Transcript Multi-disciplinary Design Optimization

Srinivasan Memorial Lecture
The Aeronautical Society of India, Trivandrum
VSSC
K. Sudhakar
Centre for Aerospace Systems Design & Engineering
Department of Aerospace Engineering
Indian Institute of Technology
Mumbai 400 076
June 27, 2003
“I would love to visit IIT Bombay and get briefed”
Dr. S Srinivasan
May 17, 1999
Breakfast table at SHAR Guest House
Years 1996-1998
• AR&DB Centres
– CFD
– Composites
– Systems Design & Engineering ? ?
• Aerospace Design as a discipline in Universities
–
–
–
–
Specialization dropped
Courses had tapered off
Design, build Or Open ended problems shunned
No research interest among faculty
• IIT Bombay decides to take a plunge!
– What made it fail earlier?
Aerospace Systems Design and Engineering
in Universities
• System Level Studies
• Masters Level Specialisation
• Design Optimization / MDO
• At CASDE we also . . . . .
System Level Studies
2001
2000
Instrumented. 2.5 kg, 1.6 m.
Videography. 0.9 kg, 0.6 m.
2002
MAV
Solar. 0.13 kg, 0.25 m.
MAV Challenges / Preparations
2 kg, 0.6 m Autonomous Video-platform
Low Reynolds number flows
Wind tunnel balance
Miniaturisation using COTS
Construction methods
Propulsion system (60% weight)
Autonomous missions  HILS
Torque sensor setup
254
Propeller test facility
50 gm force.
580
•
•
•
•
•
•
12
Torque
sensor
55
All dimensions
are in mm
Launch Vehicle Simulator from VSSC
H/W In Loop Simulator for MAV
•
•
•
•
Flight Dynamics & Sensor models
On-board Computer ?
Hobby grade actuators
Way Point Navigation
– ADDR
– ADDR + GPS
• Out of window display
@16
MHz
4 68332
RC servo
actuators
Overflying
Mumbai
RAM 1elevator,
MB, FLASH
256
kB
Aileron,
rudder,
throttle
Autonomous
Flight@: 100
4 Way
Points
8 x 12 bit ADC
kHz
15 PWM / 25 DIO
30 gm; 50 x 75 x 12 mm
Problem opened up for C&G specialists
INS-GPS Module, M Tech thesis in EE
Flapping Wing Flight
Flapping Wing Vehicle
• Unsteady wing aerodynamics with prescribed .
motion in flapping & twisting -VLM.
• Coupled aeroelastic analysis. Arrive at structural
definition.
• Tailoring to get desired twisting by only flapping
actuation.
• Construction of the wing
Average Thrust Vs Frequency of flap
50
Average Thrust (Newtons)
40
30
20
10
0
0
0.2
0.4
0.6
0.8
• Design and build the flapping mechanism
-10
-20
M Tech in robotics group.
Frequency of flap (Hz)
1
1.2
1.4
Flapping to Induce Twisting
• Wing spar to be rigid rod. Used for flapping
• Outer sleeve has low and tailored torsional stiffness
• Wing strips mounted on outer sleeve
Flapping to Induce Twisting
• Wing spar & flapping hinge rigid and one piece.
• Wing surface - film
IMS Laboratory
M Tech Specialisation in
Systems Design & Engineering
Design Optimization - I
Optimization laboratory
Design Optimization - II
3
Cruise for 3000 Km at
best range M ≥ 0.74
4
Descend to
1500 m
5
1
2
Loiter 45 min
Climb to 11000 m (Reserve)
at best
ROC ≥ 11 m/s
Takeoff at sea level
d ≤ 2150 m
6
7
8
Land at sea level
d ≤ 1220 m
Modeling & Simulation
Applied Mechatronics
Systems Engineering Principles
Design Optimization
MDO
Design Optimization / MDO
• Airborne Early Warning System
– Complex system, simple models.
• Maneuver Load Control
– Existing system, database driven
• Hypersonic Launch Vehicle
– New system, simple models, system analysis
• Aero-elastic Wing Design
– Simple models
– Intermediate level models
– FEM + VLM
MDO
• System analysis
– Ownership of disciplinary analysis?
– Integration strategy?
– Human & technical issues
• Strategies that will
– Accommodate above concerns
– Allow bringing in science based, compute intensive
analysis
Integration Issues
I cannot find the correct
tuning parameters!
Why do you want my
program?
System Designer’s Nightmare!
I have a new version of
analysis software
You have to know my code to
be able to execute it!
MDO Frameworks
• Commerical Frameworks
– iSIGHT
– Phoenix Integration
– Dakota (Sandia labs)
Design Optimization Course
during 2003 will be offered
using
CASDE MDO-Framework
• CASDE MDO-Framework
http://www.casde.iitb.ac.in/MDO/framework/
Multi-disciplinary Design Optimization
• 3D-Duct Design
– Parametrization, meshing, simple analysis
– CFD (NS)
?
• Wing or Vehicle
– CFD (NS / Euler)
?
• Hypersonic Nozzle Design
– CFD (Euler)
?
Optimization
Minimise
f (x)
x  n
h (x)  0
h  m
g (x)  0
g  k
Subject to;
Feasible designs  S   n
Optimization – Design Space Search
• Brute force. Grid the space, evaluate function,
sort to identify minima.
• Evolutionary. Still too many function calls.
– Genetic algorithms
– Simulated annealing
• Gradient based methods
– Local optima
– Small number of function calls if gradients good!
– Suited for compute intensive problems.
Brute Force Search
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X2
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         
         
         
X1
GA / SA Search


 

X2
 





X1
Gradient Based
Gradient of functions
Required!
X2



X1
 f 
 x 
 f1 


x 2 

f (x) 






 f 
 x n 
How to evaluate gradients?
Consider design of wings;
– Design variables, x = [b, C]
– Objective function, f(x) = CL
Analysis is CFD
– Give values to x = [b, C]  Wing  mesh
– Run a CFD code and generate pressure distribution
– Integrate pressures on body  CL
How to evaluate
C L
C L
 ?;
?
b
C
Methods to Evaluate Gradients?
• Finite difference method. Easy to implement, but
problematic?
• Complex variables approach, requires source
• ADIFOR – Automatic DIfferentation in FORtran;
requires source. Analytical accuracy
• Surrogate Modeling – Surface fits
– Response Surface Method (RSM / DOE)
– Design & Analysis of Computer Experiments
Finite Differenced Gradients?
Finite Difference Method
n design variables  (n+1) CFD runs
b
o
, Co 
 C oo
L
b
o
, C o 
 CLo
;
b
o
, C o 
 C oL
;
C L
CL0  C 00
L

b

C L
C 0L  C 00
L

C

f ( x  x )  f ( x )
f ' (x) 
 0.5 f ( x ) x
x
Problem with Finite Differencing?
Only (n+1) CFD runs?
Iterative
Convergence
Criteria
CL
b
Correct step size for FDM is important!
Will demand more CFD runs!
Complex Variable Approach
subroutine func (x, f)
real x, f
subroutine func(x, f)
complex x, f
Evaluate f{x + i e} ; e << 1
f(x) = Real Part { f(x + i e) }
- f”(x) e2 / 2
df/dx = Imag Part { f(x+ i e) } / e - f ”’(x) e2 / 6
CPU time up by 3, RAM up by 2
User Supplied Gradients
Complex Analysis
Code in Fortran
Manually extract
sequence of
mathematical
operations
Manually differentiate
mathematical
functions - chain rule
FORTRAN
source code
that can evaluate
gradients
Code the complex
derivative evaluator
in Fortran
User Symbolic Maths
Complex Analysis
Code in FORTARN
Manually extract
sequence of
mathematical
operations
Use symbolic math
packages to automate
derivative evaluation
FORTRAN
source code
that can evaluate
gradients
Code the complex
derivative evaluator
in Fortran
Automatic Extraction of Formulae
Complex Analysis
Code in FORTARN
Parse and
extract the sequence
of mathematical
operations
Use symbolic math
packages to automate
derivative evaluation
FORTRAN
source code
that can evaluate
gradients
Code the complex
derivative evaluator
in Fortran
Gradients by ADIFOR
Complex Analysis
Code in FORTARN
Automated
Differentiation
Package
FORTRAN
source code
that can evaluate
gradients
Surrogate Modeling
DOE / RSM modeling in physical experiments.
experimental point
y
RSM. Least Square Fit.
y = a0 + a 1 x + a2 x 2 . . .
Fitted model is smooth and easily differentiable.
Curse of dimensionality! 2k function evaluations
Sequential RSM.
x
Design & Analysis of Computer Experiments
• Regression fit + Stochastic process
• Single global fit
• Variability in prediction known and exploitable
x = Computer exp
DACE Fit
x
x
x
x
x
Estimates of
Predictive error
Building Models Using DACE - An Idea!
x
x
x
x
x
x x
x x = Computer exp
DACE Fit
5% predictive
error
Use multi-modal GA to identify ‘n’ highest peaks.
Test if they are higher than 5%
Add computer experiments at those spots
We Also . . . .
•
•
•
•
Travelling course on design
Schools Outreach Programme
Design Competition - ‘Design, Build, Fly’
KVPY Scheme for encouraging innovators of
tomorrow
• Practical training for other engineering college
students
People