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

Model-Based Systems Engineering Center. 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. Presentation Overview.

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

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  1. Model-BasedSystems EngineeringCenter Model-Based Systems Engineeringwith SysML:Problem Definition, Simulation and Optimization Chris Paredis Associate DirectorModel-Based Systems Engineering Center Georgia Tech chris.paredis@me.gatech.edu

  2. 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

  3. Model-Based Systems EngineeringMoving from Documents to Models Software Manufacturing Analysis ProjectManagement Marketing • Power plant • Transmission • Brakes • Chassis • … CAD

  4. Model-Based Systems EngineeringMoving from Documents to Models Software ImplicitDependenciesbetweenDocuments Manufacturing Analysis ProjectManagement Marketing • Power plant • Transmission • Brakes • Chassis • … CAD

  5. Model-Based Systems EngineeringMoving from Documents to Models Software Manufacturing Analysis ProjectManagement System Model Marketing • Power plant • Transmission • Brakes • Chassis • … CAD

  6. Model-Based Systems EngineeringWhat Kinds of System Models? Requirements Dynamic Performance Structure / Physical Architecture Control Input Power Equations Vehicle Dynamics Engine Transmission Driveline Integrated System ModelMust Address MultipleAspects of a System System Model Behavior / Functional Architecture Start Shift Accel Brake Models are more formal, complete & semantically rich (Adapted from OMG SysML Tutorial)

  7. The Payoff for MBSE Models are more formal, complete & semantically rich • 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

  8. 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) Knowledge/Beliefs Ideas Preferences Alternatives Outcomes Selection Criterion: E[u] Decision Theory (Figure Adapted from G. Hazelrigg) Maximize E[u] Most PreferredSystem Alternative

  9. 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

  10. SysML: A Key Enabler for MBSE The Systems Modeling Language (OMG SysMLTM)is a visual, general purpose modeling language • 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

  11. (Source: Friedenthal, www.omgsysml.org) definition Pillars of SysML — 4 Main Diagram Types 1. Structure 2. Behavior 4. Requirements 3. Parametrics

  12. (Source: Friedenthal, www.omgsysml.org) definition Pillars of SysML — 4 Main Diagram Types 1. Structure 2. Behavior use 4. Requirements 3. Parametrics

  13. (Source: Friedenthal, www.omgsysml.org) use definition Pillars of SysML — 4 Main Diagram Types 1. Structure 2. Behavior interaction 4. Requirements 3. Parametrics

  14. (Source: Friedenthal, www.omgsysml.org) use definition Pillars of SysML — 4 Main Diagram Types 1. Structure 2. Behavior interaction state machine 4. Requirements 3. Parametrics

  15. (Source: Friedenthal, www.omgsysml.org) state machine use definition Pillars of SysML — 4 Main Diagram Types 1. Structure 2. Behavior interaction activity/ function 4. Requirements 3. Parametrics

  16. (Source: Friedenthal, www.omgsysml.org) state machine activity/ function use definition Pillars of SysML — 4 Main Diagram Types 1. Structure 2. Behavior interaction 4. Requirements 3. Parametrics

  17. (Source: Friedenthal, www.omgsysml.org) state machine activity/ function use definition Pillars of SysML — 4 Main Diagram Types 1. Structure 2. Behavior interaction 4. Requirements 3. Parametrics

  18. (Source: Friedenthal, www.omgsysml.org) Cross Connecting Model Elements 1. Structure 2. Behavior 4. Requirements 3. Parametrics

  19. (Source: Friedenthal, www.omgsysml.org) Cross Connecting Model Elements 1. Structure 2. Behavior allocate 4. Requirements 3. Parametrics

  20. (Source: Friedenthal, www.omgsysml.org) Cross Connecting Model Elements 1. Structure 2. Behavior allocate 4. Requirements 3. Parametrics

  21. (Source: Friedenthal, www.omgsysml.org) Cross Connecting Model Elements 1. Structure 2. Behavior allocate satisfy 4. Requirements 3. Parametrics

  22. (Source: Friedenthal, www.omgsysml.org) allocate Cross Connecting Model Elements 1. Structure 2. Behavior satisfy 4. Requirements 3. Parametrics

  23. (Source: Friedenthal, www.omgsysml.org) allocate Cross Connecting Model Elements 1. Structure 2. Behavior value binding satisfy 4. Requirements 3. Parametrics

  24. (Source: Friedenthal, www.omgsysml.org) allocate value binding Cross Connecting Model Elements 1. Structure 2. Behavior satisfy 4. Requirements 3. Parametrics

  25. (Source: Friedenthal, www.omgsysml.org) allocate value binding verify Cross Connecting Model Elements 1. Structure 2. Behavior satisfy 4. Requirements 3. Parametrics

  26. 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

  27. Formal Models + Model Transformations Stage-Gate Documents Transformation Transformation Transformation Project Management Metrics Simulation &Optimization

  28. refers to refers to Source Metamodel Transformation Specification Target Metamodel conforms to executes conforms to reads writes Source Model Transformation Engine Target Model 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 repeatedmodeling patterns • Tool interoperation • Document generation • Consistency checking • Dependency propagation (Czarnecki, K., & Hellen, S., 2006)

  29. 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 conforms to SysML+SysML4Modelicametamodel conforms toModelicametamodel SysML Tool XMI(SysML4Modelica) XMI(Modelica) Modelica abstract syntax QVT(normative) OMC Tool-Specific Repository Modelica.mo file

  30. SysML-ModelCenter TransformationExecuting SysML Parametric Analyses / Optimizations Transformation • Through ModelCenter, include and executea wide range of engineering analyses in SysML • Trace requirements and design models to analysis System Properties Analysis Model

  31. 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

  32. Architecture Exploration Framework Problem Definition Components SysML SysML GenerateArchitecture Expl. Problem Topology Analysis Variable FidelityModel Selection LinearModels SysML SysML GAMS / AMPL / AIMMS GenerateAlgebraic Design Problem Mixed-IntegNonlin Solver Algebraic Analysis NonlinearModels SysML SysML Design Explorer Monte Carlo + Kriging Modelica GenerateDynamic Design Problem OptimizationSolver Uncertainty Quantification Dynamic Analysis DynamicModels Problem Formulation Problem Solution Transformation

  33. Given: Component models Objectives / preferences Find: Best system architecture Best component parameters (Best controller) engine Excavator pump_vdisp accum v_3way cylinder System Architecture Explorationfor a Hydraulic Excavator How to connect and size these?

  34. Specify Allowable/Required Components A Component may be abstract, representing multiple sub-classes Multiplicities for optional components Specify the required connectors in IBD

  35. Specify Allowable/Required Connections Connectors blank  not allowed 1  required +  optional + + 1 1 1 1 Note: mock-up – under development

  36. Associate Tests with Requirements

  37. Define Tests in a Solution-Independent Fashion

  38. Define Test Protocols as Activities

  39. Domain Knowledge: Model Libraries Component Structure Algebraic Linear/Nonlinear DAE — Modelica

  40. Model Transformations to Domain Knowledge • When cylinder is used, other corresponding models are often used also  Capture the reuse pattern

  41. Model Transformations to Domain KnowledgeDefining the Reuse Patterns in SysML

  42. Transformation to Mixed Integer (Linear) Program • Composition of component models • Decision variables for component & connector selection  Efficient filtering of architecture alternatives System Model Generation of AIMMS – CPLEX models through transformation AIMMS – CPLEX

  43. Step 1: Create a Superstructure All potential components All potential connections

  44. Step 2: Linearization of Constitutive Equations τmax τ(1) τ(2) τ(0) Binary Variable ω τ(3)

  45. Step 3: Generate Connection Equations A C • 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 B Model is nonlinear Difficult to solve Continuous Variables Binary Variable

  46. Step 3: Generate Connection Equations A C • 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 B Model is linear  Can be solved very quickly

  47. 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

  48. 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

  49. Architecture Exploration Framework Problem Definition Components SysML SysML GenerateArchitecture Expl. Problem Topology Analysis Variable FidelityModel Selection LinearModels SysML SysML GAMS / AMPL / AIMMS GenerateAlgebraic Design Problem Mixed-IntegNonlin Solver Algebraic Analysis NonlinearModels SysML SysML Design Explorer Monte Carlo + Kriging Modelica GenerateDynamic Design Problem OptimizationSolver Uncertainty Quantification Dynamic Analysis DynamicModels Problem Formulation Problem Solution Transformation

  50. Model-BasedSystems EngineeringCenter Key Take-Aways • Model-Based Systems Engineering (MBSE) • Key for meeting tomorrow’s demands on complexity & functionality • SysML • The leading standardized language for supporting MBSE • Formal models enable model transformation • Extract information, documents, analyses from SysML models • Efficient solution of Architecture Exploration Problems • Formal problem definition  optimization at different levels of abstraction

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