NASA Contractor Report 4328 Aircraft Design for Mission Performance Using Nonlinear Multiobjective Optimization Methods Augustine R. Dovi and Gregory A. Wrenn CONTRACT NASI-19000 OCTOBER 1990 https://ntrs.nasa.gov/search.jsp?R=19900020068 2018-07-04T04:23:29+00:00Z
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Formulation of the Mission/Performance Optimization Problem
Description of the Analysis System for Mission Performance
DESCRIPTION OF OBJE(TrlVE FUNCTION FORMULATION METHODS
Envelope Function Formulation (KSOPT)Global Criterion Formulation
Utility Function Formulation Using a Penalty Function Method
RESULTS AND DISCUSSION
Single Objective Function OptimizationParametric Results of the Design SpaceMultiobjective OptimizationComparison of Two Objective With Single Objective DesignsComparison of Three Objective With Single Objective DesignsComparison with Overall Best Single Objective Designs
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6
677
8
81010101111
CONCLUSIONS
REFERENCES
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LIST OF TABLES
Table la:
Table lb:
Table 2:
Table 3:
Table 4:
Table 5:
Multiobjective Cases
Single Objective Cases
Single Objective Design Results
Two Objective Design Results
Three Objective Design Results
Best Single Objective Results
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LIST OF FIGURES
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Objectives, Design Variables and Constraints
Mission Profile
FLOPS Primary Modules
Single Objective Optimization Change From Initial Conditions
Ramp Weight as a Function of Aspect Ratio and Thickness Ratio
Mission Fuel as a Function of Aspect Ratio and Thickness Ratio
Mach (L/D) as a Function of Aspect Ratio and Thickness Ratio
Two Objective Optimization Compromise From SingleObjective Cases
Three Objective Optimization Compromise From SingleObjective Cases
Two Objective Optimization Compromise From Best SingleObjective Cases
Three Objective Optimization Compromise From Best SingleObjective Cases
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SUMMARY
A new technique which converts a constrained optimization problem to an
unconstrained one where conflicting figures of merit may be simultaneously considered has
been combined with a complex mission analysis system. The method is compared with
existing single and multiobjective optimization methods. A primary benefit from this new
method for multiobjective optimization is the elimination of separate optimizations for each
objective, which is required by some optimization methods. A typical wide body transport
aircraft is used for the comparative studies.
INTRODUCTION
Aircraft conceptual design is the process of determining an aircraft configuration
which satisfies a set of mission requirements. Engineers within several diverse disciplines
including but not limited to mass properties, aerodynamics, propulsion, structures and
economics perform iterative parametric evaluations until a design is developed.
Convention limits each discipline to a subset of configuration parameters, subject to a
subset of design constraints, and typically, each discipline has a different figure of merit.
Advanced design methods have been built into synthesis systems such that
communication between disciplines is automated to decrease design time 1,2. Each
discipline may select its own set of design goals and constraints resulting in a set of
thumbprint and/or carpet plots from which a best design may be selected. In addition, the
conceptual design problem has been demonstrated to be very amenable to the use of formal
mathematical programming methods, and these algorithms have been implemented to
quickly identify feasible designs 3,4,5.
Thepurposeof thisreportis to investigate the use of multiobjective optimization
methods for conceptual aircraft design where conflicting figures of merit are considered
simultaneously. Three multiobjective methods6,7, 8 have been combined with a complex
mission analysis system 5. Trade-offs of the methods are compared with single objective
results. In addition parametric results of the design space are presented. The aircraft
chosen for this investigation is a typical wide body transport.
GENERAL MULTIOBJECTIVE OPTIMIZATION
The constrained multiobjective optimization problem stated in conventional
formulation is to
minimize Fk(X), k = 1 to number of objectives (1)
such that,
gj(X) _<o, j = 1 to number of constraints
and
xli < xi < xUi i = 1 to number of design variables
where,
X = {Xl,X2,X 3.... Xn}T n = number of design variables
The fundamental problem is to formulate a definition of Fk(X), the objective vector,
when its components have different units of measure thereby reducing the problem to a
single objective. Several techniques have been devised to approach this problem 7. The
methods selected for study in this report transform the vector of objectives into a scalar
2
functionof thedesignvariables.Theconstrainedminimumfor this functionhasthe
propertythatoneormoreconstraintswill beactiveandthatanydeviationfrom it will cause
atleastoneof thecomponentsof theobjectivefunctionvectorto departfrom its minimum,
Figure 1. Objectives, Design Variables and Constraints
Taxi out,
PRIMARY MISSION PROFILE
Takeoff, Climb atmaximum I Ca,uise-climb at desigrat.ed ]O_d,_te-of-climb to long- [ Math number ]constantrange cruisealtitude " __CLidle
RESERVE PROFILE DOMESTIC OPERATIONS
Climb, I Long range ertme, [ Descend
] altitude and Mach ]nmnber
Taxi in, I
Figure 2. Mission Profile
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/
AnalysisControl
md
Figure 3. FLOPS Primary Modules
SINGLE OBJECTI VE OPTIMIZATIONCHANGE FROM INITIAL CONDITIONS
• WE If.wt"f
rl FU_,B k/O
g
Figure 4
RAMPWEIGHT AS A FUNCTION OF
ASPECT RATIO AND THICKNESS RATIO
l.It
Figure $
MISSION FUEL AS A FUNCTION OF
ASPECT RATIO AND THICKNESS RATIO
m dI4110
Figure 6
MACH (L/D) AS A FUNCTION OF ASPECT
RATIO AND THICKNESS RATIO
u _wm
Figure 7
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TWO OBJECTIVE OPTIMIZATION
COMPROMISE FROM SINGLE OBJECTIVE CASES
,°1 _r • WEIGHT
[] FUEL
xl",b
KSOPT PF GLOBAL
CASE I CASE 3 CASE 5
Figure 8
IO
6
-rU
CC
.=
TWO OBJECTIVE OPTIMIZATION COMPROMISEFROM BEST SINGLE OBJECTIVE CASES
• WEIGHT (CASE 7)
[] FUEL (CASE 12)
KSOPT
Figure 10
Z,(
THREE OBJECTIVE OPTIMIZATION
COMPROMISE FROM SINGLE OBJECTIVE CASES
40,
• WEIGHT
[] FUEL Z
I_ LID
30
20 _
• -_ r-
KSOPT PF GLOBAL
CASE 2 CASE 4 CASE 6
Figure 9
40
3O
Z
__ 20
z
10'
THREE OBJECTIVE OPTIMIZATION COMPROMISEFROM BEST SINGLE OBJECTIVE CASES
• WEIGHT (CASE 7)
[] FUEL (CASE 12) .
KSOPT PF GLOBAL
Figure 11
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1. Report No.
NASA CR-4328
Report Documentation Page
2. Government Accession No.
4. Title and Subtitle
Aircraft Design for Mission Performance UsingNonlinear Multiobjective Optimization Methods
7. Author(s)
Augustine R. Dovi and Gregory A. Wrenn
9. Performing Organization Name and Address
Lockheed Engineering & SciencesHampton, VA 23666
12. Sponsoring Agency Name and Address
NASA Langley Research CenterHampton, VA 23665
3. Recipient's Catalog No.
5. Report Date
October 1990
6. Performing Organization Code
8. Performing Organization Report No.
10. Work Unit No.
505-63-01
11. Contract or Grant No.
NAS1-1900013. Type of Report and Period Covered
Contractor Report
15. Supplementary Notes
Company
14. Sponsoring &gency Code
Langley Technical Monitor: Jaroslaw Sobieski
16. Abstract
A new technique which converts a constrained optimization problem to anunconstrained one where conflicting figures of merit may be simultaneouslyconsidered has been combined with a complex mission analysis system. Themethod is compared with existing single and multiobjective optimization methods.A primary benefit from this new method for multiobjective optimization is theelimination of separate optimizations for each objective, which is required bysome optimization methods. A typical wide body transport aircraft is used forthe comparative studies.