aiaa 99-3798 multidisciplinary design optimization ... · aiaa 99-3798 multidisciplinary design...

AIAA 99-3798

Multidisciplinary Design OptimizationTechniques: Implications and Opportunities forFluid Dynamics Research

Thomas A. Zang and Lawrence L. GreenNASA Langley Research CenterHampton, VA 23681

30th AIAA Fluid Dynamics ConferenceJune 28 – July 1, 1999 / Norfolk, VA

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https://ntrs.nasa.gov/search.jsp?R=20040087025 2020-06-07T13:00:13+00:00Z

AIAA-99-3798

1American Institute of Aeronautics and Astronautics

MULTIDISCIPLINARY DESIGN OPTIMIZATION TECHNIQUES:IMPLICATIONS AND OPPORTUNITIES FOR FLUID DYNAMICS

RESEARCH

Thomas A. Zang* and Lawrence L. Green†

NASA Langley Research Center, Hampton VA 23681

Abstract

A challenge for the fluid dynamics community is toadapt to and exploit the trend towards greatermultidisciplinary focus in research and technology.The past decade has witnessed substantial growth inthe research field of Multidisciplinary DesignOptimization (MDO). MDO is a methodology for thedesign of complex engineering systems andsubsystems that coherently exploits the synergism ofmutually interacting phenomena. As evidenced by thepapers, which appear in the biannualAIAA/USAF/NASA/ISSMO Symposia onMultidisciplinary Analysis and Optimization, theMDO technical community focuses on vehicle andsystem design issues. This paper provides anoverview of the MDO technology field from a fluiddynamics perspective, giving emphasis tosuggestions of specific applications of recent MDOtechnologies that can enhance fluid dynamics researchitself across the spectrum, from basic flow physics tofull configuration aerodynamics.

Introduction

The phrase "multidisciplinary design optimization"does not admit a universally accepted interpretation.For some, it encompasses all of the aerospace designprocess used in industry and perforce has been in use

∗ Head, Multidisciplinary Optimization Branch,Associate Fellow, AIAA† Research Engineer, Multidisciplinary OptimizationBranch, Senior Member, AIAA_______________Copyright © 1999 by the American Institute ofAeronautics and Astronautics, Inc. No copyright isasserted in the United States under Title 17, U.S.Code. The U.S. Government has a royalty-freelicense to exercise all rights under the copyrightclaimed herein for Governmental Purposes. All otherrights are reserved by the copyright owner.

since the advent of aviation. For others, it refers to aparticular set of computational technologies of fairlyrecent provenance that enable enhanced designprocesses in which (1) there is more knowledge aboutthe design available earlier in the design cycle; and (2)there is more freedom to alter the design later in thedesign cycle. Consistent with the latter perspective1,we adopt here the definition: Multidisciplinary DesignOptimization (MDO) is a methodology for design andanalysis of complex engineering systems andsubsystems which coherently exploits the synergismof mutually interacting phenomena. The stress is on asystematic methodology, rather than heuristic or adhoc approaches, and on exploiting interdisciplinaryinteractions to achieve a better overall system thancan be achieved by ignoring the interactions. MDOmethods treat interdisciplinary interactions asopportunities rather than as nuisances or liabilities.

Probably the earliest MDO developmentsrecognizable from our current perspective occurred inthe 1970s. By the early 1980s there was a sufficientlylarge community of researchers to warrant the start ofa continuing biannual symposium onMultidisciplinary Analysis and Optimization, and by1989 the AIAA had established its TechnicalCommittee on MDO. In 1992 it assumedcosponsorship of this biannual Symposium. Themost recent Symposium2 consisted of several hundredtechnical papers. A healthy fraction of these papersinvolved aerodynamics. But it was not always thus.The roots of MDO lie within the structuresdiscipline, and until about 1990 the aerodynamicsdiscipline was usually a passive player inMDO—serving merely as a source of loads forstructural optimization processes. (Of course,optimization had been applied to airfoil design manyyears ago.3)

The crucial development that furnished aerodynamicswith its bona-fide MDO credentials was aerodynamicssensitivity analysis. (A sensitivity derivative is thederivative of an output quantity with respect to an


input quantity; a simple example for a computationalfluid dynamics (CFD) code is the derivative of the liftwith respect to the thickness of a particular airfoilsection.) At a 1986 conference Sobieski4 challengedthe aerodynamics community to develop a generalsensitivity analysis capability, and the first papers onexact aerodynamic sensitivity analysis appeared a fewyears afterwards.5–8 Of course, there had been earlierrelated developments. Sensitivity analysis of a limitedsort was implicit in the aerodynamic optimizationmethods utilizing adjoint equations9,10 that originatedin the late 1970s. Brute-force finite differences hadcertainly been employed for a number of years, butthe development of efficient methods for solving theexact sensitivity equations was essential for accuracyand robustness. Aerodynamic optimization with exactaerodynamic sensitivities has now become almostroutine.11 We are even beginning to seedemonstrations of combined aerodynamic-structuraloptimization of aircraft using nonlinear CFD (Euleror Navier-Stokes) and full finite-element models ofthe structure,12 as well as the first steps towardsearlier integration of the controls discipline intodesign by using aerodynamic sensitivity analysis forestimating stability and control derivatives.13

Most MDO applications to date have been at the levelof vehicle design. A significant portion of this forumis more interested in the performance of vehiclecomponents and in basic flow physics issues. Ouraim in this paper is to describe the MDO technologyfield and to propose some opportunities for exploitingthese technologies in fluid dynamics research andapplications at the vehicle, the component, and theflow physics levels. For the most part, we willconfine our references to that portion of the literaturethat has a strong fluid dynamics connection. We willalso usually refer to recent articles, in archival formwhenever feasible, from which lines of research canbe traced back; our choice of references does notimply priority. Those interested in a recent broadsurvey of MDO, complete with an extensive referencelist, should consult Sobieski & Haftka.14 A recentspecial issue of Journal of Aircraft15 was devoted toMDO; it contains 28 papers covering bothmethodology and applications, including a half-dozenpapers focusing on aerodynamics. Several individualpapers from this volume will be cited below asgeneral references for certain areas of MDO. Aninformative set of papers on applications of MDO inindustry was presented at the 7thAIAA/USAF/NASA/ISSMO Symposium onMultidisciplinary Analysis and Optimization.16–26

In this paper we shall first give an overview of twospecific MDO applications. These two examples willserve as a background for the subsequent discussion ofthe contents of the "MDO discipline." Then we shallcomment on some opportunities and implications forfluid dynamics research.

MDO Examples

Let us start then with two examples of NASA-industry MDO technology demonstrations. We willuse these both as settings for discussion of the MDOdiscipline and to point out some practical issues.

Aerospike Nozzle

In 1995 the MDO Branch at NASA Langley andRocketdyne, Inc. started a joint development of MDOmethods, focused on the design of the nozzle of anaerospike engine,27 an engine concept used for the X-33. Fig. 1 illustrates the two-dimensional physicalmodel of the nozzle employed in this study, and Fig.2 illustrates the design variables for the nozzlestructure and for the nozzle ramp geometry. The flowon the nozzle ramp was computed by a marchingEuler method, and the structural response (stress,deformation, buckling) by a commercial finite-element code; the base flow region was represented bya simple model, and a lookup table was used toestimate the gross lift-off weight (GLOW) of thelaunch vehicle from the engine specific impulse (Isp)and thrust-to-weight ratio (T/W). The nozzle structurewas parameterized by 14 structural design variablesand the nozzle ramp by 5 geometry variables. Theinitial geometry design variables were selected fromprevious Rocketdyne design studies on aerospikenozzles that used conventional design methods andwere expected to be close to an optimizedaerodynamic shape.

Fig. 1 Aerospike nozzle physical model.

In this idealized problem the "single disciplinedesign" is produced by first fixing the structural shapeand optimizing the nozzle contour for maximumthrust, and then fixing the nozzle contour and


optimizing the structural sizing variables forminimum weight. The full "multidisciplinary design"permits both the aerodynamic and structural designvariables to be optimized simultaneously. Thecomparison between results from the two approaches,illustrated in Fig. 3, is a clear example ofmultidisciplinary synergy achieved by the MDOmethod. It achieves a better overall system (lowerGLOW) by sacrificing some thrust for lower engineweight. Even greater gains are possible from theMDO method when the nozzle length is permitted tovary. We emphasize that this was a technologydevelopment study and did not impact the actual X-33engine, as that design was fixed by the time thisstudy was complete.

Fig . 2 Aerospike nozzle designparameters.

F ig . 3 Impact of MDO on aerospikenozzle.

The aerospike nozzle application was implementedseparately at both Rocketdyne and NASA Langley. Atboth sites it took two to three engineers severalmonths to assemble the multidisciplinary analysis,

wrap a simple optimizer on top of it, and ensure thatboth sites were obtaining identical results from theanalysis as well as the optimization. This applicationhas a small enough scale that it could be implementedin an academic environment by a small team or evenby a single individual with the right skills.

High-Speed Civil Transport

From the inception of the High PerformanceComputing and Communications Program in late1991, NASA Langley's application focus underNASA's Computational Aerosciences element hasbeen on demonstrating MDO for a high-speed civiltransport (HSCT). A series of increasingly complexapplications has been developed. The complexity isassociated both with increasing fidelity of the analysiscodes, e.g., from vortex-lattice (WINGDES) tomarching Euler (ISAAC) to global Euler (CFL3D)codes, and with increasing complexity of the designproblem. Table 1 lists the salient characteristics ofthe two applications that have been completed—HSCT 228 and HSCT 333—along with the onecurrently under development—HSCT 4.29,30

F i g . 4 Some geometric design variablesfor HSCT 4.

Fig. 4 illustrates some of the planform (geometry)and wing section design variables of the HSCT 4application. As Table 1 indicates, there are alsoseveral hundred structural sizing design variables. Theproblem definition of this application drew upon priorHSCT applications at NASA Langley dating back tothe HiSAIR (High-Speed Airframe IntegrationResearch) Pathfinder problem.31 It was heavilyinfluenced by discussions over a period of severalyears with industry engineers working on HSCTdesigns under the auspices of the NASA High SpeedResearch Program, as well as by long-standinginteractions with MDO researchers at GeorgiaInstitute of Technology, Stanford University andVirginia Polytechnic Institute and State University.

The HSCT 4 problem is far more complex than theaerospike nozzle problem. Even with the benefit of


more than 6 years of experience with several related,but smaller scale, HSCT MDO applications, theNASA Langley team of roughly ten members (civil

servants and contractors) took over 2 years to define,assemble, and debug just the HSCT 4 analysisprocess.

Table 1. NASA Langley HPCCP Applications 1991–1999

Application HSCT 2 (1994) HSCT 3 (1997) HSCT 4 (1999)Design Variables 5 7 271Constraints 6 6 31868Major Codes

AerodynamicsStructuresPerformancePropulsion

WINGDESELAPSRange equationEngine deck

ISAACCOMETRange equationEngine deck

CFL3D, USSAEROGENESISFLOPSENG10

Analysis Processes(without looping)

10 20 70

Analysis ControlMajor Loops

Load conditionsMission conditionsProcess (with loops)Total time

Weight Conv.,Trim21

(10) (minutes)

Weight Conv.,Aeroelastic, Trim21

(100) (hours)

Aeroelastic, Trim

710

(1000) (1 day)

Optimization Cycle(ndv+1) #analysis processes

Total time/cycle (100) (10 minutes)

(1000) (3 hours)

(100,000) (3 days)

Design VariablesGeometryStructures

Total

325

347

27244271

ConstraintsGeometryAerodynamicsPerformanceWeightsStructures

Total

-2--46

216-1024520 (per load condition)31868 (7 loadconditions)

Table 2. MDO Conceptual Elements26

InformationManagement andProcessing

Analysis Capabilities andApproximations

DesignFormulations andSolutions

Management andCulturalImplementation

• MDO Framework andArchitecture• Databases, Data Flow,and Standards• ComputingRequirements• Design SpaceVisualization

• Analysis and SensitivityCapability• Parametric Geometric Modeling• Approximation and CorrectionProcesses• Breadth vs. Depth Requirements• Effective Inclusion of High-Fidelity Analyses/Tests

• Design ProblemObjectives• Design ProblemDecomposition andOrganization• OptimizationProcedures and Issues

• Organizational Structure• MDO Operation in IPDTeams• Acceptance, Validation,Cost & BenefitsTraining


MDO Conceptual Elements

Our list of the components of MDO methodology isinfluenced by what methods are needed to achievemultidisciplinary synergy in practice.Multidisciplinary analysis, even when accompaniedby optimization, does not suffice by itself. In otherwords, MDO does not consist merely of linkingtogether disciplinary analysis tools and wrapping anoptimizer around them. This may well be the mannerin which most multidisciplinary optimizationproblems have been approached, including the twoexamples in the previous section, but as thisoverview will demonstrate, there are many alternativeapproaches.

A delineation of the contents of the "MDO discipline"has progressed through three generations, evolvingfrom an academic perspective to an industryperspective. The first proposal was an individual onemade by Sobieski.32 A modified version was used atNASA Langley for several years.33 Recent activitiesby the AIAA MDO Technical Committee have ledGiesing & Barthelemy26 to propose a third generationMDO taxonomy summarized here in Table 2. Thelatter paper has the distinction of including adiscussion of the state-of-the-art of each element inindustrial applications. Note also the fourth majorcategory, Management and Cultural Implementation.This new category (absent from the first twogenerations) acknowledges explicitly the nontechnicalchallenges that must be addressed in order for MDO tobe adopted in industry.

Our discussion of the MDO conceptual elements iscomplementary to that of Giesing & Barthelemy.Whereas they focused on the industry perspective, weshall focus on the research and methods developmentperspective.

For future reference, we state here in abstract termsthe general optimization problem:

min f(x,u(x))

s.t. h(x,u(x)) = 0 (1)

g(x,u(x)) 0

in terms of design variables x, the state variables u(from the corresponding multidisciplinary analysisproblem), the objective function f, the equalityconstraints h, and the inequality constraints g.

Information Management and Processing

The general category of information management andprocessing refers to the enabling information

technology infrastructure for MDO; many of the newdevelopments have originated in computer sciencetechnology advancements. The issues discussed heremay not be as critical for adaptation of MDOtechniques to enhance investigations of basic flowphysics, but they grow more significant as fluiddynamics strives to become more closely linked withother disciplines.

A theme that permeates this section is the desirabilityof automating as much of the MDO process as isfeasible. Nevertheless, let us stress that MDO doesnot purport to furnish a push-button designcapability. Rather, MDO seeks to provide the humandesigner with improved tools for achieving betterdesigns. The MDO tools should be used to assist thedesigner by automating routine tasks, by furnishinguseful information on interdisciplinary trades, and byconducting design space searches.

MDO Framework and Architecture

The phrase MDO framework and architecture refers tothe abstract design (architecture) and the specificsoftware tools for implementing and controlling(framework) a multidisciplinary design process. Forthose MDO practitioners who have attemptedsignificant applications, such as the aerospike nozzleand even more so the sequence of HSCT applications,the need for appropriate architectures and usefulframeworks is abundantly clear. Well over 90% of thehuman effort on the implementation of theseapplications went into preparing the analysis codesfor use in a multidisciplinary application and intolinking these codes together in the proper controlsequence.

A variety of framework research activities have beenconducted, and several commercial frameworks arenow on the market.34 Although none of thesecommercial frameworks yet presents a completesolution, their progress in the past few years has beenimpressive. Our advice to any group contemplating anontrivial MDO application is to acquire the bestavailable frameworks rather than hard-wiring theapplication or attempting an in-house frameworkdevelopment activity. We would especially cautionfluid dynamics researchers to avoid succumbing to thetemptation to build their own frameworks; leave thistask to the information technology specialists. Aboveall, exploit tools that automate the repetitiousactivities involved in preparing the analysis codes forintegration.

The HSCT 4 application is obviously a significantsoftware development activity. The ad hoc"configuration management" approaches typically


used in the research community are not feasible forthis scale of problem. On the other hand, the rigoroussoftware engineering methods applied to thedevelopment of flight critical software are surelyoverkill. The HSCT 4 team is currentlyexperimenting with the use of formal configurationmanagement procedures and utilities35 in the hopes ofeffectively managing the software development whilepermitting the experimentation necessary for aresearch project. As might be expected, this use offormal configuration management initially met withconsiderable resistance from the team members. Astime has passed, however, and more and more teammembers have been affected by problems arising frommultiple, uncontrolled versions of other members'software, greater acceptance has developed.

Databases, Data Flow, and Standards

Development of the problem definition for an MDOresearch application is quite challenging. In theapplication of MDO methods in an industry settingone often seeks to make an incremental improvementin an existing design process. Here the existingdisciplinary and interdisciplinary processes are likelyto have well-understood and well-documented dataflow, interfaces, and standards. In the research case,there is unlikely to be an existing process that canserve as a starting point. Researchers, especially thosewith no prior experience on diverse, multidisciplinaryteams, typically have little appetite for the extendeddiscussions, compromises, and documentationnecessary to achieve the detailed problem definitionessential for implementation. The aerospike nozzleapplication was still small enough that it couldreasonably be developed without a formalrequirements document, but the HSCT 4 applicationsorely needed such a document. The HSCT 4 teameventually assembled a detailed requirementsdocument. It took nearly 100 pages just to define theanalysis process, the tools used, and the data flow.The requirements document necessarily went throughseveral drafts as the process understanding evolved. Ittook more than a year to extract this definition fromthe researchers on the team. The overall processwould have been more efficient had time for this beenset aside at the very start of HSCT 4, but it is next toimpossible to persuade researchers of the value of thisprocess until they have seen firsthand theconsequences of delaying the requirements definition.

Managing the sheer volume of data for the HSCT 4application is quite a challenge. More than 10 GBytesof data is exchanged in a single execution of theanalysis process. The volume of data exchange for afull system sensitivity analysis is estimated to exceed

one TByte. A formal database system is usedjudiciously in the HSCT 4 implementation.30

Computing Requirements

The aerospike nozzle application was run on severalUltraSPARC™ workstations and typically took a dayto reach an optimal solution. Even for this relativelysmall-scale application, automation of the individualprocesses was essential to achieve this 1-dayturnaround. For the HSCT 4 application, it takesroughly a day to generate a single analysis on aworkstation even with full automation of the entireprocess. This can possibly be reduced to several hoursby use of parallel processing, but load balancing isvery challenging for this heterogeneous application.Bear in mind that the workhorse aerodynamic code formost of the HSCT 4 computations is a (linear) panelcode (USSAERO); in order to keep the computationaltime within reasonable bounds, the nonlinear codeCFL3D (in Euler mode) is used only for occasionalnonlinear corrections. Recall from Table 1 that thereare approximately 70 distinct subprocesses in theHSCT 4 application and that numerous iterativeloops between subprocesses are needed to enforce fullmultidisciplinary consistency. Such iterations arecharacteristic of multidisciplinary problems.

And yet, the complexity of the HSCT 4 problempales in complexity beside the industry designprocess. In practice, thousands of load conditions(rather than a mere seven), higher fidelity analyses(such as Reynolds-averaged Navier-Stokescomputations), and many more effects, such asflutter, controls, layout, propulsion, manufacturing,and operations, must be examined even at thepreliminary design stage. Hence, for the foreseeablefuture, MDO applications will have to considercarefully the computing requirements.

Design Space Visualization

The sophisticated graphical tools presently availablefor flow field visualization are not particularly usefulfor MDO applications: detailed flow-field features areof far less interest than representations of the effectsof the design variables upon the overall systemobjective(s) and constraints. Suffice it to be said herethat what tools do exist for this purpose are woefullyinadequate. The fluid dynamics community couldcertainly make a useful contribution by demonstratinghow to provide intuitive views of the optimizationprocess to the fluids and systems specialists.


Analysis Capabilities and Approximations

The analysis capabilities that are needed for MDOapplications go beyond what is usually included intraditional discipline analysis tools, where the one-of-a-kind analysis paradigm often prevails. This sectionwill discuss some techniques that the "MDOdiscipline" has promoted because of their genericutility.

Analysis and Sensitivity Capability

From the MDO perspective it is important that eachsignificant disciplinary analysis code be robust,automated (or at least readily automated),computationally efficient, well documented, andequipped with accurate, efficient sensitivity analysis.The first three requirements in the preceding list arenecessary to permit timely incorporation into amultidisciplinary analysis system. A major trap ofcurrent tool development is the dependence ongraphical user interfaces (GUIs) for the input,execution, and output of CFD and especially gridgeneration codes. GUIs are appropriate for initialproblem setup and for off-line visualization andinterpretation, but their use in other portions of theanalysis process embedded within optimization loopsis a dead end. The documentation must target thegeneral user whose main interest is the vehicle andnot the esoterica of fluid dynamics. The requirementfor sensitivity analysis is driven by the use ofgradient-based optimization at the system level.

Fortunately, pre-processing tools for equippinganalysis codes with accurate and efficient sensitivityanalysis capability are nearing maturity. One suchtool is ADIFOR (Automatic Differentiation ofFortran), developed by Argonne National Laboratoryand Rice University.36,37 (A similar tool, ADIC,handles C code.38) ADIFOR works as apreprocessor— it accepts as input a Fortran codealong with specifications of the input and outputvariables, and it produces as output an augmentedFortran code that contains the original analysiscapability plus the capability for computing thederivatives of all the specified output quantities withrespect to all the specified input quantities.Applications of ADIFOR to nonlinear CFD codesbegan in 199139 and have involved a close interactionwith the ADIFOR tool developers. When ADIFOR3.0 is officially released in 1999, it will also containthe capability to produce the adjoint code.37 Recentexperience37,40 indicates that a complete multigrid,multiblock, turbulent CFD code can be equipped withsensitivity analysis capability in less than a week byusing ADIFOR (assuming that the code is written in

the Fortran 77 ANSI standard). The typical time forequipping by hand a laminar Navier-Stokes code withquasi-analytic sensitivity analysis appears to be abouta year. Of course, the hand-coded algorithm will bemore efficient in terms of both CPU time andcomputer memory, by factors of perhaps 3 to 10.

Another attractive alternative is the use of thecomplex variable technique.41,42 Each of these threeapproaches—hand-coded sensitivities, automaticdifferentiation, and the complex variabletechnique—has its place, but there is certainly noexcuse today for not providing sensitivity analysiscapability along with the CFD tools. Someexploratory work has been performed on obtainingaccurate second derivatives from CFD codes,43 and theforthcoming ADIFOR 3.0 tool will include Hessian-generation capability.

A number of CFD groups have developed adjointcapabilities for their codes. There has been somequestion recently about precisely how to defineadjoints appropriately, especially in the presence offlow or grid discontinuities or singularities. Havingwitnessed first hand44 the enormous impact numericalanalysis had upon spectral methods in the 1980s, thefirst author became a firm believer in the advantagesof the weak formulation of numerical methods. Wetherefore have little hesitation in recommending thework of Lewis45 for resolving these debates for thosewho prefer to derive the adjoint first and thendiscretize the equations.

One can choose first to derive the sensitivityequations from the basic continuous equations of theproblem and then discretize them or else first todiscretize the basic continuous equations and thenderive the sensitivity equations from this discreteproblem. (Automatic differentiation tools such asADIFOR compute the sensitivities from the discreteequations.) While the jury is still out on just whenthe sensitivities (or adjoints) need to be derived fromthe discrete equations, we side with those who placegreater importance on having gradients consistentwith the function evaluation. This avoids thepossibility that inconsistent gradients would point theoptimizer in the wrong direction in some delicatesituations. In our view, consistency in the(unreachable) limit of sufficiently fine discretizationmay mollify some mathematicians but is perilous forthe practitioner.

An important but rather underdeveloped area,especially for fluid dynamics, is smart reanalysis.46

This term refers to efficient reanalysis techniques thatminimize the computations required in simulating a


system with perturbed input parameters. There is noreason to believe that the best that can be done inCFD is to redo the entire computation with the initialcondition taken from the previous solution, or even alinear extrapolation of the previous solution based onthe sensitivity derivatives.

Parametric Geometric Modeling

Parametric geometric modeling is a prerequisite forfull use in optimization of common geometry anddiscretization models. The models need to beconsistent across the disciplines even formultidisciplinary analysis. The different types ofmodels that are needed just in the HSCT 4 applicationare shown in Fig. 5, taken from the work ofSamareh.47 Note that the various analysis processesuse different features and different levels of detail. Theadditional requirement that the underlying commonmodel be parametric is essential for effective use ofoptimization in design processes. Ideally, thecommon model should be tied directly to acommercial computer-aided design (CAD) system,with the input to the MDO processes coming directlyout of the CAD representation and the improvedmodel output from the MDO process importeddirectly back into the CAD representation. Thepresent barriers to this goal are discussed at length bySamareh.48

Fig. 5 HSCT geometry models.

In the meantime, stopgap measures must beemployed. In the aerospike nozzle application,27

MATLAB™ scripts were used in a novel way toparameterize a conventional NASTRAN™ model ofthe structure. In the HSCT 4 application, the CADrepresentation was exported to a NURBS (nonuniformrational B-spline) representation and shapedeformation methods47 were applied to yield theparameterization illustrated above in Fig. 4.

For fluid dynamics applications, the focus is on thesurface geometry (outer mold line) model of thevehicle and on the field grid for the CFDcomputations. Keep in mind the importance ofobtaining accurate sensitivity derivatives of theperformance measure f (a functional of the CFDsolution u) with respect to the model parameters x.The following notional equation indicates thecomponents that contribute to the overall sensitivity:

f

x=

f

u

u

v

v

s

s

x , (2)

where v represents the volume grid and s the surfacegrid. Although there has been enormous progress onequipping CFD codes with accurate sensitivities withrespect to the flow variables ( f/ u, u/ v), there hasbeen more limited progress on inserting this featureinto volume grid generation codes49 (for ∂v/∂s), andno analytical capability exists for extracting from aCAD system the sensitivity of the surface withrespect to the model parameters ( s/ x). There is noconceptual difficulty in doing this extraction; CADvendors have not yet felt a compelling need forproviding this capability. The approach used inHSCT 4 includes analytical sensitivities of theparameterized NURBS representation.

The message for those contemplating optimizationwith CFD tools is to choose surface modeling, gridgeneration, and flow solver tools that provideparametric and sensitivity analysis capabilities.

Approximation & Correction Processes

While most disciplinary specialists envision that theirsophisticated tools would be incorporated directly intoMDO processes, the sober reality is that the lengthyrun times of many of these disciplinary codes,especially CFD codes, preclude their direct use.(Recall the time it takes for a single multidisciplinaryanalysis in HSCT 4.) In practice, heavy use is madeof approximation and corrections processes. Theapproach is to rely on a lower fidelity model for mostof the computations, but to invoke the high-fidelitymodel occasionally for corrections.

The use of variable-fidelity approximations50 is nowquite common. Fig. 6 illustrates the basic idea. Thinkof the high-fidelity model as a Navier-Stokes CFDcode, with f and ∇f representing the objectivefunction and its gradient with respect to the designvariables, as evaluated using the high-fidelity model.Let a and ∇a denote the approximate objectivefunction and gradient, as evaluated using the lowerfidelity model. Many choices are available for thelower fidelity model. It could be a simpler physical


model, such as an Euler code, a panel code, or avortex-lattice code; alternatively, it could be a formalapproximation (what has been called a metamodel insome quarters51), such as a response surface, a neuralnetwork, or a kriging approximation. In the past fewyears there has been considerable work toward puttingvariable-fidelity approximations on a soundmathematical footing.52,53 There are now variable-fidelity optimization algorithms that have beenproven to converge to the solution of the high-fidelityproblem. However, the available mathematical resultsdo not address the practical issue of whether the high-fidelity model will be invoked sufficientlyinfrequently in the variable-fidelity approximation toyield an overall reduction in computational time(compared with always invoking the high-fidelitymodel). The empirical experience with these rigorousmethods is still too limited for any conclusions to bedrawn at this point.

Fig. 6 Variable-fidelity approximation.

F i g . 7 E r r o r estimates for a Boussinesqproblem.56

A related area of research is devoted to developingrigorous error estimates for the approximations.Patera and his colleagues54–56 have pioneered thiswork for CFD applications. Fig. 7 illustrates thecurrent focus of this group. Note that the designquestion is not the traditional: Given input heat flux

q = 1, what is T , but rather what is T and what arethe upper and lower bounds due to discretizationerrors? This work provides rigorous, quantitativebounds on the chosen figure of merit. These boundsare obtained from global calculations on a coarse gridand local calculations on a more highly refined grid;consequently, the computational cost of obtaining thebounds in addition to the coarse-grid solution isessentially the cost of the coarse-grid solution. In this

example, T initial represents the mean value of thetemperature as computed on the initial, coarse mesh,

and T adapted represents the improved value of thetemperature as computed on the adaptively refinedmesh. The methodology relies upon the solution ofan adjoint equation for each output function ofinterest. It also provides a rigorous context foradapting the grid in precisely those regions thatproduce the greatest errors in the figure or merit.

Breadth vs. Depth Requirements and EffectiveInclusion of High-Fidelity Analyses/Tests

The most difficult decision for any MDO applicationis how to strike the right balance between the breadthof the effects that are considered and the depth of thetools used to analyze the effects. The narrower thebreadth and the shallower the analysis tools, the morelikely the application is to produce an unrealisticdesign. The broader the breadth and the deeper theanalysis tools, the less likely the application is everto be completely implemented or to yield timelycomputational results.

Design Formulations and Solu tions

The use of the word "optimization" in conjunctionwith design often conjures up the impression that thedesigner is seeking a mathematically optimal solutionto his problem. In reality, the designer's goal is oftento improve an existing design. In this case the phrase"design improvement" better characterizes the goalthan does "optimization." Here formal optimizationtechniques are utilized more to guide movement in thedirection of an improvement to the design than tolocate the mathematical optimum.

Design Problem Objectives

In practice, there is considerable art to specifying thedetails of the problem statement, Eq. (1).Optimization is notorious for finding the weaknessesin the analysis codes and the problem formulation. Inthe context of aerodynamics, casual optimizationfrequently drives the solution towards regimes inwhich the CFD code is unreliable (e.g., highlyseparated flow) or for which the surface geometry


model or the volume grid breaks down. A relateddifficulty for CFD-based optimization is that greatcare must be exercised in parameterizing the surface.Virtually everyone who has attempted aerodynamicwing design has been disconcerted by spanwisecorrugations in the "optimal" wing. Arian andTa'asan57 have provided a mathematical explanation ofthis phenomenon. They demonstrated that it is aninherent difficulty. Only well-chosenparameterizations or constraints can mitigate thistendency.

In most cases the precise problem formulationevolves in the course of the investigation. Thismakes methods that are able to reuse informationfrom previous optimization formulations quite useful.

Design Problem Decomposition & Organization

An MDO method for a given problem consists of anMDO formulation and an optimization algorithm.58

The former deals with problem decomposition, andmathematical issues such as equivalence to theoriginal problem and to alternative formulations aregermane. The latter deals with the solution proceduresapplied to the MDO formulation, and the propertiesof optimization algorithms as applied to theformulation are of interest.

F i g . 8 Multidisciplinary feasible (MDF)formulation.

We shall use a coupled aerodynamics-structuresproblem to illustrate a few of the many formulations(decompositions) that have been proposed. The mostobvious formulation is to stay with the originalproblem statement by constructing a fullmultidisciplinary analysis of the problem andwrapping an optimizer around it (Fig. 8). Thismultidisciplinary feasible (MDF) approach has thefeature that at each cycle of the optimization, thecurrent trial point is a consistent solution to themultidisciplinary analysis (MDA) problem. If there isa significant coupling between the disciplines, thesolution of the MDA problem requires iterations(usually of fixed-point type) through all the

disciplinary codes. The use of the word "feasible" inthe name of the MDF formulation may bemisleading. It is feasible only in the sense that themultidisciplinary analysis is consistent with respectto all the disciplines; the consistent multidisciplinaryanalysis may still represent a point infeasible withrespect to the optimization problem (some constraintsare violated).

Fig. 9 Individual discipline feasible (IDF)formulation.

The MDF formulation is hardly the only approach,however. Fig. 9 illustrates the individual disciplinefeasible (IDF) formulation.59 At each optimizationcycle IDF requires feasible solutions for eachdiscipline analysis but not for the fullmultidisciplinary analysis. The disciplinary couplingvariables become part of the design variable set inIDF and compatibility constraints are added at thesystem level; consistent multidisciplinary analysis isguaranteed only at the convergence of theoptimization.

Fig . 10 Col laborat ive opt imizat ion (CO)formulation.

Numerous multilevel formulations have beendeveloped, including concurrent subspaceoptimization (CSSO),60 collaborative optimization(CO),61 MAESTRO,62 and bilevel integrated systemssynthesis (BLISS).63 Multilevel methods aredistinguished by using optimization both at the upperor system level and at the lower or subsystems levels.Fig. 10 illustrates the CO formulation (a two-levelformulation). Note that at the subsystem


(disciplinary) level, the optimization problem is not atraditional discipline optimization problem, but ratheran optimization to reduce the incompatibility betweenthe variables shared by the disciplines. Thisformulation permits considerable disciplinaryautonomy. Fig. 11 illustrates the MAESTROformulation. Along with most of the other multilevelformulations, it uses more traditional disciplineoptimization problems at the subsystem levels andpermits some degree of disciplinary autonomy aswell.

Fig. 11 MAESTRO formulation.

Some of these formulations, such as CO and IDF,dispense completely with the requirement to performa full MDA. Others, such as CSSO and BLISS onlyrequire occasional uses of full MDA. At least twoclassifications for MDO formulations have beenproposed,59,64 but not every extant MDO formulationfits cleanly into either classification system.

One should not lose sight of the point that theformulations discussed above (aside from MDF)remain merely candidate approaches until proven to beequivalent to the MDF formulation and to be practicalin the sense that they can be coupled with an effectiveoptimization algorithm. Thorough discussions of themathematical properties of the CO formulation65 andthe MAESTRO formulation62 are available.MAESTRO has been proven rigorously to beequivalent to MDF, whereas there are some subtledifficulties with CO.

The choice of formulation should be stronglyinfluenced by the nature of the coupling between thedisciplines. This interdisciplinary coupling may becharacterized in two dimensions. The coupling isnarrow if few variables are interchanged and broad ifmany variables are interchanged. The coupling isweak if a consistent multidisciplinary analysis can beachieved in a small number of iterations and strong ifmany iterations are needed. For problems with weak,

narrow coupling, just about any formulation appearsto work. For problems with strong, broad coupling,only the MDF and the MAESTRO formulationsapply. The effectiveness of the various MDOformulations is very much an open question for theother two combinations.

Another aspect of problem decomposition, whichbecomes increasingly important as the number ofsubprocesses involved in the design process increases,is the identification of the best sequence for executingthe individual subprocesses. One needs to recognizethat in complex design processes there is both feed-forward and feedback of information. There are usuallysubprocesses that depend upon the information fromdownstream subprocesses. This dependence can onlybe handled iteratively. Tools for assisting in theoverall structuring of the design process areavailable.66

Optimization Procedures and Issues

A wide variety of optimization algorithms andsoftware67–69 is available for solving the particularMDO formulations. There is certainly quite aselection of gradient-based optimization algorithms.The main issue with these is ensuring that accurateand efficient derivative information (sensitivityanalysis) is available from all the codes. Sobieski70

has provided an algorithm—the generalized sensitivityequations—for combining the constituent disciplinarysensitivities into the full multidisciplinarysensitivities for the MDF formulation. Especiallywhen there are iterative subprocesses involved in theMDA, just validating that the system sensitivities arecorrect is quite time consuming.

Most optimization software assumes completecontrol over the calls to the analysis and sensitivityanalysis (gradients) processes as illustrated in the lefthalf of Fig. 12. For most multidisciplinary problemsthe analysis and sensitivity analysis calls are quitetime consuming, and this "direct insertion" approachis prohibitively expensive. This problem is notinherent in the optimization algorithms, but is due tothe inadequate user control provided by many of thesoftware packages. Many MDO practitioners prefer toexert more control over the optimization and haveadopted the sequential approximate programming(SAP) approach71 illustrated in the right half of Fig.12. This approach couples the optimization softwarewith an approximation; the figure illustrates anapproximation based on zero- and first-orderinformation, but the method has been used with avariety of approximations. Not only does the SAPapproach usually reduce the number of invocations of


the expensive analysis and sensitivity analysiscomputations, but it also provides readily for periodichuman intervention whenever the approximation isupdated. The SAP approach is so common in currentMDO applications that one is hard pressed to find acomplex application that used the direct insertionapproach. The aerospike nozzle application used thedirect insertion approach to optimization, whereas theplan for HSCT 4 is to use the SAP approach. Thecomputational demands of the former weresufficiently modest to permit use of direct insertion.

Fig . 12 Direct insertion and sequentialapproximate programming (SAP)approaches.

In many MDO applications involving aerodynamicsmodeled at the nonlinear CFD level, the run-time ofthe aerodynamics code dominates the overall run-timeof the MDA. Because nonlinear CFD codes areinvariably solved via iterative methods, the MDFformulation yields an iterative CFD process nestedinside the iterative optimization process. This has ledseveral groups72–76 to propose turning theaerodynamics optimization process "inside out" andnesting the optimization iterations inside the CFDiterations. Fig. 13, loosely taken from Newman etal.77 illustrates the multidisciplinary extension of thissimultaneous analysis and design (SAND) procedureas it would appear for an aerodynamics-structuresproblem. This approach has met with demonstrablesuccess for some structures problems,78 but has yet toreach its full potential for aerodynamics, let alone forcoupled aerodynamics-structures problems. Robuststrategies for ensuring convergence have yet to bedemonstrated for flows with discontinuities. Onebarrier to acceptance of this approach is that if theoptimization process is stopped short of convergence,as might occur if one simply runs out of time, onemay not have a feasible solution to the individualdisciplinary problems, let alone one to the completemultidisciplinary problem. This consideration appears

to have limited the use of this approach within thestructures discipline.

Fig. 13 Simultaneous analysis and design(SAND) algorithm.

One cannot yet provide reliable guidelines onmatching the method to the problem. (Remember thatan MDO method consists of both a formulation andan algorithm.) Some comparisons are available in theoriginal papers cited above for these methods. Therehave been the beginnings of third-party comparisonsbetween methods.58 However, these comparisons areinvariably on quite simple problems due to thetremendous effort required to implement even oneMDO method on a complex problem. NASA Langleyhas established the MDO Test Suite,79 a collection ofMDO problems, has to serve as test cases.

There is an increasing selection of availableoptimization methods that do not exploit gradientinformation. These include novel pattern searchmethods,80 evolutionary algorithms81 (includinggenetic algorithms and simulated annealing methods),and discrete search methods. Such methods appear tohave significant difficulties with problems with alarge number of variables and constraints. Sinceformulations such as CO, IDF, BLISS and CSSO alladd a large number of constraints to the original MDFformulation, non-gradient-based methods may havedifficulty with the alternative formulations.

Finally, we should mention that most MDOproblems have multiple objective functions, ratherthan a single objective function for a dominantdiscipline plus constraints for the remainingdisciplines. An obvious, but simplistic, approach isto construct a single weighted objective function outof all the objective functions. More promisingapproaches are available.82 Perhaps these will


ultimately prove useful for applications toaerodynamic multipoint optimization.

Management and Cultural Implementation

In many respects the technical challenges within theMDO field pale against the organizational and culturalbarriers the research community faces. Giesing andBarthelemy26 discuss this from an industryperspective. Here we'll just comment on some teamissues that arise in a government research laboratory.In a research environment, discipline specialistsparticipating in MDO applications naturally want touse the latest tools from their discipline, but thesetools usually are not yet robust enough for inclusionin an automated process and take large amounts ofcomputer time. Researchers, however, receive verynegative feedback from their discipline peers if theyresort to use of established tools that are more suitedfor a complex MDO application.

Another common obstacle is that developing amultidisciplinary problem statement, which includesdetailed process definition along with specific toolselection, takes considerable time. (It took well over ayear to arrive at the final technical definition of theHSCT 4 application.) This process is excruciating formost researchers. Researchers from a disciplineaccustomed to a dominant role in the organizationfind it especially difficult to make the compromisesthat are essential for an effective team. In alllikelihood, more prospective MDO research projectshave come to naught for human reasons than fortechnical ones. We have begun to make systematicstudies of these issues.83–85

Fluid Dynamics for a Multidisciplinary Age

Here we shall reinforce some of our earlier commentsand point out some potential new opportunities forfluid dynamics research.

Sensitivity Analysis

Our principal message is a recapitulation ofSobieski's 1986 call for aerodynamic sensitivityanalysis,4 but with a twist: whereas Sobieskirecommended that sensitivity analysis should be astandard feature of the CFD codes to be used invehicle design, our recommendation is that sensitivityanalysis should also be a standard feature of the codesused to study flow physics.

Sensitivity derivatives are useful for a variety ofpurposes beyond their obvious use in gradient-basedoptimization. Consider an issue that has recently

received significant attention—uncertainty analysis.There are many contributions to the uncertainty inresults from CFD codes.86 Certainly spatial andtemporal discretization, iterative convergencetolerances, artificial viscosity, transition andturbulence modeling, and plain coding errors all mustbe examined. Some aspects of these and other sourcesof errors can be quantified through sensitivityanalysis. Figure 14 illustrates how sensitivityderivatives can be used to estimate the effect ofuncertainties in flow variables, such as Mach numberM and angle of attack α, upon the uncertainties inoutputs such as the lift coefficient. We haveperformed some preliminary calculations for theuncertainties in CFD outputs for a high-lift case87

with M = 0.2 and α = 19˚, which is near maximumlift. The computations were performed by the CFL3Dcode augmented with sensitivity derivatives by theADIFOR tool. These calculations suggest that for

these conditions ∂CL/∂M = (1) and ∂CL/∂ =(10-3).

Figure 14 Uncertainty analysis viasensit ivit ies .

The use of sensitivities in this context goes farbeyond quantification of the effect of flow fielduncertainties. They can be used to determine theeffects upon the code outputs arising from variationsin any input variable or continuous parameter of aCFD code. Obvious examples are the uncertaintiesfrom transition onset location, transition regionextent, turbulence model coefficient, surfacemanufacturing variability, and elastic surfacedeflections. One can, of course, compute thesesensitivities with the finite-difference approach, i.e.,by performing one additional CFD run for eachdesired sensitivity with a small perturbation in theappropriate input or parameter variable. But a CFDcode equipped with sensitivity analysis can computeall the desired sensitivities in the same run as theoriginal analysis, usually far more efficiently and


always more accurately. The accuracy suffers whenfinite differences are used to estimate the sensitivitiesbecause one is forced to subtract nearly equalnumbers; with the other approaches the sensitivityderivatives are obtained from the most significantdigits of the computation. As noted above, one canhand-code the sensitivities, use the complex variablemethod, or employ automatic differentiation.

The use of automatic differentiation for obtainingsensitivities from CFD codes with respect to Machnumber, angle of attack, turbulence model coefficient,some algorithmic parameters such as artificialviscosity coefficients, and geometry perturbations hasalready been demonstrated 6 years ago.88 The accuracyproblems with the finite-difference approach tosensitivities can be severe for transition andturbulence modeling coefficients, as models for thesephenomena tend to be nonanalytic. Nevertheless, theautomatic differentiation approach was conclusivelyshown to yield the correct sensitivities. This may bethe only viable approach if one wishes to tune themodel coefficients by what amounts to a gradient-based optimization method.

Some preliminary calculations we have performed fora multielement airfoil near maximum lift, such asillustrated in Figure 14, suggest that first derivativesalone may not suffice for accurate estimation of theeffect upon forces and moments of inherentuncertainty in tunnel settings. Contributions fromsecond derivatives may also be needed. Park et al.40

reached a similar conclusion in their use of sensitivityderivatives to estimate control effectiveness. Secondderivatives may be obtained fairly easily bycombining the complex variable technique with useof ADIFOR or by exploiting the forthcomingHessian capability of ADIFOR, although thecomputational expense will be high. This secondderivative capability should provide fluid dynamicistswith a variety of new opportunities.

The example above was for a (nearly) steady flow.Sensitivities can be useful for time-dependent fluiddynamical problems as well. A meteorologicalapplication89 of automatic differentiation has beenmade to the computation of propagation of smalldisturbances in time-dependent nonlinear simulationcodes.

Recent trends suggest that the CFD tools of choicefor the next decade will have sensitivity analysis aswell as rigorous discretization error estimates (recallthe work leading to Fig. 7). Together these willprovide the user with a firm handle on many aspectsof the uncertainties in the code results.

Sensitivity analysis is clearly applicable to the taskof computing stability and control derivatives fromCFD codes. Most past attempts at this have simplyused the CFD code to mimic how these quantities areapproximated, by what amounts to finite differencingor curve fitting, in wind tunnel experiments and flighttests. Why not use sensitivity analysis to solve theexact equations that govern the stability and controlcoefficients?40,90

Aerodynamic Design Methods

There has been significant progress this decade ingradient-based aerodynamic design methods, with themost efficient methods utilizing hand-codedsensitivities and adjoints (although no one has yetbeen masochistic enough to produce a hand-codedadjoint that includes the turbulence model). The nextchallenge in this line is to adapt these methods tomultidisciplinary problems, e.g., to aerodynamics-structures problems. This extension is notstraightforward. If one is using a loose couplingbetween aerodynamics and structures codes, there willbe many surface interface variables, and therequirement for sensitivities for each of thesevariables diminishes the advantage of the adjointmethods.91 This difficulty can be avoided if onedevelops a tightly coupled aerodynamics-structurescode, but the tools of choice for the structurescommunity are commercial codes, and one does nothave access to the source code.

The gradient-based optimization methods that havebeen the focus of much of this paper are certainly notalways the method of choice for aerodynamic designproblems. Inverse design methods are often far moreefficient. For example, the DISC and CDISC92

methods can typically match a desired pressuredistribution at an additional cost that is less than 10%of the underlying cost of a single analysis, and ruleshave been developed that allow reasonable guesses fordesired pressure distributions and for incorporation ofa variety of constraints. Generally speaking, however,this approach is confined to situations in which thedesign variables and the objective function are takenfrom the same surface; they don't apply, for example,to the design of the shape of an engine nacelle tooptimize the performance of a wing. When effectiveestimates of desired pressure distributions cannot bemade and for cases in which there may be many localminima, the DACE (Design and Analysis ofComputer Experiments) approach used in the3DOPT93 tool and/or methods such as geneticalgorithms can be used to explore the design space.The DACE and genetic algorithm approaches do


suffer, however, from the curse of dimensionality,rapidly becoming impractical as the number of designvariables increases. (Parallel processing can reduce theimpact of the curse of dimensionality.) Gradient-basedoptimization appears the best choice when a desiredpressure distribution is not available, when multiplesurfaces are involved, when there are a large numberof design variables, or when one is content with alocal minimum.

Inverse aerodynamic design methods do not appear tohave yet been used effectively in multidisciplinaryoptimization problems. Surely they can be exploitedsomehow in multilevel MDO methods. But even inthe context of their use in aerodynamic optimizationthere is an opportunity, using techniques developedfor structural optimization, 94 to apply sensitivityanalysis to these inverse design methods to addresssuch issues as sensitivity of the optimal design withrespect to parameters.

Aerodynamic design methods generally view theproblem deterministically. A different perspective istaken by optimization methods that seek to accountexplicitly for uncertainties. This "optimization underuncertainties" approach arose in the civil engineeringcommunity and is starting to make inroads in parts ofaeronautics. Two distinct aspects of this approach arereliability-based design95–97 and robust design.98,99 Inthe former case one designs to a prescribed probabilityof failure, whereas in the latter case one seeksrelatively flat local optima, i.e., designs that remaineffective (robust) in a broad neighborhood of theputative optimal point. In both cases one needs tocharacterize the distribution of uncertainties. Forreliability-based design one is most interested in thetail of the distribution, whereas for robust design oneis most interested in its low-order moments. One canforesee fluid dynamics applications in bothareas—reliability-based approaches to theaerodynamics of systems which operate in anuncertain environment and robust design approachesto the fluid dynamics of devices which cannot bemodeled at all accurately.

Aerodynamic Approximations

Accurate, but affordable, approximations toaerodynamic analyses are desperately needed for fluiddynamics to make an impact in broad MDOprocesses. A wide variety of approximations havebeen used for MDO problems in general50,51,55,60 andfor aerodynamics optimization. 100,101 This varietyincludes response surfaces, neural networks, DACEmodels, kriging methods, and low-fidelity methods.Approximations are especially needed for time-

dependent problems. The aeroservoelastic communityhas developed a variety of methods that they callreduced-order models.102–104 Some aspects of thesemodels are useful for purely fluid dynamics problemsas well. An approach that may be intriguing to partsof the turbulence physics community is the use ofproper orthogonal decompositions in design.105

Experimental Validation

Experimental validation of aerodynamic optimizationis very challenging. There is as yet no satisfactoryapproach to experimental validation of the predictionsof optimization studies, at least with respect to shapedesign variables. The issue here is not just validatingthe performance predictions of a specific "optimized"design, but rather experimentally exploring the designspace in a neighborhood of the supposed optimum todetermine whether it is indeed an optimal design. Theobvious difficulty is that testing the region around theoptimal design requires an inexpensive, rapidcapability to make specific small changes in theshape of the test article and to retest it. Similardifficulties beset experimental validation ofsensitivity analyses.

A Cultural Reminder

If a multidisciplinary approach to a problem is tohave any hope of producing a beneficial, synergisticresult, then there must be genuine interdependencyamong the contributing disciplines. Thisinterdependency of disciplines invariably requires thatthe individual members of the multidisciplinary teambe interdependent upon each other, i.e., that they be atrue team and not just a working group in which theteam leader merely collates isolated, independentcontributions.85 This requirement is probably thelargest barrier that any fluid dynamicist mustovercome before entertaining serious thoughts ofconducting multidisciplinary research; mostresearchers are very uncomfortable depending onsomeone else. This discomfort barrier is one reasonthere are so many examples of very simple structurescodes linked to state-of-the-art CFD codes and somany examples of sophisticated finite-element codesobtaining the loads from vortex-lattice codes. Thereare few opportunities for synergy in such approaches.

The fluid dynamicist who wishes to participate inmultidisciplinary activities should ensure that hisanalysis tools are design oriented: that they containsensitivity analysis, use approximations to themaximum extent possible, allow for rapid reanalysis,


are robust, are built on parametric model descriptions,and are automated. The fluid dynamics researchershould also be prepared to invest considerable time inunderstanding the other disciplines and to participatefully in the arduous process of defining themultidisciplinary problem.

Acknowledgment

The views expressed in this paper are the fruit of ourexperiences over the past five years in theMultidisciplinary Optimization Branch at the NASALangley Research Center. We are grateful to all of thebranch members for what they have taught us. We areespecially indebted to Drs. Natalia Alexandrov, Jean-François Barthelemy, Perry Newman and JarekSobieski for their comments on the paper.

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53 Alexandrov, N. M., Dennis, J. E., Jr., Lewis, R.M., and Torczon, V., "A Trust Region Frameworkfor Managing Use of Approximation Models inOptimization," Structural Optimization, Vol. 15, No.1, 1998, pp. 16–23.54 Yesilyurt, S., and Patera, A. T., "Surrogates fornumerical simulations: optimization ofeddy–promoter heat exchangers," ComputationalMethods of Applied Mechanical Engineering, Vol.121, 1995, pp. 231–257.55 Otto, J. C., Paraschivoiu, M., Yesilyurt, S., andPatera, A. T., "Bayesian-ValidatedComputer–Simulation Surrogates for Optimizationand Design: Error Estimates and Applications,"IMACS Journal of Applied Numerical Mathematics,in press.56 Machiels, L., Peraire, J., and Patera, A. T.,"Output Bound Approximations for PartialDifferential Equations: Application to theIncompressible Navier-Stokes Equations," Proc.Istanbul Workshop on Industrial and EnvironmentalApplications of Direct and Large Eddy NumericalSimulation, edited by S. Biringen, Springer-Verlag,New York, 1998.57 Arian, E., and Ta'asan, S., "Analysis Of TheHessian For Aerodynamic Optimization: InviscidFlow," NASA CR-198328, ICASE Report No. 96-28, Apr. 1996.58 Alexandrov, N. M., and Kodiyalam, S., "InitialResults of an MDO Evaluation Study," AIAA Paper98-4884, 7th AIAA/USAF/NASA/ISSMOSymposium on Multidisciplinary Analysis andOptimization, St. Louis, MO, 1998.59 Cramer, E. J., Dennis, J. E., Jr., Frank, P. D.,Lewis, R. M., and Shubin, G. R., "ProblemFormulation for Multidisciplinary Optimization,"SIAM Journal of Optimization, Vol. 4, No. 4, 1994,pp. 754–776.60 Batill, S. M., Stelmack, M. A., and Sellar, R. S.,"Framework for Multidisciplinary Design Based onResponse–Surface Approximations," Journal ofAircraft, Vol. 36, No. 1, 1999, pp. 287–297.61 Braun, R., Moore, A., and Kroo, I., "Use of theCollaborative Optimization Architecture for LaunchVehicle Design," AIAA Paper 96-4018, 6th

AIAA/NASA/ISSMO Symposium onMultidisciplinary Analysis and Optimization,Bellevue, WA, 1996.62 Alexandrov, N. M., "Multilevel and MultiobjectiveOptimization in Multidisciplinary Design," AIAAPaper 96-4122, 6th AIAA/NASA/ISSMOSymposium on Multidisciplinary Analysis andOptimization, Bellevue, WA, 1996.


63 Sobieszczanski-Sobieski, J., Agte, J., andSandusky, R. Jr., "Bi-Level Integrated SystemSynthesis," AIAA Paper 98-4916, 7th

AIAA/USAF/NASA/ISSMO Symposium onMultidisciplinary Analysis and Optimization, St.Louis, MO, 1998.64 Balling, R. J., and Sobieszczanski-Sobieski, J.,"Optimization of Coupled Systems: A CriticalOverview of Approaches," AIAA Paper 94-4330, 5th

AIAA/NASA/USAF/ISSMO Symposium onMultidisciplinary Analysis and Optimization, PanamaCity, FL, 1994.65 Alexandrov, N. M., and Lewis, R. M., "Analyticaland Computational Aspects of CollaborativeOptimization," Optimization and Engineering,submitted.66 Rogers, J. L., "Tools and Techniques forDecomposing and Managing Complex DesignProjects," Journal of Aircraft, Vol. 36, No. 1, 1999,pp. 266–274.67 Gill, P. E., Murray, W., and Wright, M. H.,Practical Optimization, Academic Press, New York,1981.68 Haftka, R. T., and Gürdal, Z., Elements ofStructural Optimization, Kluwer, Dordrecht, 1993.69 Haim, D., Giunta, A. A., Holzwarth, M. M.,Mason, W. H., Watson, L. T., and Haftka, R. T.,"Comparison of Optimization Software Packages foran Aircraft Multidisciplinary Design OptimizationProblem," Design Optimization: International Journalfor Product and Process Improvement, Vol. 1, No. 1,1999, pp. 9–23.70 Sobieszczanski-Sobieski, J., "Sensitivity ofComplex, Internally Coupled Systems," AIAAJournal, Vol. 28, No. 1, 1990, pp. 153–160.71 Schmit, L. A. Jr., and Farshi, B., "SomeApproximation Concepts for Structural Synthesis,"AIAA Journal, Vol. 12, No. 5, 1974, pp. 692-699.72 Rizk, M. H., "Optimization by Updating DesignParameters as CFD Iterative Flow Solutions Evolve,"Multidisciplinary Applications of CFD, edited by O.Baysal, ASME-FED, Vol. 129, Winter AnnualMeeting, 1991, pp. 51–62.73 Iollo, A., Kuruvila, G., and Ta'asan, S.,"Pseudotime Method for Shape Design of EulerFlows," AIAA Journal, Vol. 34, No. 9, 1996, pp.1807–1813.74 Gumbert, C. R., Hou, G. J.-W., and Newman. P.A., "Simultaneous Aerodynamic Analysis and DesignOptimization (SAADO) for a 3-D Rigid Wing,"AIAA Paper 99-3296, 14th AIAA CFD Conference,Norfolk, VA, 1999.

75 Ghattas, O. N., and Orozco, C. E., "A ParallelReduced Hessian SQP Method for ShapeOptimization," Multidisciplinary DesignOptimization: State of the Art, edited by N. M.Alexandrov and M. Y. Hussaini, SIAM, Philadelphia,1997, pp. 133–152.76 Reuther, J., Jameson, A., Alonso, J. J.,Rimlinger, M. J., and Saunders, D., "ConstrainedMultipoint Aerodynamic Shape Optimization usingan Adjoint Formulation and Parallel Computers,Parts 1 & 2," Journal of Aircraft, Vol. 36, No. 1,1999, pp. 51–60 & pp. 61–74.77 Newman, P. A., Hou, G. J.-W., and Taylor, A. C.III: Observations Regarding use of Advanced CFDAnalysis, Sensitivity Analysis, and Design Codes inMDO," Multidisciplinary Design Optimization: Stateof the Art, edited by N. M. Alexandrov and M. Y.Hussaini, SIAM, Philadelphia, 1997, pp. 263–279.78 Haftka, R., and Kamat, M., "SimultaneousNonlinear Structural Analysis and Design,"Computational Mechanics, Vol. 4, No. 6, 1989, pp.409–416.79 Padula, S. L., Alexandrov, N. M., and Green, L.L., "MDO Test Suite at NASA Langley ResearchCenter," AIAA Paper 96-4028, 6th

AIAA/NASA/ISSMO Symposium onMultidisciplinary Analysis and Optimization,Bellevue, WA, 1996.80 Lewis, R. M., and Torczon, V., "Pattern SearchAlgorithms for Bound Constrained Minimization,"SIAM Journal of Optimization, in press.81 Hajela, P., "Nongradient Methods inMultidisciplinary Design Optimization—Status andPotential," Journal of Aircraft, Vol. 36, No. 1, 1999,pp. 255–265.82 Stadler, W., ed., Multicriteria Optimization inEngineering and in the Sciences, Plenum Press, NewYork, 1988.83 Barthelemy, J.-F., Waszak, M. R., Jones, K. M.,Silcox, R. J., Silva, W. A and Nowaczyk, R.H.,"Charting Multidisciplinary Team External Dynamicsusing a Systems Thinking Approach," AIAA Paper98-4939, 7th AIAA/USAF/NASA/ISSMOSymposium on Multidisciplinary Analysis andOptimization, St. Louis, MO, 1998.84 Waszak, M. R., Barthelemy, J.-F., Jones, K. M.,Silcox, R. J., Silva, W. A and Nowaczyk, R.H.,"Modeling and Analysis of Multidiscipline ResearchTeams at NASA Langley Research Center: ASystems Thinking Approach," AIAA Paper 98-4940,ibid.


85 Nowaczyk, R. H., and Zang, T. A., "FactorsRelated to Successful Engineering Team Design,"AIAA Paper 98-4941, ibid.86 Roache, P. J., "Quantification of Uncertainty inComputational Fluid Dynamics," Annual Review ofFluid Mechanics, Vol. 29, 1997, pp. 123–160.87 Rumsey, C. L., Gatski, T. B., Ying, S. X., andBertelrud, A., "Prediction of High-Lift Flows usingTurbulent Closure Models," AIAA Journal, Vol. 36,No. 5, 1998, pp. 765–774.88 Green, L. L., Newman, P. A., and Haigler, K. J.,"Sensitivity Derivatives for Advanced CFDAlgorithms and Viscous Modeling Parameters viaAutomatic Differentiation," Journal of ComputationalPhysics, Vol. 125, No. 2, 1996, pp. 313–324.89 Bischof, C. H., Pusch, G. D., and Knoesel, R.,"Sensitivity Analysis of the MM5 Weather Modelusing Automatic Differentiation," Computers inPhysics, Vol. 10, No. 6 1996, pp. 605-612.90 Godfrey, A. B., and Cliff, E. M., "DirectCalculation of Aerodynamic Force Derivatives,"AIAA Paper 98-0393, 36th AIAA Aerospace ScienceMeeting, Reno, NV, Jan. 1998.91 Newman, P. A., Hou, G. J.-W., Jones, H. E.,Taylor, A. C. III and Korivi, V. M., "Observationson Computational Methodologies for Use in Large-Scale, Gradient-Based Multidisciplinary Design,"AIAA Paper 92-4753, 4th AIAA/USAF/NASA/OAISymposium on Multidisciplinary Analysis andOptimization, Cleveland, OH, 1992.92 Campbell, R. L., "Efficient Viscous Design ofRealistic Aircraft Configurations," AIAA Paper 98-2539, 29th AIAA Fluid Dynamics Conference,Albuquerque, NM, 1998.93 Herling, W., LeDoux, S., and Ratcliff, R.,"Application Studies using the 3DOPT IntegratedDesign System," AIAA Paper 98-4720, 7th

AIAA/USAF/NASA/ISSMO Symposium onMultidisciplinary Analysis and Optimization, St.Louis, MO, 1998.94 Barthelemy, J.-F., and Sobieszczanski-Sobieski, J.,"Optimum Sensitivity Derivatives of ObjectiveFunctions in Nonlinear Programming," AIAAJournal, Vol. 21, No. 6, 1983, pp. 913–915.95 Shiao, M. C., and Chamis, C. C., "Optimizationof Adaptive Intraply Hybrid Fiber Composites withReliability Considerations," NASA TM-106632,Aug. 1994.96 Cruise, T. A., ed., Reliability-Based MechanicalDesign, Marcel Dekker, New York, 1996.97 Xiao, Q., Seus, R. H., and Rhodes, G. S., "Multi-disciplinary Wing Shape Optimization with UncertainParameters," AIAA Paper 99-1601, 40th

AIAA/ASCE/AHS/ASC Structures, StructuralDynamics and Materials Conference, St. Louis, MO,1999.98 Chen, W., Allen, J. K., Tsui, K.-L., and Mistree,F., "A Procedure for Robust Design: MinimizingVariations Caused by Noise Factors and ControlFactors," ASME Journal of Mechanical Design, Vol.118, No. 4, 1996, pp. 478–485.99 Kowal, M. T., and Mahadevan, S., "Uncertainty-based Multi-disciplinary Optimization," AIAA Paper98-4915, 7th AIAA/USAF/NASA/ISSMOSymposium on Multidisciplinary Analysis andOptimization, St. Louis, MO, 1998.100 Knill, D. L., Giunta, A. A., Baker, C. A.,Grossman, B., Mason, W. H., Haftka, R. T., andWatson, L. T., "Response Surface ModelsCombining Linear and Euler Aerodynamics forSupersonic Transport Design," Journal of Aircraft,Vol. 36, No. 1, 1999, pp. 75–86.101 Rai, M. M., and Madavan, N. K., "Application ofArtificial Neural Networks to the Design ofTurbomachinery Airfoils," AIAA Paper 98-1003, 36th

AIAA Aerospace Science Meeting, Reno, NV, Jan.1998.102 Livne, E., "Integrated AeroservoelasticOptimization: Status and Direction," Journal ofAircraft, Vol. 36, No. 1, 1999, pp. 122–145.103 Karpel, M., "Reduced-Order Models for IntegratedAeroservoelastic Optimization," Journal of Aircraft,Vol. 36, No. 1, 1999, pp. 146–155.104 Silva, W. A., "Reduced-Order Models Based onLinear and Nonlinear Aerodynamic ImpulseResponses," AIAA Paper 99-1262, 40th

AIAA/ASCE/AHS/ASC Structures, StructuralDynamics and Materials Conference, St. Louis, MO,1999.105 Dowell, E. H., Hall, K. C., Thomas, J. P.,Florea, R., Epureanu, B. I., and Heeg, J., "ReducedOrder Models in Unsteady Aerodynamics," AIAAPaper 99-1261, 40th AIAA/ASCE/AHS/ASCStructures, Structural Dynamics and MaterialsConference, St. Louis, MO, 1999.

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