Approximated models for aerodynamic coefficients estimation in a multidisciplinary design environment

In this paper variable fidelity analyses are investigated. Moreover different kind of approximations to be used in a wide multidisciplinary design environment for aircraft design are built. In order to obtain the surrogate models used in the main design process, a proper framework is built by different design of experiments techniques for process and variables management. Approximated models for the estimation of aerodynamic coefficients are evaluated on design spaces of different dimensions and considering different set of variables (i.e. geometric parameters and flight conditions). They are mainly based on the hybrid combination of Vortex Lattice Method (VLM) models representing the basic low fidelity analysis) and 3D finite volume Computational Fluid Dynamics models (representing the basic high fidelity analysis). Different strategies for the evaluation of the surrogate model are considered and an original methodology for the model construction is here presented

The ROMES method for statistical modeling of reduced-order-model error

This work presents a technique for statistically modeling errors introduced by reduced-order models. The method employs Gaussian-process regression to construct a mapping from a small number of computationally inexpensive `error indicators' to a distribution over the true error. The variance of this distribution can be interpreted as the (epistemic) uncertainty introduced by the reduced-order model. To model normed errors, the method employs existing rigorous error bounds and residual norms as indicators; numerical experiments show that the method leads to a near-optimal expected effectivity in contrast to typical error bounds. To model errors in general outputs, the method uses dual-weighted residuals---which are amenable to uncertainty control---as indicators. Experiments illustrate that correcting the reduced-order-model output with this surrogate can improve prediction accuracy by an order of magnitude; this contrasts with existing `multifidelity correction' approaches, which often fail for reduced-order models and suffer from the curse of dimensionality. The proposed error surrogates also lead to a notion of `probabilistic rigor', i.e., the surrogate bounds the error with specified probability