIGN THE TEST - ESIRE AR AM ETER S (C, C,...) R - MOEL CONFIGRATIONS (S) - TEST TECHNIQE (S) - MEASREMENTS REQIRE - SECIFIC INSTRM ENTATION - CORRECTIONS TO E ALIE ETERMINE ERROR SORCES AFFECTING RESLTS YES ESTIMATE EFFECT OF THE ERRORS ON RESLTS IMROVEMENT OSSILE? NO NCERTAINTY ACCETALE? NO NO YES NO TEST IMLEMENT TEST START TEST RESLTS ACCETALE? NO MEASRE- MENT SYSTEM ROLEM? YES YES NO CONTINE TEST SOLVE ROLEM ROSE ACHIEVE? YES ESTIMATE ACTAL ATA NCERTAINTY OCMENT RESLTS - REFERENCE CONITION - RECISION LIM IT - IAS LIMIT - TOTAL NCERTAINTY

5 Temnolog Accuac: cloene beween meaued and ue value Eo: dffeence beween meaued and ue value nceane ():( emae of he eo (95% confdence level) ƒ δ oal eo β β ba eo a eo (β) ε pecon eo ƒ a lm () ƒ econ eo (ε) ƒ econ lm () ƒ Toal eo (δ β ε) FREQENCY OF OCCRRENCE ; WXH δ N β δ N ; N ε ε N (a) wo eadng ε N ε ; N ; ; ; WXH µ MAGNITE OF ; (b) nfne numbe of eadng

6 opagaon of eo Meauemen em: numenaon, daa acquon and educon, opeaonal envonmen ELEMENTAL ERROR SORCES 1 INIVIAL MEASREMENT SYSTEMS ƒelemenal eo ouce (, ) fo each vaable popagae o he eul hough daa educon equaon X, X, (X, X,..., X ) 1 X, MEASREMENT OF INIVIAL VARIALES ATA RECTION EQATION, EXERIMENTAL RESLT

Eo ouce Idenfcaon and quanfcaon of eo: condeaon of he ep and envonmen of he epemen MOEL FIELITY AN TEST SET: - A bul geome - Hdodnamc defomaon - Suface fnh - Model poonng TEST ENVIRONMENT: - Calbaon

7 Eo ouce Idenfcaon and quanfcaon of eo: condeaon of he ep and envonmen of he epemen MOEL FIELITY AN TEST SET: - A bul geome - Hdodnamc defomaon - Suface fnh - Model poonng TEST ENVIRONMENT: - Calbaon veu e - Spaal/empoal vaaon of he flow - Seno nallaon/locaon - Wa ll ne fe e nce - Flud and facl condon CONTRITIONS TO ESTIMATE NCERTAINITY SIMLATION TECHNIQES: - Inumenaon nefeence - Scale effec ATA ACQISITION AN RECTION: - Samplng, fleng, and ac - Cuve f - Calbaon

8 ncean popagaon equaon One vaable ( X ) (X ) ue d d dx δ X X X ue X ( X ) ( X ) ue δ X d dx

9 ncean popagaon equaon Two vaable, he h h e of meauemen ((, ) (, ) ue β ε β [ N ε [ N ε \ N β \ N ue β ε [ WXH µ [ [ N µ \ [ \ N N N \ N \ WXH ue ( ue ) ( ue ) R β N ε N The oal eo n he h deemnaon of WXH N ue ( β ε ) ( β ε ) δ (1)

10 ncean popagaon equaon A meaue of A meaue of δ ( ) N N N 1 1 lm δ σ δ ε ε ε ε β β β β δ σ σ σ σ σ σ σ c S S S b b b u Ku c Subung (1) n (), and aumng no coelaed ba/pecon eo () σ ae no nown; ue emae fo he vaance and covaance of he dbuon of he oal, ba, and pecon eo The oal uncean of he eul a a pecfed level of confdence (K fo 95% confdence level) (3)

11 ncean popagaon equaon Genealzng (3) fo Genealzng (3) fo vaable vaable X ( ) A C A C,,, 1 ( ) ( ) ( ) ( ) 1 1 A A C A C C C C env coeffcen Eample:

12 Sngle and mulple e Sngle e: one e of meauemen (X( 1, X,, X j ) fo Mulple e: man e of meauemen (X( 1, X,, X j ) fo The oal uncean of he eul (ngle and mulple) (4) : deemned n he ame manne fo ngle and mulple e : deemned dffeenl fo ngle and mulple e

13 a lm (ngle and mulple e) gven b: gven b: ƒsenv coeffcen X ƒ : emae of calbaon, daa acquon, daa educon, concepual ba eo fo X ƒ : emae of coelaed ba lm fo X and X L ( ) ( ) α α 1 α

14 econ lm (ngle e) econ lm of he eul (end o end): S : coveage faco ( fo N > 10) S : he andad devaon fo he N eadng of he eul econ lm of he eul (ndvdual vaable): ( 1 ) : he pecon lm fo X S

15 econ lm (mulple e) The aveage eul: econ lm of he eul (end o end): : coveage faco ( fo N > 10) S : andad devaon fo M eadng of he eul 1 M M 1 S M M ( ) 1 1 S M econ lm of he eul (ndvdual vaable): 1/ ( 1 ) : coveage faco ( fo N > 10) S : andad devaon fo M eadng of he vaable S M

16 Implemenaon eemne daa educon equaon: (X 1, X,, X j ) Conuc he bloc dagam Conuc daa-eam dagam Idenf, emae, and eablh elave gnfcance of he ba lm fo he ndvdual vaable Emae pecon lm (end-o o-end pocedue ecommended) Calculae oal uncean ung equaon (4) Repo oal eo, ba and pecon lm fo he fnal eul

17 Eample: Te degn F d F b S p h e e f a l l n g a e m n a l v e l o c l F g V A phee of damee fall a emnal veloc V (fall dance λ, fall me ) hough a clnde flled wh 99.7% aqueou glcen oluon of den, vco µ, and nemac vco ν ( µ/). ƒ The daa educon equaon fo ν and g ν ν (,, λ, ) ( S 18λ 1) (,,, ) - -

18 Meauemen em EXERIMENTAL ERROR SORCES SHERE IAMETER FALL ISTANCE FALL TIME INIVIAL MEASREMENT SYSTEMS X, X λ, λ λ X, MEASREMENT OF INIVIAL VARIALES ν ( X, X ) ν (X, X, X, X ) λ - - g( /-1) phee 18λ ATA RECTION EQATIONS ν,,, ν ν,, EXERIMENTAL RESLTS

19 Te eul Table 1. Gav and phee den conan efnon Smbol Value Gavaonal g 9.81 m/ acceleaon en of eel 7991 g/m 3 en of eflon 148 g/m 3 Table. Tpcal e eul Tal TEFLON STEEL RESLTS T 6.4 C ν λ 0.61 m (m) (ec) (m) (ec) (g/m 3 ) (m /) Aveage Sd.ev. (S )

20 ncean aemen (mulple e) en en ƒ a lm a Lm Magnude ecenage Value Emaon S m % 0.14 % ½ numen eoluon % 0.083% La gnfcan dg M S ƒ econ lm ± ƒ Toal uncean

21 ncean aemen (mulple e) en Tem Whou coelaed ba eo Wh coelaed ba eo Magnude % Value Magnude % Value 1.48 g/m 3.30% 1.48 g/m % 0.31 g/m % 0.31 g/m % -.63 g/m % -.63 g/m % g/m % g/m % g/m % g/m % 3.13 g/m 3 0.4% 3.3% g/m 3 1.8% 96.70% 1. g/m % 0.47% g/m 3 1.9% 99.53% 17.0g/m % 16.95g/m 3 1.8%

22 ncean aemen (mulple e) Vco ν (eflon phee) ƒ a lm ν λ λ ƒ econ lm ƒ Toal uncean ν S ν ν ν M ν Tem Magnude ecenage Value l m 0.13% l m / 5.97% ν m/ 90.03% m/ 0.6% λ l m/ 3.74% ν τ ν τ ν ν m/ 0.64% 16.43% n ν ν m/ 1.43% n 83.57% ν m/ 1.57% ν ν

23 Compaon wh benchma daa en en (g/m 3 ) Refeence daa (oce & Gamble) Mulple e mehod ETco hdomee Robeon & Cowe (1997) Tempeaue (egee Celu) E 4.9% (efeence daa) and E 5.4% (ETco hdomee) Neglecng coelaed ba eo: E 1.30% aa no valdaed: E E

24 Compaon wh benchma daa Vco ν Knemac Vco (m /) 1.6e-3 1.4e-3 1.e-3 1.0e-3 8.0e-4 6.0e-4 Refeence daa (oce & Gamble) Mulple e mehod (Teflon) Cannon vcomee Robeon & Cowe (1997) Refeence daa (oce & Gamble) Mulple e mehod (Seel) Cannon vcomee Robeon & Cowe (1997) 4.0e Tempeaue (degee Celu) Tempeaue (degee Celu) E 3.95% (efeence daa) and E 40.6% (Cannon caplla vcomee) Neglecng coelaed ba eo: E E 1.57%( eflon) 1.49%( eel) aa no valdaed (unaccouned ba eo): E E

25 Recommendaon Recognon of he uncean anal (A) mpoance Full negaon of A no all phae of he eng poce Smplfed A: domnan eo ouce onl ue of pevou daa end-o o-end calbaon and emaon of eo Full documenaon: Te degn, meauemen em, daa-eam n bloc dagam Equpmen and pocedue Eo ouce condeed Emae fo ba and pecon lm and emang pocedue ealed A mehodolog and acual daa uncean emae

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