Transcript Multiobjective Modeling and Optimization in Design Progress Report Qiang Chen, Derek Dalle, Chad Griep, Jingwei Hu, Jahmario Williams, Zhenqiu Xie.

Multiobjective Modeling and
Optimization in Design
Progress Report
Qiang Chen, Derek Dalle,
Chad Griep, Jingwei Hu,
Jahmario Williams, Zhenqiu Xie
Introduction
• Optimal design of
subsonic aircraft
– Study how changes in the shape
of aircraft affect aerodynamics.
• More importantly, figure
out what to optimize.
• Apply this to quiet
supersonic aircraft.
– Investigate intricacies and
difficulties inherent in designing
a cost-effective, efficient and
quiet supersonic passenger
aircraft.
Configuration Design
Variables for Conceptual Design
• Reference wing area
• Wing sweep angle
• Wing aspect ratio
• Wing taper ratio
• Wing-thickness chord ratio
• Gross weight
• Thrust
•
•
•
•
•
Objective
Functions
Minimum gross weight
Minimum fuel burned
Maximum range
Minimum cost
Minimum NOx emissions
t
c
sweep angle
Motivation
Typical Engineer’s Method
• Establish requirements.
• Design an aircraft that
successfully meets the
requirements.
• Try to optimize by
changing one (or
several) design variable
at a time.
• Ad hoc stopping criteria
are used.
Motivation
Problems with Old Methods
• This process is slow.
• Optimization occurs too
late.
• Engineers have been
successful, but design is
based on experience.
• Some problems are too
hard.
• Real problems are
massively multiobjective.
Flight Optimization System
FLOPS (A. McCullers)
• FLOPS analyzes a
complete aircraft given a
large set of design
variables and options.
• FLOPS also does
nonlinear optimization by
minimizing Σωifi where
each fi is a single
objective function.
• We are looking for better
decision-making tools.
Relationships between design
variables and objective functions
Look at 5 main design variables:
THRUST
SWEEP
AR
TCA
SW
----------------
Maximum rated thrust per engine
Quarter-chord sweep angle of the wing
Wing aspect ratio
Wing thickness-chord ratio
Reference wing area
Objective functions: Fuel Usage, Gross
Weight and their (weighted) average.
Optimality for
Single Objective
Study sensitivity of single objective function to variations in
design variables
• FLOPS aproach
– Enter parametrically varied design variables into input file and
chose objective function to study
– Run FLOPS to analyze the inputs
– Read values of objective function from (contour plot data)
output file
• FLOPS with Matlab approach
–
–
–
–
–
Use Matlab to generate mesh of two design variables
Rewrite the input file with updated variables
Call FLOPS to analyze the inputs
Read output for objective function
Write data file and plot results
Optimality for Multiple
Objectives
• Analyze competing elements in supersonic aircraft
shape optimization (i.e., low boom versus low drag).
• Discuss condition where one objective cannot be
improved without hurting another.
Pareto optimality
• Pareto optimality (or efficiency) occurs
when one cannot decrease one objective
without increasing another. F1
• Decision making plays
an important role.
• Choose proper weights
F  w1F1  w 2 F2
F2
Not perfect curve.
• Objective functions have many local minima
(artifact of numerical procedures).
• The graph implies that we need more work on
optimization.
Using other optimization codes
• To investigate alternative formulations, we need to use
tools that are external to FLOPS.
• NPSOL (Stanford Software, Gill et al.) is a set of Fortran
subroutines for minimizing a smooth function subject to
bounds on variables, linear constraints and smooth
nonlinear constraints.
• It uses a sequential quadratic programming (SQP)
algorithm.
• Call previous Matlab codes to adjust input variables,
perform analysis and read output results.
• Use NPSOL to minimize the result (weighted objective
function)
•
Used “out of the box”, NPSOL did not
provide better results than FLOPS itself
– Price of running FLOPS is quite high
– May not be efficient enough in handling this
special problem
– May need fine tuning
•
A bootstrapping strategy of the two
codes can do quite well
Minimization Obtained
Minimum of Gross Weight
FLOPS
213554
NPSOL
221495
FLOPS + NPSOL
211920
2 * (FLOPS +
NPSOL)
210046
Progress
• Unconstrained optimal
design of subsonic aircraft.
– Done using Mathematica’s
FindMinimum command and
FLOPS
– “Optimal” designs are often
unrealistic (because of the
problem formulation).
• Once constraints are applied,
more sophisticated objective
functions can be used.
• More design variables can
also be used.
“Optimal”
Future Work
• Investigate the effects of
multiple objectives.
• Model sound and energy
produced from sonic
overpressure signal.
• Understand relationships
between aircraft design and
overpressure signal.
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• The goal is an analysis
method that could be used
with an optimization
algorithm.
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