System-of-Systems Engineering - Liophant Simulation

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Markov Chains• A Markov Chain is a directed graph in which theedge weights represent transition probabilities,and the probabilities on the edges leaving avertex sum to 1• Markov chains are used to model stochasticprocesses– For example, a Markov chain can be used to create astochastic version of the SIR model developed usingsystem dynamics– Queuing models– Bacteria growthDeveloping Methods and Techniques for System of Systems EngineeringDr. Dimitri Mavris, dimitri.mavris@ae.gatech.edu66
Markov Chains• The transition probabilitybetween state i and j isdenoted p ij• They are typicallyrepresented in atransition matrix, wherethe rows represent thepresent state and thecolumns represent thestate at the next timestepS1p 21S2p 32p 12 p 23S3Developing Methods and Techniques for System of Systems EngineeringDr. Dimitri Mavris, dimitri.mavris@ae.gatech.edu67
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Developing Methods and Techniques f
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The Aerospace Systems Design Labora
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Motivation- Emphasis on “Early-Ph
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What is a system?“A set of functi
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System of Systems• “A set or ar
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What is SoSE?• System of Systems
Page 13 and 14:
The Evolution of New Ideas“All tr
Page 15 and 16: What is needed for this New Paradig
Page 17 and 18: An Architecture-based Approach to S
Page 19 and 20: The System Alternative Space• The
Page 21 and 22: The Architecture-based Technology E
Page 23 and 24: Extension to Systems-of-Systems Ana
Page 25 and 26: Fundamental Properties of a Complex
Page 27 and 28: Enablers for Complex SoS• Design
Page 29 and 30: Design of Experiments• Design of
Page 31 and 32: Design of Computer Simulation• Co
Page 33 and 34: Agent-Based Behavioral Modeling•
Page 35 and 36: System Dynamics Modeling• System
Page 37 and 38: Discrete Event Simulations• Discr
Page 41 and 42: Surrogate ModelsWhy do we use surro
Page 43 and 44: Challenges to Surrogate Modeling fo
Page 45 and 46: Fitting Modal ResponsesDeveloping M
Page 51 and 52: Pareto Optimal Solutions in Many Di
Page 53 and 54: Interactive Electronic Design Revie
Page 55 and 56: Collaboration and Integration in So
Page 57 and 58: Concluding Remarks• System of Sys
Page 59 and 60: Selecting a DesignDeveloping Method
Page 61 and 62: A New Paradigm Shift: Simulation Ba
Page 63 and 64: Which are simple? Which arecomplica
Page 65: What is a Markov Chain• Markov Ch
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System-of-Systems Engineering - Liophant Simulation

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