A Surrogate-based Adjustment Factor Approach to Multi-Fidelity Design Optimization

Abstract

The conceptual and preliminary design stages of aircraft design have traditionally been two separate, time intensive design phases. However, the concept of dialable/multi-fidelity design is one in which the gap between these two phases, conceptual and preliminary design, is bridged by introducing physics into the design process at an earlier stage than traditionally possible. This introduction of physics at an earlier stage eliminates the need for separate conceptual and preliminary design phases and consequently reduces total design time. The concept of multi-fidelity design does however pose certain obstacles such as determining how and when to “dial” or switch between different fidelity models. This paper explores the ability to apply an adjustment factor to the response of the low-fidelity model so as to “correct” the low-fidelity model. In doing so, the “corrected low-fidelity” model becomes more representative of the high-fidelity model. This process is employed within a Trust Region Model Management optimization routine. A surrogate model is constructed on the calculated adjustment factors available at high-fidelity simulation points with corresponding low-fidelity simulations. This surrogate serves the purpose of determining an adjustment factor given any design point (thus a function of design variables) that is then utilized in correcting the low-fidelity simulation at a corresponding design point. It is shown that optimization on the high-fidelity as well as corrected low-fidelity models converge to the same local optimum. Employing the proposed multi-fidelity methodology results in converging to the high-fidelity optimum in an order of magnitude fewer highfidelity function evaluations. This paper outlines the Trust Region Model Management optimization,surrogate modeling, and adjustment factor procedures. These procedures are then demonstrated on two different demonstration optimization problems. The first of these demonstration problems is a purely academic test case while the second consists of optimizing a geometrically nonlinear, tapered, cantilever beam.