16.842: tradespace exploration and concept selection · pugh matrix steps 1. choose or develop the...
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16.842
16.842 Fundamentals of Systems Engineering
1
Lecture 5 – Tradespace Exploration and Concept Selection
Prof. Olivier de Weck
October 9, 2009
16.842
V-Model – Oct 9, 2009
Systems EngineeringOverview
Stakeholder Analysis
RequirementsDefinition
System ArchitectureConcept Generation
Tradespace ExplorationConcept Selection
Design DefinitionMultidisciplinary Optimization
System IntegrationInterface Management
Verification andValidation
CommissioningOperations
Lifecycle Management
Cost and ScheduleManagement
Human Factors System
Safety
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Outline
Decision AnalysisIssues in Concept SelectionSimple Methods of Concept Selection
Pugh MatrixMulti-Attribute Utility
Non-DominancePareto Frontiers, Multiobjective Optimization
Tradespace ExplorationContribution from SEARI
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ConceptSynthesis
ConceptScreening
ConceptSelection
SystemDesign
Conceptual Modeling &
Optimizationmetric 1
met
ric2
DecisionMaking
Design Modeling &
Optimization
variable x1
met
ric3
x1*
Need Qualitative Quantitative
“Optimal”Design
System Architecture System Design
System Architecture Design
SRRPDR
CDR
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Decision Analysis
Methods and Tools for ranking (and choosing) among competing alternatives (courses of action)Components of a decision
alternativescriteriavalue judgmentsdecision maker (individual or group) preferences
A
B
C
• cost• performance• risk
C(A)=1.1, +P(A)=0.8, -R(A)=1.5, 0
1.B2.C3.A
BCA
0
ordinal scale
cardinal scale
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Issues in Concept Selection
multiple criteria – how to deal with them ?what if there are ties between alternatives?group decision making versus individual decision making?
relates to stakeholder analysis
uncertaintyright criteria?right valuation? are the best alternatives represented?
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Simple Methods of Concept Selection
Pugh MatrixUses +, 0, - to score alternatives relative to a datumNamed after Stuart Pugh
Utility AnalysisMaps criteria to dimensionless Utility (0 1)Rooted in Utility Theory (von Neumann-Morgenstern 1944)
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Pugh Matrix Steps1. Choose or develop the criteria for comparison.
Based on a set of system requirements and goals.
2. Select the Alternatives to be compared.The alternatives are the different ideas developed during concept generation. All concepts should be compared at the same level of generalization and in similar language.
3. Generate Scores.Use the “best” concept as datum, with all the other being compared to it for each criterion.If redesigning an existing product, then the existing product can be used as the datum.
Evaluate each alternative as being better (+), the same (S, o), or worse (-) relative to the datum.If the matrix is developed with a spreadsheet like Excel, use +1, 0, and -1 for the ratings.If it is impossible to make a comparison, more information should be developed.
4. Compute the total scoreThree scores will be generated, the number of plus scores, minus scores, the overall total.The overall total is the number of plus scores- the number of minus scores. The totals should not be treated as absolute in the decision making process but as guidance only.
5. Variations on scoring
A number of variations on scoring Pugh’s method exist.For example a seven level scale could be used for a finer scoring system where:+3 meets criterion extremely better than datum +2, +1, 0, -1, -2, -3
Source: http://www.enge.vt.edu/terpennyAdapted from
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Pugh Example (Simple)
+
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+
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1 2 3 4 5 6 7 8 9 10 11
A
B
C
D
E
F
Σ+
Σ−
ΣS
Concept
Criteria
Image by MIT OpenCourseWare.
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Pugh Example (Complex)
SDM Thesis, Feb 2003
Idea or Need
Expansion
Initial Possible Feasible Promising
Selection
Screening
Filtering
Concept generation and selection process
Thesis study region
Image by MIT OpenCourseWare.
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Architectural Space
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Filtered Concepts
Reactor
Fuel
Temp
Conversion
Exchange
Reactor
Fuel
Temp
Conversion
Exchange
Reactor
Fuel
Temp
Conversion
Exchange
LM
UO2
UO2 UO2 UO2 UO2 UO2 UO2 UN UN UN UN UN UN UO2 UO2 UO2 UO2 UO2 UO2 UN UN UN UNUNUN UN UN
M M M H H H M M M H H H M M M H H H M M M H H H
UO2 UO2 UO2 UO2 UO2 UO2 UO2 UO2 UO2 UO2 UO2UN UN UN UN UN UN UN UN UN UN UN UN
LM LM LM LM LM LM LM LM LM LM LM LM LM LM LM LM LM LM LM LM LM LM LM
B
D D D D D D D D D D D D
R TE B R TE B R TE B R TE B R TE B R TE B R TE B R TE
B
D
HP HP HP HP HP HP HP HP HP HP HP HP HP HP HP HP HP HP HP HP HP HP HP HP
D D D D D D D D D D D
R TE B R TE B R TE B R TE B R TE B R TE B R TE B R TE
GC GC GC GC GC GC GC GC GC GC GC GC GC GC GC GC GC GC GC GC GC GC GC GC
M M M H H H M M M H H H M M M H H H M M M
UO2 UO2 UO2 UO2 UO2 UO2 UN UN UN UNUNUN UN UN UO2 UO2 UO2 UO2 UO2 UO2 UN UN UN UN UN UN
B
D D D D D D D D D D D D
R TE B R TE B R TE B R TE B R TE B R TE B R TE B R TE
M M M H H H M M M H H H M M M H H H H H HM M M
H H H
Direct HP and LM
Direct TE and RankineGC with TE and RankineHigh temperature UO2Remaining Concepts
Liquid Metal
Gas CooledHeat PipeMedium
High
Brayton
RankineThermoelectricDirect
Indirect
LM
GC
HP
M
H
X
X
X
X
X
B
R
TEDI
Image by MIT OpenCourseWare.
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Concept Screening Matrix (Pugh)
Reactor
Conversion Device
Heat Exchange
Fuel
Operating Temp.
TRL
Infrastructure
Complexity
Strategic Value
Schedule
Launch Packaging
Power
Specific Power
Lifetime
Payload Interaction
Adaptability
Sum “+”
Sum “0”
Sum “-”
Net Score
Rank
LM LM LM LM LM LM LM LM LM HP HP HP HP HP HP HP HP HP GC GC GC GC GC GC
B
M
0 0
0 0
0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0000
0
0
0
0
0
0
0
0
0
0
0 0 0
0
0 0 0
0
0
0
0
00 000
0
0 0
00
0
0
00
00
0
0 0 0 0 0
0 0 0 0 0 0
0
0
0
0
0
0
00
0 0 0 0 0 0 0 0
0 0
0 0 0 0 0 00 0 0 0
0
0
0
0
0 0
0
0000
00
0 0 0 0
0 0
M M M M M M M M M M M M M M M
B B R R R TE TE TE B B B R R R TE TE TE B B B B B B
| | | | | | | | | | | | | | | | | | | | | DDD
UO2 UO2 UO2 UO2 UO2 UO2 UO2 UO2UN UN UN UN UN UN UN UN UN UN UN UN UN UN UN UN
HHHHHHHH
+
+
+ +
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++
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++++
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2 2
2 22
2 2 2 2 2 2 2
2 2-5 -4-3-3-3-3-3-3 -3 -3 -3-2 -2 -1-1 1 -2
2 2 2 2
2
55
5 5 5 5 5 5 5
55 5
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5 55 5
544
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3 3
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6 6
6 8
11
66666666
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3 3 3
3
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11 1 4
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LM = Liquid MetalHP = Heat PipeGC = Gas Cooled
B = BraytonR = RankineTE = Thermoelectric
I = IndirectD = Direct
M = MediumH = High
Criteria
Concept Combinations
Promising concepts
SP-100 Reference
Image by MIT OpenCourseWare.
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What is Pugh Matrix for?
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Challenges
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Role of the Facilitator
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Critique
Ranking of alternatives can depend on the choice of datumWeighting: Some criteria may be more important than others
See stakeholder analysisCan implement a “weighted” version of the Pugh method, but need to agree on weightings
Multiattribute Utility Analysis and Pugh Method may yield different rank order of alternativesThe most important criteria may be intangible and missing from the listPersonal Opinion
Pugh Method is useful and simple to use. It stimulates discussion about the important criteria, set of alternatives,…Should not be used as the ONLY means of concept filtering and selection
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Utility TheoryUtility is defined as
In economics, utility is a measure of the relative happiness or satisfaction (gratification) gained by consuming different bundles of goods and services. Given this measure, one may speak meaningfully of increasing or decreasing utility, and thereby explain economic behavior in terms of attempts to increase one's utility. The theoretical unit of measurement for utility is the util.
Generally map criteria onto dimensionless utility [0,1] intervalCombine Utilities generated by criteria into overall utility
Consumption Set X (mutually exclusive alternatives)
ℜaXU : Ranks each member of the consumption set
A
B
C
• cost• performance• risk
BCA
0
cardinal scale
Utility U1
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Utility Function Shapes
Ji
Ui
Ji
Ui Ui
Ji
Ui
JiMonotonicincreasingdecreasing
StrictlyConcaveConvex
ConcaveConvex Non-monotonic
Cook:Smaller-is-better (SIB)Larger-is-better (LIB)
Nominal-is-better (NIB)
Range-is-better (RIB)
-
Messac:
Class 1SClass 2S
Class 3S Class 4S
(this is almostnever seenIn practice)
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Aggregated Utility
The total utility becomes the weighted sum of partial utilities:
Attribute Ji
customer 1customer 2customer 3
Caution: “Utility” is a surrogate for “value”, but while “value”has units of [$], utility isunitless.
interviews
Combine single utilitiesinto overall utility function:
Steps: MAUA1. Identify Critical Objectives/Attrib.2. Develop Interview Questionnaire3. Administer Questionnaire4. Develop Aggregate Utility Function5. Determine Utility of Alternatives6. Analyze Results
(performance i)
Ui(Ji)
ki’s determined during interviewsK is dependent scaling factor
… sometimes called multi-attribute utility analysis (MAUA)
1.0
E.g. two utilities combined: ( )1 2 1 2 1 2 1 1 2 2, ( ) ( ) ( ) ( )U J J Kk k U J U J kU J k U J= + +
1 2 1 2(1 ) /K k k k k= − −For 2 objectives:
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Notes about Utility Maximization
• Utility maximization is very common and well accepted• Usually U is a non-linear combination of criteria J• Physical meaning of aggregate objective is lost (no units)• Need to obtain a mathematical representation for U(Ji) for
all i to include all components of utility• Utility function can vary drastically depending on decision
maker …e.g. in U.S. Govt change every 3-4 years• Requires formulation of preferences apriori
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Example: Space Tugs (2002-2004)
A satellite that has the ability to change the orbitalelements ( ) of a target satellite by a predefined amount without degrading its functionalityin the process.
, , , , ,e iα ω νΩ
- Waiting in Parking Orbit- Tasking and Orbital Transfer- Target Search and Identification- Rendezvous and Approach- Docking and Capture- Orbital Transfer- Release and Status Verification- Return to Parking Orbit or Next Target
Typical Mission ScenarioTypical Mission Scenario
Image by MIT OpenCourseWare.
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Total ΔV capability
System Attributes (Objectives)
- where it can goCalculated from simple model (rocket equation)
Response time - how fast it can get thereBinary - electric is slow - some astrodynamics
Mass of observation/grappling equipment -what it can do when it gets there
Based solely on payload mass
Vehicle wet and dry mass - cost driversCalculated from simple models - scaling relationships
Combineinto aUtility[0,1]
KeepCost
separate[M$]
McManus, H. L. and Schuman, T. E., "Understandingthe Orbital Transfer Vehicle Trade Space," AIAA-2003-6370, Sept. 2003.
(MATE Method)
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What is Utility ?
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
0 2000 4000 6000 8000 10000 12000ΔV [m/s]
ΔV si
ngle
-attr
ibut
e U
tility
Leo-Geo
Leo-Geo RT
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Low (300 kg) Medium (1000 kg) High (3000 kg) Extreme(5000 kg)
Cap
abili
ty S
ingl
e-A
ttri
bute
Util
ity
ΔV - Utility : where it can goPayload mass utility: whatit can handle
Response time utility binary (electric bad)Total Utility a weighted sum
Examples will stress ΔV, then capability
Cost estimated from wet and dry mass
Weights:- Capability 0.3- DV 0.6-Time 0.1-Sum: 1.0
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0
500
1000
1500
2000
2500
3000
3500
4000
0.00 0.20 0.40 0.60 0.80 1.00
Utility (dimensionless)
Trade SpaceFreebirdBiprop GEO tenderBiprop LEO 2 tenderLEO 4A TenderBiprop GEO tugElectric GEO CruiserSCADS
711 kg dry mass, 1112 kg wet massIncludes return of tug to safe orbitA reasonable, versatile system
Electric GEO Cruiser
Biprop LEO tender
680.18 kg dry mass; 1403.6 kg wet massReasonable size and mass fraction
Cost[M$]
Space Tug Tradespace Analysis
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Trade Space Analysis
Hits a “wall” of either physics (can’t change!) or utility (can)
0.00
500.00
1000.00
1500.00
2000.00
2500.00
3000.00
3500.00
4000.00
0.00 0.20 0.40 0.60 0.80 1.00
Utility (dimensionless)
Low BipropMedium BipropHigh BipropExtreme BipropLow CryoMedium CryoHigh CryoExtreme CryoLow ElectricMedium ElectricHigh ElectricExtreme ElectricLow NuclearMedium NuclearHigh NuclearExtreme Nuclear
Cost
($M
)
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Non-Dominance
Non-Dominance, Pareto FrontierMultiobjective Optimization
Preferences enter aposteriori
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History – Vilfredo Pareto
Born in Paris in 1848 to a French Mother and Genovese FatherGraduates from the University of Turin in 1870 with a degree in Civil Engineering
Thesis Title: “The Fundamental Principles of Equilibrium in Solid Bodies”While working in Florence as a Civil Engineer from 1870-1893, Pareto takes up the study of philosophy and politics and is one of the first to analyze economic problems with mathematical tools. In 1893, Pareto becomes the Chair of Political Economy at the University of Lausanne in Switzerland, where he creates his two most famous theories:
Circulation of the ElitesThe Pareto Optimum
“The optimum allocation of the resources of a society is not attained so long as it is possible to make at least one individual better off in his own estimation while keeping others as well off as before in their own estimation.”Reference: Pareto, V., Manuale di Economia Politica, Societa Editrice Libraria, Milano, Italy, 1906. Translated into English by A.S. Schwier as Manual of Political Economy, Macmillan, New York, 1971.
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Properties of optimal solution
( ) ( )*optimal if
for and for S
≥
∈ ≠
*
*
x J x J x
x x x*This is why multiobjective optimization is alsosometimes referred to as vector optimization
x* must be an efficient solution
S∈x is efficient if and only if (iff) its objective vector(criteria) J(x) is non-dominated
A point is efficient if it is not possible to move feasiblyfrom it to increase an objective without decreasing at leastone of the others
S∈x
(maximization)
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Dominance (assuming maximization)Let be two objective (criterion) vectors.
Then J1 dominates J2 (weakly) iff
More precisely:
z∈1 2J , J
1
2i
z
JJ
J
J
⎡ ⎤⎢ ⎥⎢ ⎥=⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦
M and ≥ ≠1 2 1 2J J J J
1 2 1 2 and for at least one i i i iJ J i J J i≥ ∀ >
Also J1 strongly dominates J2 iff
More precisely: >1 2J J
1 2 i iJ J i> ∀
R
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Dominance - Exercisemax{range}min{cost}max{passengers}max{speed}
[km][$/km][-][km/h]
7587 6695 3788 8108 5652 6777 5812 7432321 211 308 278 223 355 401 208112 345 450 88 212 90 185 208950 820 750 999 812 901 788 790
#1 #2 #3 #4 #5 #6 #7 #8
MultiobjectiveAircraft Design
Which designs are non-dominated ? (5 min)
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ProcedureAlgorithm for extracting non-dominated solutions:Pairwise comparison
7587 > 6695321 > 211 112 < 345950 > 820
Score#1
Score#2#1 #2
1 00 10 11 0
2 vs 2Neither #1 nor #2 dominate each other
7587 > 6777321 < 355 112 > 90950 > 901
Score#1
Score#6#1 #6
1 01 01 01 0
4 vs 0Solution #1 dominatessolution #6
In order to be dominated a solution musthave a ”score” of 0 in pairwise comparison
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Domination Matrix
1 2 3 4 5 6 7 8
12345678
12000001
Solution 2 dominatesSolution 5
0 0 0 0 1 1 2 0
Shows which solution dominates which othersolution (horizontal rows) and (vertical columns)
Solution 7 is dominatedby Solutions 2 and 8
Row Σ
j-th row indicateshow manysolutionsj-th solutiondominates
Column Σ
k-th column indicatesby how many solutionsthe k-th solution is dominated
Non-dominated solutions have a zero in the column Σ !
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Pareto-Optimal vs non-dominated
max (J1)
min(J2)TrueParetoFront
ApproximatedPareto Front
D ND PO
All pareto optimal points are non-dominatedNot all non-dominated points are pareto-optimal
√√√ √
It’s easier to show dominatedness than non-dominatedness !!!
Obtaindifferentpoints fordifferent weights
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Conclusions
During Conceptual DesignUse Pugh-Matrix Selection
When detailed mathematical models not yet available, but qualitative understanding exists
During Preliminary DesignUse Utility Analysis
Especially for non-commercial systems where NPV may not be easy to calculate
Use Non-dominanceGenerate many designs for each concept, apply Pareto filter
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16.842 Fundamentals of Systems EngineeringFall 2009
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