1 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. Model-Based Systems Engineering with SysML: Problem Definition, Simulation and Optimization

1MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.

Model-Based Systems Engineeringwith SysML:Problem Definition, Simulation and Optimization

Chris ParedisAssociate DirectorModel-Based Systems Engineering CenterGeorgia [email protected]

M BS EModel-BasedSystems EngineeringCenter


Presentation Overview

Model-Based Systems Engineering– Overview and motivation– The Systems Modeling Language (OMG SysMLTM)

Model Transformation for Simulation and Optimization

System Architecture Exploration– Transforming SysML models into analysis and optimization

models


Model-Based Systems EngineeringMoving from Documents to Models

Software

Manufacturing

ProjectManagement

Marketing

Analysis

CAD

• Power plant• Transmission• Brakes• Chassis• …



Software

Manufacturing

ProjectManagement

Marketing

Analysis

CAD


ImplicitImplicitDependenciesDependencies

betweenbetweenDocumentsDocuments



Software

Manufacturing

ProjectManagement

Marketing

Analysis

CAD


System Model


Integrated System ModelMust Address MultipleAspects of a System

Model-Based Systems EngineeringWhat Kinds of System Models?

Models are more formal, complete & semantically richModels are more formal, complete & semantically rich

Requirements

Engine Transmission Driveline

Structure / Physical Architecture

Start Shift Accel Brake

Behavior / Functional Architecture

Power Equations

Control Input

Dynamic Performance

Vehicle Dynamics

System Model

(Adapted from OMG SysML Tutorial)

Mass

Cost

Manufacturing

Reliability


The Payoff for MBSE

Improved communication

less ambiguous, more consistent Improved complexity management

traceability, abstraction, decomposition Improved design quality

more efficient and effective exploration Improved knowledge reuse

integrated model libraries

Models are more formal, complete & semantically richModels are more formal, complete & semantically rich


Summary: Making Better Decision

Goal of MBSE: Improve Efficiency & Rationality– Efficient = Perform the SE process with fewer resources– Rational = Make better decisions with available information

(Be consistent with designer’s beliefs and preferences)

(Figure Adapted from G. Hazelrigg)

Alternatives Outcomes

Maximize E[u]

Most PreferredSystem Alternative

IdeasKnowledge/Beliefs

Preferences

Decision Theory

Selection Criterion: E[u]






models


SysML: A Key Enabler for MBSE

What Can be Expressed in SysML?– All the information and knowledge needed for the

application of a systems development methodology

Specification Analysis Design Verification Validation

Hardware Software Data Personnel Procedures Facilities

The Systems Modeling Language (OMG SysMLTM)is a visual, general purpose modeling language

The Systems Modeling Language (OMG SysMLTM)is a visual, general purpose modeling language


Pillars of SysML — 4 Main Diagram Types

definition

bdd [package] VehicleStructure [ABS-Block Definition Diagram]

«block»Traction Detector

«block»Brake

Modulator

«block»Library::Electro-Hydraulic

Valve

«block»Library::

Electronic Processor

«block»Anti-Lock Controller

d1 m1



«block»Brake

Modulator


Valve

«block»Library::



d1 m1

1. Structure 2. Behavior

4. Requirements 3. Parametrics

(Source: Friedenthal, www.omgsysml.org)


Pillars of SysML — 4 Main Diagram Types

definition



«block»Brake

Modulator


Valve

«block»Library::



d1 m1

use

ibd [block] Anti-LockController [Internal Block Diagram]

d1:Traction Detector

m1:Brake Modulator

c1:modulator interface



m1:Brake Modulator






Pillars of SysML — 4 Main Diagram Types(Source: Friedenthal, www.omgsysml.org)

definition



«block»Brake

Modulator


Valve

«block»Library::



d1 m1

use



m1:Brake Modulator




interaction

sd ABS_ActivationSequence [Sequence Diagram]

d1:TractionDetector

m1:BrakeModulator

detTrkLos()

modBrkFrc()

sendSignal()

modBrkFrc(traction_signal:boolean)

sendAck()


d1:TractionDetector

m1:BrakeModulator

detTrkLos()

modBrkFrc()

sendSignal()


sendAck()




d1:TractionDetector

m1:BrakeModulator

detTrkLos()

modBrkFrc()

sendSignal()


sendAck()

definition



«block»Brake

Modulator


Valve

«block»Library::



d1 m1

use



m1:Brake Modulator




interaction

state machine

stm TireTraction [State Diagram]

Gripping Slipping

LossOfTraction

RegainTraction


Gripping Slipping

LossOfTraction

RegainTraction




d1:TractionDetector

m1:BrakeModulator

detTrkLos()

modBrkFrc()

sendSignal()


sendAck()

definition



«block»Brake

Modulator


Valve

«block»Library::



d1 m1

use



m1:Brake Modulator




interaction

state machine


Gripping Slipping

LossOfTraction

RegainTractionactivity/function

act PreventLockup [Activity Diagram]

DetectLossOf Traction

Modulate BrakingForce

TractionLoss:




TractionLoss:




d1:TractionDetector

m1:BrakeModulator

detTrkLos()

modBrkFrc()

sendSignal()


sendAck()

definition



«block»Brake

Modulator


Valve

«block»Library::



d1 m1

use



m1:Brake Modulator




interaction

state machine


Gripping Slipping

LossOfTraction

RegainTractionactivity/function




TractionLoss:

par [constraintBlock] StraightLineVehicleDynamics [Parametric Diagram]

:AccellerationEquation[F = ma]

:VelocityEquation[a = dv/dt]

:DistanceEquation[v = dx/dt]

:BrakingForceEquation

[f = (tf*bf)*(1-tl)]

tf: bf:tl:

f:

F:

c

a:a:

v:

v:

x:






[f = (tf*bf)*(1-tl)]

tf: bf:tl:

f:

F:

c

a:a:

v:

v:

x:




d1:TractionDetector

m1:BrakeModulator

detTrkLos()

modBrkFrc()

sendSignal()


sendAck()

definition



«block»Brake

Modulator


Valve

«block»Library::



d1 m1

use



m1:Brake Modulator




interaction

state machine


Gripping Slipping

LossOfTraction

RegainTraction

req [package] VehicleSpecifications [Requirements Diagram - Braking Requirements]

Braking Subsystem Specification

Vehicle System Specification

id=“102”text=”The vehicle shall stop from 60 mph within 150 ft on a clean dry surface.”

«requirement»StoppingDistance

id=”337"text=”Braking subsystem shall prevent wheel lockup under all braking conditions.”

«requirement»Anti-LockPerformance

«deriveReqt»








«deriveReqt»

activity/function




TractionLoss:






[f = (tf*bf)*(1-tl)]

tf: bf:tl:

f:

F:

c

a:a:

v:

v:

x:


Cross Connecting Model Elements








«deriveReqt»




TractionLoss:






[f = (tf*bf)*(1-tl)]

tf: bf:tl:

f:

F:

c

a:a:

v:

v:

x:



m1:Brake Modulator


1. Structure 2. Behavioract PreventLockup [Swimlane Diagram]

«allocate»:TractionDetector

«allocate»:BrakeModulator

allocatedTo«connector»c1:modulatorInterface



TractionLoss:

act PreventLockup [Swimlane Diagram]






TractionLoss:












«deriveReqt»




TractionLoss:






[f = (tf*bf)*(1-tl)]

tf: bf:tl:

f:

F:

c

a:a:

v:

v:

x:



m1:Brake Modulator








TractionLoss:







TractionLoss:


allocatedFrom«activity»DetectLosOfTraction

d1:TractionDetector

allocatedFrom «activity»Modulate BrakingForce

m1:BrakeModulator

allocatedFrom«ObjectNode»TractionLoss:

c1:modulatorInterface



d1:TractionDetector


m1:BrakeModulator



allocate












«deriveReqt»






SatisfiedBy«block»Anti-LockController



«deriveReqt»









«deriveReqt»




TractionLoss:






[f = (tf*bf)*(1-tl)]

tf: bf:tl:

f:

F:

c

a:a:

v:

v:

x:



m1:Brake Modulator










TractionLoss:



d1:TractionDetector


m1:BrakeModulator



allocate











«deriveReqt»









«deriveReqt»









«deriveReqt»




TractionLoss:






[f = (tf*bf)*(1-tl)]

tf: bf:tl:

f:

F:

c

a:a:

v:

v:

x:



m1:Brake Modulator










TractionLoss:



d1:TractionDetector


m1:BrakeModulator





d1:TractionDetector


m1:BrakeModulator



satisfies«requirement»Anti-LockPerformance



d1:TractionDetector


m1:BrakeModulator




allocate

satisfy











«deriveReqt»









«deriveReqt»




TractionLoss:






[f = (tf*bf)*(1-tl)]

tf: bf:tl:

f:

F:

c

a:a:

v:

v:

x:



m1:Brake Modulator








TractionLoss:



d1:TractionDetector


m1:BrakeModulator





d1:TractionDetector


m1:BrakeModulator





allocatedFrom«activity»DetectLosOf Traction

d1:TractionDetector

valuesDutyCycle: Percentage


m1:BrakeModulator






d1:TractionDetector



m1:BrakeModulator




allocate


satisfy











«deriveReqt»




TractionLoss:






[f = (tf*bf)*(1-tl)]

tf: bf:tl:

f:

F:

c

a:a:

v:

v:

x:



m1:Brake Modulator








TractionLoss:



d1:TractionDetector


m1:BrakeModulator





d1:TractionDetector


m1:BrakeModulator






d1:TractionDetector



m1:BrakeModulator






d1:TractionDetector



m1:BrakeModulator




allocate






[f = (tf*bf)*(1-tl)]

tf: bf:tl:

f:

F:

m:

a:a:

v:

v:

x:

v.Position:

v.Weight:v.chassis.tire.

Friction:v.brake.abs.m1.

DutyCycle:v.brake.rotor.BrakingForce:






[f = (tf*bf)*(1-tl)]

tf: bf:tl:

f:

F:

m:

a:a:

v:

v:

x:

v.Position:




value binding










«deriveReqt»

satisfy











«deriveReqt»




TractionLoss:






[f = (tf*bf)*(1-tl)]

tf: bf:tl:

f:

F:

c

a:a:

v:

v:

x:



m1:Brake Modulator








TractionLoss:



d1:TractionDetector


m1:BrakeModulator





d1:TractionDetector


m1:BrakeModulator






d1:TractionDetector



m1:BrakeModulator




allocate






[f = (tf*bf)*(1-tl)]

tf: bf:tl:

f:

F:

m:

a:a:

v:

v:

x:

v.Position:









[f = (tf*bf)*(1-tl)]

tf: bf:tl:

f:

F:

m:

a:a:

v:

v:

x:

v.Position:









[f = (tf*bf)*(1-tl)]

tf: bf:tl:

f:

F:

m:

a:a:

v:

v:

x:

v.Position:




value binding










«deriveReqt»

satisfy







TractionLoss:






[f = (tf*bf)*(1-tl)]

tf: bf:tl:

f:

F:

c

a:a:

v:

v:

x:



m1:Brake Modulator








TractionLoss:



d1:TractionDetector


m1:BrakeModulator





d1:TractionDetector


m1:BrakeModulator






d1:TractionDetector



m1:BrakeModulator




allocate






[f = (tf*bf)*(1-tl)]

tf: bf:tl:

f:

F:

m:

a:a:

v:

v:

x:

v.Position:









[f = (tf*bf)*(1-tl)]

tf: bf:tl:

f:

F:

m:

a:a:

v:

v:

x:

v.Position:









[f = (tf*bf)*(1-tl)]

tf: bf:tl:

f:

F:

m:

a:a:

v:

v:

x:

v.Position:














«deriveReqt»









«deriveReqt»








«deriveReqt»




VerifiedBy«interaction»MinimumStoppingDistance






«deriveReqt»

satisfy par [constraintBlock] StraightLineVehicleDynamics [Parametric Diagram]





[f = (tf*bf)*(1-tl)]

tf: bf:tl:

f:

F:

m:

a:a:

v:

v:

x:

v.Position:




verify

value binding






models


Formal Models + Model Transformations

Stage-Gate Documents

Project Management Metrics

Transformation

Transformation

Simulation &Optimization

System Model

Transformation


Model Transformation

Transformation Specification isalso a Model automated generation of transformation engine code

Origins– Model Driven Architecture/

Engineering Tools

– MOFLON, QVTo, ATL, GME/GReAT, VIATRA2, Kermeta,…

Example Usages:– Automation of repeated

modeling patterns– Tool interoperation– Document generation– Consistency checking– Dependency propagation

Source Metamodel

Source Model

Target Metamodel

Target Model

conforms to conforms to

Transformation Specification

Transformation Enginereads writes

refers to refers to

executes

(Czarnecki, K., & Hellen, S., 2006)


SysML-Modelica Transformation SpecificationRepresenting Hybrid Continuous/Discrete Dynamics in SysML

OMG standard for integrating SysML and Modelica Transformation is specified in QVT (Query/View/

Transformation) – an OMG specification

Modelica abstract syntax

XMI(SysML4Modelica)

conforms toSysML+

SysML4Modelicametamodel

SysML Tool

Modelica.mo file

Tool-Specific Repository

QVT(normative)

XMI(Modelica)

conforms toModelica

metamodel

OMC


SysML-ModelCenter TransformationExecuting SysML Parametric Analyses / Optimizations

Through ModelCenter, include and execute a wide range of engineering analyses in SysML

Trace requirements and design models to analysis

Transformation

System Properties

Analysis Model






models


SysML

SysML

SysML

Architecture Exploration Framework

Problem Definition

GenerateAlgebraic Design

Problem

SysML

GenerateArchitecture

Expl. Problem

Components

SysML

GenerateDynamic Design

Problem

SysML

Problem Formulation Problem Solution

Topology Analysis

Dynamic Analysis

Uncertainty Quantification

Mixed-IntegNonlin Solver

Algebraic Analysis

OptimizationSolver

Monte Carlo + KrigingDesign Explorer Modelica

GAMS / AMPL / AIMMS

Variable FidelityModel Selection

NonlinearModels

DynamicModels

LinearModels

Transformation


System Architecture Explorationfor a Hydraulic Excavator

Given:– Component models– Objectives / preferences

Find:– Best system architecture– Best component

parameters– (Best controller)

Excavator

pump_vdisp

cylinder

accum

How to connect and size these?

engine

v_3way


Specify Allowable/Required Components

A Component may be abstract, representing multiple sub-classes

Multiplicities for optional components

Specify the required connectors in IBD

Hydraulic Subsystem Hydraulic Subsystem[Block] ibd [ ]

arm

bucket

boomL

swing

armHousing

bucketHousing

boomLHousing

boomRHousingboomR

fuel

bucketCylinder : Cylinder

A B

rod housing

boomCylinderRight : Cylinder

A B

rod housing

armCylinder : Cylinder

A B

rod housing

swingMotor : FixedDisplacementMotor

P : Hydraulic

T : Hydraulic

rotational : Rotational

boomCylinderLeft : Cylinder

A B

rod housing

valveBlock : ValveBlock [0..4]A

B

P1T1

P2T2

powerUnit : PowerUnit [1..4]

P [1] T


mover : PrimeMover [1..4]

out : Rotational

fuelIn : Fuel


Specify Allowable/Required Connections

Connectors blank not allowed 1 required

+ optional

1 1

1 1

Note: mock-up – under development

+ +


Associate Tests with Requirements


Define Tests in a Solution-Independent Fashion

Hydraulic Subsystem Hydraulic Subsystem[Block] ibd [ ]

arm

bucket

boomL

swing

armHousing

bucketHousing

boomLHousing

boomRHousingboomR

fuel

bucketCylinder : Cylinder

A B

rod housing

boomCylinderRight : Cylinder

A B

rod housing

armCylinder : Cylinder

A B

rod housing

swingMotor : FixedDisplacementMotor

P : Hydraulic

T : Hydraulic


boomCylinderLeft : Cylinder

A B

rod housing

valveBlock : ValveBlock [0..4]A

B

P1T1

P2T2

powerUnit : PowerUnit [1..4]

P [1] T


mover : PrimeMover [1..4]

out : Rotational

fuelIn : Fuel


Define Test Protocols as Activities


Domain Knowledge: Model Libraries

Component Structure Algebraic Linear/Nonlinear DAE — Modelica


Model Transformations to Domain Knowledge

When cylinder is used, other corresponding models are often used also

Capture the reuse pattern


Model Transformations to Domain KnowledgeDefining the Reuse Patterns in SysML


Transformation to Mixed Integer (Linear) Program

Composition of component models

Decision variables for component & connector selection

Efficient filtering of architecture alternatives

System Model

AIMMS – CPLEXGeneration of AIMMS – CPLEX models through transformation


Step 1: Create a Superstructure

All potential connections

All potential components


Step 2: Linearization of Constitutive Equations

τmaxτ(2)

τ(3)

τ(1)

τ(0)

max 0 1 2 30 1 2 3

0 1 2 3(0) (1) (2) (3)

0 1 2 3 1

0 1 (1)sgmt

1 2 (2)sgmt

2 3 (3)sgmt

(1) (2) (3) 1sgmt sgmt sgmt

Binary Variable

ω


Step 3: Generate Connection Equations

Kirchhoff’s Laws:– A.flow + flowAC = 0– B.flow + flowBC = 0– C.flow – flowAC – flowBC = 0– A.pressure = B.pressure = C.pressure

When considering optional connections:– A.flow + flowAC * existsAC = 0– B.flow + flowBC * existsBC = 0– C.flow – flowAC * existsAC – flowBC * existsBC = 0– (A.pressure - C.pressure) * existsAC = 0– (B.pressure - C.pressure) * existsBC = 0

A

B

C

Binary Variable

Continuous Variables

Model is nonlinear Difficult to

solve


Step 3: Generate Connection Equations

Kirchhoff’s Laws:– A.flow + flowAC = 0– B.flow + flowBC = 0– C.flow – flowAC – flowBC = 0– A.pressure = B.pressure = C.pressure

When considering optional connections:– flowAC <= existsAC * upperBound– flowAC >= - existsAC * upperBound – flowBC <= existsBC * upperBound– flowBC >= - existsBC * upperBound

Model is linear Can be solved very quickly

A

B

C


Step 4: Solve Mixed-Integer Linear Equations

Potentially 4 Pumps, 4 Valves, 4 Cylinders, 1 Motor 4 Motion Phases Generated MIP Problem: 7147 Constraints & 2175

Variables Solution time: < 10 minutes


So What?

Express complex problems in domain-specific language– Multiple perspectives, multiple operational phases, …

Transform problem into declarative equations– Efficient formulation much larger problems than

can be formulated manually– Efficient solution take advantage of knowledge of the

mathematical structure of the equations

Same problem definition can be reused at different levels of abstraction

Goal is NOT to find the optimal solution in one step… but to filter out the poor solutions so that more accurate and more expensive models can be applied selectively


SysML

SysML

SysML

Architecture Exploration Framework

Problem Definition

GenerateAlgebraic Design

Problem

SysML

GenerateArchitecture

Expl. Problem

Components

SysML

GenerateDynamic Design

Problem

SysML

Problem Formulation Problem Solution

Topology Analysis

Dynamic Analysis

Uncertainty Quantification

Mixed-IntegNonlin Solver

Algebraic Analysis

OptimizationSolver

Monte Carlo + KrigingDesign Explorer Modelica

GAMS / AMPL / AIMMS

Variable FidelityModel Selection

NonlinearModels

DynamicModels

LinearModels

Transformation


1. Model-Based Systems Engineering (MBSE)– Key for meeting tomorrow’s demands on complexity & functionality

2. SysML– The leading standardized language for supporting MBSE

3. Formal models enable model transformation– Extract information, documents, analyses from SysML models

4. Efficient solution of Architecture Exploration Problems– Formal problem definition optimization at different levels of

abstraction

M BS EModel-BasedSystems EngineeringCenter

Key Take-Aways


Acknowledgments

Sponsors– John Deere– Ford Motor Company– Lockheed Martin– National Science

Foundation– Siemens

Collaborators– Leon McGinnis– Russell Peak– Peter Fritzson– Roger Burkhart– Sandy Friedenthal

Grad Students / Postdocs– Aditya Shah (Deere)– Alek Kerzhner– Axel Reichwein– Ben Lee– Brian Taylor– Kevin Davies– Roxanne Moore– Sebastian Herzig– Wladimir Schamai (EADS)