ModelBased Systems Engineering Center ModelBased Systems Engineering with

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

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

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

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

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

Model-Based Systems Engineering What Kinds of System Models? Requirements Dynamic Performance Structure / Physical Architecture Engine Transmission Control Input Driveline Integrated System Model Must Address Multiple Aspects of a System Power Equations Vehicle Dynamics System Model Behavior / Functional Architecture Start Shift Accel Brake Models are more formal, complete & semantically rich (Adapted from OMG Sys. ML Tutorial) 2008 -2011 Copyright © Georgia Tech. All Rights Reserved. MBSE 6

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

Summary: Making Better Decision Ideas Alternatives Knowledge/ Beliefs Outcomes Preferences Selection Criterion: E[u] Decision Theory Maximize E[u] (Figure Adapted from G. Hazelrigg) u Most Preferred System Alternative 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) 2008 -2011 Copyright © Georgia Tech. All Rights Reserved. MBSE 8

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

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

(Source: Friedenthal, www. omgsysml. org) Pillars of Sys. ML — 4 Main Diagram Types 1. Structure 2. Behavior definition 4. Requirements 2008 -2011 Copyright © Georgia Tech. All Rights Reserved. 3. Parametrics MBSE 11

(Source: Friedenthal, www. omgsysml. org) Pillars of Sys. ML — 4 Main Diagram Types 1. Structure definition 2. Behavior use 4. Requirements 2008 -2011 Copyright © Georgia Tech. All Rights Reserved. 3. Parametrics MBSE 12

(Source: Friedenthal, www. omgsysml. org) Pillars of Sys. ML — 4 Main Diagram Types 1. Structure 2. Behavior interaction definition use 4. Requirements 2008 -2011 Copyright © Georgia Tech. All Rights Reserved. 3. Parametrics MBSE 13

(Source: Friedenthal, www. omgsysml. org) Pillars of Sys. ML — 4 Main Diagram Types 1. Structure 2. Behavior interaction state machine definition use 4. Requirements 2008 -2011 Copyright © Georgia Tech. All Rights Reserved. 3. Parametrics MBSE 14

(Source: Friedenthal, www. omgsysml. org) Pillars of Sys. ML — 4 Main Diagram Types 1. Structure 2. Behavior interaction state machine activity/ function definition use 4. Requirements 2008 -2011 Copyright © Georgia Tech. All Rights Reserved. 3. Parametrics MBSE 15

(Source: Friedenthal, www. omgsysml. org) Pillars of Sys. ML — 4 Main Diagram Types 1. Structure 2. Behavior interaction state machine activity/ function definition use 4. Requirements 2008 -2011 Copyright © Georgia Tech. All Rights Reserved. 3. Parametrics MBSE 16

(Source: Friedenthal, www. omgsysml. org) Pillars of Sys. ML — 4 Main Diagram Types 1. Structure 2. Behavior interaction state machine activity/ function definition use 4. Requirements 2008 -2011 Copyright © Georgia Tech. All Rights Reserved. 3. Parametrics MBSE 17

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

(Source: Friedenthal, www. omgsysml. org) Cross Connecting Model Elements 1. Structure 2. Behavior ate c allo 4. Requirements 2008 -2011 Copyright © Georgia Tech. All Rights Reserved. 3. Parametrics MBSE 19

(Source: Friedenthal, www. omgsysml. org) Cross Connecting Model Elements 1. Structure 2. Behavior ate c allo 4. Requirements 2008 -2011 Copyright © Georgia Tech. All Rights Reserved. 3. Parametrics MBSE 20

(Source: Friedenthal, www. omgsysml. org) Cross Connecting Model Elements 1. Structure 2. Behavior ate c allo satisfy 4. Requirements 2008 -2011 Copyright © Georgia Tech. All Rights Reserved. 3. Parametrics MBSE 21

(Source: Friedenthal, www. omgsysml. org) Cross Connecting Model Elements 1. Structure 2. Behavior ate c allo satisfy 4. Requirements 2008 -2011 Copyright © Georgia Tech. All Rights Reserved. 3. Parametrics MBSE 22

(Source: Friedenthal, www. omgsysml. org) Cross Connecting Model Elements 1. Structure 2. Behavior ate c allo satisfy value binding 4. Requirements 2008 -2011 Copyright © Georgia Tech. All Rights Reserved. 3. Parametrics MBSE 23

(Source: Friedenthal, www. omgsysml. org) Cross Connecting Model Elements 1. Structure 2. Behavior ate c allo satisfy value binding 4. Requirements 2008 -2011 Copyright © Georgia Tech. All Rights Reserved. 3. Parametrics MBSE 24

(Source: Friedenthal, www. omgsysml. org) Cross Connecting Model Elements 1. Structure 2. Behavior ate c allo value binding satisfy verify 4. Requirements 2008 -2011 Copyright © Georgia Tech. All Rights Reserved. 3. Parametrics MBSE 25

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

Formal Models + Model Transformations Stage-Gate Documents Transformation Tr an sf or Transformation m at io n Project Management Metrics Simulation & Optimization 2008 -2011 Copyright © Georgia Tech. All Rights Reserved. MBSE 27

Model Transformation Source Metamodel refers to Transformation Specification conforms to Source Model refers to executes reads Target Metamodel conforms to writes Transformation Engine Target Model (Czarnecki, K. , & Hellen, S. , 2006) u u Transformation Specification is also a Model automated generation of transformation engine code Origins u – Automation of repeated modeling patterns – Tool interoperation – Document generation – Consistency checking – Dependency propagation – Model Driven Architecture/ Engineering u Example Usages: Tools – MOFLON, QVTo, ATL, GME/GRe. AT, VIATRA 2, Kermeta, … 2008 -2011 Copyright © Georgia Tech. All Rights Reserved. MBSE 28

Sys. ML-Modelica Transformation Specification Representing Hybrid Continuous/Discrete Dynamics in Sys. ML u u OMG standard for integrating Sys. ML and Modelica Transformation is specified in QVT (Query/View/ Transformation) – an OMG specification conforms to Sys. ML+ Sys. ML 4 Modelica metamodel conforms to Modelica metamodel XMI (Sys. ML 4 Modelica) XMI (Modelica) Sys. ML Tool QVT (normative) Tool-Specific Repository 2008 -2011 Copyright © Georgia Tech. All Rights Reserved. Modelica abstract syntax OMC Modelica. mo file MBSE 29

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

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

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

System Architecture Exploration for a Hydraulic Excavator u Given: – Component models – Objectives / preferences u Excavator Find: – Best system architecture – Best component parameters – (Best controller) engine pump_vdisp accum cylinder v_3 way How to connect and size these? 2008 -2011 Copyright © Georgia Tech. All Rights Reserved. MBSE 33

Specify Allowable/Required Components A Component may be abstract, representing multiple sub-classes Multiplicities for optional components Specify the required connectors in IBD 2008 -2011 Copyright © Georgia Tech. All Rights Reserved. MBSE 34

Specify Allowable/Required Connections Connectors blank not allowed 1 required + optional + + 1

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

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

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

Domain Knowledge: Model Libraries Component Structure 2008 -2011 Copyright © Georgia Tech. All Rights

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

Model Transformations to Domain Knowledge Defining the Reuse Patterns in Sys. ML 2008 -2011

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

Step 1: Create a Superstructure All potential components All potential connections 2008 -2011 Copyright

Step 2: Linearization of Constitutive Equations τmax τ(1) τ(2) τ(0) τ(3) 2008 -2011 Copyright

Step 3: Generate Connection Equations u Kirchhoff’s Laws: – – u A. flow + flow. AC = 0 B. flow + flow. BC = 0 C. flow – flow. AC – flow. BC = 0 A. pressure = B. pressure = C. pressure A C B When considering optional connections: – – – A. flow + flow. AC * exists. AC = 0 B. flow + flow. BC * exists. BC = 0 C. flow – flow. AC * exists. AC – flow. BC * exists. BC = 0 (A. pressure - C. pressure) * exists. AC = 0 (B. pressure - C. pressure) * exists. BC = 0 Model Continuous Variables 2008 -2011 Copyright © Georgia Tech. All Rights Reserved. Binary Variable MBSE is nonlinear Difficult to solve 45

Step 3: Generate Connection Equations u Kirchhoff’s Laws: – – u A. flow + flow. AC = 0 B. flow + flow. BC = 0 C. flow – flow. AC – flow. BC = 0 A. pressure = B. pressure = C. pressure A C B When considering optional connections: – – flow. AC <= exists. AC * upper. Bound flow. AC >= - exists. AC * upper. Bound flow. BC <= exists. BC * upper. Bound flow. BC >= - exists. BC * upper. Bound Model is linear Can be solved very quickly 2008 -2011 Copyright © Georgia Tech. All Rights Reserved. MBSE 46

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

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 u 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 2008 -2011 Copyright © Georgia Tech. All Rights Reserved. MBSE 48

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

Model-Based Systems Engineering Center Key Take-Aways 1. Model-Based Systems Engineering (MBSE) – Key for meeting tomorrow’s demands on complexity & functionality 2. Sys. ML – The leading standardized language for supporting MBSE 3. Formal models enable model transformation – Extract information, documents, analyses from Sys. ML models 4. Efficient solution of Architecture Exploration Problems – Formal problem definition optimization at different levels of abstraction 2008 -2011 Copyright © Georgia Tech. All Rights Reserved. MBSE 50

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