project 2e: model-based systems engineering for efficient ... · •formulated tb3 optimization as...

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

5

10

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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60

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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

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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