Several Nominal Distances for Rotorcraft Gaussian Process Metamodels in the Presence of Categorical Alternatives

Designers desire to enable in early design stages more sophisticated but also computationally burdensome simulation tools to obtain better performing initial designs that are more valuable in subsequent design stages. The Hamming nominal distance has been used to build efficient Gaussian process metamodels, called mixed-integer-categorical (MIC) surrogates, that leverage trends which are similar across categorical alternatives in typical engineering objectives. This paper proposes and studies other nominal distances for constructing these MIC surrogates. These meta-models based on the proposed nominal distances are built and their performance indicators are compared when modeling a noise-free canonical function and the computationally noisy UH60A hover power consumption with a choice of several airfoil sections which represents the categorical variable. This paper shows that the use of the Hamming distance and the intrinsic distance, based on an underlying parametrization in the categorical variable, are the most efficient nominal distance for implementing MIC metamodels when approximating the noise-free canonical function and the UH60A hover power consumption.