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
6
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
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