Adaptive Polynomial Response Surfaces and Level-1 Probability Boxes for Propagating and Representing Aleatory and Epistemic Components of Uncertainty

摘要

When analyzing and predicting stochastic variability in a population of devices or systems, it is important to segregate epistemic lack-of-knowledge uncertainties and aleatory uncertainties due to stochastic variation in the population. This traditionally requires dual-loop Monte Carlo (MC) uncertainty propagation where the outer loop samples the epistemic uncertainties and for each realization, an inner loop samples and propagates the aleatory uncertainties. This results in various realizations of what the aleatory distribution of population response variability might be. Under certain conditions, the various possible realizations can be represented in a concise manner by approximate upper and lower bounding distributions of the same shape, composing a "Level 1" approximate probability box (L1 APbox). These are usually sufficient for model validation purposes, for example, and can be formed with substantially reduced computational cost and complication in propagating the aleatory and epistemic uncertainties (compared to dual-loop MC). Propagation cost can be further reduced by constructing and sampling response surface models that approximate the variation of physics-model output responses over the uncertainty parameter space. A simple dimension- and order- adaptive polynomial response surface approach is demonstrated for propagating the aleatory and epistemic uncertainties in a L1 APbox and for estimating the error contributed by using the surrogate model. Sensitivity analysis is also performed to quantify which uncertainty sources contribute most to the total aleatory-epistemic uncertainty in predicted response. The methodology is demonstrated as part of a model validation assessment involving thermal-chemical-mechanical response and weld breach failure of sealed canisters weakened by high temperatures and pressurized by heat-induced pyrolysis of foam.