Uncertainty quantification using nonparametric quantile estimation and metamodeling
In many applications, particularly in the engineering field, the need to consider uncertainties is recognized. To reduce the number of necessary simulations, metamodels can be used. We present a novel method on the basis of metamodels, that allows us to model not only the deterministic responses, but also the propagation of uncertainty in the entire design space. Our procedure makes it possible to determine the robust optimum quickly with common multi-criteria optimization algorithms. The novel approach offers the possibility to include the tolerance of the metamodel in the calculation. We introduce a new class of robustness measures that characterizes the propagation of uncertainty more accurately than usual: the median as measure of central tendency and the difference between median and a high quantile q as measure of dispersion. This allows the user to adjust the degree of robustness to his wishes via q. It can handle even extremely skewed distributions in an appropr iate way. For the determination of the quantiles we use a novel combination of sampling scheme and nonparametric quantile estimation. This enables a fast computation on a local level. The suitability of the proposed proceeding is proved on several examples. The applicability is demonstrated on a real life example from automotive industry.