/

NASA Technical Memorandum 107314

AIAA-96-4163

A General-Purpose Optimization Engine for

Multi-Disciplinary Design Applications

Surya N. Patnaik

Ohio Aerospace Institute

Cleveland, Ohio

Dale A. Hopkins and Laszlo Berke

Lewis Research Center

Cleveland, Ohio

Prepared for the

Sixth Multidisciplinary Analysis and Optimization Symposium

cosponsored by AIAA, NASA, and USAF

Bellevue, Washington, September 4-6, 1996

National Aeronautics and

Space Administration

GENERALmPURPOSE OPTIMIZATION ENGINE FOR

MULTIDISCIPLINARY DESIGN APPLICATIONS

Surya N. Patnaik,* Dale A. Hopkins, and Lazlo Berke

National Aeronautics and Space Administration

Lewis Research Center

Cleveland, Ohio 44135

Abstract

A general purpose optimization tool for

multidisciplinary applications, which in the literature

is known as COMETBOARDS, is being developed

at NASA Lewis Research Center. The modular

organization of COMETBOARDS includes several

analyzers and state-of-the-art optimization algorithms

along with their cascading strategy. The code

structure allows quick integration of new analyzers

and optimizers. The COMETBOARDS code reads

input information from a number of data files,

formulates a design as a set of multidisciplinary

nonlinear programming problems, and then solves the

resulting problems. COMETBOARDS can be used to

solve a large problem which can be defined through

multiple disciplines, each of which can be further

broken down into several subproblems. Alternatively,

a small portion of a large problem can be optimized

in an effort to improve an existing system. Some of

the other unique features of COMETBOARDS

include design variable formulation, constraint

formulation, subproblem coupling strategy, global

scaling technique, analysis approximation, use of

either sequential or parallel computational modes,

and so forth. The special features and unique

strengths of COMETBOARDS assist convergence

and reduce the amount of CPU time used to solve

the difficult optimization problems of aerospace

industries. COMETBOARDS has been successfully

used to solve a number of problems, including

structural design of space station components, design

of nozzle components of an air-breathing engine,

configuration design of subsonic and supersonic

aircraft, mixed flow turbofan engines, wave rotor

topped engines, and so forth. This paper introduces

the COMETBOARDS design tool and its versatility,

which is illustrated by citing examples from

structures, aircraft design, and air-breathing

propulsion engine design.

Introduction

A multidisciplinary optimization engine, which

in the literature is known as COMETBOARDS, is

being developed at NASA Lewis Research Center for

the design of structural components, subsonic and

supersonic aircraft configuration design, and airbreathing propulsion engine design. The

COMETBOARDS design tool has provision to

accommodate up to ten different disciplines; each of

these can have a maximum of five subproblems. The

design tool in other words can optimize a system

which can be defined in terms of fifty optimization

subproblems. Each subproblem can be defined with

its own design variables, constraints, and an

objective function. Computation at the subproblem

level can be carried out either in sequential or in

parallel computational modes. Interdisciplinary

coupling, an important strategy for successful

solution of the problem, is accomplished through

coupling at the design variable level and through

local and global constraint formulations. On the

other hand, by appropriate data specification,

COMETBOARDS can also be used to examine the

optimality of a small portion of a much larger design

problem.

The COMETBOARDS system first formulates the

design as a nonlinear mathematical programming

problem, reading data from specified input files, and

then solves the resulting problem. Problem

formulation can utilize a number of analysis tools

available in its 'Analyzers' module. Representative

analysis tools currently available in

COMETBOARDS include, RPK/NASTRAN 1 for

structural analysis, NASA Engine Performance

Program (NEPP) 2 for air-breathing engine

performance analysis, and Flight Optimization

Systems (FLOPS) 3 for aircraft performance analysis.

The code allows soft-coupling and quick integration

of new analyzers. COMETBOARDS solution

*Ohio Aerospace Institute, Cleveland, Ohio

"This paper is declared a work of the U.S. Government

and is not subject to copyright protection in the United States."

1

American Institute of Aeronautics and Astronautics
techniquexploitsseveralof its uniquestrengths,

whichare availablein its 'Optimizers'module.

COMETBOARDSis writtenin Fortran77language

andtestedin CrayandConvexcomputersandinSGI

and Sun Unix workstations. Successful

COMETBOARDSsolutionsfor a numberof diverse

industrial problems,from different disciplines

corroboratetherobustnessandversatilityof the

designtool.With augmentationandimprovement,

the researchlevel optimization capability of

COMETBOARDShasthepotentialof becominga

robustdesigntoolfortheaerospaceindustry.

Thispaperincludesanoverviewof thedesign

tool COMETBOARDS.Threeapplications(one

each,from structures,aircraft design,and airbreathingpropulsionengineconcepts)aregivento

illustrate the versatility and robustnessof

COMETBOARDS.

COMETBOARD$ Design Tool

The modular organization of COMETBOARDS is

depicted in Fig. 1. The key features of

COMETBOARDS include its multidisciplinary

nature (with a separate objective, constraints, and

variables for each discipline, which can be further

broken down into several subproblems), substructure

optimization (with coupling strategy available in

sequential as well as in parallel computational

modes), state-of-the-art optimization algorithms and

their cascading 4 strategies, and analysis

approximations by means of linear regression

analysis and neural network. The COMETBOARDS

modular organization is like a test bed, and a user

has considerable flexibility such as (1) solving a

problem by using available analyzers and optimizers

in the code, (2) adding analyzers through softcoupling into COMETBOARDS and then solving

problems, (3) checking out the performance of new

analyzers, (4) checking out the performance of a

new optimizer utilizing the 40 or so problems

available in the COMETBOARDS solved-examplestest-bed; just to mention a few. Space does not

permit the description of the other features and

unique strengths of the design tool

COMETBOARDS, some aspects of which can be

found in Refs. [5, 6, and 7]. Only the cascade

strategy required to optimize aircraft and engine

problems is described next.

Cascade Optimization Strategy

COMETBOARDS provides for the solution of

difficult optimization problems by means of a

cascade strategy. The basic cascade concept is an

attempt to solve a complex problem by using more

than one optimizer, when individual optimizers face

difficulties. The cascade concept and its flow

diagram are depicted in Fig. 2. A COMETBOARDS

user has considerable flexibility in developing a

cascade strategy, by selecting a number of

optimizers (currently about one dozen different

nonlinear programming algorithms are available),

their convergence criteria, analysis approximations,

and the amount of random perturbations between

optimizers. Consider for the purpose of illustration,

the cascade concept, first optimizer, followed by

several other optimizers, shown in Fig. 2(a).

Individual convergence criteria can be specified for

each optimizer; for example, a coarse stop criteria

may be sufficient for the first optimizer, while a fine

stop criteria can be stipulated for the last optimizer.

Likewise approximate analysis may suffice for the

first optimizer, reserving an accurate analyzer for the

final optimizer. The amount of pseudo random

perturbations for design variables between the

optimizers may be specified at the discretion of the

user.

Substructure Optimization Strategy

Design optimization of large structural systems

can be attempted by using the substructuring strategy

available in COMETBOARDS. In this strategy the

original structure is divided into several smaller

substructures. The design of the entire structure can

be accomplished by repeated optimizations of the

substructures. Substructure optimization can use

either sequential or parallel computational platforms.

The substructure optimization strategy available

in COMETBOARDS is illustrated by considering the

example of the support system of the long spacer

structure of the International Space Station as shown

in Fig. 3. The support system, which for analysis is

idealized by shell elements, is divided into four

segments and four substructures as depicted in Fig. 3.

Substructure (1) includes all shell elements within

segments 3 and 4, substructure (2) includes all shell

elements within segments 4 and 1, substructure

(3) includes all shell elements within segments 1

and 2, and substructure (4) includes all shell

elements within segments 2 and 3. The substructuring

process incorporates adequate design variable

coupling, which is essential for the success of the

strategy. Notice, for example, the coupling between

the first and fourth substructures through the

elements in segment 4, which are common to both.

The thickness of all shell elements within a

segment were grouped to obtain a single active

design variable. Thus, each substructure has two

active design variables; namely, substructure

(1) contains the third and fourth design variables,

substructure (2) contains the fourth and the first

design variables, and so forth.

The behavior constraints were separated into

local and global sets. Separation of behavior

2

American Institute of Aeronautics and Astronautics
constraintsintolocalandglobalsetsis essential for

convergenceof thesubstructurestrategy8. Thefirst

setincludedthelocalstressconstraintsassociated

with each substructure;thesewere reducedby

following the constraintsformulationscheme

availablein thedesigntoolCOMETBOARDS. The

othersetincludedglobaldisplacement constraints

whichwereconsideredcommonforallsubstructures.

Thefinaloptimumresultsforthesupportsystem

wereobtainedafterthreecompletedesigncycles,

which totaled solutions of 12 optimization

subproblems. Thesubstructuredesignsequenceis

depictedinFig.4. Notice,forexample,thereduction

in theweightof substructure(1)in Fig.4, between

cycles! and2, andbetweencycles2 and3.In first

two cyclesthereis a considerablerductionin the

weight,whileconvergenceoccurreduringthenext

twocycles.Othersubproblemcharacteristicsfollow

thepatternwithsomedeviations.

Optimumresultsfor theproblemareshownin

TableI. Theoptimumweightforthesupportsystem

obtainedby usingthe substructuretechniqueis

34.71lb; therearethreeactiveconstraints.The

optimumresult is in goodagreementwith the

optimumsolutionof 34.68lb whichwasobtained

whentheentirestructurewasdesignedasa single

unit.Likewisethevaluesof thedesignvariablesat

the optimum,shownin TableI, agreedwhen

substructuringand single-stepoptimizationwere

used. Bothtechniquesproducedthe samethree

activeconstraints.

Design Optimization of Supersonic Aircraft Concept

Design optimization of both subsonic and

supersonic aircraft concepts has been attempted

successfully through a soft-coupling of the Flight

Optimi-zation Systems (FLOPS) as the analyzer and

COMETBOARDS as the optimizer. The FLOPS

analyzer through input data specifications can be

used to analyze both subsonic and supersonic

aircraft. The FLOPS analyzer uses several different

disciplines to predict aircraft performance. The

different disciplines available in a modular form

include weight, aerodynamics, engine cycle

analysis, propulsion data interpolation, mission

performance, takeoff and landing, noise footprint,

and cost. The combined design tool with FLOPS as

the analyzer and COMETBOARDS as the optimizer

has been successfully used to solve a number of

subsonic and supersonic aircraft problems. The

example of a supersonic aircraft is given here to

illustrate COMETBOARDS capability.

The takeoff gross weight is considered as the

merit function of the aircraft problem. Six

independent design variables are considered; they

are (1) engine thrust (in lb), (2) wing size (in sq ft),

(3) engine turbine inlet temperature (in °R),

(4) engine overall pressure ratio, (5) bypass ratio,

and (6) fan pressure ratio. The six critical behavior

constraints included are (1) landing approach

velocity, (2) takeoff field length, (3) missed

approach, (4) second segment climb, (5) jet

velocity, and (6) compressor discharge temperature.

The resulting multidisciplinary optimization

problem has distorted design space since both

design variables and constraints varied over a very

wide range. For example an engine thrust design

variable (which is measured in kip) is immensely

different from the bypass ratio variable (which is a

small number). Likewise, landing velocity constraint

(in knots) and field length limitation (in thousands of

ft) differ both in magnitude and in units of measure.

The difficult nature of the design problem is further

compounded because of the statistical and empirical

equations, the smoothing techniques, and so forth,

employed in the FLOPS analyzer. In other words, the

FLOPS analyzer can be numerically unstable for

some combinations of design variables, especially

for a supersonic aircraft. The unique features of

COMETBOARDS, especially the scaling and the

cascade strategy, assisted the convergence of the

difficult problem.

To examine the robustness of the

COMETBOARDS-FLOPS combined design tool, six

different aircraft design test cases with different

starting points and variable bounds were devised at

NASA Langley Research Center. Only five cases

will be given in this paper. All the test problems

have been solved by using NASA Lewis'

COMETBOARDS. Optimum solutions for all five

cases are given in Table II. This table reveals the

following:

(1) Both COMETBOARDS and another

optimizer successfully solved all five test cases.

(2) Optimum solutions obtained by both

COMETBOARDS and other optimizers were

comparable. The average COMETBOARDS optimum

solution at 666,550.0 lb was about 1 percent lighter

than the other optimizers results at 673,273.0 lb.

(3) Optimum values for the design variables

obtained using COMETBOARDS and other

optimizers codes compared well with minor

differences. Likewise constraint values agreed well

between the two design tools, except for the second

segment climb thrust (SSFOR). When

COMETBOARDS was used, SSFOR was at 21.72 Ib,

while the other optimizer resulted in a value of

607 lb.

The optimum solution obtained has been verified

graphically in Fig. 5. The optimum lies at the

intersection of three active constraints, namely,

compressor discharge temperature, jet velocity, and

second segment climb thrust. With respect to design

3

American Institute of Aeronautics and Astronautics
variables, bypass ratio, and fan pressure ratio, the

unconstrained minimum condition is achieved

without any active constraint.

Desi_ma of a Mixed flow Turbofan Engine for HighSpeed Civil Transport System

Design optimization of air-breathing engines for

high-speed civil transport applications has been

developed through a soft-coupling of the NASA

Engine Performance Program (NEPP) with the

optimization tool COMETBOARDS. The combined

COMETBOARDS-NEPP computer simulation is an

attempt to optimize the design of multimission

variable cycle engines with specified hardware

components and configurations with designated

interconnections. The solution to the nonlinear

engine design problem when attempted through any

one of the dozen robust optimizers available in

COMETBOARDS could provide a feasible optimum

solution for only a portion of the aircraft flight regime

because of a large number of mission points (defined

through altitudes, Mach numbers, and power setting

combinations) with diverse constraints (specified on

pressure ratios, temperatures, speed corrections,

mass flow rates, etc.) and over all ill-conditioned

design space. Utilization of the unique strengths of

COMETBOARDS (such as the cascade strategy,

global scaling technique, design variables, and

constraint formulations) successfully solved a

number of difficult engine design optimization

problems.

The COMETBOARDS solution for a 122-

mission-point turbofan engine is given here as the

last numerical example. The 122 mission points for

the mixed flow turbofan (MFTF) engine is depicted

in Fig. 6. The design optimization of the MFTF

engine required the solution of a sequence of 122

optimization subproblems, one for each mission

point. For each mission point, the thrust of the engine

was considered as the merit function. The following

important active design variables were considered:

pressure balance in the mixer, R-values for fans and

compressors, fan speed, and so forth. The important

constraints considered were the following: the

maximum speed of the compressor, acceptable surge

margin for the compressor, the discharge

temperatures, the mixer entrance Mach number, and

so forth. The most reliable individual optimization

algorithm available in COMETBOARDS could

provide feasible results for only a portion of the 122-

mission-point flight envelope because of the

sequence of a large number of optimization

subproblems, diverse constraint types, and overall illconditioning of the design space. A four optimizer

cascade strategy could successfully solve the engine

design problem for the entire 122-mission-point flight

envelope. Furthermore, the cascade strategy

converged to the same global solution when begun

from different design points. The cascade solution

was normalized with respect to the NEPP results,

which were obtained by using an individual

optimizer and manual interventions. The normalized

solution, which is shown in Fig. 7, was found to be

superior for most of the 122 mission points, except

for a few cases for which both (COMETBOARDS

and NEPP) optimum results agreed. For flights

around mission point 70, COMETBOARDS results

for optimum thrust were about 10 percent higher than

the NEPP solution. In brief, the cascade optimization

strategy successfully solved the 122- mission-point

mixed-flow turbofan engine design problem.

Conclusions

COMETBOARDS, with its unique strengths

and strategies, has been used successfully to solve

a number of problems from structures, aircraft, and

air-breathing propulsion engines. Successful

COMETBOARDS solutions for three difficult

examples (i.e., (1) design optimization of a support

system solved by using substructuring capability,

(2) supersonic aircraft configuration optimization,

and (3) mixed flow turbofan thrust optimization)

illustrate the versatility of the code. The cascade

strategy of COMETBOARDS was required to

generate solutions for the aircraft and engine

problems. COMETBOARDS, which is written in

Fortran 77 language with parallel computational

facility, is available in the Cray-YMP and Unix

workstations. With some enhancements and

modifications, the research level COMETBOARDS,

which has been found robust and reliable for

multidisciplinary design applications has the

potential of becoming a useful design tool for

aerospace industry.

References

1. RPK/NASTRAN, COSMIC, University of

Georgia, Athens, GA.

2. Kiann, J.N.; and Snyder, C.A.: NEPP

Programmers Manual. NASA TM-106575, 1994.

3. McCullers, L.A.: FLOPS: Aircraft Configuration

Optimization Including Optimized Flight Profiles.

NASA CP-2327, 1984.

4. Patnaik, S. N.; Coronets R. M.; and Hopkins, D.A.:

A Cascade Optimization Strategy for Solution of

Difficult Multidisciplinary Design Problems.

AIAA/ASME/ASCE/AHS/ASC 37th Structures,

Structural Dynamics, and Materials Conference,

April 15-17, 1996, Salt Lake City, UT.

4

American Institute of Aeronautics and Astronautics
5.Guptiil, J.D.; et al.: COMETBOARDSUser's

Manual,NASATM-4537,1996.

6.Patnaik,S.N.;et ai.: ComparativeEvaluationof

DifferentOptimizationAlgorithmsfor Structural

DesignApplications.Int. Jnl. Num. Meth.

OfEngr.,Vol.39,pp.1761-1774, 1996.

7.Patnaik,S.N.;Gendy,A.S.;andHopkinsD.A.:

DesignOptimizationof LargeStructural Systems

WithSubstructuringin a ParallelComputational

Environment. Computer Systems in Engineering.

Vol. 5, No.4-6, pp. 425--440, 1994.

8. Gendy, A..S.; et al.: Issues in Substructure

Optimization.WCSMO-1 ,Structural a n d

Multidisciplinary Optimization, pp. 857-862,

1995.

Table I.-Optimum Design Of Support System

Design cycle number

0 (initial)

1

(a) Weight

3 (optimum)

Substructurin_

Weight,

lb

No substructufing

54.35 54.35

34.04

2 34.74

34.71

34.68 (optimum)

Substructure

(b) Design

Design variables,

in.

variables

Optimum design

Initial Substructurin 8

I 0.2 0.1277

II 0.2 0.1298

In 0.2 0.1765

IV 0.2 0.0264

No substructuring

0.1277

0.1295

0.1766

0.0263

Table II.-Optimum Design for Five NASA Langley Research

Center Supersonic Aircraft Test Cases

Test cases Takeoff gross weight

(normalized)

COMETBOARDS Other optimizers

I 0.99997 1.01785

2 1.00004 1.00184

3 1.00005 1.02855

4 0.99996 1.00200

5 0.99997 1.00019

Average 1.0 (666,550.0 lb) 1.00019 (673273.0 ib)

5

American Institute of Aeronautics and Astronautics
Fig. 1 .--Organization of COMETBOARDS design tool.

Initial First

design optimizer

Initial

design

,,I Optimum ',,

I I I

First I Second I I Last

optimizer I optimizer I Ioptimizer

I I I

I I I

start

solution

Next optimizer

design tn sequence

start

Random

Design iterations

(a) (b)

Fig. 2.--Cascade strategy in COMETBOARDS. (a) Cascade concept. (b) Flow diagram.

Check

No

Yes
I

I

I

Fig. 3.-Support of long spacer structure of lnternational Space

Station"

0 25 50 75 100 125

Number of design iterations

Fig. 4.-Convergence characteristics of substructure optimization of support system.

S1 substructure i; Cycle i Complete

optimization cycle i for substructures
0700t//11 

0.600

.o_

o.6oo

m 0.430

0.40

0.300 ._ \ ._ \ \._ \ .\ \ ._ _ •

3.00 3.25 3.50

3

(a)

Fan pressure ratio

70.0_

60.0_

41,500 _ _;'x,_\ _ _ _/

40.0_ _ _ i i i i i7.00 8.25 9.50 10.75

8,150

Wing area

(c)

12.00

._o 0.0250

0.0230

,=

21.5

0.0210

O.

0.0190 °

0.0170 !_\_,_- _"

2.800 2.900

(b)

3.000 3.1 O0 3.200

2950 °R

Turbine inlet temperature

CDT Compressor discharge temperature

TOFL Takeoff field length

V App Approach velocity

V Jet Jet velocity

X Optimum solution

Fig. 5.mGraphical verification of optimum design of supersonic aircraft. (a) Fan pressure ratio.

(b) Turbine inlet temperature. (c) Wing area.
5.0xl 04

4.0

3.0

e"

"O

,_ 2.0

m

-- • •

• •

1.0-- • •

i•

0.00 0.25 0.50

4_

I I I I I I I

0.75 1.00 1.25 1.50 1.75 2.00 2.25

Mach number

Fig. 6.--Flight envelope for High-Speed Civil Transport mixed flow

turbofan engine.

2

5

E

Q.

0

"0

._

0

Z

1.10

1.05

1.00

0.95

Solution

COM ETBOARDS

NEPP optimizer

I I I I

25 50 75 100

Number of mission points

Fig. 7.--122 mission points for mixed flow turbofan

(MFTF) engine.

I

125

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1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED

August 1996 Technical Memorandum

4. TITLE AND SUBTITLE 5. FUNDING NUMBERS

A General-Purpose Optimization Engine for Multi-Disciplinary

Design Applications

6. AUTHOR(S)

Surya N. Patnaik, Dale A. Hopkins, Laszlo Berke

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Lewis Research Center

Cleveland, Ohio 44135-3191

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, D.C. 20546-0001

WU-505--63-5B

8. PERFORMING ORGANIZATION

REPORT NUMBER

E- 10409

10. SPONSORING/MONITORING

AGENCY REPORT NUMBER

NASA TM-107314

AIAA-96-4163

11. SUPPLEMENTARY NOTES

Prepared for the Sixth Multidisciplinary Analysis and Optimization Symposium cosponsored by AIAA, NASA, and

USAF, Bellevue, Washington, September 4-6, 1996. Surya N. Patnaik, Ohio Aerospace Institute, 22800 Cedar Point

Road, Cleveland, Ohio 44142; Dale A. Hopkins and Laszlo Berke, NASA Lewis Research Center. Responsible person,

Dale A. Hopkins, organization code 5210, (216) 433-3260.

12a. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified - Unlimited

Subject Category 39

This publication is available from the NASA Center for AeroSpace Information, (301) 621--0390.

12b. DISTRIBUTION CODE

13. ABSTRACT (Maximum 200 words)

A general purpose optimization tool for multidisciplinary applications, which in the literature is known as COMETBOARDS,

is being developed at NASA Lewis Research Center. The modular organization of COMETBOARDS includes several

analyzers and state-of-the-art optimization algorithms along with their cascading strategy. The code structure allows quick

integration of new analyzers and optimizers. The COMETBOARDS code reads input information from a number of data files,

formulates a design as a set of multidisciplinary nonlinear programming problems, and then solves the resulting problems.

COMETBOARDS can be used to solve a large problem which can be defined through multiple disciplines, each of which can

be further broken down into several subproblems. Alternatively, a small portion of a large problem can be optimized in an

effort to improve an existing system. Some of the other unique features of COMETBOARDS include design variable formulation, constraint formulation, subproblem coupling strategy, global scaling technique, analysis approximation, use of either

sequential or parallel computational modes, and so forth. The special features and unique strengths of COMETBOARDS

assist convergence and reduce the amount of CPU time used to solve the difficult optimization problems of aerospace

industries. COMETBOARDS has been successfully used to solve a number of problems, including structural design of space

station components, design of nozzle components of an air-breathing engine, configuration design of subsonic and supersonic

aircraft, mixed flow turbofan engines, wave rotor topped engines, and so forth. This paper introduces the COMETBOARDS

design tool and its versatility, which is illustrated by citing examples from structures, aircraft design, and air-breathing

propulsion engine design.

14. SUBJECT TERMS

Multi-disciplinary optimization; Nonlinear programming algorithms and cascade substructure; Parallel computation

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