Method to Facilitate High-Dimensional Design Space Exploration Using Computationally Expensive Analyses

Abstract

The emergence of adjoint design methods has been a breakthrough in the field of aerodynamic shape optimization. The strength of such methods lies in the fact that the adjoint formulation effectively removes the curse of dimensionality by drastically reducing the cost of computing the gradient. However, the curse of dimensionality is still very much alive when it comes to design space exploration, where gradient-free methods cannot be avoided. In attempt to solve this problem, this work presents a method called latent space gradient transformation, which facilitates gradient-free exploration for cases where function evaluations are expensive and dimensionality is high. The method builds upon previous work by applying principal component analysis to gradient information, something that had not been done before. This yields a low-rank transformation that maps a high-dimensional design space onto an equivalent, low-dimensional space in which gradient-free methods become more affordable. Concepts and limitations are discussed through analytical examples, and the method is tested on an overwing nacelle integration problem. Results showed that the method is cost-effective, requiring only 150 gradient samples to successfully reduce the problem from 145 design variables to less than 20, with an error of 10 drag counts on average and 25 drag counts at worst with 95% confidence.