Research Overview

Systems Realization Laboratory

© 2008, Chris Paredis

Research Overview

Chris Paredis

Systems Realization LaboratoryProduct and Systems Lifecycle Management Center

G.W. Woodruff School of Mechanical EngineeringGeorgia Institute of Technology

www.srl.gatech.edu www.pslm.gatech.edu

Systems Realization Laboratory© 2008, Chris Paredis

Research Scope, Context, and Foundation Model-Based Systems Engineering

1. Reusable Analysis Models Defined in SysML

2. Predictive Trade-off Models

3. Variable Fidelity Analysis

4. Capturing Synthesis Knowledge as Graph Transformations

5. Risk Management in Systems Engineering

Summary

Presentation Overview

2


Research Area• Modeling and Simulation in Design

Application Focus: Systems engineering• Fluid power systems• Mechatronic systems

Research Focus• Decision theory• Modeling and Simulation• Information technology

Research Scope and Context

3


Product Development: A Decision-Based Perspective

4

Concept

Development Design

Production

& Testing

Sales &

Distribution

Maintenance

& Support

Portfolio

Planning

Decisions

Evaluate Alternatives

GenerateAlternatives

Select Alternative

KnowledgeInformation

GenericDecisionProcess

Modeling and Simulation Provides Informationin Support of Decisions


A Generic Design Decision

5

Decision

nA

11O

12O

1kO

21O

22O

2kO

1nO

2nO

nkO

11( )U O

12( )U O

1( )kU O

21( )U O

22( )U O

2( )kU O

1( )nU O

2( )nU O( )nkU O

Select iAwhere

is maximum

[ ]E U

Select iASelect iAwhere

is maximum

[ ]E U

1A

2A

Alternatives Outcomes(Attributes)

Preferences


Uncertainty

Why are Design Decisions Difficult?

Decision

nA

11O

12O

1kO

21O

22O

2kO

1nO

2nO

nkO

11( )U O

12( )U O

1( )kU O

21( )U O

22( )U O

2( )kU O

1( )nU O

2( )nU O( )nkU O

Select iAwhere

is maximum

[ ]E U

Select iASelect iAwhere

is maximum

[ ]E U

1A

2A

Uncertainty

Alternatives Outcomes(Attributes)

Preferences

Limited Resources

Infinite number of

alternatives


Integration of Design Product & Design Process

Goal: maximize overall utility• Must consider process in utility assessment

Value trade-offs between product and process• Decrease expected utility of product to reduce expected cost of

process• "Optimal" solution is guaranteed not to be optimal from a pure

product perspective

Information Economics• Meta-level decision:

How to frame your design problem?

Cost Value Cost Value

7


Systems Approach to Product Development

The systems approach provides a balanced trade-off between product and process objectives

Systematic decomposition• Large, flexible, yet manageable design space

Decoupling• Limit the risk due to unexpected interactions• Enable collaborative engineering

Helps us deal with complexity

8


Model-based Systems Engineering (MBSE)

Effective and Efficient Analysisof Alternatives• Model from different

perspectives• Model at different levels of

abstraction• Model reuse & modularity• Optimization with grid-computing

Effective Generationof Alternatives• Graph transformations for

generating plausible system architectures

• Automated generation of system models

9

Requirements & Objectives

Executable Simulations

System Behavior Models

Design Optimization

System Alternatives

ModelLibraries

MBSE: Model formally all aspects of a systems engineering problem

MBSE: Model formally all aspects of a systems engineering problem

Systems Realization Laboratory© 2008, Chris Paredis10

MBSE: Example Problem

Given:• Primary components• Decision objectives / preferences

Find:• Best system topology• Best component parameters

Given:• Primary components• Decision objectives / preferences

Find:• Best system topology• Best component parameters

Very large search and optimization problem• Many competing

objectives• Many topologies• Many component

types/sizes• Many control

strategiesExcavator

pump_vdisp

cylinder

accum

How to size and connect these?

engine

v_3way

10


Which decisions should be made at each point in the product development process?• How should decisions be ordered in a decision sequence?• How should the decisions be framed? Which decision alternatives

should one consider?

Which information should be used in support of these decisions?• How accurate should the information be?• How do we trade off accuracy versus cost?

Which tools allow us to obtain this information most cost effectively?• Which Information Technologies can be used to reduce the cost of

information?• Is it cost effective to use repositories of reusable models?

Research Questions

11








Summary


12



Formal Representation of Engineering Analysis Models in SysML

Student: Jonathan Jobe

Reusable Analysis Models

14

Multi-Aspect Component Models

• Components are the reusable elements of design

• MAsCoMs:– Group all models related to

single fluid power component– Multiple disciplines and levels

of abstraction– Modular– Formal & unambiguous

• Systems Modeling Language (OMG SysMLTM)

– Formally model systems design information, from requirements through testing

15

How to use MAsCoMs?

Design Concept Schematics

-Hydraulic System

ISO 1219Fluid Power Graphics

Log Splitter Design Example

16

Log Splitter—Model Composition

17

Automatic Translationfrom SysML to Modelica

Formal Graph Transformations Modelica

SysML








Summary


18



Reusable Models for Predicting the Performance of Design Concepts

Student: Rich Malak

Predictive Trade-off Models


Decision Chains: From Concept to Detail

DesignDecision

Alternative 1

Alternative 2

Alternative 3

Alternative n

...

One-Shot Decision A Chain of Decisions

Decision3.1

Decision1

Decision3.2

Alternative 1

Alternative 2

Alternative 3

Alternative 4

Decision3.3

Alternative…

Alternative…

Decision3.4

Alternative n-1

Alternative n

Decision2.1

Decision2.2

Concept 2.1

Concept 2.2

Concept 3.1

Concept 3.2

Concept 3.3

Concept 3.4

20


Decision Chains: From Concept to Detail

DesignDecision

Alternative 1

Alternative 2

Alternative 3

Alternative n

...

One-Shot Decision A Chain of Decisions

Decision3.1

Decision1

Decision3.2

Alternative 1

Alternative 2

Alternative 3

Alternative 4

Decision3.3

Alternative…

Alternative…

Decision3.4

Alternative n-1

Alternative n

Decision2.1

Decision2.2

Concept 2.1

Concept 2.2

Concept 3.1

Concept 3.2

Concept 3.3

Concept 3.4

Decision2.1

Alternative 1

Alternative 2

Alternative 3

Alternative 4

Each Concept = Set of Design Alternatives

21


Modeling Set-Based Design Concepts

What is the appropriate gear ratiofor the differential?

…it depends• On the other drivetrain

components• On manufacturing and

cost considerations• On the details of

differential itself

How do we best model a subsystem conceptto support decision making at the systems level?

22


Functional and Preference Attributes

What is important about the differential?• Gear ratio• Maximum torque• Maximum speed• Size, mass• Cost

What is NOT important about the differential?• Working principle• Detailed dimensions• Manufacturing processes

Functional Attributes

Preference Attributes

Only important to the extent that theyinfluence the preference attributes

Model Preference Attributes as Function of Key Functional Attributes

23


Predictive Tradeoff Model: Hydraulic Cylinder Key functional attributes

• Bore diameter

• Stroke length

Predicted preference attributes• Mass

• Cost

stroke

mass

borecost

stroke

mass

borecost utility

stroke

bore pumpdisp

Raw Cylinder Data Predictive Cylinder Model System Tradeoffs

stroke

mass

borecost

stroke

mass

borecost

stroke

mass

borecost utility

stroke

bore pumpdisp



Taking Designer Preferences into Account

Not all feasible designs are preferred: Pareto optimality

Non-dominated set (efficient frontier). Every point is optimal under some tradeoff

0.95 0.96 0.97 0.98 0.99 1

200

250

300

350

400

Reliability

Cos

t ($)

Valid Designs: Planetary Gear TrainFeasible Designs: Planetary Gear TrainFeasible, but dominated. No engineer will choose these

Care only about non-dominated set

25


Parameterized Efficient Sets

2.61222.9375

3.25003.5789

3.8750

0.95

0.96

0.97

0.98

0.99

1

180

200

220

240

260

280

300

320

340

360

Torque Ratio

Reliability

Co

st (

$)

No problem-independent preference for gear ratio.Solution: find efficient set as function of gear ratio.

Gear Ratio

26


Combining Multiple Concepts with the same Functionality

Blue reverted gear train

dominates at gear ratios < 5

Redplanetary gear train

dominates at gear ratios > 5

Best concept can be identified after consideringsystems-level tradeoff for gear ratio and other attributes.

33.5

44.5

55.5

6

0.940.95

0.960.97

0.980.99

1

150

200

250

300

350

400

450

500

Torque RatioReliability

Co

st (

$)

Gear Ratio

33.5

44.5

55.5

6

0.940.95

0.960.97

0.980.99

1

150

200

250

300

350

400

450

500

Torque RatioReliability

Co

st (

$)

Gear Ratio

27


Another Example: Small 4-stroke Engines

Some engines are dominated• E.g. same torque, mass,

power, but lower price

Not all combinationsof the functional attributes are feasible• Clustering algorithms

are used to define the feasible set(Support Vector Machines)

3D Projection of Small Engine Data (6D)(Clustering and Domination)

non-dominatedtradeoffs

max torque

dominatedtradeoffs

Cluster ID

mass

max power

3D Projection of Small Engine Data (6D)(Clustering and Domination)

non-dominatedtradeoffs

max torque

dominatedtradeoffs

Cluster ID

mass

max power

28

Project 2E Webcast - 23 July 2008 29

Predictive Tradeoff Modeling:Making System-Level Decisions

System Model

Utility Model

Other Components

…

Pump Attributes:• max displacement• max speed• efficiency• mass• price

Cylinder Attributes:• bore diam.• stroke length• mass• price

Engine Attributes:• max power• max speed• max torque• efficiency• mass• price

Typical Iterative Loop(optimization / search)

Often more than technical performance

• E.g., price/cost, mass, “-ilities” (reliability, usability,…)

Attribute values for a given component are not independent How to formalize the dependencies efficiently and effectively?

Attribute values for a given component are not independent How to formalize the dependencies efficiently and effectively?


Making System-Level Decisions with Predictive Models

stroke

mass

borecost

stroke

mass

borecost utility

stroke

bore pumpdisp


stroke

mass

borecost

stroke

mass

borecost

stroke

mass

borecost utility

stroke

bore pumpdisp


Engine & Pump

Hydraulic Cylinder & Ram

Directional Control Valve

Log Loading & Splitting Area

Engine & Pump

Hydraulic Cylinder & Ram

Directional Control Valve

Log Loading & Splitting Area

stroke

mass

borecost

stroke

mass

borecost utility

stroke

bore pumpdisp


stroke

mass

borecost

stroke

mass

borecost

stroke

mass

borecost utility

stroke

bore pumpdisp


Engine

Load

Engine

Load



Adaptive Kriging Models

Students: Alek Kerzhner, Roxanne Moore

Efficient Design Optimization under Uncertainty

3232

Motivating Study:Backhoe Dig-Cycle

• Optimization under uncertainty

• LatinHyperCube sampler used to predict expected value

• Kriging model used in conjunction with sampler to generate response surface to reduce computational cost

optimizer

Latin Hypercube + Kriging response surface

Objectives:• Maximize Efficiency• Minimize Cost

Design variables:• bore diameters• pump max disp

Adaptive Kriging Models

• Why Surrogate Models?– Without Kriging: 50 optimizer iterations*

7 evaluations per iteration*1000 LHS samples = 350,000 runs

– With Kriging: 2000 seeding runs + 100 extra runs = 2,100 runs!

• Adaptive Kriging model– Kriging: computational complexity is O(n4)– Adaptive approach: keep n small

• Many localized (small) response surfaces• Automatically requests additional simulations • Automatically regenerates response surface

3333


The Information Economic Challenge

Level of Exploration / Optimization

Levelof

FidelityLevel of Effort

Required


The Information Economic Challenge

Level of Exploration / Optimization

Levelof

FidelityLevel of Effort

Required


Variable Fidelity Modeling

Low fidelity for broad explorationidentify promising regions of design space

High fidelity for detailed optimization

Feasible solutions

x1

x2

A

B

C

x1

Obj








Summary


37



Formal Representation of Domain-Specific Knowledge

Student: Alek Kerzhner

Capturing Synthesis Knowledge as Graph Transformations


Most Knowledge Can Be Representedas Graphs or Graph Transformations

Requirements & Objectives

SysML

Executable Simulations

Dymola

System Behavior Models SysML

Topology Generation using Graph Transf

Model Composition using Graph Transf

Model Translation using Graph Transf

Design Optimization ModelCenter

System Alternatives

MAsCoMs SysML

Simulation Configuration using Graph Transf

Hydraulic_Subsystem Schematic[Block] ibd [ ]

actuator : Double-ActingCylinder

a : FlowPort

b : FlowPorthousing : FlowPort

rod : FlowPort

valve : 4port3wayServoValve

cylA : FlowPort

cylB : FlowPort

portP : FlowPort

portT : FlowPort

pump : FDpump

discharge : FlowPort

suction : FlowPort

housing : FlowPort

inputShaft : FlowPort

tank-to-pump : Line

a : FlowPort

b : FlowPort

pump-to-valve : Line

a : FlowPort

b : FlowPort

valve-to-cylP1 : Line

a : FlowPort

b : FlowPort

valve-to-cylP2 : Line

a : FlowPort

b : FlowPortfilter : Filter

in : FlowPort

out : FlowPort

valve-to-filter : Line

a : FlowPort

b : FlowPort

filter-to-tank : Line

a : FlowPort

b : FlowPort

tank : Tank

return : FlowPort

sump : FlowPort

hydraulics

world

x

y

Dig Cycle

Arm

Boom

Sw ing

BucketTraj

systemalternative

behaviormodel

simulationconfiguration


MOFLON: Meta-Modeling & Graph Xform Tool

Define graph transformationsin Storyboards:activity diagrams + graphs

Easily integrated with SysMLtools(through standardized JMI interface)

Capture domain-specific knowledge

40


Generative Grammar for Design Synthesis

Graph Transformation rules to generate systems

Generate random system alternatives by applying rules in randomized order

Improve system alternatives through evolutionary search algorithms

41


Composition of Multi-Aspect Models

System ModelsMACM

Repository

ArchitectureOptimization

Perspective A

Perspective CPerspective B

AutomatedComposition

42








Summary


43



Trading off Product Quality and Risk versus Design Process Costs

Student: Stephanie Thompson

Risk Management in Systems Engineering


Maximize expected utility! Of what?• Product (artifact) utility• Product + Design Process utility

Instead of “What configuration of the product gives us the best product

utility?” we should ask

“What can we do now to give us the best balance of product and process utility later?”

Frame of Reference

45


When is it valuable to perform additional analyses to reduce risk?

When is it valuable to perform detailed uncertainty analysis? In which order should the analyses be performed? How many design concepts should one carry forward in

parallel? …

Approach: • Investigate simplified design scenario for which a theoretically

optimal design process can be determined• Generalize these theoretical insights toward practical guidelines

Questions To Answer

46


Simple Illustration Problem – Problem Definition

Two Concepts• Designer must choose concept

A or B• The utilities of concepts A and

B are uncertain

Two Analyses• Low quality (LQ) and high

quality (HQ) analyses to refine the utility estimates

• LQ is cheaper, but the HQ is more precise.

• Cost of analyses reduces expected utility.

47

2~ ,iuu N

Lu u

Hu u

2~ 0,N

2~ 0,N


Normal distributions:• The utilities of A and B, and uncertainties of analyses are all

distributed normally.• All derived conditional distributions are also Normal

Limited scope of decision tree• The low quality analyses have already been performed for both

concepts, reducing the size of the decision tree. • In further work, the decision tree will include branches to perform the

low quality analyses.

Simplifying Assumptions

48


Decision Tree of Design Process

49

Select A

Select B

HQ A

HQ B HQ A

HQ B

Select A

Select A

Select B

Select B

Select B

Select B

Select A

Select A

ALp u

BLp u

|A AL

A

u up u

|B BL

B

u up u

|A AH L

AHu u

p u

|B BH L

BHu u

p u

|B BH L

BHu u

p u

|A AH L

AHu u

p u

|A AL

A

u up u

|B BL

B

u up u

| ,A A AH L

A

u u up u

| ,B B BH L

B

u u up u

| ,A A AH L

A

u u up u

| ,B B BH L

B

u u up u

uA

uB

uA-cHQA

uB-cHQA

uA-cHQB

uB-cHQB

uA-cHQA-cHQB

uA-cHQA-cHQB

uB-cHQA-cHQB

uB-cHQA-cHQB

| ,A A AH L

A

u u up u

| ,B B BH L

B

u u up u


Apply Bayes’ Theoremto derive conditional probabilities

All distributions end up being Normal:

Probability Distributions for Chance Events

50

|

,x Y y

Y

p x yp x

p y

2 2 2 2

| 2 2 2 2~ ,

L

u L uu u

u u

up u N

2 2 2 2 2 2 2 2

| 2 2 2 2~ ,

H L

u L u uu u H

u u

up u N

2 2 2 2

| 2 2 2 2~ ,

H

u H uu u

u u

up u N

2 2 2 2 2 2 2 2

| 2 2 2 2~ ,

L H

u H u u du u L

u u

up u N

2 2 2 2 2 2 2 2 2

| , 2 2 2 2 2 2 2 2 2 2 2 2~ ,

L H

u L u H uu u u

u u u u

u up u N


Decision Map

51

Nominal Parameters:

μA = μB = 100

σ2A = σ2

B = 502

HQ costs = 10

σ2L = 452

σ2H = 52








Summary


52


Summary

53

Overall Research ThemeHow can one design systems better at a lower cost?

Guiding PrincipleMaximize utility of both product and process

Increase the value – Decrease the cost

Solution PrinciplesUtility theory

Modularity in components and modelsFormal knowledge capture and reuseGraph manipulation & transformation

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