On the Application of Differential Geometry to MDO

Abstract

Multidisciplinary Design Optimization (MDO) is a methodology for optimizing large coupled systems. Over the years, a number of different MDO decomposition strategies, known as architectures, have been developed, and various pieces of analytical work have been done on MDO and its architectures. However, MDO lacks an overarching paradigm which would unify the field and promote cumulative research. In this paper, we propose a differential geometry framework as such a paradigm: differential geometry comes with its own set of analysis tools and a long history of use in theoretical physics. We begin by outlining some of the mathematics behind differential geometry and then translate MDO into that framework. This initial work gives new tools and techniques for studying MDO and its architectures while producing a naturally arising measure of design coupling. The framework also suggests several new areas for exploration into and analysis of MDO systems. At this point, analogies with particle dynamics and systems of differential equations look particularly promising for both the wealth of extant background theory that they have and the potential predictive and evaluative power that they hold.

Differential Geometry and Design Coupling in MDO

“…While the metric tensor could be tested for use in either of these applications, it is really meant more as a tool for further MDO analysis; obtaining the metric tensor requires a lot of work for a coupling suspension technique, and it is really meant to do a lot more. See our previous and forthcoming papers 2,34 for further discussion of what that analysis might look like.…”