Useful Tips for Presenting Data and Measurement Un……

E2,95% 9.01 0.12GPa
University of Florida Mechanical and Aerospace Engineering 8
Level 2: Uncertainty Propagation
• Law of Propagation of Uncertainties (LPU):
• Explain important terminology and definitions
– NIST vs. ISO vs. ASME/ASTM – Oberkampf definitions of model uncertainty (not included)
• Experimental scenarios and corresponding methods
2 2 2
2
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Level 3: NIST Component Measurement Uncertainty Table
University of Florida Mechanical and Aerospace Engineering
n n q 2 q 2 u (q) u ( pi ) i 1 pi i 1 j 1 pi n 2
q p j
u ( pi , p j )
– where, p are the inputs (components) and q is the output
• Conclusion: The interpretation of ± u is not consistent within a field, let alone between fields
– It is very important to explain the statistical relevance of the uncertainty bounds!!!
• Avoid use of ambiguous ± notation without explanation • Pet peeve: CV coefficient of variation s x x – COV = covariance
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• Use terms carefully!
– Error vs. Uncertainty: Error is the deviation from the true value and measured value (never known), which is estimated as uncertainty – Bias vs. variability (will explain later)
NIST Classification of Measurement Uncertainties
• Uncertainty classification:
– Random uncertainty / variability – scatter in the measurements (v) – Systematic uncertainty / bias – systematic departure from the true value (b)
University of Florida Mechanical and Aerospace Engineering
6
Uncertainty Analysis Example
• Consider our transverse modulus work (E2)
• Hooke’s Law:
P E2 Ae 2
• Thickness and width are correlated
E E E E v ( E2 ) 2 vT 2 ( P) 2 vT 2 (e 2 ) 2 vT 2 (t ) 2 vT 2 ( w) P t w e 2
2 2 2 2 2
E E E E E E b2 ( E2 ) 2 bT 2 ( P) 2 bT 2 (e 2 ) 2 bT 2 (t ) 2 bT 2 ( w) 2 2 2 bT (t )bT ( w) P t w t w e 2
University of Florida Mechanical and Aerospace Engineering
7
Level 1: Total Uncertainty
• In general,
U X 95 t95 (v X ) 2 (bX ) 2
– where, vX and bX were propagated from component uncertainties t95 = Student’s t distribution at 95% confidence level (depends on # of DOF)
– Type A – calculated by statistical methods (it is useful to explain the design of experiments and the number of samples involved) – Type B – determined by other means, such as estimate from experience or manufacturers specifications
• E2 Example:
– Uncertainty contributors were analyzed for each of the components of E2 – Random and systematic effects propagated separately – Only systematic uncertainties can have correlated effects
2
m = 75 ± 5 g What is the meaning of ± 5 ?
• • • • • Best guess by experimenter Half the smallest division of measurement Standard deviation: Standard error: m = /n Expanded uncertainty of ± 2 or ± 3 (95% or 99% confidence interval) • Standard uncertainty: u • Combined standard uncertainty: uc
University of Florida Mechanical and Aerospace Engineertainty Precisely
• Choose a standard for presenting uncertainty (I prefer NIST), and reference the standard • Explain the source of the uncertainty
b B 2
Range is at 95% (2) level of a normal distribution
xt = true value of specimen m = experimental population average x = experimental sample average vx = random error of sample bx = systematic error of sample
• Type of evaluation:
– Type A – calculated by s v x sx x statistical methods N – Type B – determined by other means, such as estimate from experience
P = Load A = Area A w t
2
1
e2 = transverse strain
• We will work through this problem backwards
Total Uncertainty Bias & Variability Components Contributors
– – – – Uncertainty propagation Crossed vs. nested factors (ANOVA vs. VCA) p-values Interlaboratory Studies (not included)
University of Florida Mechanical and Aerospace Engineering
– Either design the experiments properly or match the corresponding method to the data you already have
Useful Tips for Presenting Data and Measurement Uncertainty Analysis
Ben Smarslok
University of Florida Mechanical and Aerospace Engineering
1
Outline
• Why is presenting data properly important?