Design Optimization
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Today’s Lecture
• Introduction to Design Optimization
o What is it?
o How does it work?
What kind of methods are available?
o How can it be used for System Design?
o Some examples of Design Optimization applied to engineering systems
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Introduction
What is System Design?
Examples of Engineering Systems
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Introduction (2)
• Aircraft System Design
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Introduction (3)
Cost Group
Propulsion Group
Pilots Choice
Fuselage Group
Optimum Design
Empennage Group
Wing Group
Weight Group
Undercarriage Group
Weapon Group
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Traditional Design Hierarchy
Mission
Requirements
•General arrangement and performance
•Representative Configurations
•General internal layout
Conceptual
Design
Conceptual
Baselines
•Optimization
•Parametric
•1st level analysis
Preliminary
Design
•Sophisticated analysis
•Problem Decomposition
•Disciplinary Optimization
Selected
Baseline
Detailed
Design
 May lead to Sub-optimal designs
•Systems Specifications
•Detailed Subsystems
•Internal Arrangements
•Process Design
Production
Baseline
Production
and Support
Source: AIAA MDO White Paper, 1991
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Traditional Approach To Product Development
100%
CONCEPTUAL
100%
PRELIMINARY
100%
DETAILED
100%
KNOWLEDGE ABOUT DESIGN
• AERODYNAMICS
• PROPULSION
• STRUCTURES
• CONTROLS
• MANUFACTURING
• SUPPORTABILITY
• COST
DESIGN FREEDOM
TIME INTO DESIGN PROCESS
•
Short Conception phase + unequal distribution of disciplines
o
o
•
limited scope for optimization & assessing impact of inter-disciplinary
couplings.
Correction of later problems
o
o
Costly/ Lost Time/ Futile
Solutions limited to specific discipline
Source: AIAA MDO White Paper, 1991
The Design Process Paradigm Shift
100%
CONCEPTUAL
100%
PRELIMINARY
GOAL
100%
DETAILED
100%
KNOWLEDGE ABOUT DESIGN
• AERODYNAMICS
• PROPULSION
• STRUCTURES
• CONTROLS
• MANUFACTURING
• SUPPORTABILITY
GOAL
• COST
DESIGN FREEDOM
TIME INTO DESIGN PROCESS
Design process reorganized to gain information earlier and to retain design freedom longer
•
•
•
•
More up-front design
More evenly distributed efforts of disciplines in early design
Alleviate paradox
Design decisions/trade-off reordered
Source: AIAA MDO White Paper, 1991
Modernizing Design
•
•
How do we achieve this
improvement?
One way is to implement
numerical optimization
o
•
Aircraft Design Example
o
o
o
•
Integrate all of the different
analysis methods that drive the
design
Aerodynamics
Structures
Performance
Implement numerical
optimization algorithms
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Aerodynamics
Structures
Performance
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Design Optimization
• Design Optimization definition:
o Design Optimization consists of mathematical processes for
determining the maximum or minimum of a function
o OR: Make something the best it possibly could be
• Components of a Design Optimization Problem
o
o
o
o
Design Variables
Objective Functions
Constraint Functions
System Equations
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Objective Functions
• In order to select between design alternatives, we
need a measure of ‘goodness’ that allows us to
compare different designs quantitatively
• We need to be able to estimate this numerically
• Objective functions need to be chosen carefully
o Should reflect the major design goal of the system
o If we choose the wrong objective function, the results will be useless
• The objective function will lead the design to
being the best possible in that category
• Example: If we’re designing an airplane, we could
use the following
o Weight, speed, range, or any other measurable quantity
• Objective functions are represented as
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Objective Functions (2)
• Is there one aircraft which is best in every way?
The lightest, fastest, most efficient, cheapest?
• We can only make one thing the best at a time
• That thing is the objective function
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Design Variables
• Design variables are parameters we can change
to adjust the design
• Optimization is the process of choosing the design
variables that yield an optimum design with
respect to the objective function
• We need to select the design variables carefully
o They should be independent of each other
o They should affect the objective function in a significant way
• Design variables are represented by
• is a vector
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Design Variables (2)
• Aircraft Wing Design Example
• Objective function: maximize L/D
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Constraint Functions
• Almost all engineering design problems have
constraints
• Some constraints are simply boundaries of design
variables, which are easy to handle
o For example, we might know that the wing span should be between 7
and 10 meters
• Some constraints are implicit
o For example, maximum speed > 200 kts
o This is a quantity that is calculated by some equations or analysis
programs, not simple limits on the design variables
• Some are equality constraints
o For example, Lift=Weight
• Some are inequality constraints
o For example Weight < 600 kg
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Constraint Functions (2)
• Aircraft Design Example
Constraints
Endurance
>
8 hours
Rate of climb
>
4.5 m/s
Takeoff distance
<
300 m
Landing distance
<
350 m
Static margin
>
10%
Range
>
1500 km
Weight
<
600 kg
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System Equations
• Equations that calculate the performance of the
system that is being designed
• System equations
o
o
o
o
read in a
Calculate
Calculate
Calculate
set of design
the objective
the values of
the values of
• Examples
variables as input
function value
each equality constraint
each inequality constraint
o Finite element method (can calculate weights, stiffness, and stress)
o CFD aerodynamics (calculates drag, pressure distribution, etc)
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System Equations (2)
• VLM Aerodynamics
Solver
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• FEM Structural Solver
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Problem Statement
• Minimize
• By varying
• Subject to
•
•
•
•
,
objective function
equality constraint functions
inequality constraint functions
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Simple Examples
• Unconstrained
optimization
• The optimizer begins
at an initial point
• Steps are taken that
reduce the value of
until the a minimum
value is reached
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Simple Examples (2)
• Constrained
optimization
• Such that
• Steps are taken that
reduce the value of
until the a minimum
value is reached that
doesn’t violate the
constraint
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Engineering Examples
• 18 Bar Truss
o Load applied along each top node
• What is the best design?
o How thick should each beam be?
o How long should each beam be? (where to we put the connecters)
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Engineering Examples (2)
• We need to define the structure
in terms of a set of design
variables
• We can alter these variables to
try and search for better designs
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Engineering Examples (3)
• We have represented the structure as a set of 12
design variables
• Now we need to set up our optimization problem
• What makes one truss design better than
another?
• We need to select an objective function
o We decide that a lighter design is better
o Minimize mass=sum(each element length x each element thickness x density)
• What are the design constraints?
o The truss shouldn’t break when certain loads are applied to it
o Stress < yield stress in each element
o Stress < buckling stress in each element
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Engineering Examples (4)
•Now we can select or develop an optimization
program and run it to find the best design
•The optimization algorithm gives us the x values
corresponding to the position of each node and the
thickness of each beam
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Methods
• How can we determine what the optimum
design is?
• There are many computational methods available
for doing so
o
o
o
o
o
o
o
Random search
Simplex method
Bisection method
Newton’s method
Genetic Algorithms
Sequential Quadratic Programming
Many others
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Classification of
Optimizers
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Additional Examples
• Topology
Optimization
• Each square is a
design variable
that is either 1 or
0
• Can result in
highly optimized
structural designs
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Additional Examples (2)
• Regional Jet Conceptual Design
• Objective Function: minimize fuel consumption
• Constraints:
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Additional Examples (3)
• System Equations
o VLM Aerodynamics solver
o Performance Equations
o Weight Equations
o Aircraft configuration
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Additional Examples (3)
• Design Variables
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Additional Examples (4)
• Constraints
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Additional Examples (5)
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Aircraft Design Case Study
Deterministic
P=0.80
P=0.99
Boeing 737-800
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