Signomial programming for aircraft design

Abstract

Due to the coupled nature of aircraft system design, it is important to consider all major subsystems when optimizing a configuration. This, however, is easier said than done, particularly because each individual subsystem model can be arbitrarily complex. By restricting an optimization problem to have a certain mathematical structure, significantly more effective and tractable solution techniques can be used. Geometric programming, an example of one such technique, guarantees finding a globally optimal solution. Although it has been shown that geometric programming can be used to solve some conceptual aircraft design problems, the required formulation can prove too restrictive for certain relationships. Signomial programming is a closely related relaxation of geometric programming that offers enhanced expressiveness, but without the guarantee of global optimality. Despite this, solution methods for signomial programs are disciplined and effective. In the present work, signomial programming models are proposed for optimal preliminary sizing of the vertical tail, horizontal tail, fuselage, landing gear, and wing of a commercial aircraft with a tube-and- wing configuration. These models are then combined together to produce a full aircraft optimization model. Signomial programming's relaxed formulation allows it to handle some of the key constraints in tail, fuselage, landing gear, and wing design, and therefore an improvement in fidelity over geometric programming models is achieved. The models are readily extensible and easily combined with other models, making them effective building blocks for future work. A primary contribution of this work is to demonstrate signomial programming as a viable tool for multidisciplinary aircraft design optimization.