Polynomial-Chaos–Kriging with Gradient Information for Surrogate Modeling in Aerodynamic Design

Abstract

This paper proposes a variant of gradient-enhanced surrogate model based on polynomial-chaos–kriging (PCK) to assist aerodynamic design exploration. The main aim is to improve the accuracy of kriging when gradient information is available via the adjoint method. In contrast to the standard gradient-enhanced kriging (GEK), the gradient information is used to enrich both the trend function and the stochastic part, using the polynomial-chaos expansion (PCE) as the trend function. The optimal polynomial terms are selected by scanning through various polynomial orders in which the coefficients are calculated by means of the generalized least squares or the least angle regression algorithm. The performance of the gradient-enhanced PCK (GEPCK) was compared with GEK, gradient-enhanced PCE (GEPCE), and their nongradient counterparts on a set of analytical and a suite of aerodynamic problems consisting of aerodynamic design exploration of a blended-wing–body configuration, an inviscid transonic flow over an airfoil, and a low-fidelity aerostructural wing design. The results show notable improvements obtained by GEPCK in terms of performance and robustness compared with other gradient-enhanced surrogate models. Based on these results, it can be concluded that enhancing the trend part with gradient is highly beneficial in improving the accuracy of the kriging surrogate model.