ACDL Faculty

Karen E. Willcox

Charles Stark Draper Assistant Professor of Aeronautics and Astronautics

Phone: (617) 253-3503
Office: MIT Room 37-447

Research Interests:

Reduced-Order Modeling: Reduced-order modeling is a powerful technique in which small yet accurate models of complicated systems are derived. The basic idea is to start with a high-order model (e.g. a CFD model of a fluid flow), extract a reduced-space basis which captures the desired dynamics accurately, and project the high-order system onto the reduced space to obtain a low-order model. By considering the inputs and outputs that are relevant for the particular application, a huge reduction in the number of states can be obtained, e.g. for a two-dimensional Euler aeroelastic model a reduction from 300,000 to 200 flow states was achieved while retaining the required accuracy. The basis can be calculated via a variety of methods, including eigenmodes, proper orthogonal decomposition, Arnoldi methods and balanced truncation.

Multidisciplinary Design Optimization: MDO is a tool which has been used successfully throughout the design process to enable improvements in aircraft performance. By simultaneously considering the effects of aerodynamics, structural dynamics and controls, and the complicated interaction between them, substantially improved performance can be achieved. The concept of MDO can be extended beyond just including the engineering disciplines. In current design practices, optimal is almost exclusively synonymous with minimum weight. If accurate cost models can be developed and integrated to an optimization framework, then we can begin to consider the trade-offs between performance and cost, and arrive at solutions that are more favorable.

Design Space Visualization: The most effective use of MDO is not as a "push-button" tool where one can specify the problem and get the "best" answer. Instead, MDO is a valuable complement to other design tools, and as such should be constructed to provide relevant information for informed design decisions rather than just a solution to a problem. Rather than being used to eke out a 5% improvement in the design solution (where model fidelity is often an issue anyway), MDO ought to be used as a way of gaining insight to the design space, quantitatively identifying rrades and finding innovative design options. Often, in practical applications, it is the solution concept suggested by the optimizer but not the actual details of the design that are more interesting. In this research, we are developing methodology to improve the way in which designers can use MDO. By coupling the optimizer with a visualization framework, we aim to automatically convey important information about the design space, such as:

System Design for Value: As the aerospace industry moves from the era of "Higher, Faster, Farther" to the challenge of "Better, Faster, Cheaper" the definition of best design has evolved considerably. The best strategy is that which optimizes value to the enterprise including not only the aircraft manufacturer, but also the suppliers, the airlines, the consumers and the community. How do we make the best decisions, not only at a detailed design level, but also at a program level (e.g. on fleet mix or speed)? Moreover, how do we quantify the value of intangibles such as system commonality, quietness or environmental impact?

Blended-Wing-Body: The Boeing BWB is a revolutionary concept for transport that integrates wing, fuselage, engines, and tail to achieve a substantial improvement in performance over a conventional transport. This aircraft provides not only many exciting technical challenges, but also many thought-provoking opportunities to revolutionize the way aircraft are designed and built.


Teaching Interests:

16.060 Principles of Automatic Control

A junior-level core Aero/Astro class taught with Prof. Deyst and Prof. Markey.

16.888 Multidisciplinary System Design Optimization

A new graduate-level class taught with Prof. de Wech.

Mathematics for Aerospace Engineers

An initiative to improve the math skills of Aero/Astro undergraduates. Funded b the MIT Alumni Fund.


Other Activities:

Member of the AIAA MDO Technical Committee.

Associate faculty fellow of the Singapore-MIT Alliance.

Board member MIT Muddy Charles Pub.

Publications of Prof. Willcox

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Last modified: October 24, 2002.