ABSTRACT Title of Document: SYSTEM MODELING AND TRACEABILITY APPLICATIONS OF THE HIGRAPH FORMALISM Kevin Fogarty, Master of Science in Systems Engineering, 2006 Directed By: Dr. Mark Austin, Department of Civil and Environmental Engineering, and The Institute for Systems Research, University of Maryland at College Park One of the most important tools for a systems engineer is their system model. From this model, engineering decisions can be made without costly integration, fabrication, or installations. Existing system modeling languages used to create the system model are detailed and comprehensive, but lack a true ability to unify the system model by showing all relationships among all components in the model. Higraphs, a type of mathematical graph, allow systems engineers to not only represent all required information in a system model, but to formally show all relationships in the model through hierarchies, edges, and orthogonalities. With a higraph system model, all relationships between system requirements, components, and behaviors are formalized allowing for a “smart” model that can be queried for custom sets of information that, when presented to the systems engineer, will aid in engineering decisions.SYSTEM MODELING AND TRACEABILITY APPLICATIONS OF THE HIGRAPH FORMALISM By Kevin Fogarty Thesis submitted to the Faculty of the Graduate School of the University of Maryland, College Park, in partial fulfillment of the requirements for the degree of Master of Science in Systems Engineering 2006 Advisory Committee: Dr. Mark Austin, Chair Dr. John Baras, Committee Member Dr. David Lovell, Committee Member© Copyright by Kevin Fogarty 2006i Dedication This paper is dedicated to Brayden Thomas. May you grow up to be strong and faithful, and may you get to experience and learn all this world has to offer.ii Acknowledgements I would like to acknowledge the following people, all of whom contributed to this paper. Dr. Mark Austin, University of Maryland at College Park. • Associate Professor, Department of Civil and Environmental Engineering, and • Faculty, The Institute for Systems Research Dr. Austin, in his role as the thesis advisor, has provided overall guidance, editorial comment, and technical input to this thesis. Dr. Austin served as the Chair of this Thesis Committee. Dr. John Baras, University of Maryland at College Park. • Professor, Department of Electrical and Computer Engineering, • Founding Director, The Institute for Systems Research, and • Director, Maryland Hybrid Networks Center Dr. Baras served as a member of this Thesis Committee, and has provided technical input to this thesis. Dr. David Lovell, University of Maryland at College Park. • Associate Professor, Department of Civil and Environmental Engineering, andiii • Faculty, The Institute for Systems Research Dr. Lovell served as a member of this Thesis Committee, and has provided technical input to this thesis. Chad Rivera, University of Maryland at College Park. • Past student, Master’s of Engineering, Systems Engineering Program Mr. Rivera worked with Mr. Fogarty on a paper that served as the initial effort to research the higraph formalism as a tool for system modeling and traceability.iv Table of Contents Dedication ..................................................................................................................i Acknowledgements ...................................................................................................ii Table of Contents .....................................................................................................iv List of Tables............................................................................................................vi List of Figures .........................................................................................................vii Chapter 1: Introduction..............................................................................................1 Section 1.1: Introduction and Objectives................................................................1 Section 1.2: Organization of Thesis........................................................................3 Section 1.3: Contributions......................................................................................5 Chapter 2: Introduction to Higraphs...........................................................................6 Section 2.1: Higraph Definition .............................................................................6 Section 2.2: Existing Mathematical and Logical Models of Higraphs ...................13 Section 2.3: Existing Uses of Higraphs ................................................................19 Chapter 3: Existing System Modeling Languages ....................................................22 Section 3.1: The Unified Modeling Language ......................................................22 Subsection 3.1.1: What is The Unified Modeling Language? ...........................22 Subsection 3.1.2: Weaknesses of UML 1.x .....................................................25 Subsection 3.1.3: What is UML 2.0?................................................................26 Subsection 3.1.4: Weaknesses of UML 2.0 ......................................................28 Section 3.2: The Systems Modeling Language .....................................................29 Subsection 3.2.1: What is the Systems Modeling Language .............................29 Subsection 3.2.2: Weaknesses of SysML and Higraphs Areas of Improvement 34 Chapter 4: Using Higraphs for Systems Modeling ...................................................40 Section 4.1: Requirements Modeling with Higraphs.............................................40 Section 4.2: Structure Modeling with Higraphs....................................................49 Section 4.3: Behavior Modeling with Higraphs....................................................58 Section 4.4: System Level Modeling and Connectivity with Higraphs..................70 Section 4.5: Higraph Deficiencies ........................................................................74 Chapter 5: Formal Modeling of Higraphs................................................................80 Section 5.1: Extended Mathematical and Logical Modeling of Higraphs..............80 Section 5.2: Software Representations of Higraph Models