Nondeterministic Kriging for Engineering Design Exploration

In this paper, the nondeterministic kriging (NDK) method is proposed, aiming for the applications of engineering design exploration, especially when only a limited number of random samples is available from either nondeterministic simulations or physical experiments under uncertainty. To handle nondeterministic data, the proposed NDK method uses separate aleatory and epistemic uncertainty processes. In a general situation in which resources are limited in generating random samples, an aleatory variance is assessed via a local regression kernel process. It is often found that a prediction model built with a conventional kriging suffers from the overfitting issue, which becomes worse with noisy and random data. The proposed NDK method can provide physically meaningful insights into both the main trend and the prediction uncertainty of system behaviors by capturing uncertainty in the sample data and suppressing the numerical instability. The predicted uncertainty from the proposed approach can be represented in terms of distinguishable aleatory and epistemic uncertainties, which will be useful in a decision-making process for an adaptive model building and design exploration. The potential benefits of using the proposed NDK method are demonstrated with multiple numerical examples, including mathematical and aircraft concept design problems.