Managing Gradient Inaccuracies while Enhancing Optimal Shape Design Methods

A major focus of aircraft design is the enhancement of CFD-based optimal shape design methods with improved solution accuracies from mesh adaptation, or efficient gradient calculations from adjoint formulations. The key goal of these enhancements is to increase the accuracy of the solution while reducing the computational wall-time. This study is specifically interested in quantifying the impact of mesh adaptation and approximate gradients from continuous adjoint methodologies while performing Gradient Based Optimization (GBO) or Surrogate Based Optimization (SBO). In the course of this work we have discovered conditions in which these various gradient methods can actually degrade the performance of the optimizer. For example, we have observed that bias errors from continuous adjoint gradients, which are traditionally acceptable for GBO methods, are not acceptable for basic SBO methods, which make a stronger assumption of objective-gradient correlation. We have also observed that applying mesh adaptation to continuous adjoint solutions can exacerbate this error enough to effect GBO convergence rates. In attempting to improve the convergence of the optimizers, we have built several approaches to better condition gradient accuracies. In one approach we filter the surface sensitivities before projecting them into a parameterized design space. In another approach, we build surrogate models capable of learning the noise of the system. This paper will present the work completed towards developing these methods, and will provide examples in the form of analytical test cases and demonstrative aerodynamic problems.