Practical Appropriate Fidelity Optimization for Large-scale Multidisciplinary Aircraft Design

Abstract

Numerical optimization has been successfully applied to multidisciplinary design optimizations such as aerostructural wing design. These optimizations consist of over a thousand design variables constraints, and include expensive simulations such as computational fluid dynamics within the optimization loop. Nevertheless, by using gradient-based optimizers together with efficient gradient computation techniques, researchers have been able to tackle these challenging large-scale problems.

However, longstanding challenges remain. These optimizations tend to require direct user input, manually tuning various optimization parameters to obtain convergence. The optimizations are slow and computationally expensive, often using thousands of processors for several days at a time. As aircraft designers move toward using more expensive, higher-fidelity tools in design, the computational cost will only increase in the future.

To address these challenges, this dissertation contains three main contributions. First, a novel geometric parameterization is presented. Based on sensitivity analysis, the parameterization is also able to automatically scale the newly-generated design variables, suitably for gradient-based optimization. This approach is demonstrated on two aerodynamic shape optimizations, and is shown to perform comparably to the manual approach requiring trial and error.

Second, an adaptive error control scheme is developed to reduce the computational cost of optimizations. The function error due to convergence of the solver is estimated using an adjoint-derived approach. The error is then adapted during optimization, allowing for loose solver convergence at the beginning of the optimization, thereby reducing computational cost. The approach is demonstrated on two aerodynamic shape optimizations, showing between 30%-50% cost savings.

Third, an appropriate fidelity optimization framework is developed, suited for gradient-based multidisciplinary design optimizations. This framework uses a sequential approach, and begins by quantifying the errors present in each fidelity at the discipline level. The errors are then propagated to the system-level objective and constraints. An optimization is started using the lowest fidelity, and these errors are used to terminate the low-fidelity optimizations at an appropriate time. The errors are also used to select the next appropriate fidelity, by performing a tradeoff between error reduction and computational cost increase. A new optimization is then started using the selected fidelity, and the process is repeated until the high-fidelity optimum is reached.

The approach is then demonstrated on two aerostructural optimizations, including the XRF1 aircraft with over 900 design variables and 900 constraints. The aircraft is analyzed at four flight conditions, and there are a total of over 300,000 possible fidelity combinations. Through the use of the appropriate fidelity framework, cost savings of between 44% and 64% were realized.