Assessing Engineering Uncertainties

1. Assessing Engineering Uncertainties G. E. Mattingly NIST Fluid Flow Group Leader (20+yrs), Retired and, currently, Adjunct Professor of Mechanical Engineering The Catholic University of America (CUA) Washington, D. C. and Flow Measurement and Uncertainty Instructor and Consultant and NIST/NVLAP Assessor for “Flow” E-mail: gemattingly@verizon.net Phone (301) 461-3637 Keynote Address - Mech-Aero 2014 Philadelphia, PA Sept 8, 2014

2. Assessing Engineering Uncertainties Keynote Outline: Importance of engineering uncertainties Definition of Uncertainty…according to VIM 1 & GUM 2 Nature of measurements (“scatter”, random, systematic, etc.) Uncertainty assessment strategies: replicating measurements to obtain “satisfactory” average, assessing “scatter” (and “stability” of result), understanding contributions of component measurements, categorizing and combining the different types of uncertainties, specifying uncertainty result (confidence levels, degrees of freedom.. for national & international acceptance), displaying the whole uncertainty assessment process & the result. Example 1 “VIM” = International Vocabulary for Metrology; see: www.bipm.org 2 “GUM” = Guide for Uncertainty in Measurement; see: www.bipm.org

3. Nature of measurements – “Scatter” Characteristics: ….”imprecise” ….”precise, but not accurate!” … that its’ “tight” doesn’t mean its right! …. “precise and accurate!” Accuracy implies precision, but not “vice versa”!

4. Expanded Uncertainty, …..U(q) is the total or overall uncertainty…. …where k is the coverage factor, selected to produce specific levels of confidence for the Expanded Uncertainty; k=1 (68% confidence), k = 2 (95% confidence), k=3 (99% confidence), etc. Uncertainty assessment strategies: VIM & GUM Categorization and Combination of Uncertainties: “Type A and Type B Uncertainties”: Type A uncertainties are determined using “statistics”; Type B uncertainties are determined using “techniques other than statistics”, i.e., “estimates”, guesses, guru-ship, etc. Combined Uncertainty….. uc(q) produced by RSS of all Type A and B uncertainties for “q”, i.e. ] [ where k=2 (95% C.L.) (Msm’t Avg)

5. Uncertainty assessment strategies…..for “q(x,y)” where x, y are component measurements: 1 1 or: Note: a.) partial derivatives are “Sensitivity Coefficients”, and b.) since intervals can be positive or negative, we square to get:

6. where When take sums over all replicated data and divide by n-1: a) terms become “sample” variances and b) term becomes the “sample” covariance, i.e., When there is no correlation between x and y: …for both Type A and Type B uncertainties for x and y.

7. Since many engineering measurements are products or quotients, the uncertainty assessment is simplified using “relative” uncertainties: …ratios are dimensionless fractions or “percentages of readings” …i.e., the “relative sensitivity coefficients are the exponents” and squaring produces relative variances and covariances:

8. Therefore, we can write the relative uncertainty as: where: If define the correlation coefficients, via: then: When there are no correlation effects …for both Type A and Type B relative uncertainties for x, y and z.

9. How can measurements be “assured”?…by ”Traceability” to accepted standards….i.e., NIST in the US or NMIs elsewhere. Traceability: (VIM) … property of the result of a measurement or the value of a standard whereby it can be related to stated references, usually national or international standards through an unbroken chain of comparisons (calibrations) all having stated uncertainties. … i.e., traceability is a “chain” of measurements that connect practical measurements to acceptable references, where the “links” are tests that compare lab measurement capabilities.

10. Standards for SI Units Maintained by NMIs (NIST) Standards for Derived Units Maintained by NMIs (NIST) • SRMs • SRD, etc. The U.S.National Metrological Pyramid • Mass • Length • Time • Temperature • Electric Current • Am’t of Substance (mole) • Candela www.nist.gov • Volume • Pressure • Flow • Force • Air Speed • Humidity • Density www.nist.gov • Acceleration • Voltage, etc. • Transfer Standards Calibration Services • Global Time Service and Special Tests www.nist.gov • (Accredited?) Sensor Mfgrs1 Applications • (Accredited?) Testing Labs1 • US Industries • Gov’t Agencies • Academia etc. 1 For “ lab accreditation” details, see: “NVLAP” via: www.nist.gov

11. Example:Liquid Flow Measurement Using a “bucket & stopwatch” method: Liquid Flow Liquid Flow If 10 liters in 10 secs  1 l/sec Since “weighing” is more accurate than “volume-ing”, can use a scale to weigh: If 10 kg in 10 secs  1 kg/sec If density is 1 gm/cc  1 l/sec Scale SS In general:

12. Squaring…to create positive quantities and noting that these “independent” measurements are not correlated, gives: Interpret…for improving measurement uncertainty…. • Measurement strategy: • Replicate V-dot measurements • Quantify Type A uncertainty for V-dot • Determine Type B uncertainties for component measurements • Combine uncertainties according to VIM/GUM • Select Coverage Factor for “confidence” and “DoF” • Present results for all to understand, believe, and accept.

13. Presenting the uncertainty assessment…for easy understanding

16. Conclusions • Engineering uncertainties are critical in today’s world to quantify the quality of our engineering measurements, • Quantifying uncertainties according to the VIM & GUM assures the acceptability of the process nationally and internationally, • The VIM & Gum method is simple to understand and to apply, and • Tabulating the whole process makes the uncertainty assessment clear, understandable, and acceptable to all.

17. The End Old metrological saying: In God we trust…. all others need to bring good data!....with an uncertainty statement in accord with the VIM & GUM