Systems of Systems Engineering and Mathematics

Systems of Systems Engineering and Mathematics

|1| Systems of SystemsEngineering and Mathematics Laura Antul Judith Dahmann JSD 8 2017 The MITRE Corporation. All rights reserved. |2| Topics What is Systems Engineering? What is Systems of Systems (SoS) Engineering? How can mathematics contribute to Systems of Systems Engineering? 2017 The MITRE Corporation. All rights reserved. JSD 8 |3| Systems Engineering |4| What is SE? Definition of Systems and SE A system is a construct or collection of different elements that together produce results not obtainable by the elements alone. [1]

Systems Engineering is an engineering discipline whose responsibility is creating and executing an interdisciplinary process to ensure that the customer and stakeholder's needs are satisfied in a high quality, trustworthy, cost efficient and schedule compliant manner throughout a system's entire life cycle. [1] [1]"What is Systems Engineering", Incose.org, 2017. [Online]. Available: http://www.incose.org/AboutSE/WhatIsSE. [Accessed: 15- Jul- 2017]. 2017 The MITRE Corporation. All rights reserved. JSD 8 |5| MIT: Systems Introduction Characteristics [2] Interaction Hierarchical Emergent Dynamic Interdisciplinary Application Domain Examples [2] Aerospace Communication systems Information systems [2]Q. Hommes, P. Hale and D. Erickson, "ESD.33 Systems Engineering Lecture 1 Course Introduction", MIT, 2010. 2017 The MITRE Corporation. All rights reserved. JSD 8 |6|

MIT: Systems Introduction (cont.) Process Models [2] Waterfall Spiral INCOSE VEE [2]Q. Hommes, P. Hale and D. Erickson, "ESD.33 Systems Engineering Lecture 1 Course Introduction", MIT, 2010. 2017 The MITRE Corporation. All rights reserved. JSD 8 |7| SEBoK: Systems Engineering Overview Project Lifecycle [3] SE Scope [3] [3]"Systems Engineering Overview - SEBoK", Sebokwiki.org, 2017. [Online]. Available: http://sebokwiki.org/wiki/Systems_Engineering_Overview. [Accessed: 15- Jul- 2017]. 2017 The MITRE Corporation. All rights reserved. JSD 8 |8| System of Systems Engineering (SoSE) |9| Overview of SoS Definition of SoS and SoSE

System of Systems is a set or arrangement of systems that results when independent and useful systems are integrated into a larger system that delivers unique capabilities. [4] Systems of Systems Engineering is the process of planning, analyzing, organizing, and integrating the capabilities of a mix of existing and new systems into a system-of-systems capability that is greater than the sum of the capabilities of the constituent parts. [4] [4]Department of Defense, "US Defense Acquisition Guidebook", Defense Acquisition University, 2008. 2017 The MITRE Corporation. All rights reserved. JSD 8 | 10 | MITRE: Overview of SoS (cont.) Characteristics [5] Operational independence of constituent systems Managerial independence of constituent systems Geographical distribution Evolutionary development Emergent behavior Type [6] Directed Acknowledged Collaborative Virtual [5]Maier, M. (1998); "Architecting Principles for Systems-of-Systems"; Systems Engineering, Vol. 1, No. 4 (pp 267-284). [6]ISO/IEC/IEEE International Standard - Systems and software engineering -- System life cycle processes," in ISO/IEC/IEEE 15288 First edition 2015-05-15 , vol.,

no., pp.1-118, May 15 2015 doi: 10.1109/IEEESTD.2015.7106435 2017 The MITRE Corporation. All rights reserved. JSD 8 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7106435&isnumber=7106434 | 11 | MITRE: Overview of SoS (cont.) Socio-Technical (Disaster Response) Scope [7] Technical Socio-Technical Enterprise Domain [7] Mission Platform Information Technology [7]NATO STO, "System of Systems Characterization and Types", NATO STO, 2015. 2017 The MITRE Corporation. All rights reserved. JSD 8 | 12 | MITRE: Am I dealing with a SoS? Challenges Autonomy, Interdependencies,

SoS Authorities and Emergence Leadership Testing, Validation and Constituent Systems Perspectives Learning Capabilities and Requirements SoS Principles 2017 The MITRE Corporation. All rights reserved. JSD 8 | 13 | MITRE: Understanding SOP Acknowledged SoS in the DoD [8] Come into existence when something occurs that is important enough to trigger recognition of the SoS and bring into play management and governance processes which cut across established individual systems boundaries. [8]J. S. Dahmann and K. J. Baldwin, "Understanding the Current State of US Defense Systems of Systems and the Implications for Systems Engineering," 2008 2nd Annual IEEE Systems Conference, Montreal, Que., 2008, pp. 1-7. doi: 10.1109/SYSTEMS.2008.4518994 [9] Office of the Under Secretary of Defense for Acquisition, Technology and Logistics (OUSD AT&L) 2008. Systems of Systems Systems Engineering Guide: 2017 The MITREfor Corporation. All rights reserved. JSD of 8 Systems Environment, Washington, DC: Pentagon, (forthcoming).

Considerations Systems Engineering in a System | 14 | MITRE: Implementer View SoSE Wave Model [10] A wave model [11] of SoS SE unwinds the trapeze model and then maps the core elements to a more familiar view of SoS SE as a series of six timesequenced major steps in implementing an SoS SE process. This model has several driving characteristics that reflect the attributes of SoS: Multiple Overlapping Iterations of Evolution, Ongoing Analysis, Continuous Input from External Environment, Architecture Evolution, and Forward Movement with Feedback. Note: Flexibility evident by multiple arrows pointing to the same step in the model [10]Dahmann, J., Rebovich, G., Lane, J. A., Lowry, R., & Baldwin, K. (2011). An Implementers View of Systems Engineering for Systems of Systems. Proceedings of IEEE International Systems Conference. Montreal. [11] The concept of 'Wave Planning' developed Dr David Dombkins, see Dombkins, David. Complex Project Management, Booksurge Publishing, South Carolina: 2007. 2017 The MITRE

Corporation. Allwas rights reserved.by JSD 8 | 15 | INCOSE: SoS Pain Points Study Origins of Pain Points [12] Survey Conducted in 2012 38 Respondents 65 Pain Points Major Challenge Areas Identified [12]Dahmann, J. (2014), 1.4.3 System of Systems Pain Points. INCOSE International Symposium, 24: 108121. doi:10.1002/j.23345837.2014.tb03138.x 2017 The MITRE Corporation. All rights reserved. JSD 8 | 16 | Quantitative Analysis Method for System of Systems Architectures | 17 | As-is for Evaluating Architectures

2017 The MITRE Corporation. All rights reserved. JSD 8 | 18 | SoS Analysis of Alternatives Establish baseline SoS architecture Generate SoS architecture alternatives SoS graph abstraction and network analysis MIP contribution: inform prioritization of alternatives using lightweight analytics Detailed evaluation with M&S environment Informed architecture selection 2017 The MITRE Corporation. All rights reserved. JSD 8 | 19 | Robustness Metric (Algebraic Connectivity Value)

Represents average difficulty of isolating a node Second smallest eigenvalue of a Laplacian Matrix Inputs: Degree Matrix Diagonal matrix that contains the number of nodes adjacent to a given node Adjacency Matrix Symmetric matrix that contains a 1 if two given nodes are adjacent and 0 otherwise Reference: H. Mehrpouyan, B. Haley, A. Dong, I. Y. Tumer, and C. Hoyle, "Resiliency analysis for complex engineered system design," Artificial Intelligence for Engineering Design, Analysis and Manufacturing, vol. 29, no. 01, pp. 93108, Jan. 2015. 2017 The MITRE Corporation. All rights reserved. JSD 8 | 20 | Identifying Resilient SoS Architectures Architecture 1 Architecture 2 Robustness Metric Value: Robustness Metric Value: 0.5858 2017 The MITRE Corporation. All rights reserved. JSD 8 0.8299

| 21 | Example Derivation of Algebraic Connectivity Value | 22 | Example: Deriving Adjacency Matrix Sub HDR SATCOM (1) Integrated Combat System (3) Bow Sensor (5) Adjacency Matrix Representation Tow Sensor (2) External Comms

(4) Torpedo (6) 2017 The MITRE Corporation. All rights reserved. JSD 8 1 2 3 4 5 6 1 0 0 1 1 0

0 2 0 0 1 0 0 0 3 1 1 0 0 1 1

4 1 0 0 0 0 0 5 0 0 1 0 0 0 6

0 0 1 0 0 0 | 23 | Example: Deriving Degree Matrix Adjacency Matrix (A) Degree Matrix (D) 1 2 3 4 5

6 1 2 3 4 5 6 1 0 0 1 1 0 0 1

2 0 0 0 0 0 2 0 0 1 0 0 0 2 0

1 0 0 0 0 3 1 1 0 0 1 1 3 0 0

4 0 0 0 4 1 0 0 0 0 0 4 0 0 0

1 0 0 5 0 0 1 0 0 0 5 0 0 0 0

1 0 6 0 0 1 0 0 0 6 0 0 0 0 0

1 Sum row or column (e.g. Degree of node 3 is 4) 2017 The MITRE Corporation. All rights reserved. JSD 8 | 24 | Example: Deriving Laplacian Matrix Degree Matrix (D) Adjacency Matrix Laplacian Matrix 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

1 2 0 0 0 0 0 1 0 0 1 1 0 0 1 2 0 -1 -1 0 0 2 0 1 0 0 0 0 3 0 0 4 0 0 0 2 0 0 1 0 0 0 0 0 0 0 -1 -1

4 0 0 0 1 0 0 5 0 0 0 0 1 0 4 1 0 0 0 0 0 1 0 0 5 0 0 1 0 0 0 2 0 1 -1 3 -1 -1 4 4 -1 0 0 5 0 0 -1 0 1 0 6 0 0 0 0 0 1 6 0 0 1 0 0 0 6 0

0 0 1 2017 The MITRE Corporation. All rights reserved. JSD 8 3 1 1 0 0 1 1 0 -1 | 25 | Example: Calculating Eigenvalues 0 When l = 0, 0.486, 1, 2.428, or 5.086 Therefore, 0.486 is the algebraic connectivity value 2017 The MITRE Corporation. All rights reserved. JSD 8 | 26 | Summary Systems of Systems Engineering is a growing area of practice

Mathematics provides a core foundation for SoS analysis and engineering 2017 The MITRE Corporation. All rights reserved. JSD 8

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