project 2e: model-based systems engineering for efficient ... · •formulated tb3 optimization as...
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Approach: Model-Based Systems Engineering
Project 2E: Model-Based Systems Engineering for Efficient Fluid PowerInvestigators: Chris Paredis, Alek Kerzhner, Ben Lee, Roxanne Moore, Isabelle Bouchard, Jayme
Walton, Chris Min, Yaro Vasyliv (Georgia Tech)
What fluid power-related
question is being answered?
What progress has been made?
Georgia Institute of Technology | Milwaukee School of Engineering | North Carolina A&T State University | Purdue University | University of Illinois, Urbana-Champaign | University of Minnesota | Vanderbilt University
CCEFP
Project 2E
• How can one most effectively
represent design knowledge
about fluid power systems?
• Can one significantly reduce the
time and effort required to formulate
and solve fluid power design
problems through composition and
re-use of synthesis and analysis
models?
• How can one capture analysis
knowledge about fluid power
components from multiple
disciplinary perspectives and at
multiple levels of abstraction?
• How can one use fluid power
models at different levels of fidelity
to search the system design space
• ModelCenter Framework
SysML
SysML
SysML
Problem
Definition
Generate
Algebraic Design
Problem
SysMLAlgebraic
Models
Generate
Architecture
ComponentsSysML
Generate
Dynamic Design
Problem
SysMLDynamic
Models
SysML Model exchanged in XMIMagicDraw SysML Editor
GAMS SolverMOFLON Transformation Engine
Topology
Analysis
Dynamic
Analysis
Uncertainty
Quantification
Mixed-Integ
Nonlin Solver
Algebraic
Analysis
Optimization
Solver
Monte Carlo + KrigingDesign Explorer Modelica
GAMS
Variable Fidelity
Model Selection
SysML and ModelCenter
• Implemented integration between SysML authoring tool and ModelCenter.
• Allows designers to explicitly define their problem in SysML and then perform
design exploration in ModelCenter.
Capture
Knowledge
For Domain
The Problem Given:• Knowledge about the domain
• Objectives / preferences
Find:• Best system architecture
• Best component parameters
Excavator
pump_vdisp
cylinder
accum
How to connect and size
these components?
engine
v_3way
Why is this a hard problem?
• Many competing objectives
• Many potential system alternatives
• Many component types/sizings
• Large Amount of Domain Knowledge
• Large Optimization Problem
Predict
Outcomes
Maximize E[u]
Most Preferred
System Alternative
Ideas Knowledge Preferences
Decision TheoryDecision Theory
Generate
AlternativesSelection Criterion:
E[u]
Based on Decision Theory. Want to make
rational decisions efficiently.
MagicDraw ModelCenter
50
100
150
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15
20
0
2
4
6
x 109
E pump displacementB pump displacement
Exp
ec
ted P
rofit
Expected
Profit [$/rev] x108
How does this fit into the
Center’s overall strategy?
On which test bed will it
be demonstrated?
Who are the industry and university collaborators?
to search the system design space
most efficiently?
• Enable designers to make efficient
and effective comparisons of
different system architectures
relative to their preferences for
system-level trade-offs � Efficient
Systems and Compact Integrated
Systems
• Enable the evaluation of the impact
of introducing new component
technologies � Efficient
Components
• Enable the fluid-power industry to
predict the impact of technology
trends on overall system
performance � Efficient Systems
and Compact Integrated Systems
• The model-based systems
engineering approach for fluid-
power systems will be used to
perform a thorough exploration of
the space of system architectures
for both TB1 (Excavator) and TB3
(Hydraulic Hybrid Passenger
Vehicle)
Industry
Deere & Co.,Sauer-Danfoss,
Lockheed Martin, No Magic Inc.,
Phoenix Integration
University
Linköping University,
Univ. of Darmstadt,
Univ. of Stuttgart, Univ. of Bath
Publications• Kerzhner and Paredis, "Model-Based System Verification: A Formal Framework for Relating Analyses, Requirements, and
Tests ", 4th International Workshop on Multi-Paradigm Modeling - MPM'10, October 2010.
• Malak and Paredis, “Using Support Vector Machines to Formalize the Valid Input Domain of Predictive Models for
Systems Design Problems,” in Journal of Mechanical Design,
• Malak and Paredis, "Using Parameterized Pareto Sets to Model Design Concepts." Journal of Mechanical Design.
• Shah, Kerzhner, Schaefer and Paredis, "Multi-View Modeling to Support Embedded Systems Engineering in SysML." in
Graph Transformations and Model-Driven Engineering - Essays Dedicated to Manfred Nagl LNCS 5765, Springer-Verlag,
Berlin/Heidelberg (2010).
• Shah, A. A., C. J. J. Paredis, Burkhart, R., and Schaefer, D., “Combining Mathematical Programming and SysML for
Component Sizing of Hydraulic Systems,” Proceedings of IDETC/CIE 2010. Montreal, Quebec, Canada, 2010.
Hydraulic Hybrid Vehicle (TB3)
• Formulated TB3 optimization as value-driven design problem.
• Performed design exploration to maximize expected profit.
Variable Optimization Framework
• Implemented and tested framework on base-cases.
% market
max vel = 120mph
price = $12,000
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-10
-5
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X
Y(X
)
Truth
MSE
low fidelity
high fidelity
fit
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-0.1
0
0.1
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X
E[V
(I(X
))]
low fidelity VOI
high fidelity VOI
Model 1 Samples
Model 2 Samples
x
Y(x)
Variable
Accuracy Data
from q models
Fit Gaussian
Process- Based
Surrogate Model
x
Y(x)
x
Y(x)
Select next point and
analysis using Value of
Information Metric
Sequential Sampling and
Updating
Define Problem
in SysML
Generate
Synthesis
Problem &
Sizing Problem
Formulate Problem Solve ProblemCompilation
MINLP
Represet knowledge about domain in
logical constraints + algebraic constraints:
• isConnected(x,y) <=> isConnected(y,x).
• (x.flow+y.flow)*isConnected(x,y)=0
Define
Problem
Generate
Alternatives
Predict
Outcomes
Select Most
Preferred
Alternative
Capture knowledge about the domain in
information models to allow for review
and reuse.
Explicitly define the problem in information models.
Use models at varying levels of fidelity during
optimization to predict outcomes. Use Value of
Information to choose locations to explore.
Compile problem formulation into a MINLP
problem. Solving problem gives both
plausible alternatives and initial sizings.
Value-Driven Design perspective where the
objective is to maximize value design provides.
MagicDraw ModelCenter
Problem
Description Executable
Simulations
Executable
Simulations
Executable
Simulations
Demand Model Expected Profit
Customer
Demand
Utility
Engine Size
Pump/Motor
Size
Transmission
Ratios
Accumulator
Size
Hydraulic Oil
Market
Perception
Weather
Manufacturing
Defects
Driver
Behavior
Price
Safety
Reliability
Top Speed
Fuel Economy
Noise
Production
Cost
Acceleration
Terrain
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
-10
-5
0
5
10
X
Y(X
)
Truth
MSE
low fidelity
high fidelity
fit
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
1
2
3
4
5
6
7
X
E[V
(I(X
))]
low fidelity VOI
high fidelity VOI
50
100
150
5
10
15
20
0
2
4
6
x 109
E pump displacementB pump displacement
Expecte
d P
rofit
Profit [$/rev] x108
Deterministic Profit