不确定度量化
外推法
敏感性分析
离散化
不确定度分析
不确定性传播
测量不确定度
计算机科学
数学
数学优化
算法
机器学习
统计
模拟
数学分析
作者
Christopher J. Roy,William L. Oberkampf
标识
DOI:10.1016/j.cma.2011.03.016
摘要
An overview of a comprehensive framework is given for estimating the predictive uncertainty of scientific computing applications. The framework is comprehensive in the sense that it treats both types of uncertainty (aleatory and epistemic), incorporates uncertainty due to the mathematical form of the model, and it provides a procedure for including estimates of numerical error in the predictive uncertainty. Aleatory (random) uncertainties in model inputs are treated as random variables, while epistemic (lack of knowledge) uncertainties are treated as intervals with no assumed probability distributions. Approaches for propagating both types of uncertainties through the model to the system response quantities of interest are briefly discussed. Numerical approximation errors (due to discretization, iteration, and computer round off) are estimated using verification techniques, and the conversion of these errors into epistemic uncertainties is discussed. Model form uncertainty is quantified using (a) model validation procedures, i.e., statistical comparisons of model predictions to available experimental data, and (b) extrapolation of this uncertainty structure to points in the application domain where experimental data do not exist. Finally, methods for conveying the total predictive uncertainty to decision makers are presented. The different steps in the predictive uncertainty framework are illustrated using a simple example in computational fluid dynamics applied to a hypersonic wind tunnel.
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