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.