Docstoc

Multi-disciplinary Design Optimization

Document Sample
Multi-disciplinary Design Optimization Powered By Docstoc
					      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

                          2000                           2001




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
               580




                        12
                                                           50 gm force.
                             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             4 68332 @16 MHz
                               RC servo actuators
                            Overflying Mumbai
                               RAM MB, FLASH 256 kB
                             Aileron,1elevator, rudder, throttle
• Out of window display        8 x 12 bit Flight : 4 Way Points
                            AutonomousADC @ 100 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           Average Thrust Vs Frequency of flap


  definition.                                  50


                                               40

• Tailoring to get desired twisting by only flapping
                    Average Thrust (Newtons)
                                               30


  actuation.                                   20



• Construction of the wing                     10


                                                0
                                                     0   0.2       0.4       0.6       0.8           1   1.2   1.4

• Design and build the flapping mechanism      -10


                                               -20

  M Tech in robotics group.                                              Frequency of flap (Hz)
          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
                                                       Cruise for 3000 Km at
                                                        best range M ≥ 0.74
                                                   3                      4
Design Optimization - I                                                   Descend to
                                                                           1500 m
Optimization laboratory                                       Loiter 45 min
                                                                               5
                                              Climb to 11000 m (Reserve)

Design Optimization - II         1        2
                                                   at best
                                               ROC ≥ 11 m/s
                                                                               6
                                                                                7      8
                           Takeoff at sea level                            Land at sea level
                              d ≤ 2150 m                                     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        Design Optimization Course
  – iSIGHT                     during 2003 will be offered
                                         using
  – Phoenix Integration         CASDE MDO-Framework
  – Dakota (Sandia labs)


• 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
Subject to;
           h (x)  0   h  m
           g (x)  0   g  k

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

              
              
              
              

X2
              
              
              
              
              
              

               X1
             GA / SA Search


                           


                

X2             


                                   


                               
               
                       X1
         Gradient Based


                          Gradient of functions
                          Required!

                                       f 
X2                                    x 
                                       f1 
         
                                            
                             f (x)   x 2 
                                            
                                           
                                            
                                       f 
                 X1
                                       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

                                         C L  C0  C 00
  b   o
           , C o        Co      ;         L       L

                                          b       
                             L


                                         C L  C 0  C 00
  b   o
           , C o        C o     ;         L       L

                                         C        
                              L




            f ( x  x )  f ( x )
  f ' (x)                          0.5 f ( x ) x
                    x
       Problem with Finite Differencing?

Only (n+1) CFD runs?

                                              Iterative
                         CL                   Convergence
                                              Criteria




                                          b

Correct step size for FDM is important!
Will demand more CFD runs!
          Complex Variable Approach

 subroutine func (x, f)          subroutine func(x, f)
 real 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

                            Manually extract
Complex Analysis             sequence of
 Code in Fortran             mathematical
                              operations


                          Manually differentiate
                              mathematical
                          functions - chain rule

   FORTRAN
                            Code the complex
  source code
                           derivative evaluator
that can evaluate
                                in Fortran
    gradients
             User Symbolic Maths

                            Manually extract
Complex Analysis             sequence of
Code in FORTARN              mathematical
                              operations

                           Use symbolic math
                          packages to automate
                          derivative evaluation

    FORTRAN
   source code              Code the complex
 that can evaluate         derivative evaluator
     gradients                  in Fortran
    Automatic Extraction of Formulae

                              Parse and
Complex Analysis         extract the sequence
Code in FORTARN           of mathematical
                              operations


                          Use symbolic math
                         packages to automate
                         derivative evaluation

    FORTRAN
                          Code the complex
   source code
                         derivative evaluator
 that can evaluate
                              in Fortran
     gradients
           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.



                                  y
   experimental point

    RSM. Least Square Fit.
    y = a0 + a1 x + a2 x2 . . .

                                                    x
Fitted model is smooth and easily differentiable.
Curse of dimensionality! 2k function evaluations
Sequential RSM.
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 = Computer exp
                                               DACE Fit
         x                     x x
     x            x        x
 x




                                                 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

				
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
views:3
posted:2/8/2012
language:
pages:40