Sequential Laplacian regularized V-optimal design of experiments for response surface modeling of expensive tests: An application in wind tunnel testing

In an increasing number of cases involving estimation of a response surface, one is often confronted with situations where there are several factors to be evaluated, but experiments are prohibitively expensive. In such scenarios, learning algorithms can actively query the user or other resources to determine the most informative settings to be tested. In this article, we propose an active learning methodology based on the fundamental idea of adding a ridge and a Laplacian penalty to the V-optimal design to shrink the weight of less significant factors, while looking for the most informative settings to be tested. To leverage the intrinsic geometry of the factor settings in highly nonlinear spaces, we generalize the proposed methodology to local regression. We also propose a simple sequential design strategy for efficient determination of subsequent experiments based on the information from previous experiments. The proposed methodology is particularly suited for problems involving expensive experiments with a high standard deviation of the error. We apply the proposed methodology to a simulated wind tunnel testing and compare the result with an existing practice. We also evaluate the estimation accuracy of the proposed methodology using the paper helicopter case study. Finally, through extensive simulated experiments, we demonstrate the performance of the proposed methodology against classic response surface methods in the literature.