UC San Diego

Aerospace vehicle design is a complex process involving multiple engineering disciplines such as aerodynamics, structures, propulsion, and controls. This complexity led to the emergence of multidisciplinary design optimization (MDO), a field that employs numerical optimization methods to improve the designs of engineering systems while simultaneously considering multiple disciplines. Integrating all disciplines significantly increases the problem's complexity, which motivates the use of gradient-based optimization methods with analytical computation of the derivatives. This approach has demonstrated considerable success in tackling practical large-scale MDO problems with hundreds of design variables. Recent applications can be found in the conceptual design of electrified aircraft, unmanned aerial vehicles, and launch vehicles. Presently, most MDO applications formulate and solve deterministic optimization problems in which the objective and constraint functions do not consider randomness. However, real-world scenarios introduce uncertainties arising from factors like variations in operating conditions, parameter fluctuations, and manufacturing discrepancies. Incorporating these uncertainties into MDO problems transforms them into MDO under uncertainty (MDOUU) problems. Addressing well-defined MDOUU problems can enhance the robustness and reliability of MDO-optimized designs in real-world scenarios. This dissertation presents a suite of graph-accelerated uncertainty propagation methods, designed to tackle various forward uncertainty quantification (UQ) and MDOUU problems. At the core of these methods lies a new computational graph transformation method called Accelerated Model Evaluations on Tensor Grids using Computational Graph Transformations (AMTC). AMTC leverages the sparsity in the computational graphs of multidisciplinary systems to accelerate tensor-grid evaluations. This approach has been effectively combined with the non-intrusive polynomial chaos method to tackle UQ and MDOUU problems, with several extensions devised to address higher-dimensional problems within this framework. Towards the end, this dissertation also includes a case study on a laser-beam-powered aircraft design problem. This study offers a comparative analysis between the results of MDO and MDOUU, while also demonstrating the efficacy of graph-accelerated uncertainty propagation methods in addressing large-scale MDOUU problems.