Publications
Propagating and combining aleatory uncertainties characterized by continuous random variables and sparse discrete realizations from random functions
This paper presents a practical methodology for propagating and combining the effects of random variations of several continuous scalar quantities and several random-function quantities affecting the failure pressure of a heated pressurized vessel. The random functions are associated with stress-strain curve test-to-test variability in replicate material strength tests (uniaxial tension tests) on nominally identical material specimens. It is demonstrated how to effectively propagate the curve-to-curve discrete variations and appropriately account for the small sample size of functional data realizations. This is coordinated with the propagation of aleatory variability described by uncertainty distributions for continuous scalar quantities of pressure-vessel wall thickness, weld depth, and thermal-contact factor. Motivated by the high expense of the pressure vessel simulations of heating, pressurization, and failure, a simple dimension-and order-adaptive polynomial response surface approach is used to propagate effects of the random variables and enable uncertainty estimates on the error contributed by using the surrogate model. Linear convolution is used to aggregate the resultant aleatory uncertainty from the parametrically propagated random variables with an appropriately conservative probability distribution of aleatory effects from propagating the multiple stress-strain curves for each material. The response surface constructions, Monte Carlo sampling of them for uncertainty propagation, and linear sensitivity analysis and convolution procedures, are demonstrated with standard EXCEL spreadsheet functions (no special software needed).