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What is MDAO?
Modern aircraft are extremely complex systems with millions of moving parts. To design an aircraft is a monumental effort, requiring thousands of engineers, technicians and support staff. As with any major project, sub-tasks be spun off of the main design effort, often arranged by the technical expertise of small groups of subject matter experts. These disciplines become the core of the technical work that goes into the aircraft.
However each discipline has a vested interest in making its own sub-task as easy as possible, often leading to conflict. This this satirical illustration from from aircraft designer C. W. Miller illustrates the fundamental issue:
Anyone who has ever worked on an aircraft program knows how quickly a productive design process can descend into political squabbling between discipline groups. A well run program must establish a framework or architecture to evaluate disciplines against each other in a technical and unbiased fashion. The field of Multi-Disciplinary Analysis and Optimization (MDAO) studies how do best solve this problem.
In summary, research in MDAO tends to involve the following general components:- A complex design problem, broken down into smaller discipline sub-problems
- Disciplines that interact and conflict (ie, gain in one corresponds to loss in another)
- Separate discipline analysis modules which are generally expensive to evaluate
- A desire to minimize or maximize some objective function (weight, drag, cost etc)
- Implementation in a numeric optimization computational architecture
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What is the Current State of Research in MDAO?
While formal mathematical optimization began to make its way into engineering design in the 1970s, the modern field of MDAO traces its origins to the early 1990s. The November 1994 paper Problem Formulation for Multidisciplinary Optimization by Cramer et. al. was one of the first to use modern terminology in application to a coupled aerodynamic and structural analysis for an aircraft wing. Almost 20 years later, a survey paper by Lambe and Martins Multidisciplinary Design Optimization: A Survey of Architectures filled in many of the gaps left by the original Cramer paper, and provides us with a great starting point to understand the current state of MDAO.
During the 20 years spanned between Cramer and Lambe/Martins, the focus of the research community remained squarely on integrating large scale analysis codes together into a common architecture, which can then be wrapped by an optimizer. Cramer states:
We feel that the all-at-once (AAO) [or fully integrated] approach remains theoretically attractive because of the probability that it will be the least expensive computationally. Unfortunately, it requires a higher degree of software integration than is likely to be achieved in the near future for realistic applications.
Lambe and Martins make a very similar statement:
In engineering design, software for discipline analysis often operates in a black-box fashion, directly computing the coupling variables while hiding the discipline-analysis residuals and state variables. Even if the software can be modified to return the residuals, the cost and effort required may be excessive. Therefore, most practical MDO problems require an architecture that can take advantage of existing discipline-analysis software.
Even today, the state of the art when it comes to applied MDAO remains the tying together of various analysis tools. This approach is very reasonable. Developing an analysis tool is a massive undertaking to begin with, but perhaps more importantly trust in an analysis tool is built over years of use and hundreds of validations. To violate the bounds of the black box is to open a Pandora's Box of unforeseen problems.
And yet, this approach which was intended to save headaches has still proven to be problematic, particularly when it comes to optimization. As illustrated in this figure from Mark Drela (given in a presentation in 2011), the introduction of black box analysis models introduces false optima:
Recent literature has continued to suggest that taking a more integrated approach to MDAO is not only possible, but leads to better designs. Hoburg's paper Geometric Programming for Aircraft Design Optimization took a radical new approach: Rather than treating analysis models as fixed black boxes, leading to arbitrarily hard optimization formulations that must be wrapped with a general non-linear solver, we can instead fit our analyses into a fast and efficient optimization scheme. Hoburg's work culminated in GPkit, a software for MDAO which allows users to write their design problems using an optimization first approach. The resulting dozen or so papers have time and again demonstrated that by prioritizing optimization in addition to analysis, and by exploiting structure in our design spaces, the practice of MDAO begins align with expectation. -
What Research do I Contribute to the MDAO Community?
In my work, I seek to bridge the gap between "classical" MDAO and the novel approach originally proposed by Hoburg. Core to this idea is that integrating black box analyses into a structured optimization framework may provide a happy medium between the two approaches. My Master's Thesis proposed a methodology to include black box analysis tools into a framework that was otherwise compatible with the novel methods available in GPkit. My design tool Corsair, a loose acronym for Concurrent Optimization and Analysis for AIRcraft (expected release in 2021, beta testing available on request), continues to build out capability where GPkit left off, extending to a broader and more general set of black boxes, and introducing hybrid optimization schemes which are more in line with the classical MDAO literature. A number of pending publications will outline the full spectrum of methods from fully integrated optimization first approaches to non-linear analysis first architectures, and propose numerical methods which fill the existing gaps. Take a look at my work in Optimization Methods for more information on these new algorithms.