1. 1 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. Model-Based Systems Engineering with SysML: Problem Definition, Simulation and Optimization Chris Paredis Associate Director Model-Based Systems Engineering Center Georgia Tech chris.paredis@me.gatech.edu Model-Based Systems Engineering Center

2. 2 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. Presentation Overview u Model-Based Systems Engineering –Overview and motivation –The Systems Modeling Language (OMG SysML TM ) u Model Transformation for Simulation and Optimization u System Architecture Exploration –Transforming SysML models into analysis and optimization models

3. 3 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. Model-Based Systems Engineering Moving from Documents to Models Software Manufacturing Project Management Marketing Analysis CAD Power plant Transmission Brakes Chassis …

4. 4 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. Model-Based Systems Engineering Moving from Documents to Models Software Manufacturing Project Management Marketing Analysis CAD Power plant Transmission Brakes Chassis …

5. 5 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. Model-Based Systems Engineering Moving from Documents to Models Software Manufacturing Project Management Marketing Analysis CAD Power plant Transmission Brakes Chassis … System Model

6. 6 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. Integrated System Model Must Address Multiple Aspects of a System Model-Based Systems Engineering What Kinds of System Models? Models 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)

7. 7 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. The Payoff for MBSE uImproved communication  less ambiguous, more consistent uImproved complexity management  traceability, abstraction, decomposition uImproved design quality  more efficient and effective exploration uImproved knowledge reuse  integrated model libraries Models are more formal, complete & semantically rich

8. 8 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. Summary: Making Better Decision u 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 Preferred System Alternative Ideas Knowledge/ Beliefs Preferences Decision Theory Selection Criterion: E[u]

9. 9 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. Presentation Overview u Model-Based Systems Engineering –Overview and motivation –The Systems Modeling Language (OMG SysML TM ) u Model Transformation for Simulation and Optimization u System Architecture Exploration –Transforming SysML models into analysis and optimization models

10. 10 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. SysML: A Key Enabler for MBSE u What Can be Expressed in SysML? –All the information and knowledge needed for the application of a systems development methodology u Specification u Analysis u Design u Verification u Validation u Hardware u Software u Data u Personnel u Procedures u Facilities The Systems Modeling Language (OMG SysML TM ) is a visual, general purpose modeling language

11. 11 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. Pillars of SysML — 4 Main Diagram Types definition 1. Structure2. Behavior 4. Requirements3. Parametrics (Source: Friedenthal, www.omgsysml.org)

12. 12 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. Pillars of SysML — 4 Main Diagram Types definition use 1. Structure2. Behavior 4. Requirements3. Parametrics (Source: Friedenthal, www.omgsysml.org)

13. 13 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. Pillars of SysML — 4 Main Diagram Types (Source: Friedenthal, www.omgsysml.org) definition use 1. Structure2. Behavior 4. Requirements3. Parametrics interaction

14. 14 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. Pillars of SysML — 4 Main Diagram Types (Source: Friedenthal, www.omgsysml.org) definition use 1. Structure2. Behavior 4. Requirements3. Parametrics interaction state machine

15. 15 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. Pillars of SysML — 4 Main Diagram Types (Source: Friedenthal, www.omgsysml.org) definition use 1. Structure2. Behavior 4. Requirements3. Parametrics interaction state machine activity/ function

16. 16 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. Pillars of SysML — 4 Main Diagram Types (Source: Friedenthal, www.omgsysml.org) definition use 1. Structure2. Behavior 4. Requirements3. Parametrics interaction state machine activity/ function

17. 17 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. Pillars of SysML — 4 Main Diagram Types (Source: Friedenthal, www.omgsysml.org) definition use 1. Structure2. Behavior 4. Requirements3. Parametrics interaction state machine activity/ function

18. 18 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. Cross Connecting Model Elements 1. Structure2. Behavior (Source: Friedenthal, www.omgsysml.org) 4. Requirements3. Parametrics

19. 19 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. Cross Connecting Model Elements 1. Structure2. Behavior allocate (Source: Friedenthal, www.omgsysml.org) 4. Requirements3. Parametrics

20. 20 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. Cross Connecting Model Elements 1. Structure2. Behavior 4. Requirements3. Parametrics allocate (Source: Friedenthal, www.omgsysml.org)

21. 21 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. Cross Connecting Model Elements 1. Structure2. Behavior 4. Requirements3. Parametrics allocate satisfy (Source: Friedenthal, www.omgsysml.org)

22. 22 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. Cross Connecting Model Elements 1. Structure2. Behavior allocate (Source: Friedenthal, www.omgsysml.org) satisfy 4. Requirements3. Parametrics

23. 23 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. Cross Connecting Model Elements 1. Structure2. Behavior allocate value binding (Source: Friedenthal, www.omgsysml.org) satisfy 4. Requirements3. Parametrics

24. 24 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. Cross Connecting Model Elements 1. Structure2. Behavior allocate value binding (Source: Friedenthal, www.omgsysml.org) satisfy 4. Requirements3. Parametrics

25. 25 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. Cross Connecting Model Elements 1. Structure2. Behavior allocate (Source: Friedenthal, www.omgsysml.org) 4. Requirements3. Parametrics satisfy verify value binding

26. 26 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. Presentation Overview u Model-Based Systems Engineering –Overview and motivation –The Systems Modeling Language (OMG SysML TM ) u Model Transformation for Simulation and Optimization u System Architecture Exploration –Transforming SysML models into analysis and optimization models

27. 27 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. Formal Models + Model Transformations Stage-Gate Documents Project Management Metrics Transformation Simulation & Optimization Transformation

28. 28 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. Model Transformation u Transformation Specification is also a Model  automated generation of transformation engine code u Origins –Model Driven Architecture/ Engineering u Tools –MOFLON, QVTo, ATL, GME/GReAT, VIATRA2, Kermeta,… u 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 Transformation Specification Transformation Engine readswrites refers to executes (Czarnecki, K., & Hellen, S., 2006)

29. 29 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. SysML-Modelica Transformation Specification Representing Hybrid Continuous/Discrete Dynamics in SysML u OMG standard for integrating SysML and Modelica u Transformation is specified in QVT (Query/View/ Transformation) – an OMG specification Modelica abstract syntax XMI (SysML4 Modelica) conforms to SysML+ SysML4Modelica metamodel SysML Tool Modelica.mo file Tool-Specific Repository QVT (normative) XMI (Modelica) conforms to Modelica metamodel OMC

30. 30 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. SysML-ModelCenter Transformation Executing SysML Parametric Analyses / Optimizations u Through ModelCenter, include and execute a wide range of engineering analyses in SysML u Trace requirements and design models to analysis Transformation System Properties Analysis Model

31. 31 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. Presentation Overview u Model-Based Systems Engineering –Overview and motivation –The Systems Modeling Language (OMG SysML TM ) u Model Transformation for Simulation and Optimization u System Architecture Exploration –Transforming SysML models into analysis and optimization models

32. 32 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. SysML Architecture Exploration Framework Problem Definition Generate Algebraic Design Problem SysML Generate Architecture Expl. Problem Components SysML Generate Dynamic Design Problem SysML Problem Formulation Problem Solution Topology Analysis Dynamic Analysis Uncertainty Quantification Mixed-Integ Nonlin Solver Algebraic Analysis Optimization Solver Monte Carlo + KrigingDesign ExplorerModelica GAMS / AMPL / AIMMS Variable Fidelity Model Selection Nonlinear Models Dynamic Models Linear Models Transformation

33. 33 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. System Architecture Exploration for a Hydraulic Excavator u Given: –Component models –Objectives / preferences u Find: –Best system architecture –Best component parameters –(Best controller) Excavator pump_vdisp cylinder accum How to connect and size these? engine v_3way

34. 34 MBSE 2008-2011 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

35. 35 MBSE 2008-2011 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 + +

36. 36 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. Associate Tests with Requirements

37. 37 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. Define Tests in a Solution-Independent Fashion

38. 38 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. Define Test Protocols as Activities

39. 39 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. Domain Knowledge: Model Libraries Component StructureAlgebraic Linear/NonlinearDAE — Modelica

40. 40 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. Model Transformations to Domain Knowledge u When cylinder is used, other corresponding models are often used also  Capture the reuse pattern

41. 41 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. Model Transformations to Domain Knowledge Defining the Reuse Patterns in SysML

42. 42 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. Transformation to Mixed Integer (Linear) Program u Composition of component models u Decision variables for component & connector selection  Efficient filtering of architecture alternatives System Model AIMMS – CPLEX Generation of AIMMS – CPLEX models through transformation

43. 43 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. Step 1: Create a Superstructure All potential connections All potential components

44. 44 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. Step 2: Linearization of Constitutive Equations τ max τ(2) τ(3) τ(1) τ(0) Binary Variable ω

45. 45 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. Step 3: Generate Connection Equations u Kirchhoff’s Laws: –A.flow + flowAC = 0 –B.flow + flowBC = 0 –C.flow – flowAC – flowBC = 0 –A.pressure = B.pressure = C.pressure u 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 A B B C C Binary Variable Continuous Variables Model is nonlinear  Difficult to solve

46. 46 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. Step 3: Generate Connection Equations u Kirchhoff’s Laws: –A.flow + flowAC = 0 –B.flow + flowBC = 0 –C.flow – flowAC – flowBC = 0 –A.pressure = B.pressure = C.pressure u 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 A B B C C

47. 47 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. Step 4: Solve Mixed-Integer Linear Equations u Potentially 4 Pumps, 4 Valves, 4 Cylinders, 1 Motor u 4 Motion Phases u Generated MIP Problem: 7147 Constraints & 2175 Variables u Solution time: < 10 minutes

48. 48 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. So What? u Express complex problems in domain-specific language –Multiple perspectives, multiple operational phases, … u 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 u Same problem definition can be reused at different levels of abstraction u 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

49. 49 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. SysML Architecture Exploration Framework Problem Definition Generate Algebraic Design Problem SysML Generate Architecture Expl. Problem Components SysML Generate Dynamic Design Problem SysML Problem Formulation Problem Solution Topology Analysis Dynamic Analysis Uncertainty Quantification Mixed-Integ Nonlin Solver Algebraic Analysis Optimization Solver Monte Carlo + KrigingDesign ExplorerModelica GAMS / AMPL / AIMMS Variable Fidelity Model Selection Nonlinear Models Dynamic Models Linear Models Transformation

50. 50 MBSE 2008-2011 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 Model-Based Systems Engineering Center Key Take-Aways

51. 51 MBSE 2008-2011 Copyright © Georgia Tech. All Rights Reserved. Acknowledgments u Sponsors –John Deere –Ford Motor Company –Lockheed Martin –National Science Foundation –Siemens u Collaborators –Leon McGinnis –Russell Peak –Peter Fritzson –Roger Burkhart –Sandy Friedenthal u Grad Students / Postdocs –Aditya Shah (Deere) –Alek Kerzhner –Axel Reichwein –Ben Lee –Brian Taylor –Kevin Davies –Roxanne Moore –Sebastian Herzig –Wladimir Schamai (EADS)