Specialist Committee on Uncertainty Analysis Joel T. Park, Ph. D., - - PowerPoint PPT Presentation

Specialist Committee on Uncertainty Analysis

Joel T. Park, Ph. D., Chairman, USA Ahmed Derradji Aouat, Ph. D., Secretary, Canada Baoshan Wu, China Shigeru Nishio, Ph. D., Japan

25th ITTC, Fukuoka, Japan 15 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)

Summary Recommendations

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, USA Ahmed Derradji Aouat, Ph. D. Sec., IOT, Canada Erwan Jacquin, BEC, France Baoshan Wu, CSSRC, China Shigeru 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, 2008 Kobe University, Kobe, Japan, September 12, 2008

6

Objectives of General Procedure

Simple and useable procedure tailored to ITTC hydrodynamics testing Specific guidance on application of uncertainty to experimental naval hydrodynamics Self-contained without need for consultation with reference documents ITTC 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 mean

Conventional statistical definitions: Ross (2004)

• p. 203, AIAA (1999) p. 7, ASME (2005) p. 6

∑

=

>= <

n k k

x n x

1

) / 1 (

∑

=

> < − − =

n k k x

x x n s

1 2 2

) ( )] 1 /( 1 [ n s s u

x x A

/ = =

> <

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 relationship Combined uncertainty

– Law of propagation of uncertainty – Sensitivity coefficient – Independent – Correlated (weight set)

Expanded uncertainty

– Coverage factor, k – Student t

∑

=

∂ ∂ =

n i i i c

x u x f y u

1 2 2 2

) ( ) / ( ) ( 95 % , 2 ), (

%

= = = k y ku U

c %

t k = ) , , , (

2 1 N

x x x f y K =

i i

x f c ∂ ∂ ≡ /

∑ ∑

= =

≡ =

N i i N i i i c

y u x u c y u

1 2 1 2 2

) ( )] ( [ ) (

∑

=

=

N i i i c

x u c y u

1

) ( ) (

10

Relative Uncertainty Propeller

Reynolds number Advance ratio Thrust coefficient

) /(ND V J =

2 2 2 2

) / ( ) / ( ) / ( ] / [ D u N u V u J u

D N V J

− + − + = ) /(

4 2D

N T KT ρ =

2 2 2 2 2 2

) / ( 16 ) / ( 4 ) / ( ) / ( ) / ( ] / [ D u N u u t T u K u

D N t T T KT

− + − + − ∂ ∂ + = ρ ρ μ ρ / VD ReD =

2 2 2 2 2

) / ( ) / ( ) / ( ) / ( ] / ) ( [ μ ρ

μ ρ

u D u V u u Re Re u

D V D D c

− + + + =

11

Numerical Evaluation of Sensitivity Coeff.

Central difference for uncertainty Numerical sensitivity coefficient Jitter program, Moffat (1982)

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

1 1 N i i N i i i i

x x u x x f x x u x x f Z y u K K K K − − + = = ) ( /

i i i

x u Z c =

12

Reporting Uncertainty Specific for U

Give full description of how measurand Y was defined State 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

Outliers Inter-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)

x x f y β α + = = ) ( β β α β α / B , / A where By A / ) y ( ) y ( f x 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

• n 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

• f estimate, & outliers

– Identify cause of outliers – Compute calibration uncertainty

Compare results to previous calibration

– Hypothesis test of slope & intercept

Update computer slope & intercept 3-point calibration check @ computer with test software

18

Uncertainty Elements for Instrument Cal.

Uncertainty in reference standard: NMI traceable Uncertainty in curve fit Type 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 Output (V)

• 10
• 8
• 6
• 4
• 2

2 4 6 8 10

Intercept: +0.0052 V Slope: -0.09143 V/deg SEE: 0.0362 V r: 0.999968 Linear Regression Increasing Roll Angle Decreasing Roll Angle

Reference Angle (deg)

• 100-80 -60 -40 -20 0

20 40 60 80 100

Standardized Residuals

• 6
• 4
• 2

2 4 6

Intercept: -0.056 deg Slope: -10.9370 deg/V SEE: 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 (

w a

ρ ρ / mg F − =

∑

=

=

n i i m

u u

1

21

Equations for LDA Calibration

LDA optical calibration Rotating disk calibration Uncertainty equations

ω π r V 2 =

2 2 2 2 2

) 2 ( ) 2 (

ω

π πω u r u u

r V

+ =

2 2 2

) / ( ) / ( ) / ( ω

ω

u r u V u

r V

+ =

f D D

f f V δ λ θ = = ] / ) 2 / (sin 2 [ r V c r V c π ω πω 2 / , 2 /

2 1

= ∂ ∂ = = ∂ ∂ =

ITTC 7.5-01-03-02 (2008)

22

LDV Velocity Uncertainty

Axial LDA Velocity (m/s)

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 mm Rotational Velocity Uncertainty Radial Uncertainty LDA 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 0.041 fr 0.062 0.26 0.0018 0.035 δf

• 0.16
• Angle
• 0.011 0.017 0.0022

fD 0.026 0.36 0.20 0.010 Curve 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) procedure Present procedure developed from the guideline

• f Visualization Society of Japan recommendation

(PIV-STD project, Nishio, et al., 1999)

u ΔX/Δt u δ α + = ) (

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

2 2 2 c

) / ( ) / ( t u u x u u u u

t x u

∂ ∂ + ∂ ∂ + =

26

PIV Calibration Uncertainty

27

Summary of Uncertainty for Velocity u

Parame- ter Cate- 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)

26.8 0.204 (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 description Calibration – See procedure for details

– Force and mass – Resistance – Towing speed

30

Revised Procedure

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

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

General Guidelines for Uncertainty Analysis in 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 GUM ISO GUM AIAA AIAA 5 pp 16 pp

31

UA in Resistance in Tow Tank Tests

Total resistance coefficient

– Data reduction equation – Uncertainty equation

) /( 2

2

SV R C

T T

ρ =

2 2 2 2 2

) / ( ) / ( ) / 2 ( )] / )( / [( ) / ( S u R u V u u t C u

S T RT V t T CT

+ + + ∂ ∂ = ρ ρ

ITTC 7.5-02-01-02 (2008)

32

Prohaska method Intercept & its standard deviation from linear regression theory Example from CSSRC

– 0.1574±0.0097 (±6.2 %)

Additional terms from CF & CT at x = 0

Form Factor

6 4 1 1 < < ≤ + = − n . Fr k C / bFr C / C

F n F T

Fr4/CF

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

CT/CF - 1

0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32

Slope: 0.1924 k: 0.1574 SEE: 0.0105 r: 0.977 Linear Fit +/-95% Prediction Limit +/-95% Confidence Limit Model Data

1

F T

− = C / C k

33

Other Elements of Final Report

Terms of reference Uncertainty analysis symbols Other activities History of uncertainty analysis Recommendation INC-1 (1980) Importance of uncertainty analysis Repeatability 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 properties Uncertainty in PMM procedure

35

Recommendations

Adopt 2 revised and 3 new procedures from UAC Adopt 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 slides Uncertainty analysis - 11 slides Calibration data - 4 slides LDV data - 1 slide PIV details on displacement & magnification uncertainties - 2 slides Resistance testing - 8 slides Repeatability - 2 slides Youden 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 1297 ASME 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

• f 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 means

Giacomo (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

2 i

s

i

ν

2 i

u

45

Expanded Uncertainty

Combined standard uncertainty, uc (y): universal expression of measurement uncertainty Expanded uncertainty, U: inclusion of large fraction of values

– Coverage factor, k – Measurement result – Large interval

) (y ku U

c

= U y Y ± = U y Y U y + ≤ ≤ −

46

Law of Propagation of Uncertainty

General law of propagation of uncertainty General law for uncorrelated data

) , ( ) ( ) ( 2 ) ( ) (

1 1 1 1 2 2 2 j i j i j N i N i j i N i i i c

x x r x u x u c c x u c y u

∑ ∑ ∑

− = + = =

+ = ) , ( =

j i x

x r

∑

=

=

N i i i c

x u c y u

1 2 2 2

) ( ) (

47

Correlated Input Quantities (cont.)

Special case for perfectly correlated data

– Weight set for calibration of force

1 ) , ( + =

j i x

x r

2 1 2

) ( ) ( ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = ∑

= N i i i c

x u c y u

∑

=

=

N i i i c

x u c y u

1

) ( ) (

Flow Diagram for Jitter Program

Read xi , δ xi Subroutine f = f(x1 ,…xi ,…, xN ) i = 1 δ g = 0 Subroutine ci = ¶ f/¶ xi e = (δ xi ¶ f/¶ xi )2 δ g = δ g + e i = i + 1 i < N δ f = (δ g)1/2 Print f, δ f Stop Start Yes No Moffat (1982)

Flow Diagram for Subroutine ¶ f/¶ xi

Moffat (1982) Return Subroutine ci = ¶ f/¶ xi Subroutine F+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 estimates All measurements NMI traceable Uncertainty estimates from post-processing code suitable for inclusion in final report Comparison 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 future Supplements 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 assessment

BIPM, 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

2 2 2 2 1 2 1 2 1

2

− −

= = + + ≤ ≤ + −

N , N xx xx

F c , t c where ) s c c ( See ) x ( f y ) s c c ( 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

Voltage Output (Vdc)

• 8
• 6
• 4
• 2

2 4 6 8

Columbia SN 1649 Intercept: -0.0847 V Slope: +7.9294 V/g 4/27/05 H. W. Reynolds Linear Regression Accelerometer Data

Reference Acceleration (g)

• 1.0
• 0.5

0.0 0.5 1.0

Acceleration Residual (g)

• 0.015
• 0.010
• 0.005

0.000 0.005 0.010 0.015

Columbia SN 1649 Intercept: +0.0107 g Slope: +0.12611 g/V 4/27/05 H. W. Reynolds +/-95 % Confidence Limit Accelerometer Data

55

Tunnel Speed

Main Drive Motor Speed (rpm)

10 20 30 40 50 60

Tunnel Velocity (m/s)

5 10 15 20

Linear Fit LDA Data 26 Oct 2000 y = a + bx a = -0.164 m/s b = 0.3199 m/s/rpm r = 0.999961

Main Drive Motor Speed (rpm)

10 20 30 40 50 60

Velocity Residual (m/s)

• 0.10
• 0.05

0.00 0.05 0.10

y = a + bx a = -0.164 m/s b = 0.3199 m/s/rpm r = 0.999961 LDA Data 26 Oct 2000

56

Non-Linear Tunnel Speed

Main Drive Motor Speed (rpm)

10 20 30 40 50 60

Velocity Residual (m/s)

• 0.10
• 0.05

0.00 0.05 0.10

26 Oct 2000 Low Range, y = a + bx a = -0.1314 b = 0.3231 r = 0.999973 High Range, y = a + bxc a = 0.0679 b = 0.2749 c = 1.0359 r = 0.9999983 LDA Data, High Range LDA Data, Low Range +/-95 % Prediction Limit

57

LDV Calibration Data

Reference Velocity (m/s)

5 10 15 20

LDV Velocity (m/s)

5 10 15 20

y = a + bx a = 0.0007 b = 0.98488 r = 0.99999985 SEE = 0.00286 m/s Linear Regression LDV Data 07 May 01

Reference Velocity (m/s)

5 10 15 20

Velocity Residual (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: -0.0007 Slope: 1.01535 Focal L: 1600 mm Beam Space: 115 mm Wavelength: 514.5 nm +/-95 % Prediction Limit LDV Data 07 May 01 Outlier 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 0.204 0.204 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 Procedures

State of art, UA in resistance tests before 25th ITTC

Five (5) QM procedures

7.5 - 02 - 01 - 02 (1999) 5 pages Uncertainty 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 pages Uncertainty Analysis, Example for Resistance Test 7.5 - 02 - 02 - 03 (2002) 5 pages Uncertainty Analysis Spreadsheet for Resistance Measurements 7.5 - 02 - 02 - 04 (2002) 4 pages Uncertainty Analysis Spreadsheet for Speed Measurements 7.5 - 02 - 02 - 05 (2002) 5 pages Uncertainty Analysis Spreadsheet for Sinkage and Trim Measurements 7.5 - 02 - 02 - 06 (2002) 4 pages Uncertainty Analysis Spreadsheet for Wave Profile Measurements

Step-by-step process with high

• perability

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 to 1) 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 UAC

Review 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 report a) Traceability of measurements to NMI (NIST in USA) b) Mass uncertainty correlated not uncorrelated c) Terminology on calibration and acquisition is confusing – Recommend following new UA procedure on calibration d) Uncertainty in water temperature appears to be low e) Clarification needed on computation of uncertainty from repeat tests f) Alternate approach on carriage speed uncertainty suggested.

69

Repeatability

Sequence Number

2 4 6 8 10 12 14 16

Wave Amplitude (mm)

170 180 190 200 210 220

Senix Gage #6 201 +/-11 mm Average +/-95 % Confidence Limit Wave Amplitude Data Outlier Data

Test Sequence Number

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/s Lab 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

KT, 10ΔKQ

• 0.2

0.0 0.2 0.4 0.6 0.8 1.0

KT 4th Order Polynomial KQ 4th Order Polynomial KQ Data, 1000 rpm KT Data, 1000 rpm 10 May 2002

J

0.0 0.5 1.0 1.5

ΔKT

• 0.04
• 0.02

0.00 0.02 0.04

+/-95 % Prediction Limit KT, 1000 rpm, 10 May 2002 All Historical Data

Donnelly and Park (2002)

71

Youden Plot for Turbine Meters

Lab F

Dirritti, et al. (1993)

72

Carl Friedrich Gauss

Born 30 April 1777 in Brunswick, Germany Died 23 Feb 1855 in Gottingen, Germany Predicted position of Ceres in 1801 by least squares Director of Gottingen Observatory in 1807 Least squares method from normal pdf in 1809 Pioneer in measurement error Ranked 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, 2009 Vail Cascade Resort and Spa

1300 Westhaven Drive Vail, Colorado 81657-3890 USA

Call for Papers

Symposium Abstracts 12/12/08 Forum Abstracts 02/13/09