Experimentation, Validation, and Uncertainty Analysis for Engineers

By H. Coleman, W. Steele, Mariana Buzhuga. 2009

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Estimation of Uncertainty for Contour Method Residual Stress Measurements (2015, background): “The model error is assumed to have a Gaussian distribution, which has been found to be appropriate for many experimental error sources [9], and implies that one standard deviation represents a confidence interval of 68%.”
PIV uncertainty quantification by image matching (2013, methodology): “…about the measurement result which contains the measurand at a given confidence level; this is done by multiplying δ̂ by a coverage factor k: U = k · δ. (5) Coleman and Steele (2009) report that the variable δ̂ as computed in (4) is not normally distributed, but rather follows the t distribution…”
Estimation of uncertainty bounds for individual particle image velocimetry measurements from cross-correlation peak ratio (2013, methodology): “The treatment of uncertainty in this work will follow the ISO Guide to the Expression of Uncertainty in Measurement [18] (GUM), as adapted by Coleman and Steele in Experimentation, Validation, and Uncertainty Analysis for Engineers [19].”
PIV uncertainty propagation (2016, background): “Secondly, σy provides a measure of the uncertainty Uy of y for a single measurement given the standard uncertainties Uxi of each input variable xi (Coleman and Steele 2009): ( ) ⎛ ⎝ ⎜ ⎞ ⎠ ⎟∑ ∑ ∑ ρ δ δ= ∂ ∂ + ∂ ∂ ∂ ∂= = − = + U F x U F x F x x x U U2 ,y i N i x i N j i N i j i j x x 2 1 2 2 1 1 1 i…”