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