Dr. Rob McDonald Lockheed Martin Endowed Professor Cal Poly, SLO UT Austin AIAA

Multidisciplinary Design and Optimization (MDO)

Natural Evolution of that Other Engineering Activity.

Dr. Rob McDonaldLockheed Martin Endowed Professor

Cal Poly, SLO

UT Austin AIAA

Core Engineering Activities

• Analysis– Given a system, how do we expect it to perform?

• Test– Given a system, how does it perform?

• Design– Given a desired performance, what system do we want?

Design is an inverse problem.

Design is inherently different from Analysis & Test.

Complex Systems

• Systems are becoming more complex– Larger systems– Systems of systems– Networks, connections, & interactions– Longer life cycles – longer development cycles– Higher cost

• There are more constraints than ever before– Emissions– Noise– Safety

• Systems perspective not just for the system

Reconnaissance/ObservationFederal observation balloon Intrepid being inflated. Battle

of Fair Oaks, Va., May 1862. National Archives.

Multi-mission Aircraft

1942 1952 1970 1983 1991 1996 20040

5

10

15

20

25

30

3

8

23

26 26 26 26

3

89

8 87

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US Carrier Air Wing Composition

# of Missions# of Aircraft Types

YearData compiled from Borer 2006

Stick and Rudder?

Communications

US Soldiers

Complex Systems

• Systems are becoming more complex– Larger systems– Systems of systems– Networks, connections, & interactions– Longer life cycles – longer development cycles– Higher cost

• There are more constraints than ever before– Emissions– Noise– Safety

• Systems perspective not just for the system

Q: How do you analyze & design complex systems?A: SDAO / MDAO

NASA's Aeronautics Plan

-Lisa Porter

“The Systems Analysis, Design, and Optimization team has identity at Levels 2 through 4...”

- SFW Reference Document, Collier et.al.

NASA's Aeronautics Plan

-Bill Haller

“The Systems Analysis, Design, and Optimization team has identity at Levels 2 through 4...”

- SFW Reference Document, Collier et.al.

NASA's Aeronautics Plan

-Lisa Porter

Not Just NASA

• DARPA• ONR• NAVAIR• AFRL• FAA• Industry

– Lockheed– Boeing– Northrop Grumman– Pratt & Whitney– General Electric

• etc.

Core Engineering Activities

• Analysis– Given a system, how do we expect it to perform?

• Test– Given a system, how does it perform?

• Design– Given a desired performance, what system do we want?

Design is an inverse problem.

Design is inherently different from Analysis & Test.

Analysis

A – Model.X – Input Vector.A – Output Vector.

Design

Given a system, how do we expect it to perform?

Given a desired performance, what system do we want?

ΔX – Change Mechanism.X0 – Initial Guess.A* – Desired Output.

AA

X

AA

A*X0

ΔX X

Multidisciplinary Analysis (MDA)

– System.A – Component.X – Input Vector.A – Output Vector.a1 – Feedforward Interaction.b2 – Feedback Interaction.

MDA Techniques focus on the challenges of this problem.

System Decomposition & IntegrationConvergence & Consistency

Model ApproximationInformation/Data ManagementParallelization & Acceleration

Error PropagationValidation

etc.

AA

X

B B

C C

a1

b2

b1

Multidisciplinary Design Optimization(MDO)

MDO Techniques focus on the challenges of this problem.

All of the challenges of MDA.+

Design ExplorationOptimization

Constraints & RequirementsTradeoff

Robust DesignDecision Making

VisualizationSensitivities & Growth

etc.

AA

B B

C C

a1

b2

b1

A*B*C* X

0

ΔX

Familiar Challenges

x

f Has anyone never……performed an analysis?

Familiar Challenges

Has anyone never……changed an input and

analyzed multiple cases?…wished it was easier?

x

f

Parametric Analysis & Automation.

Familiar Challenges

Has anyone never……fit a curve to the points?

…plotted the resulting curve?…estimated the curve’s error?

Metamodeling / Surrogates & Visualization.Response Surface Equation,

Least Squares Regression, Spline Interpolation, Neural Networks, Gaussian Processes, Radial Basis Functions.

x

f

Familiar Challenges

Has anyone never……wanted to explore a space more dimensions, but thought “There must be a better way

to pick the points”?x

fy

x

fy

Familiar Challenges

Has anyone never……wanted to do the same in

more dimensions, but thought “There must be a better way

to pick the points”?

Design of Experiments.Face Centered Cubic, Orthogonal Arrays,

Latin Hypercube, Monte Carlo.Not to mention parallelization.

Familiar Challenges

Has anyone never……estimated a derivative?…used that derivative to

predict behavior?

Sensitivity Analysis.Finite Difference, Adjoint Methods, Automatic Differentiation,

System Sensitivity Analysis.

x

f

Familiar Challenges

Has anyone never……looked for the maximum or

minimum of the curve? Subject to constraints?

Optimization.Constrained Optimization, Gradient Based, Conjugate Gradient,

Penalty Function, Stochastic Optimization, Genetic Algorithms, Synthetic Annealing,

x

f

x

f

Familiar Challenges

Has anyone never……been uncertain of inputs?

…been uncertain of the analysis?

Robust Design, Uncertainty & Error Propagation.

Familiar Challenges

Has anyone never……faced competing

objectives?

Decision Making.Pareto Frontier, Non-Dominated Solution,

MADM, MODM, SAW, TOPSIS.

$

f

Natural Evolution of Design

AA

A*X0

ΔX Xx

f

1942 1952 1970 1983 1991 1996 20040

5

10

15

20

25

30

3

8

23

26 26 26 26

3

89

8 87

6

US Carrier Air Wing Composition

# of Missions# of Aircraft Types

Year

1. Evolution of Complex Systems

2. MDO as the Solution to the Complexity of Systems

3. MDO as a Core Engineering Activity

4. MDO as a Toolbox for Familiar Challenges

Questions?

Thanks,

Rob McDonald