Verification, validation and uncertainty quantification are becoming increasingly important with the great attention to high-credibility modeling and simulation in industrial software. However, traditional validation frameworks are deficient under epistemic uncertainty, and multiple uncertainties are difficult to quantify, which desiderates to be resolved for measures of agreement between computation and experiment. In this study, a comprehensive validation framework with a unified area metric is proposed to validate numerical simulation under aleatory and epistemic uncertainties.
The mathematical formulation of validation framework, credibility index and its numerical solution is derived, including the effects of epistemic uncertainty, which can determine the agreement level of different simulations by providing the quantitative credible evidence. Regarding the issue of multidimensional uncertainties in credibility analysis, a dimension reduction strategy with active subspaces is integrated to conduct the uncertainty propagation and obtain the response distribution more efficiently.
The proposed approach is illustrated by a one-dimensional response function and a practical aerodynamic analysis case of 12 uncertainties. The comprehensive validation framework is reasonable by comparing the computation with wind tunnel experiments and proved to be quite effective for the agreement measures, thus providing a potential template for tackling the widely existing computation validation problems subject to different types of uncertainties.
Engineers and analysts traditionally rely on a large number of tests to validate the modeling results, which is a repetitive process of designing, testing, verifying, redesigning, retesting and revalidating that can extend the development process for years and increase costs significantly. With respect to validate high-credibility numerical simulation, this paper presents a comprehensive validation metric for the modeling and simulation under aleatory and epistemic uncertainties.
