Optimal Aircraft Design Decisions Under Uncertainty Using Robust Signomial Programming

Abstract

Aircraft design benefits from optimization under uncertainty since design feasibility and performance can have large sensitivities to uncertain parameters. Legacy methods of uncertainty protection do not adequately explain the tradeoffs between feasibility and optimality, and they require prior engineering knowledge that may not be available for new system concepts. Furthermore, stochastic optimization over parameter distributions is computationally intractable for solving high-dimensional nonlinear design optimization problems. This paper proposes an efficient solution method for engineering design optimization problems under uncertainty using robust signomial programs (RSPs). Signomial programs (SPs) have demonstrated potential in solving multidisciplinary optimization problems, and the formulation of RSPs enables conceptual design that captures parametric uncertainty with probabilistic guarantees of constraint satisfaction. The proposed method transforms stochastic optimization problems to deterministic problems by considering the worst-case robust counterpart of each design constraint over a parameter uncertainty set, provided that each constraint is SP representable. The RSP formulation extends an existing robust geometric program (RGP) formulation by allowing difference-of-log-convex constraints that appear in many design problems. The RSP is solved efficiently and deterministically using a sequence of local RGP approximations. RSPs are then applied to unmanned aircraft design, and they are used to rigorously explore the tradeoff between robustness and optimality in design decisions.