1 mbse 2008-2011 copyright © georgia tech. all rights reserved. model-based systems engineering...
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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
2MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
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
3MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
Model-Based Systems EngineeringMoving from Documents to Models
Software
Manufacturing
ProjectManagement
Marketing
Analysis
CAD
• Power plant• Transmission• Brakes• Chassis• …
4MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
Model-Based Systems EngineeringMoving from Documents to Models
Software
Manufacturing
ProjectManagement
Marketing
Analysis
CAD
• Power plant• Transmission• Brakes• Chassis• …
ImplicitImplicitDependenciesDependencies
betweenbetweenDocumentsDocuments
5MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
Model-Based Systems EngineeringMoving from Documents to Models
Software
Manufacturing
ProjectManagement
Marketing
Analysis
CAD
• Power plant• Transmission• Brakes• Chassis• …
System Model
6MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
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
7MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
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
8MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
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]
9MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
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
10MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
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
11MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
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
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
1. Structure 2. Behavior
4. Requirements 3. Parametrics
(Source: Friedenthal, www.omgsysml.org)
12MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
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
use
ibd [block] Anti-LockController [Internal Block Diagram]
d1:Traction Detector
m1:Brake Modulator
c1:modulator interface
ibd [block] Anti-LockController [Internal Block Diagram]
d1:Traction Detector
m1:Brake Modulator
c1:modulator interface
1. Structure 2. Behavior
4. Requirements 3. Parametrics
(Source: Friedenthal, www.omgsysml.org)
13MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
Pillars of SysML — 4 Main Diagram Types(Source: Friedenthal, www.omgsysml.org)
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
use
ibd [block] Anti-LockController [Internal Block Diagram]
d1:Traction Detector
m1:Brake Modulator
c1:modulator interface
1. Structure 2. Behavior
4. Requirements 3. Parametrics
interaction
sd ABS_ActivationSequence [Sequence Diagram]
d1:TractionDetector
m1:BrakeModulator
detTrkLos()
modBrkFrc()
sendSignal()
modBrkFrc(traction_signal:boolean)
sendAck()
sd ABS_ActivationSequence [Sequence Diagram]
d1:TractionDetector
m1:BrakeModulator
detTrkLos()
modBrkFrc()
sendSignal()
modBrkFrc(traction_signal:boolean)
sendAck()
14MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
Pillars of SysML — 4 Main Diagram Types(Source: Friedenthal, www.omgsysml.org)
sd ABS_ActivationSequence [Sequence Diagram]
d1:TractionDetector
m1:BrakeModulator
detTrkLos()
modBrkFrc()
sendSignal()
modBrkFrc(traction_signal:boolean)
sendAck()
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
use
ibd [block] Anti-LockController [Internal Block Diagram]
d1:Traction Detector
m1:Brake Modulator
c1:modulator interface
1. Structure 2. Behavior
4. Requirements 3. Parametrics
interaction
state machine
stm TireTraction [State Diagram]
Gripping Slipping
LossOfTraction
RegainTraction
stm TireTraction [State Diagram]
Gripping Slipping
LossOfTraction
RegainTraction
15MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
Pillars of SysML — 4 Main Diagram Types(Source: Friedenthal, www.omgsysml.org)
sd ABS_ActivationSequence [Sequence Diagram]
d1:TractionDetector
m1:BrakeModulator
detTrkLos()
modBrkFrc()
sendSignal()
modBrkFrc(traction_signal:boolean)
sendAck()
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
use
ibd [block] Anti-LockController [Internal Block Diagram]
d1:Traction Detector
m1:Brake Modulator
c1:modulator interface
1. Structure 2. Behavior
4. Requirements 3. Parametrics
interaction
state machine
stm TireTraction [State Diagram]
Gripping Slipping
LossOfTraction
RegainTractionactivity/function
act PreventLockup [Activity Diagram]
DetectLossOf Traction
Modulate BrakingForce
TractionLoss:
act PreventLockup [Activity Diagram]
DetectLossOf Traction
Modulate BrakingForce
TractionLoss:
16MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
Pillars of SysML — 4 Main Diagram Types(Source: Friedenthal, www.omgsysml.org)
sd ABS_ActivationSequence [Sequence Diagram]
d1:TractionDetector
m1:BrakeModulator
detTrkLos()
modBrkFrc()
sendSignal()
modBrkFrc(traction_signal:boolean)
sendAck()
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
use
ibd [block] Anti-LockController [Internal Block Diagram]
d1:Traction Detector
m1:Brake Modulator
c1:modulator interface
1. Structure 2. Behavior
4. Requirements 3. Parametrics
interaction
state machine
stm TireTraction [State Diagram]
Gripping Slipping
LossOfTraction
RegainTractionactivity/function
act PreventLockup [Activity Diagram]
DetectLossOf Traction
Modulate BrakingForce
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:
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:
17MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
Pillars of SysML — 4 Main Diagram Types(Source: Friedenthal, www.omgsysml.org)
sd ABS_ActivationSequence [Sequence Diagram]
d1:TractionDetector
m1:BrakeModulator
detTrkLos()
modBrkFrc()
sendSignal()
modBrkFrc(traction_signal:boolean)
sendAck()
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
use
ibd [block] Anti-LockController [Internal Block Diagram]
d1:Traction Detector
m1:Brake Modulator
c1:modulator interface
1. Structure 2. Behavior
4. Requirements 3. Parametrics
interaction
state machine
stm TireTraction [State Diagram]
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»
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»
activity/function
act PreventLockup [Activity Diagram]
DetectLossOf Traction
Modulate BrakingForce
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:
18MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
Cross Connecting Model Elements
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»
act PreventLockup [Activity Diagram]
DetectLossOf Traction
Modulate BrakingForce
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:
ibd [block] Anti-LockController [Internal Block Diagram]
d1:Traction Detector
m1:Brake Modulator
c1:modulator interface
1. Structure 2. Behavioract PreventLockup [Swimlane Diagram]
«allocate»:TractionDetector
«allocate»:BrakeModulator
allocatedTo«connector»c1:modulatorInterface
DetectLossOf Traction
Modulate BrakingForce
TractionLoss:
act PreventLockup [Swimlane Diagram]
«allocate»:TractionDetector
«allocate»:BrakeModulator
allocatedTo«connector»c1:modulatorInterface
DetectLossOf Traction
Modulate BrakingForce
TractionLoss:
(Source: Friedenthal, www.omgsysml.org)
4. Requirements 3. Parametrics
19MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
Cross Connecting Model Elements
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»
act PreventLockup [Activity Diagram]
DetectLossOf Traction
Modulate BrakingForce
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:
ibd [block] Anti-LockController [Internal Block Diagram]
d1:Traction Detector
m1:Brake Modulator
c1:modulator interface
1. Structure 2. Behavioract PreventLockup [Swimlane Diagram]
«allocate»:TractionDetector
«allocate»:BrakeModulator
allocatedTo«connector»c1:modulatorInterface
DetectLossOf Traction
Modulate BrakingForce
TractionLoss:
act PreventLockup [Swimlane Diagram]
«allocate»:TractionDetector
«allocate»:BrakeModulator
allocatedTo«connector»c1:modulatorInterface
DetectLossOf Traction
Modulate BrakingForce
TractionLoss:
ibd [block] Anti-LockController [Internal Block Diagram]
allocatedFrom«activity»DetectLosOfTraction
d1:TractionDetector
allocatedFrom «activity»Modulate BrakingForce
m1:BrakeModulator
allocatedFrom«ObjectNode»TractionLoss:
c1:modulatorInterface
ibd [block] Anti-LockController [Internal Block Diagram]
allocatedFrom«activity»DetectLosOfTraction
d1:TractionDetector
allocatedFrom «activity»Modulate BrakingForce
m1:BrakeModulator
allocatedFrom«ObjectNode»TractionLoss:
c1:modulatorInterface
allocate
(Source: Friedenthal, www.omgsysml.org)
4. Requirements 3. Parametrics
20MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
Cross Connecting Model Elements
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»
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
SatisfiedBy«block»Anti-LockController
id=”337"text=”Braking subsystem shall prevent wheel lockup under all braking conditions.”
«requirement»Anti-LockPerformance
«deriveReqt»
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
SatisfiedBy«block»Anti-LockController
id=”337"text=”Braking subsystem shall prevent wheel lockup under all braking conditions.”
«requirement»Anti-LockPerformance
«deriveReqt»
act PreventLockup [Activity Diagram]
DetectLossOf Traction
Modulate BrakingForce
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:
ibd [block] Anti-LockController [Internal Block Diagram]
d1:Traction Detector
m1:Brake Modulator
c1:modulator interface
1. Structure 2. Behavior
4. Requirements 3. Parametrics
act PreventLockup [Swimlane Diagram]
«allocate»:TractionDetector
«allocate»:BrakeModulator
allocatedTo«connector»c1:modulatorInterface
DetectLossOf Traction
Modulate BrakingForce
TractionLoss:
ibd [block] Anti-LockController [Internal Block Diagram]
allocatedFrom«activity»DetectLosOfTraction
d1:TractionDetector
allocatedFrom «activity»Modulate BrakingForce
m1:BrakeModulator
allocatedFrom«ObjectNode»TractionLoss:
c1:modulatorInterface
allocate
(Source: Friedenthal, www.omgsysml.org)
21MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
Cross Connecting Model Elements
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»
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
SatisfiedBy«block»Anti-LockController
id=”337"text=”Braking subsystem shall prevent wheel lockup under all braking conditions.”
«requirement»Anti-LockPerformance
«deriveReqt»
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
SatisfiedBy«block»Anti-LockController
id=”337"text=”Braking subsystem shall prevent wheel lockup under all braking conditions.”
«requirement»Anti-LockPerformance
«deriveReqt»
act PreventLockup [Activity Diagram]
DetectLossOf Traction
Modulate BrakingForce
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:
ibd [block] Anti-LockController [Internal Block Diagram]
d1:Traction Detector
m1:Brake Modulator
c1:modulator interface
1. Structure 2. Behavior
4. Requirements 3. Parametrics
act PreventLockup [Swimlane Diagram]
«allocate»:TractionDetector
«allocate»:BrakeModulator
allocatedTo«connector»c1:modulatorInterface
DetectLossOf Traction
Modulate BrakingForce
TractionLoss:
ibd [block] Anti-LockController [Internal Block Diagram]
allocatedFrom«activity»DetectLosOfTraction
d1:TractionDetector
allocatedFrom «activity»Modulate BrakingForce
m1:BrakeModulator
allocatedFrom«ObjectNode»TractionLoss:
c1:modulatorInterface
ibd [block] Anti-LockController [Internal Block Diagram]
allocatedFrom«activity»DetectLosOfTraction
d1:TractionDetector
allocatedFrom «activity»Modulate BrakingForce
m1:BrakeModulator
allocatedFrom«ObjectNode»TractionLoss:
c1:modulatorInterface
satisfies«requirement»Anti-LockPerformance
ibd [block] Anti-LockController [Internal Block Diagram]
allocatedFrom«activity»DetectLosOfTraction
d1:TractionDetector
allocatedFrom «activity»Modulate BrakingForce
m1:BrakeModulator
allocatedFrom«ObjectNode»TractionLoss:
c1:modulatorInterface
satisfies«requirement»Anti-LockPerformance
allocate
satisfy
(Source: Friedenthal, www.omgsysml.org)
22MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
Cross Connecting Model Elements
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»
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
SatisfiedBy«block»Anti-LockController
id=”337"text=”Braking subsystem shall prevent wheel lockup under all braking conditions.”
«requirement»Anti-LockPerformance
«deriveReqt»
act PreventLockup [Activity Diagram]
DetectLossOf Traction
Modulate BrakingForce
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:
ibd [block] Anti-LockController [Internal Block Diagram]
d1:Traction Detector
m1:Brake Modulator
c1:modulator interface
1. Structure 2. Behavioract PreventLockup [Swimlane Diagram]
«allocate»:TractionDetector
«allocate»:BrakeModulator
allocatedTo«connector»c1:modulatorInterface
DetectLossOf Traction
Modulate BrakingForce
TractionLoss:
ibd [block] Anti-LockController [Internal Block Diagram]
allocatedFrom«activity»DetectLosOfTraction
d1:TractionDetector
allocatedFrom «activity»Modulate BrakingForce
m1:BrakeModulator
allocatedFrom«ObjectNode»TractionLoss:
c1:modulatorInterface
ibd [block] Anti-LockController [Internal Block Diagram]
allocatedFrom«activity»DetectLosOfTraction
d1:TractionDetector
allocatedFrom «activity»Modulate BrakingForce
m1:BrakeModulator
allocatedFrom«ObjectNode»TractionLoss:
c1:modulatorInterface
satisfies«requirement»Anti-LockPerformance
ibd [block] Anti-LockController [Internal Block Diagram]
allocatedFrom«activity»DetectLosOf Traction
d1:TractionDetector
valuesDutyCycle: Percentage
allocatedFrom «activity»Modulate BrakingForce
m1:BrakeModulator
allocatedFrom«ObjectNode»TractionLoss:
c1:modulatorInterface
satisfies«requirement»Anti-LockPerformance
ibd [block] Anti-LockController [Internal Block Diagram]
allocatedFrom«activity»DetectLosOf Traction
d1:TractionDetector
valuesDutyCycle: Percentage
allocatedFrom «activity»Modulate BrakingForce
m1:BrakeModulator
allocatedFrom«ObjectNode»TractionLoss:
c1:modulatorInterface
satisfies«requirement»Anti-LockPerformance
allocate
(Source: Friedenthal, www.omgsysml.org)
satisfy
4. Requirements 3. Parametrics
23MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
Cross Connecting Model Elements
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»
act PreventLockup [Activity Diagram]
DetectLossOf Traction
Modulate BrakingForce
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:
ibd [block] Anti-LockController [Internal Block Diagram]
d1:Traction Detector
m1:Brake Modulator
c1:modulator interface
1. Structure 2. Behavioract PreventLockup [Swimlane Diagram]
«allocate»:TractionDetector
«allocate»:BrakeModulator
allocatedTo«connector»c1:modulatorInterface
DetectLossOf Traction
Modulate BrakingForce
TractionLoss:
ibd [block] Anti-LockController [Internal Block Diagram]
allocatedFrom«activity»DetectLosOfTraction
d1:TractionDetector
allocatedFrom «activity»Modulate BrakingForce
m1:BrakeModulator
allocatedFrom«ObjectNode»TractionLoss:
c1:modulatorInterface
ibd [block] Anti-LockController [Internal Block Diagram]
allocatedFrom«activity»DetectLosOfTraction
d1:TractionDetector
allocatedFrom «activity»Modulate BrakingForce
m1:BrakeModulator
allocatedFrom«ObjectNode»TractionLoss:
c1:modulatorInterface
satisfies«requirement»Anti-LockPerformance
ibd [block] Anti-LockController [Internal Block Diagram]
allocatedFrom«activity»DetectLosOf Traction
d1:TractionDetector
valuesDutyCycle: Percentage
allocatedFrom «activity»Modulate BrakingForce
m1:BrakeModulator
allocatedFrom«ObjectNode»TractionLoss:
c1:modulatorInterface
satisfies«requirement»Anti-LockPerformance
ibd [block] Anti-LockController [Internal Block Diagram]
allocatedFrom«activity»DetectLosOf Traction
d1:TractionDetector
valuesDutyCycle: Percentage
allocatedFrom «activity»Modulate BrakingForce
m1:BrakeModulator
allocatedFrom«ObjectNode»TractionLoss:
c1:modulatorInterface
satisfies«requirement»Anti-LockPerformance
allocate
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:
m:
a:a:
v:
v:
x:
v.Position:
v.Weight:v.chassis.tire.
Friction:v.brake.abs.m1.
DutyCycle:v.brake.rotor.BrakingForce:
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:
m:
a:a:
v:
v:
x:
v.Position:
v.Weight:v.chassis.tire.
Friction:v.brake.abs.m1.
DutyCycle:v.brake.rotor.BrakingForce:
value binding
(Source: Friedenthal, www.omgsysml.org)
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
SatisfiedBy«block»Anti-LockController
id=”337"text=”Braking subsystem shall prevent wheel lockup under all braking conditions.”
«requirement»Anti-LockPerformance
«deriveReqt»
satisfy
4. Requirements 3. Parametrics
24MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
Cross Connecting Model Elements
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»
act PreventLockup [Activity Diagram]
DetectLossOf Traction
Modulate BrakingForce
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:
ibd [block] Anti-LockController [Internal Block Diagram]
d1:Traction Detector
m1:Brake Modulator
c1:modulator interface
1. Structure 2. Behavioract PreventLockup [Swimlane Diagram]
«allocate»:TractionDetector
«allocate»:BrakeModulator
allocatedTo«connector»c1:modulatorInterface
DetectLossOf Traction
Modulate BrakingForce
TractionLoss:
ibd [block] Anti-LockController [Internal Block Diagram]
allocatedFrom«activity»DetectLosOfTraction
d1:TractionDetector
allocatedFrom «activity»Modulate BrakingForce
m1:BrakeModulator
allocatedFrom«ObjectNode»TractionLoss:
c1:modulatorInterface
ibd [block] Anti-LockController [Internal Block Diagram]
allocatedFrom«activity»DetectLosOfTraction
d1:TractionDetector
allocatedFrom «activity»Modulate BrakingForce
m1:BrakeModulator
allocatedFrom«ObjectNode»TractionLoss:
c1:modulatorInterface
satisfies«requirement»Anti-LockPerformance
ibd [block] Anti-LockController [Internal Block Diagram]
allocatedFrom«activity»DetectLosOf Traction
d1:TractionDetector
valuesDutyCycle: Percentage
allocatedFrom «activity»Modulate BrakingForce
m1:BrakeModulator
allocatedFrom«ObjectNode»TractionLoss:
c1:modulatorInterface
satisfies«requirement»Anti-LockPerformance
allocate
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:
m:
a:a:
v:
v:
x:
v.Position:
v.Weight:v.chassis.tire.
Friction:v.brake.abs.m1.
DutyCycle:v.brake.rotor.BrakingForce:
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:
m:
a:a:
v:
v:
x:
v.Position:
v.Weight:v.chassis.tire.
Friction:v.brake.abs.m1.
DutyCycle:v.brake.rotor.BrakingForce:
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:
m:
a:a:
v:
v:
x:
v.Position:
v.Weight:v.chassis.tire.
Friction:v.brake.abs.m1.
DutyCycle:v.brake.rotor.BrakingForce:
value binding
(Source: Friedenthal, www.omgsysml.org)
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
SatisfiedBy«block»Anti-LockController
id=”337"text=”Braking subsystem shall prevent wheel lockup under all braking conditions.”
«requirement»Anti-LockPerformance
«deriveReqt»
satisfy
4. Requirements 3. Parametrics
25MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
Cross Connecting Model Elements
act PreventLockup [Activity Diagram]
DetectLossOf Traction
Modulate BrakingForce
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:
ibd [block] Anti-LockController [Internal Block Diagram]
d1:Traction Detector
m1:Brake Modulator
c1:modulator interface
1. Structure 2. Behavioract PreventLockup [Swimlane Diagram]
«allocate»:TractionDetector
«allocate»:BrakeModulator
allocatedTo«connector»c1:modulatorInterface
DetectLossOf Traction
Modulate BrakingForce
TractionLoss:
ibd [block] Anti-LockController [Internal Block Diagram]
allocatedFrom«activity»DetectLosOfTraction
d1:TractionDetector
allocatedFrom «activity»Modulate BrakingForce
m1:BrakeModulator
allocatedFrom«ObjectNode»TractionLoss:
c1:modulatorInterface
ibd [block] Anti-LockController [Internal Block Diagram]
allocatedFrom«activity»DetectLosOfTraction
d1:TractionDetector
allocatedFrom «activity»Modulate BrakingForce
m1:BrakeModulator
allocatedFrom«ObjectNode»TractionLoss:
c1:modulatorInterface
satisfies«requirement»Anti-LockPerformance
ibd [block] Anti-LockController [Internal Block Diagram]
allocatedFrom«activity»DetectLosOf Traction
d1:TractionDetector
valuesDutyCycle: Percentage
allocatedFrom «activity»Modulate BrakingForce
m1:BrakeModulator
allocatedFrom«ObjectNode»TractionLoss:
c1:modulatorInterface
satisfies«requirement»Anti-LockPerformance
allocate
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:
m:
a:a:
v:
v:
x:
v.Position:
v.Weight:v.chassis.tire.
Friction:v.brake.abs.m1.
DutyCycle:v.brake.rotor.BrakingForce:
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:
m:
a:a:
v:
v:
x:
v.Position:
v.Weight:v.chassis.tire.
Friction:v.brake.abs.m1.
DutyCycle:v.brake.rotor.BrakingForce:
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:
m:
a:a:
v:
v:
x:
v.Position:
v.Weight:v.chassis.tire.
Friction:v.brake.abs.m1.
DutyCycle:v.brake.rotor.BrakingForce:
(Source: Friedenthal, www.omgsysml.org)
4. Requirements 3. Parametrics
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
SatisfiedBy«block»Anti-LockController
id=”337"text=”Braking subsystem shall prevent wheel lockup under all braking conditions.”
«requirement»Anti-LockPerformance
«deriveReqt»
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
SatisfiedBy«block»Anti-LockController
id=”337"text=”Braking subsystem shall prevent wheel lockup under all braking conditions.”
«requirement»Anti-LockPerformance
«deriveReqt»
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»
req [package] VehicleSpecifications [Requirements Diagram - Braking Requirements]
Braking Subsystem Specification
Vehicle System Specification
VerifiedBy«interaction»MinimumStoppingDistance
id=“102”text=”The vehicle shall stop from 60 mph within 150 ft on a clean dry surface.”
«requirement»StoppingDistance
SatisfiedBy«block»Anti-LockController
id=”337"text=”Braking subsystem shall prevent wheel lockup under all braking conditions.”
«requirement»Anti-LockPerformance
«deriveReqt»
satisfy 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:
m:
a:a:
v:
v:
x:
v.Position:
v.Weight:v.chassis.tire.
Friction:v.brake.abs.m1.
DutyCycle:v.brake.rotor.BrakingForce:
verify
value binding
26MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
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
27MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
Formal Models + Model Transformations
Stage-Gate Documents
Project Management Metrics
Transformation
Transformation
Simulation &Optimization
System Model
Transformation
28MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
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)
29MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
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
30MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
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
31MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
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
32MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
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
33MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
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
34MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
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
rotational : Rotational
mover : PrimeMover [1..4]
out : Rotational
fuelIn : Fuel
35MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
Specify Allowable/Required Connections
Connectors blank not allowed 1 required
+ optional
1 1
1 1
Note: mock-up – under development
+ +
36MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
Associate Tests with Requirements
37MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
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
rotational : Rotational
boomCylinderLeft : Cylinder
A B
rod housing
valveBlock : ValveBlock [0..4]A
B
P1T1
P2T2
powerUnit : PowerUnit [1..4]
P [1] T
rotational : Rotational
mover : PrimeMover [1..4]
out : Rotational
fuelIn : Fuel
38MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
Define Test Protocols as Activities
39MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
Domain Knowledge: Model Libraries
Component Structure Algebraic Linear/Nonlinear DAE — Modelica
40MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
Model Transformations to Domain Knowledge
When cylinder is used, other corresponding models are often used also
Capture the reuse pattern
41MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
Model Transformations to Domain KnowledgeDefining the Reuse Patterns in SysML
42MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
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
43MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
Step 1: Create a Superstructure
All potential connections
All potential components
44MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
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
45MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
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
46MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
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
47MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
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
48MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
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
49MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
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
50MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
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
51MBSE2008-2011 Copyright © Georgia Tech. All Rights Reserved.
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)