Specialist Committee on Uncertainty Analysis

Joel T. Park, Ph. D., Chairman, USAAhmed Derradji Aouat, Ph. D., Secretary, Canada

Baoshan Wu, ChinaShigeru Nishio, Ph. D., Japan

25th

ITTC, Fukuoka, Japan15 September 2008, 15:00 –

16:15

2

Outline

Introduction– Important concepts– ISO GUM (1995)

Membership & meetings

Procedures (5)– UA procedure

(revised)– Calibration Procedure– LDV Calibration– PIV Uncertainty– Resistance Tests

(revised)SummaryRecommendations

3

Important Concepts

Measurements traceable to a National Metrology Institute (NMI)Most uncertainty from data scatter in curve fit for conventional methods– Calibration data– Thrust coefficient versus advance ratio– Residual plot of data

Most uncertainty in naval hydrodynamics in repeatability of tests– Uncontrolled element in test– Resistance tests

4

Committee Members

Joel T. Park, Ph. D., Chair, NSWCCD, USAAhmed Derradji Aouat, Ph. D. Sec., IOT, CanadaErwan Jacquin, BEC, FranceBaoshan Wu, CSSRC, ChinaShigeru Nishio, Ph. D., Kobe U., Japan Wu Derradji Jacquin Park Nisho

5

Meetings

Bassin d’Essais des Carènes, Val-de-Reuil, France, March 30 - 31, 2006.China Ship Scientific Research Center, Wuxi, China, October 23 - 25, 2006.National Research Council Canada, Institute for Ocean Technology, St. John’s, Newfoundland, Canada, June 7 - 8, 2007.U. S. National Academy of Sciences, Naval Studies Board, Washington, DC, January 30 - February 1, 2008Kobe University, Kobe, Japan, September 12, 2008

6

Objectives of General Procedure

Simple and useable procedure tailored to ITTC hydrodynamics testingSpecific guidance on application of uncertainty to experimental naval hydrodynamicsSelf-contained without need for consultation with reference documentsITTC procedure derived from ISO Guide to the Expression of Uncertainty in Measurement (1995), referred to as the ISO GUM.

ITTC 7.5-02-01-01 (2008)

7

Uncertainty Analysis Fundamentals

Type A evaluation of standard uncertainty– Average or sample mean

– Sample variance

– Standard deviation, sx– Type A standard uncertainty definition or standard

deviation of the meanConventional statistical definitions: Ross (2004) p. 203, AIAA (1999) p. 7, ASME (2005) p. 6

∑=

>=<n

kkxnx

1

)/1(

∑=

><−−=n

kkx xxns

1

22 )()]1/(1[

nssu xxA /== ><

8

Uncertainty Analysis Fundamentals (cont.)

Type B evaluation of standard uncertainty– Previous measurement data

» Density, viscosity, and vapor pressure– Experience– Manufacturer’s specifications– Handbook– National Metrology Institute (NMI) traceable

calibration: NIST in USA, NMIJ in Japan, NMi in The Netherlands, NPL in UK, PTB in Germany, NRC in Canada, KRISS in ROK

9

Uncertainty Analysis Fundamentals (cont.)

Functional relationshipCombined uncertainty– Law of propagation of uncertainty– Sensitivity coefficient– Independent

– Correlated (weight set)

Expanded uncertainty– Coverage factor, k– Student t

∑=

∂∂=n

iiic xuxfyu

1

222 )()/()(

95%,2),(% === kykuU c

%tk =

),,,( 21 Nxxxfy K=

ii xfc ∂∂≡ /

∑∑==

≡=N

ii

N

iiic yuxucyu

1

2

1

22 )()]([)(

∑=

=N

iiic xucyu

1)()(

10

Relative Uncertainty Propeller

Reynolds number

Advance ratio

Thrust coefficient

)/(NDVJ =2222 )/()/()/(]/[ DuNuVuJu DNVJ −+−+=

)/( 42DNTKT ρ=

22

2222

)/(16)/(4

)/()/()/(]/[

DuNu

utTuKu

DN

tTTKT

−+−

+−∂∂+= ρρ

μρ /VDReD =

22

222

)/()/(

)/()/(]/)([

μ

ρ

μ

ρ

uDu

VuuReReu

D

VDDc

−+

++=

11

Numerical Evaluation of Sensitivity Coeff.

Central difference for uncertainty

Numerical sensitivity coefficient

Jitter program, Moffat (1982)

)],),(,,(),),(,,(][2/1[)(

1

1

Nii

Niiii

xxuxxfxxuxxfZyu

KK

KK

−−+==

)(/ iii xuZc =

12

Reporting Uncertainty Specific for U

Give full description of how measurand Y

was definedState measurement result as Y = y ± U– Give units of y

and U

Include relative expanded uncertainty U/|y|, |y|

≠ 0

Give values of k

and uc

(y)Give approximate level of confidence for the interval y ± U

and state how determined

Provide details or reference published document

13

Specification of Numerical Results

ms

= (100.021 47 ± 0.000 79) g, where the number following the symbol ± is the numerical value of U = kuc

(y), with U determined from uc

= 0.35 mg and k = 2.26 based on the t-distribution for ν = 9 degrees of freedom, and defines an interval estimated to have a level of confidence of 95 percent.

14

Other Elements of Procedure

Pre- & post-test uncertainty analysis– Uncertainty analysis in

data processing code

OutliersInter-Laboratory Comparisons– Youden plot

Special cases– Mass measurements– Instrument calibration

» NMI traceable» End-to-end or through

system calibration

– Repeat tests

15

Calibration Theory

Linear function– Independent variable,

x, calibration value set in engineering units

– Dependent variable, y, instrument response, usually in voltage units from A/D converter

Calibration value in post-processing code for engineering units

Uncertainty from theory of Scheffe (1973) & Carroll, et al. (1988)xxfy βα +== )(

ββαβα

/B,/AwhereByA/)y()y(fx

1=−=+=−==

ITTC 7.5-01-03-01 (2008)

16

Instrument Calibration Procedure

Calibration @ 10 approximately equal increments– System calibration with computer and software for test

measurements– Calculate mean and standard deviation for each point

on the order of 100 to 1000 points (5 to 50 s at 20 Hz sampling rate)

– Document» cutoff frequency» sample rate» number of samples

– NMI traceable reference standard with known uncertainty

17

Instrument Calibration Procedure (cont.)

Regression analysis of calibration data– Slope, intercept, correlation coefficient, standard error

of estimate, & outliers– Identify cause of outliers– Compute calibration uncertainty

Compare results to previous calibration– Hypothesis test of slope & intercept

Update computer slope & intercept3-point calibration check @ computer with test software

18

Uncertainty Elements for Instrument Cal.

Uncertainty in reference standard: NMI traceableUncertainty in curve fitType A uncertainty in data collection via computer for time series– Number of samples– Average– Standard deviation– Normally negligible: large values indication of

problem

19

Vertical Gyroscope Calibration in Roll

Reference Angle (deg)

-100-80 -60 -40 -20 0 20 40 60 80 100

A/D

Out

put (

V)

-10

-8

-6

-4

-2

0

2

4

6

8

10

Intercept: +0.0052 VSlope: -0.09143 V/degSEE: 0.0362 Vr: 0.999968

Linear RegressionIncreasing Roll AngleDecreasing Roll Angle

Reference Angle (deg)

-100-80 -60 -40 -20 0 20 40 60 80 100

Sta

ndar

dize

d R

esid

uals

-6

-4

-2

0

2

4

6

Intercept: -0.056 degSlope: -10.9370 deg/VSEE: 0.396 deg

Increasing Roll Angle Data Decreasing Roll Angle Data

Calibration Theory

20

Other Elements of Calibration

Hypothesis tests– Comparison with previous calibration results

Outliers– Chauvenet’s criteria– Standardized residuals

Force calibration– Mass uncertainty

Pulse count – optical encoders– Propeller shaft speed– Carriage speed

)1( wa ρρ /mgF −=

∑=

=n

iim uu

1

21

Equations for LDA Calibration

LDA optical calibration

Rotating disk calibration

Uncertainty equationsωπ rV 2=

22222 )2()2( ωππω uruu rV +=222 )/()/()/( ωωuruVu rV +=

fDD ffV δλθ == ]/)2/(sin2[

rVcrVc πωπω 2/,2/ 21 =∂∂==∂∂=

ITTC 7.5-01-03-02 (2008)

22

LDV Velocity Uncertainty

Axial LDA Velocity (m/s)0 5 10 15 20

U95

(m/s

)

0.000

0.005

0.010

0.015

0.020

0.025

0.030

Total Uncertainty for r = 50 mmRotational Velocity UncertaintyRadial UncertaintyLDA Noise

r = 100 mm

r = 50 mm

Bean & Hall (NIST, 1999)

07 May 2001

23

Comparison of Disk Results

Element NSWC NIST NMIJ PTB r 0.061 0.0074 0.0017 0.041fr 0.062 0.26 0.0018 0.035δf --- 0.16 --- ---Angle --- 0.011 0.017 0.0022fD 0.026 0.36 0.20 0.010Curve fit 0.043 --- --- ---Combined 0.10 0.48 0.20 0.055

Expanded Uncertainty in % @ 20 m/s

24

Particle Image Velocimetry (PIV)

Example of uncertainty analysis (UA) procedurePresent procedure developed from the guideline of Visualization Society of Japan recommendation (PIV-STD project, Nishio, et al., 1999)

uΔX/Δtu δα += )(Flow speed

Image displacement

Time interval

Magnification factor

ITTC 7.5-01-03-03 (2008)

25

Accumulation for Total Performance

Accumulation for total performance by the uncertainty for the flow speed

uu

, ux

, ut

: uncertainties of u, x and t

222c )/()/( tuuxuuuu txu ∂∂+∂∂+=

26

PIV Calibration Uncertainty

27

Summary of Uncertainty for Velocity uParame-

terCate-gory Error sources u(xi

) (unit) ci(unit) ci

u(xi

) (unit)

α Magnification Factor 0.00165 (mm/pix) 1580.0 (pix/s) 2.61

ΔX Image displacement 0.204 (pix) 132.0 (mm/ pix/s) 26.8

Δt Image interval 5.39E-09 (s) 1.2 (mm/s2) 6.47E-09

δu Experiment 0.732 (mm/s) 1.0 0.732

Combined uncertainty u 26.9 (mm/s)

26.80.204 (pix)

28

Summary of PIV Calibration Results

Total number of elements: 15– Magnification: 6– Displacement: 5– Time: 2– Velocity: 2

Velocity: 0.500 ±0.054 m/s (±11 %)

Dominant terms– Mis-matching: 26.4 mm/s

Secondary terms– Magnification: 2.6 mm/s– Sub-pixel

analysis: 4.0 mm/s– Laser power

fluctuation: 3.0 mm/s

29

Guidelines for UA in Resistance Tests

Data reduction equations– Total resistance coefficient– Form factor– Others: Re, Fr, frictional, & residuary – See procedure

Measurement system descriptionCalibration – See procedure for details– Force and mass– Resistance– Towing speed

30

Revised Procedure

Uncertainty Analysis in EFD, Guidelines forResistance Towing Tank Tests (1999)

Revise QM Procedure 7.5-02-01-02 (1999)

General Guidelines for Uncertainty Analysisin Resistance Towing Tank Tests (2008)

7.5-02-01-01 (2008)Guide to the Expression of

Uncertainty in Experi- mental Hydrodynamics

7.5-02-02-01 (2002)Resistance,

Resistance Test

7.5-01-03-01 (2008)Uncertainty Analysis -

Instrument Calibrations

ISO GUMISO GUM

AIAAAIAA5 pp

16 pp

31

UA in Resistance in Tow Tank Tests

Total resistance coefficient– Data reduction equation

– Uncertainty equation)/(2 2SVRC TT ρ=

222

22

)/()/()/2(

)]/)(/[()/(

SuRuVu

utCu

STRTV

tTCT

++

+∂∂= ρρ

ITTC 7.5-02-01-02 (2008)

32

Prohaska method

Intercept & its standard deviation from linear regression theoryExample from CSSRC– 0.1574±0.0097 (±6.2 %)

Additional terms from CF & CT at x

= 0

Form Factor

6410

1

<<≤

+=−

n.Fr

kC/bFrC/C Fn

FT

Fr4/CF

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

CT/

CF -

10.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30

0.32

Slope: 0.1924k: 0.1574SEE: 0.0105r: 0.977

Linear Fit+/-95% Prediction Limit+/-95% Confidence Limit

Model Data

1FT −= C/Ck

33

Other Elements of Final Report

Terms of referenceUncertainty analysis symbolsOther activitiesHistory of uncertainty analysisRecommendation INC-1 (1980)Importance of uncertainty analysisRepeatability and reproducibility of data

34

Other Elements of Final Report (cont.)

Inter-laboratory comparisons– Youden plot

Free-running model tests– Instrument calibration– Model speed– Circle manoeuvres

Uncertainty of water propertiesUncertainty in PMM procedure

35

Recommendations

Adopt 2 revised and 3 new procedures from UACAdopt ISO (1995) as the UA standard for ITTC– Modify existing ITTC procedures to conform to ISO

(1995) by relevant committees with assistance of UAC– Adopt Annex J of ISO (1995) for ITTC symbols for

UA and VIM as dictionary– Include UA in benchmark data & review by UAC

Extend PIV procedure to include stereo PIV

36

Important Concepts

Measurements traceable to a National Metrology Institute (NMI)Most uncertainty from data scatter in curve fit for conventional methods– Calibration data– Thrust coefficient versus advance ratio– Residual plot of data

Most uncertainty in naval hydrodynamics in repeatability of tests– Resistance tests

37

Support Slides

Coleman & Steele on ISO (1995) - 5 slidesUncertainty analysis - 11 slidesCalibration data - 4 slidesLDV data - 1 slidePIV details on displacement & magnification uncertainties - 2 slidesResistance testing - 8 slidesRepeatability - 2 slidesYouden plot - 1 slide

38

Glenn Steele on ISO (1995)From: Glenn Steele [mailto:steele@me.msstate.edu] Sent: September 3, 2008 3:40 PM To: Derradji, Ahmed Cc: Hugh W. Coleman Subject: RE: 25th ITTC-Japan: Uncertainty Analysis Discussion

Ahmed,

I am responding to your phone call last week and the e-mail below. As I stated to you, Hugh Coleman and I agree that the ISO Guide is the international standard for uncertainty analysis. We state this in our book, Coleman and Steele (1999). We do not state that the guide is inappropriate for engineering experiments or tests, but instead point out the different definitions for uncertainty, Type A or B and systematic or random. Your statement below clearly summarizes my opinions expressed in our phone conservation - As far as I know, the ASME PTC 19.1 (2005) is in harmony with ISO GUM, and I think you and I agree that the ISO is the international organization, no questions. Uncertainty components types A and B of ISO-GUM look at the sources of uncertainty, while random and systematic uncertainty components of ASME PTC (2005) look at the effects of uncertainties on the test results. Ultimately, regardless what procedure one uses, the final standard uncertainty estimate should be the same.

If you have any other questions or need further clarification, please let me know.

Sincerely,

Glenn

39

Coleman & Steele (1999) on ISO (1995)

Coleman & Steele (1999) pp. 248 - 249

40

Coleman & Steele (1999) – cont.

41

ASME PTC 19.1-2005

Harmonization of this Supplement with the ISO GUM is achieved by encouraging subscripts with each uncertainty estimate to denote the ISO Type, i. e., using the subscripts of either “A” or “B.”

ASME (2005) p. 1

42

Other Adaptations of ISO (1995)

Taylor, B. N. and Kuyatt, C., 1994, “Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results”, NIST Technical Note 1297ASME PTC 19.1-2005, “Test Uncertainty”AIAA S-071A-1999, “Assessment of Experimental Uncertainty With Application to Wind Tunnel Testing

43

Recommendation INC-1 (1980)

Source: Working Group on the Statement of Uncertainties, Bureau International des Poids et Mesures (BIPM), http://www.bipm.org/Two categories of uncertainty– A. Those which are evaluated by statistical

methods for a series of observations– B. Those which are evaluated by other meansGiacomo (1981)

ISO (1995)

44

Recommendation INC-1 (1980) (cont.)

Category A characterization– Estimated variances– Number of degrees of freedom

Category B characterization– Approximation to corresponding variances

Combined uncertainty– Usual method for combination of variances– Uncertainty expressed as standard deviation

Overall uncertainty with stated factor

2is

iν

2iu

45

Expanded Uncertainty

Combined standard uncertainty, uc

(y): universal expression of measurement uncertaintyExpanded uncertainty, U: inclusion of large fraction of values– Coverage factor, k– Measurement result– Large interval

)(ykuU c=UyY ±=

UyYUy +≤≤−

46

Law of Propagation of Uncertainty

General law of propagation of uncertainty

General law for uncorrelated data ),()()(2

)()(

1

1 1

1

222

jijij

N

i

N

iji

N

iiic

xxrxuxucc

xucyu

∑ ∑

∑−

= +=

=

+=

0),( =ji xxr ∑=

=N

iiic xucyu

1

222 )()(

47

Correlated Input Quantities (cont.)

Special case for perfectly correlated data– Weight set for calibration of force

1),( +=ji xxr2

1

2 )()( ⎥⎦⎤

⎢⎣⎡= ∑

=

N

iiic xucyu

∑=

=N

iiic xucyu

1)()(

Flow Diagram for Jitter Program

Readxi , δ xi

Subroutinef = f(x1 ,…xi ,…, xN )

i = 1δ g = 0

Subroutineci = ¶ f/¶ xi

e = (δ xi ¶ f/¶ xi )2

δ g = δ g + e

i = i + 1

i < N

δ f = (δ g)1/2

Printf, δ f

Stop

Start Yes

No

Moffat (1982)

Flow Diagram for Subroutine ¶ f/¶ xi

Moffat (1982)

Return

Subroutineci = ¶ f/¶ xi

SubroutineF+ui = f(x1 ,...,xi +ui ,…, xN )F-ui = f(x1 ,...,xi -ui ,…, xN )

¶ f/¶ xi = (F+ui - F-ui )/(2ui )

50

Pre-Test Uncertainty Analysis

Data reduction program for processing data– Measurement equations– Uncertainty analysis

» Elemental uncertainty & relative importance» Combined & expanded uncertainty» Calibration factors for conversion to physical units» Type A & B estimates, for low noise instruments Type A

should be small relative to B

Planning and design of test– Selection of instrumentation for required uncertainty

results

51

Post-Test Uncertainty Analysis

Post-test data processing code same as pre-test, including uncertainty estimatesAll measurements NMI traceableUncertainty estimates from post-processing code suitable for inclusion in final reportComparison of pre-test and post-test uncertainty estimates– Post-test results consistent with pre-test estimates– Review for potential improvements and reduction of

uncertainty in future tests

52

Future of ISO (1995)

ISO (1995) to remain unchanged for near futureSupplements and other documents– Supplement 1: Propagation of distributions using a

Monte Carlo method (2008)– Supplement 2: Models with any number of output

quantities– Evaluation of measurement data –

An introduction to

the GUM– Evaluation of measurement data –

The role of

measurement uncertainty in conformity assessmentBIPM, Joint Committee for Guides in Metrology

http://www.bipm.org/en/committees/jc/jcgm/

53

Calibration Theory (cont.)

Uncertainty in calibration

Uncertainty in post-processed data

22221

2121

2 −− ==

++≤≤+−

N,N

xxxx

Fc,tcwhere)scc(See)x(fy)scc(See)x(f

Scheffe (1973)Carroll, Spiegelman, & Sacks (1988)

54

Columbia Transverse Acceleration Cal.

Reference Acceleration (g)-1.0 -0.5 0.0 0.5 1.0

Vol

tage

Out

put (

Vdc

)

-8

-6

-4

-2

0

2

4

6

8

Columbia SN 1649Intercept: -0.0847 VSlope: +7.9294 V/g4/27/05 H. W. Reynolds

Linear RegressionAccelerometer Data

Reference Acceleration (g)-1.0 -0.5 0.0 0.5 1.0

Acc

eler

atio

n R

esid

ual (

g)

-0.015

-0.010

-0.005

0.000

0.005

0.010

0.015

Columbia SN 1649Intercept: +0.0107 gSlope: +0.12611 g/V4/27/05 H. W. Reynolds

+/-95 % Confidence LimitAccelerometer Data

55

Tunnel Speed

Main Drive Motor Speed (rpm)0 10 20 30 40 50 60

Tunn

el V

eloc

ity (m

/s)

0

5

10

15

20

Linear FitLDA Data26 Oct 2000

y = a + bxa = -0.164 m/sb = 0.3199 m/s/rpmr = 0.999961

Main Drive Motor Speed (rpm)0 10 20 30 40 50 60

Vel

ocity

Res

idua

l (m

/s)

-0.10

-0.05

0.00

0.05

0.10

y = a + bxa = -0.164 m/sb = 0.3199 m/s/rpmr = 0.999961

LDA Data26 Oct 2000

56

Non-Linear Tunnel Speed

Main Drive Motor Speed (rpm)0 10 20 30 40 50 60

Vel

ocity

Res

idua

l (m

/s)

-0.10

-0.05

0.00

0.05

0.10

26 Oct 2000

Low Range, y = a + bxa = -0.1314b = 0.3231r = 0.999973

High Range, y = a + bxc

a = 0.0679b = 0.2749c = 1.0359r = 0.9999983

LDA Data, High RangeLDA Data, Low Range

+/-95 % Prediction Limit

57

LDV Calibration Data

Reference Velocity (m/s)

0 5 10 15 20

LDV

Vel

ocity

(m/s

)

0

5

10

15

20

y = a + bxa = 0.0007b = 0.98488r = 0.99999985SEE = 0.00286 m/s

Linear RegressionLDV Data 07 May 01

Reference Velocity (m/s)

0 5 10 15 20

Vel

ocity

Res

idua

l (m

/s)

-0.10

-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

Intercept: -0.0007Slope: 1.01535Focal L: 1600 mmBeam Space: 115 mmWavelength: 514.5 nm

+/-95 % Prediction LimitLDV Data 07 May 01Outlier Data

58

Parame-ter

Cate-gory Error sources u(xi

) (unit) ci(unit) ci

u(xi

) uc

α(mm/pix)

Calibra-tion

Reference image 0.70 (pix) 3.84E-04 (mm/pix2) 2.69E-04

Physical distance 0.02 (mm) 1.22E-03 (1/pix) 2.44E-05

Image distortion by lens 4.11 (pix) 3.84E-04 (mm/pix2) 1.57E-03

Image distortion by CCD 0.0056 (pix) 3.84E-04 (mm/pix2) 2.15E-06

Board position 0.5 (mm) 2.84E-04 (1/pix) 1.42E-04

Parallel board 0.035 (rad) 0.011 (mm/pix) 3.85E-04 0.00165

Uncertainty Sources & Propagation: α

59

Uncertainty Sources & Propagation: ΔX

Parame- ter Category Error sources u(xi

) (unit) ci(unit) ci

u(xi

) uc

ΔX(pix)

Acquisi-tion

Laser power fluctuation 0.0071 (mm) 3.16 (pix/mm) .0224

Image distortion by CCD 0.0056 (pix) 1.0 0.0056

Normal view angle 0.035 (rad) 0.011 (mm/pix) 3.85E-04

Reduc-tion

Mis-matching error 0.20 (pix) 1.0 0.20

Sub-pixel analysis 0.03 (pix) 1.0 0.03 0.2040.204

0.20

60

Measurement System

61

Captive vs Free Running Model Tests

Captive Model Tests vs. Free Running Model Tests (1)

In narrow sense, they usually refer to two types of manoeuvring model tests

In general sense, Captive Model Tests: resistance test, open water test, oblique towing test, rotating arm test, PMM test, ….Free Running Model Tests: seakeeping test, free model test for manoeuvring,

62

Captive vs Free Running Model Tests – cont.

From the viewpoint of measurand, hydrodynamic measurement in ITTC can be grouped primarily in three (3) types:

Hydrodynamic forces/moments measurement,

e.g., in captive model tests

Field measurement,

e.g., wake flow, pressure distribution, wave profile

Motion measurement,

e.g., in seakeeping, free model tests for manoeuvring

Captive Model Tests vs. Free Running Model Tests (2)

63

Captive vs Free Running Model Tests – cont.

The main objective of Captive Model tests is to measure the hydrodynamic forces/moments in steady motion of given condition.

Captive Model Tests vs. Free Running Model Tests (3)

Take the resistance measurement as an example to provide a general guideline for Uncertainty Analysis of captive model tests based on the ISO GUM (1995), because

1) there is only one component force (the longitudinal forces, i.e., resistance) to be measured in resistance test and,

2) it is a task for the 25th ITTC-UAC to revise the QM Procedure 7.5-02-01-02 (1999) Uncertainty Analysis in EFD, Guidelines for Resistance Towing Tank Tests

64

Captive Model Test ProceduresState of art, UA in resistance tests before 25th ITTC

Five (5) QM procedures

7.5 - 02 - 01 - 02 (1999) 5 pagesUncertainty Analysis in EFD, Guidelines for Resistance Towing Tank Tests

Concise and excellent, but as general as policy for UA in resistance tests

7.5 - 02 - 02 - 02 (2002) 18 pagesUncertainty Analysis, Example for Resistance Test

7.5 - 02 - 02 - 03 (2002) 5 pagesUncertainty Analysis Spreadsheet for Resistance Measurements

7.5 - 02 - 02 - 04 (2002) 4 pagesUncertainty Analysis Spreadsheet for Speed Measurements

7.5 - 02 - 02 - 05 (2002) 5 pagesUncertainty Analysis Spreadsheet for Sinkage and Trim Measurements

7.5 - 02 - 02 - 06 (2002) 4 pagesUncertainty Analysis Spreadsheet for Wave Profile Measurements

Step-by-step process

with high operability

To be revised as UAC task

65

Details not in Revised Procedure

Revise QM Procedure 7.5-02-01-02 (1999)

General Guidelines for Uncertainty Analysis in Resistance Towing Tank Tests (2008)

in which, 1) Uncertainties related to extrapolation and full-scale

predictions are not taken into consideration and,2) Specific details not included such as turbulence

stimulation, drag of appendages, blockage and wall effect of tank, scaling effect on form factor, and etc.

66

New Details in Revised Procedure

Revise QM Procedure 7.5-02-01-02 (1999)

General Guidelines for Uncertainty Analysis in Resistance Towing Tank Tests (2008)

in which, special attention is given to1) Uncertainties related to geometry of ship model and,2) Uncertainties in data reduction, taking the form factor ( k) by

the Prohaska’s method, as a example, where the Linear Least Square method is used as in calibration data analysis.

These can be referenced by other captive model tests.

67

Future Revisions to Related Procedurs

Revise QM Procedure 7.5-02-01-02 (1999)

General Guidelines for Uncertainty Analysis in Resistance Towing Tank Tests (2008)

Noted: 1) In the near future, the researchers and engineering in towing tank

will still follow the QM procedures (7.5-02-02-02~~06) practically, because these procedures are developed by resistance specialists and can be performed in high operability. UAC have no desire or attempt to revise these five (5) procedures by themselves.

2) Revision of these five (5) procedures will be done by the specialists in resistance or the Resistance Committee (RC), where all the valuable papers on UA in resistance tests since 2002 will be reviewed.

68

Review of Other Draft Procedures by UACReview Draft ITTC Procedure and Guidelines-Forces and Moment Uncertainty Analysis, Example for Planar Motion Mechanism Test by the Manoeuvring Committee (MC) (2008)

Noted:1) Suggestions for improvements in PMM procedure noted in UAC final

reporta) Traceability of measurements to NMI (NIST in USA)b) Mass uncertainty correlated not uncorrelatedc) Terminology on calibration and acquisition is confusing –

Recommend following new UA procedure on calibrationd) Uncertainty in water temperature appears to be lowe) Clarification needed on computation of uncertainty from repeat testsf) Alternate approach on carriage speed uncertainty suggested.

69

Repeatability

Sequence Number

0 2 4 6 8 10 12 14 16

Wav

e Am

plitu

de (m

m)

170

180

190

200

210

220Senix Gage #6201 +/-11 mm

Average+/-95 % Confidence LimitWave Amplitude DataOutlier Data

Test Sequence Number

0 5 10 15 20 25

(V -

<V>)

/<V>

(%)

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

Lab A: 2.0375 +/-0.0014 m/sLab B: 2.54903+/-0.00048 m/s

Lab A (2001)

Lab B (2006)+/-95% Confidence, A

+/-95 % Confidence, B

Carriage Speed Wave Amplitude

70

Open Water Dynamometer Results

J

0.0 0.5 1.0 1.5

K T, 1

0ΔK Q

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

KT 4th Order PolynomialKQ 4th Order PolynomialKQ Data, 1000 rpm KT Data, 1000 rpm

10 May 2002

J

0.0 0.5 1.0 1.5

ΔK T

-0.04

-0.02

0.00

0.02

0.04+/-95 % Prediction Limit

KT, 1000 rpm, 10 May 2002All Historical Data

Donnelly and Park (2002)

71

Youden Plot for Turbine Meters

Lab F

Dirritti, et al. (1993)

72

Carl Friedrich GaussBorn 30 April 1777 in Brunswick, GermanyDied 23 Feb 1855 in Gottingen, GermanyPredicted position of Ceres in 1801 by least squaresDirector of Gottingen Observatory in 1807Least squares method from normal pdf in 1809Pioneer in measurement errorRanked with Archimedes, Newton, and Euler

ASME 2009 Fluids Engineering Division Summer Meeting

http://www.asmeconferences.org/FEDSM09/Conference Chair: Joel Park, Ph. D.

August 2-5, 2009Vail Cascade Resort and Spa

1300 Westhaven DriveVail, Colorado 81657-3890 USA

Call for PapersSymposium Abstracts 12/12/08

Forum Abstracts 02/13/09