Post on 01-Jan-2016
Configuration Design of Air Breathing Hypersonic Vehicle using Numerical Optimization
2nd Progress Seminar 22nd August,2003
J. Umakant Research Student ( External)Roll No. 01401701
CASDEDept. of Aerospace EngineeringIIT, Bombay
Summary of 1st Progress Seminar – September 2002Problem Formulation* Conceived Overall Design process for Air-Breathing Hypersonic configuration * Disciplinary Interactions* Parameterization of vehicle and Analysis Modules
Review of literature of Aerospace Vehicle Design using MDO 3 Ph D thesis - McQuade : Development of CFD based GLA factors for 2D scramjet vehicle - Guinta : VCRSM of HSCT Wing - Old : Robust design of SSTO vehicle 12 Papers from 1990 onwards - Bowcutt (1999) MDO Hypersonic Vehicle Optimization - Design synthesis tools for Launch Vehicles - Papers related to approximation strategies
Fore-body optimization using engineering method with FFSQP optimizer- two design variables ( fore-body compression angles)- objective function ma / Cd subject to constraints on Mintk , L/D , h/l
I Hypersonic Technology Demonstrator Vehicle(HSTDV) - Mission - Vehicle Background
II HSTDV Configuration
- Problem Statement - Parameterization and Trade-Offs - Engineering Methods for Analysis
III Optimization and Results
IV Potential Improvements in Aerodynamic Prediction code
2nd Progress Seminar
HYPERSONIC TECHNOLOGY DEMONSTRATOR HYPERSONIC TECHNOLOGY DEMONSTRATOR
TO DEMONSTRATE AUTONOMOUS SUSTAINED FLIGHT AT HYPERSONIC SPEED
1 m DIA
ALTITUDE : 20 kmMACH NO. : 4.5
SCRAMJET TEST
RAMJET
SCRAMJETMACH NO. : 5.5
ALTITUDE : 32.5 kmMACH NO. : 6.5TEST DURATION : 400 s
DUAL MODE TEST
HSTDV Vehicle – Discipline Interactions
Integrated Engine and Airframe• Entire undersurface of the airframe forms part of the engineFore-Body • pre-compressed air to the intake , aerodynamic characteristics, volumeAfter-Body• thrust, stability characteristics , after-body volume
Aerodynamic heating, Detailed Modeling of Intake, Combustor, Nozzle , Trajectory Optimization
AERODYNAMICS
Multi-disciplinary Analysis
PERFORMANCE
PROPULSION
SIZING
OptimizerXD f , g
MDO - Implementation Issues
Mathematical modeling and Computational Expense low fidelity methods : computationally cheap but not sufficiently accurate high fidelity methods: highly accurate but computationally prohibitive
Organizational Complexity disciplinary expertise is distributed across the organization, not available centrally difficulty in data exchange
Optimization Procedures problem formulation algorithms for global optimization
Broad Strategy for HSTDV Design using MDO
I Overall Vehicle Design using Engineering Methods ( low fidelity ) - Sizing, Aerodynamics, Propulsion and Performance - Identify important design variables - Build a multidisciplinary analysis tool - Calibration factors - Numerical optimization
II Methods to create Approximate Models for High Fidelity Analysis - Design and Analysis of Computer Experiments - Data fusion ( low fidelity + high fidelity )
III Global Optimization Strategies using DACE suggested in Statistical literature.
IV Methods to take into account uncertainties in approximate model
Parameterization of HSTDV Body
XD: {1, 2, 3 , n_pl , wc , wfac_pl, tfac_pl,,Hcruise }
W_fact_fac
Wing: AR=0.6, b = 1.6m, =0.4 Tail: AR=2.3 , b = 1.4m , =0.4 Airframe thickness t = 50mm ; Lmid = 2.5 m
4 5 6 7 8 9 1 0M A C H N U M B E R
0 .1
0 .2
0 .3
0 .4
0 .5
0 .6
0 .7
0 .8
0 .9
1 .0
TO
TA
L P
RE
SS
UR
E R
EC
OV
ER
Y
S IN G L E S H O C K
2 S H O C K S
4 S H O C K S
3 S H O C K S
Fore-body Parameterization – 3 Ramp configuration
Max pnoz Sin(noz)
s.t 0.2 – pnoz/pne
noz
Lab
After-body Parameterization
1.0
0.0
noz (deg.)0 40
p noz/p
ne
Pno
z *
l ab*S
in
noz
noz (deg.)
Mne = 1.5 pne = 1.1 atmLab = 1.5m1-D P-M relationsto estimate pnoz
*noz = 17°
Parameter Potential Trade
n_planhigher body width ( volume) vs higher skin friction drag
1, 2, 3 higher f/b height (volume) vs lower intake Mach No., lower Pressure recovery, higher CL & CD
lmid higher volume vs higher skin friction drag, higher weight
lab higher a/b volume vs lower nozzle angle ( propulsive force & propulsive moment)
w_fac Higher lift, lower trim angle of attack vs higher drag, more space
w_cant Stability vs higher wave drag
t_fac higher trim deflections vs lower trim deflection, stability
Hcruise higher drag , higher ma vs lower drag , lower ma
Trade-Offs
External Configuration Model External Compression Model
Aero Model
Adjust Ballast
Mass flow of Air Capture
Thrust Model
Specific Impulse
Trim deflection , DragUpdated mass
Fuel flow rateThrust Deliverable
Performance Model
VolumeBody Discretization
TrimNo
Yes
Optimizer
f , gXD
Forebody length and height
Overall Aero &Controldata
MassC.G.
PAYLOAD : 400 kgFUEL : 250 kgTOTAL WEIGHT: 1240 kg
HYPERSONIC TECHNOLOGY DEMONSTRATOR -CONFIGURATIONHYPERSONIC TECHNOLOGY DEMONSTRATOR -CONFIGURATION
External Compression Model
External Compression Model
Oblique shock theory
M ,
Input Variables
1 , 2 , 3
Output Fore-body dimensions( l1 ,l2 ,l3 ,h1 ,h2 ,h3 )Intake Entry Conditionspintk , Mintk , ma
1
3
2
L L L
h
bb
b
12
3
1 2 3
h
h
h
1
2
3
intk
a
hM
33
int3 tantan kh
l 333 tanlh
22
23int32 tantan
tan
lhh
l k222 tanlh
11
132int321 tantan
tan
llhhh
l k
111 tanlh
Assuming shock on lip condition
Inta
ke E
ntry
Mac
h N
o.
Tot
al P
ress
ure
Rec
over
yMass flow rate ( Kg/s) Mass flow rate ( Kg/s)
First Ramp Angle 5 deg.
Calibration factor
Mass flow rate based on Euler CFD calculations is about 30% lower as
compared to the estimate from low fidelity analysis
Each Euler CFD run on a 8node P-III cluster requires 15 hours
Typical Results from External Compression model
External Configuration Model
Input Variables
1 , 2 , 3 , n_plan , wc ,
wfac_pl , tfac_pl,
External ConfigurationModel
Outputs
* Body discretization (x,y,z)
* Wing & Tail discretization
* Internal Volume
* Overall Mass (TOGW)
* Centers of gravity
External Compression Model
(l1,l2,l3 ,h1,h2,h3)
Z
x
xfb1_stn xfb2_stn xfb3_stn xmid_stn xnoz_stnx0
w
th
xstn 1 2stn
LmidLnoz
Input Parameters
* Swid_ntip = 0.1m* Lmid = 2.5m* noz = 20°* a/b = 2.0
Body Discretization
stnxfbxstnxfb _3_2
ntipwidsplstnxnosexysemi __tan*_
3tan*_2
tan*_1_2tan*__1 21
stnxfbx
stnxfbstnxfbstnxnosestnxfbzlh
ba
ysemizuh
/
ab
w =
b =
h =
External Configuration Model
w
th
xstn 1 2stn
l
dxtxl
wwtx
l
hhV
0
11 0.2*2
Mass = s * Swet ; s = 20 kg / m2 surface area density
Internal volume
body_int vol = fb1_v + fb2_v + fb3_v + midbd_v + aftbd_v
Airframe Mass
bodyaf_m = 1.2* (fb1_m + fb2_m + fb3_m + midbd_m + aftbd_m)
External Configuration Model
Xc.g. = dxxAx
xdxxAx
l
l
)()(
)()(
0
0
dxtxl
wwtdxx
l
hhtdxxA
lll
0
1
0
1
0
2)(
tw
wh
h
twwl
hhl
22
2
2322
32
11
11
Xc.g. =
bodyaf_xcg = ( fb1_m* fb1_xcg + fb2_m * fb2_xcg + fb3_m* fb3_xcg + midbd_m* midbd_xcg + aftbd_m* aftb_xcg) / bodyaf_m
Airframe Center of gravityExternal Configuration Model
TE
LE
ME
TR
Y P
AC
KA
GE
OBC
INS
ENGINE
FUEL
FUELPAYLOAD
OBC
INS
PAYLOAD
BATTERY
ACTUATORS
ACTUATORS
TOGW = bodyaf_m + equip_m + eng_m + fuel_m + wing_m + tail_m
act_xcg = xmid_stn ; act_zcg = zlh_mid
tm_xcg = xfb3_stn + 0.25*(xmid_stn-xfb3_stn) ; tm_zcg = 0.5*zlh_mid
equip_m = nc_m + bal_m + obc_m + ins_m + tm_m + tank_m
wing_m = baseline wing mass * w_fac
to_xcg = ( bodyaf_m *bodyaf_xcg + equip_m*equip_xcg + eng_m*eng_xcg + fuel_m * fuel_xcg + wing_m * wing_xcg + tail_m*tail_xcg) / TOGW
External Configuration Model
Aerodynamics Model
Aerodynamics ModelTangent Cone / Tangent Wedge Method( local surface inclination )
External Configuration Model
Vehicle geometry definition(x,y,z)
Tj
j
Overall CN , Cm , CA
Control surfacecharacteristics
Typical Aerodynamic Characteristics of HSTDV ; M =6.5
0.0 5.0 10.0 15.0 20.0 25.0
0.0
2.0
4.0
6.0
8.0
Body Alone
Complete Vehicle
CN
0.0 5.0 10.0 15.0 20.0 25.0
0.0
0.2
0.4
0.6
0.8
Cm_xcg
-8 -4 0 4 8ANGLE OF ATTACK (deg.)
0.00
0.20
0.40
0.60
0.80
AX
IAL
FO
RC
E C
OE
FF
ICIE
NT
BODY ALONE
BODY + W ING
BODY + W ING + TAIL
0.0 2.0 4.0 6.0 8.0 10.0
0.0
1.0
2.0
3.0
4.0
L/D
ANGLE OF ATTACK (deg.)
Calibration Factors (Scale factor)•Use CFD computations to generate calibration factors.•Valid within specified move limits
Fidelity of Analysis
CN Xcp/d CA m a(Kg/s)
Tangent
Cone
Method
2.028 3.911 0.431 8.1
CFD
(Euler)
1.657 3.507 0.342 5.59
Zeroth order scale factor 20% 15% 15% 30%
Higher order scale factors will be used in future studies
Basic Body, Wing & Tail Aero characteristicsPropulsive force & moment
Evaluate Static stability
Statically stable
AdjustBallast weight
Exit with tail sizeand updatedMass and C.Gtrim and trim
and trim drag
No
Yes
Trim Model
M N
AW
0.75T0.25T
Npnoz
N + Np = W Cos T = A + W Sin
Np = 0.25 T / tan noz
Mp = Np (to_xcg - x_noz) + 0.25T (to_zcg - z_noz) + 0.75T (to_zcg - z_noz)
Mtrim = Maero_cg + Mp_cg = 0
Trim Model
Thrust Model
Thrust Model
External Compression Model ma , Mintk
Thrust deliverable
Isp (M, H_cr)
Equivalence ratio = 1
f
delivsp
m
ThI
15/
fa mm
Performance - 2DOF trajectory simulation
Aerodynamics
Propulsion
Sizing
Range R
Performance Analysis
Multi-disciplinary Design Optimization for HSTDV – Problem Statement
Minimize f(XD): - (Range)/2000g1 MI / 4.0 – 1 < 0 scramjet considerations
g2 / 20.0 – 1 < 0 Aero, control and actuation
g3 L / 7.5 – 1 < 0
g4 H / 0.85 – 1 < 0 sizing
g5 W / 0.85 –1 < 0
g6 TOGW / 1325.0 – 1 < 0 system
g7 AF / Th deliv – 1 < 0. Aerodynamics & Propulsion
Optimization variables
XD: {1, 2, 3 , n_plan , wc ,
wfac_pl,tfac_pl,,Hcruise }
Side constraints3° 1 10° ; 1° 2 10° 1° 3 10° ; 3° n_pl 6° 0° wc 6° ; 0.8 wfac_pl 10.8 tfac_pl 1.1 ; 30 Hcr 35
0 4 8 12
0.0
0.2
0.4
0.6
0.8
1.0
0 4 8 12
0.0
0.2
0.4
0.6
0.8
1.0
0 4 8 12
0.0
0.2
0.4
0.6
0.8
1.0
0 4 8 12
0.0
0.2
0.4
0.6
0.8
1.0
1 2
3n_pl
Iteration number Iteration number
Results
0 4 8 12
0.0
0.2
0.4
0.6
0.8
1.0
0 4 8 12
0.0
0.2
0.4
0.6
0.8
1.0
0 4 8 12
0.0
0.2
0.4
0.6
0.8
1.0
0 4 8 12
0.0
0.2
0.4
0.6
0.8
1.0
w_c w_fac
t_fac H_cr
Iteration number Iteration number
0 4 8 12
0.0
0.2
0.4
0.6
0.8
1.0
0 4 8 12
-0.04
-0.03
-0.02
-0.01
0.00
Cruise Range g1 : MI / 4.0 – 1 < 0
0 4 8 12
-0.10
-0.08
-0.06
-0.04
-0.02
0.00
0 4 8 12
-0.06
-0.04
-0.02
0.00
g2 : / 20.0 – 1 < 0 g3 : L / 7.5 – 1 < 0
Iteration number Iteration number
Iteration number Iteration number
0 4 8 12
-0.08
-0.06
-0.04
-0.02
0.00
0 4 8 12
-0.20
-0.16
-0.12
-0.08
-0.04
0.00g4 : H / 0.85 – 1 < 0 g5 : W / 0.85 –1 < 0
0 4 8 12
-0.08
-0.06
-0.04
-0.02
0.00
0 4 8 12
-0.50
-0.40
-0.30
-0.20
-0.10
0.00
g6: TOGW / 1325.0 – 1 < 0 g7: AF / Th deliv – 1 < 0.
Iteration number Iteration number
Iteration number Iteration number
Baseline Optimum
Tail planform
Body Outline
Comparison of Initial Configuration Outline with Optimum configuration
XD Initial
Design
Setting
Optimum
Design
Setting
1 7.55 5.82
2 3.88 3.64
3 2.89 4.14
n_plan 4.50 4.00
wc 4.80 6.00
wfac_pl 0.80 0.80
tfac_pl 1.10 1.06
Hcr 31.25 31.65
Optimum design with respect to initial design* 4% increase in dry weight* 15% increase in fuel volume* 1.5% decrease in drag
• 17% increase in cruise range
Physical constraints on Mintk , and TOGW are active
R / 1 -66.02
R / 2 -89.09
R / 3 +93.75
R / n_plan +147.85
R / wc +23.75
R / wfac_pl +110.5
R / tfac_pl -13.97
R / Hcr +13.46
Sensitivity of objective function with respect to design variablesat initial design point
Optimum configuration has lower valuesfor 1 and 2 as compared to initial design.Decreasing these variables at the initialdesign point , results in a decrease in theobjective function ie, cruise range
However, the inter-play among the designvariables has resulted in a net improvement in objective function.
R / Xi = +109.69
Fidelity of Analysis
Physics Based Corrections•Improve the accuracy of the Engg. Methods like Tangent Cone through correlation factors generated using CFD •Globally valid
Equivalent Body for conical flow calculations
Actual Body
0 20 40 60 80 100 120 140 160 1800
0.02
0.04
0.06
Cp
CFDTCM
0 20 40 60 80 100 120 140 160 1800
0.05
0.1
Cp
0 20 40 60 80 100 120 140 160 180-0.2
0
0.2
Circumferential location (deg)
a = 2.5
a = 5.0
a = 7.5
Cone Body (semi-included angle 5° )
2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.50
0.005
0.01
0.015
0.02
0.025
M=3.5
M=5.0
M=6.5
Angle of attack (deg.)
Cp
Error = Cp = Cp (TCM) – Cp (CFD) at = 0°
Cone Body (semi-included angle 5° )
0 1 2 3 4 5 6 7 8 9 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Cp /
Sin
Global Correction Factor
Cp (corrected) = Cp(TCM) - Cp
Further course of Action
Focus on methods to include high fidelity analysis
Summary of methods adopted for Aerospace Vehicle Design
Various strategies have been used to address the issue of computational burden associated with high fidelity analysis
Parametric methods with RSM
Global Local Approximation
First Order Approximate Model Management
Variable Complexity Response Surface Method
Statistical Literature Design and Analysis of Computer Experiments
Design and Analysis of Computer Experiments
MotivationGiven function values Y at sampled points x , one simple way to create response surface is through linear regression i
ihhh
i xfxy In the above model, the errors are assumed independent. This assumption is justified for physical experiments.
Computer experiments are however, ‘deterministic’.
Lack of random error in computer experiments and any lack of fit is entirely due to collection of left out terms in x.
In DACE model, (i) is interpreted as (x(i)) ie., errors are correlated.
Ref: Sacks et.al. [10] Jones et.al. [11]
1yRrx 1-y ji x xxx ,dCorrR ji exp, phj
hi
h xxd
h , k
1h
ji x x
Further course of Action
DACE modeling for ma , CN, Cm and CA
Use ‘data fusion’ ( low fidelity + high fidelity) ; validation
Optimization Strategies
Robustness of design through error propagation
Design and Analysis of Computer Experiments
The correlation is high if two points x (i) and x (j) are close and low when the points are far apart.
phjh
ih xxd
h ,
k
1h
ji x x
2,1,0 hh p
ji x xxx ,dCorrR ji exp,
(Jones et.al.)
Design and Analysis of Computer Experiments
ii xx y
DACE Model
2 k ,........1 kpp ,........1 are parameters estimated by maximizing
the likelihood of the sample y = ( y(1),……, y(n) )'
(Jones et.al.)
2
1-
2
1y R1y
Rexp
2
1
2
12/22/ nn
local effect
global effect
Design and Analysis of Computer Experiments
iihh
hi xfxy
1yRrx 1-y
RSM model using regression
RSM model using DACE modeling
ri(x*) = Corr[ (x*), (x(i))] , i=1,….n
Design and Analysis of Computer Experiments
Branin test function Contours DACE response surface Quadratic surface fit
Illustration (Jones et.al.)
Design and Analysis of Computer Experiments
Global Optimization for a 1-D function using DACE model(Jones et.al.)Expected Improvement Criteria for selecting additional sample points
02
46
8
-50
0
50-3
-2
-1
0
1
Cm
DACE fit for Pitching Moment DataPredictions are at the sampled points itself
= -45° , -35° , -25° , -15° , -5° , 0° , 5° , 15°, 25° 35° , 45° = 0° , 2° , 4°, 6°,8°
-50
0
50
0
2
4
6
85.4
5.6
5.8
6
6.2
x 10-15
MSE
Mean Squared Error
0 1 2 3 4 5 6 7 8
-40
-30
-20
-10
0
10
20
30
40
0 1 2 3 4 5 6 7 8
-40
-30
-20
-10
0
10
20
30
40
(deg) (deg)
Iso-contour of actual function Iso-contours of fit surface
02
46
8
-40
-20
0
20
40-3
-2
-1
0
1
Cm
DACE fit for Pitching Moment DataPredictions are at untried points
-40-20
020
40
0
2
4
6
80
0.02
0.04
0.06
0.08
MSE
Mean Squared Error
0 1 2 3 4 5 6 7-40
-30
-20
-10
0
10
20
30
40
-2.4276
-2.4
276
-2.1241
-2.1
241
-2.1
241
-1.82
07
-1.8
207
-1.8
207
-1.51
72
-1.5
172
-1.5
172
-1.2
138
-1.2
138
-1.2
138
-0.9
103
3-0
.91
033
-0.6
068
9-0
.60
689
-0.3
034
4
-0.30344
0 1 2 3 4 5 6 7-40
-30
-20
-10
0
10
20
30
40
-2.54
26
-2.22
1
-2.22
1
-2.221
-1.89
95
-1.89
95
-1.8
995
-1.57
79-1
.5779
-1.5
779
-1.2
563
-1.2563
-1.2563
-1.2563
-0.9
347
3-0
.93
473
-0.9
347
3
-0.6
131
6-0
.61
316
-0.2
915
8-0
.29
158
(deg) (deg)
Iso-contour of actual function Iso-contours of fit surface
McQuade Ph.D thesis Univ. of Washington, 1991 Aerodynamic optimization of a 2D scramjet vehicle using CFD (Euler). Fore-body and Nozzle were separately optimized to maximize thrust.
• Engg. Models used : Oblique Shock theory, 1D Heat Addition, MOC correction factors based on 2D CFD (Euler) analysis (GLA)
Review of MDO for Aerospace Vehicles
Detailed Analysis
Approximate Problem formulation
Complete Optimization ( 1 iteration)
Convergence?
stop
Detailed Analysis
General Application of Global-Local Approximation
xf
xfx
lo
hi)(
cT
ccc xxxxx
lo
lo
hi
hicc f
f
f
fxx
No
Yes
xf
xfx
lo
hi)(
Objective : maximize the net thrustSubject to constraints on geometric parameters
CFD , 1D isentropic flow, MOC Taylor Series, GLA using 1D, GLA using MOC
Afterbody OptimizationReview of MDO for Aerospace Vehicles
Method (deg.) curve
(deg.)
FnetCFD
calls
Relative
Cost/step
Init Design
18.000 0.0050 18.05 - -
CFD 20.541 0.0032 19.71 22 1.0
1-D 26.000 0.0082 18.42 - -
MOC 26.000 0.0082 18.42 - -
Taylor 20.362 0.0031 19.71 7 0.0098
1D GLA 20.850 0.0035 19.71 7 0.0083
MOC GLA
20.563 0.0033 19.70 7 0.0109
Results
Afterbody OptimizationReview of MDO for Aerospace Vehicles
Fore-body Optimization
Objective : maximize the net thrustSubject to constraints on geometric parameters
CFD , Oblique shock theory Taylor Series, GLA based on Oblique shock
Review of MDO for Aerospace Vehicles
MDO of Air Breathing Hypersonic Vehicle
Ref: Bowcutt J.of Propulsion and Power , Nov-Dec,2001
Optimization of Vehicle Configuration for performance (range)across a specified Mach No. vs Altitude Trajectory
Optimization variables : { nose angle, engine axial location, engine cant, cowl length and chine length }
Review of MDO for Aerospace Vehicles
•Sizing•Aerodynamics•Stability & Control•Propulsion•Trajectory
Key changes in the Optimized vehicle configuration
•Engine location moved forward by 6% of vehicle length•Engine cant reduced by 2 deg•Engine cowl length reduced by 5% of vehicle length•Chine length reduced by 80% of vehicle length
The optimized vehicle, flying the same M-q trajectory as thebaseline, achieved : 46% greater air-breathing range9% improvement in effective specific impulse13% reduction in trim drag over the baseline configuration
Review of MDO for Aerospace Vehicles
Aerodynamic Lessons
Wind tunnel testing and CFD analysis was performed on theOptimized vehicle
•HABP like Engg. Codes overpredicted lower surface pressures inthe aft region of the vehicle.
•Vehicle range reduced by 6% based on W/T Aerodynamics.
•Vehicle instability levels in terms of negative static margin increasedresulting in reduction in max. flight dynamic pressure at which the vehicle could operate.
Review of MDO for Aerospace Vehicles
Hall mark of MDO
Range sensitivities to the five vehicle design parameters
chine
cowl
cant
eng
nose
lR
lR
R
xR
R
/
/
/
/
/
+ 64 nm/deg
+ 47 nm/deg
– 92 nm/deg
+ 113 nm/deg
+ 25 nm/deg
Parameter Derivative
A variation that is detrimental by itself can be beneficial when working in concert with many coupled variations.
Review of MDO for Aerospace Vehicles
Review of MDO for Aerospace Vehicles
John Robert Olds , Ph.D. thesis NCSU, 1993 Advanced Space Transportation Vehicle optimized for minimum weight. Taguchi methods was used to select initial experimental arrays. Parametric methods were used to determine the settings for design variables which minimized weight. The effect ‘noise variables’ on the objective function was included to ensure a robust design . Central Composite Design was used for the final design variables . Quadratic Response surface was created using RSM Non-linear optimizer was used to optimize the quadratic surface
Remarks Parametric methods are useful only for very early design stages where the
number of design variable are very few. Initial problem size 8 design variables
Final problem size : 3 design variables Inclusion of design constraints in the frame work is not easy.
Review of MDO for Aerospace Vehicles
Giunta , Ph.D thesis VPI & SU , 1997 HSCT configuration optimized for TOGW. Variable Complexity Response Surface Modeling. Low fidelity methods used to screen the original design space. Response Surfaces (polynomial based) using medium fidelity analysis created
for the reduced design space. RSM’s were used for function evaluations in the optimizer. Preliminary investigation on the use of Design of Computer Experiments
(Kriging) for creating response surfaces was also carried out.Remarks RSM help to smoothen out the numerical noise in analysis methods. This
ensures that the gradient calculations (search directions ) are not affected. Constraints from aerodynamics, propulsion, stability, performance. Methodology demonstrated for problem sizes of 5 to 20 design variables. Curse of dimensionality limits the problem size. Further studies are needed to investigate the capabilities of DACE modeling.
Review of MDO for Aerospace Vehicles
Summary
Various strategies have been used to address the issue of computational burden associated with high fidelity analysis
Parametric methods with RSM
Global Local Approximation
First Order Approximate Model Management
Variable Complexity Response Surface Method
Review of MDO for Aerospace Vehicles
……Summary
For problems at complete vehicle level, RSM based on linear regression has
been widely used to overcome the challenge of computational cost. Once the response surface is available, in most of the cases, an optimizer
has been used to find the minimum of the surface
Issues It may be difficult to predict the form of the linear regression.
Restriction on the number of design variables is a serious limitation.
Sample points to construct the RSM are chosen based on DoE. These
may not necessarily be in the region of interest.
Multiple starts are required in the optimization, to verify if the solution
is not a local minima.
Conceptual problem is reported on the use of RSM based on linear
regression for computer simulation experiments.