Multidelity methods for multidisciplinary system design

Abstract

Optimization of multidisciplinary systems is critical as slight performance improvements can provide significant benefits over the system's life. However, optimization of multidisciplinary systems is often plagued by computationally expensive simulations and the need to iteratively solve a complex coupling-relationship between subsystems. These challenges are typically severe enough as to prohibit formal system optimization. A solution is to use multi- fidelity optimization, where other lower-fidelity simulations may be used to approximate the behavior of the higher-fidelity simulation. Low-fidelity simulations are common in practice, for instance, simplifying the numerical simulations with additional physical assumptions or coarser discretizations, or creating direct metamodels such as response surfaces or reduced order models. This thesis offers solutions to two challenges in multidisciplinary system design optimization: developing optimization methods that use the high-fidelity analysis as little as possible but ensure convergence to a high-fidelity optimal design, and developing methods that exploit multifidelity information in order to parallelize the optimization of the system and reduce the time needed to find an optimal design. To find high-fidelity optimal designs, Bayesian model calibration is used to improve low- fidelity models and systematically reduce the use of high-fidelity simulation. The calibrated low-fidelity models are optimized and using appropriate calibration schemes convergence to a high-fidelity optimal design is established. These calibration schemes can exploit high- fidelity gradient information if available, but when not, convergence is still demonstrated for a gradient-free calibration scheme. The gradient-free calibration is novel in that it enables rigorous optimization of high-fidelity simulations that are black-boxes, may fail to provide a solution, contain some noise in the output, or are experimental. In addition, the Bayesian approach enables us to combine multiple low-fidelity simulations to best estimate the high- fidelity function without nesting. Example results show that for both aerodynamic and structural design problems this approach leads to about an 80% reduction in the number of high-fidelity evaluations compared with single-fidelity optimization methods. To enable parallelized multidisciplinary system optimization, two approaches are developed. The first approach treats the system design problem as a bilevel programming problem and enables each subsystem to be designed concurrently. The second approach optimizes surrogate models of each discipline that are all constructed in parallel. Both multidisciplinary approaches use multifidelity optimization and the gradient-free Bayesian model calibration technique, but will exploit gradients when they are available. The approaches are demonstrated on an aircraft wing design problem, and enable optimization of the system in reasonable time despite lack of sensitivity information and 19% of evaluations failing. For cases when comparable algorithms are available, these approaches reduce the time needed to find an optimal design by approximately 50%.