Cokriging is a flexible tool for constructing surrogate models on the outputs of computer models. It can readily incorporate gradient information, in which form it is named gradient-enhanced Kriging (GEK), and promises accurate surrogate models in >10 dimensions with a moderate number of sample locations for sufficiently smooth responses. However, GEK suffers from several problems: poor robustness and ill-conditionedness of the surface. Furthermore it is unclear how to account for errors in gradients, which are typically larger than errors in values. In this work we derive GEK using Bayes' Theorem, which gives an useful interpretation of the method, allowing construction of a gradienterror contribution. The Bayesian interpretation suggests the "observation error" as a proxy for errors in the output of the computer model. From this point we derive analytic estimates of robustness of the method, which can easily be used to compute upper bounds on the correlation range and lower bounds on the observation error. We thus see that by including the observation error, treatment of errors and robustness go hand in hand. The resulting GEK method is applied to uncertainty quantification for two test problems.

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After a jet engine is shut down, hot air rising inside the compressor disc cavities, secondary air systems, and the gas path annulus will result in a vertical temperature gradient. As the compressor rotor cools and contracts in the presence of this thermal gradient, it will bend, in a phenomenon known as thermal rotor bow. Starting an engine under bowed conditions can result in rubbing of the rotor and stator seals, adding heat to the rotor, exacerbating the rotor bow. This causal sequence of rubbing and bending is called the Newkirk Effect. In this study, 30 simulations of simplified compressor geometries have been run in three-dimensional unsteady conjugate heat transfer computational fluid dynamics coupled with finite element modelling, using a Sobol’ quasi-random sequence coupled with kriging interpolation to study the effects of three important geometric parameters on the thermal bow response of an engine. The three parameters, rotor length, rotor diameter, and compressor case wall thickness, were selected based on a similar screening test analysis performed by authors in a previous study. The results include response maps of each parameter with respect to rotor bow and clearance reduction onset time, duration, and severity, and show that length and case wall thickness exhibit linear responses due to their effect on stiffness, whereas diameter exhibits a non-linear response, due to the conflicting and competing effects on stiffness and vertical temperature difference.