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Integrated Systems Understanding using Bayesian Networks: Measuring the Effectiveness of a Weapon System
Pretoria
Defence, Peace, Safety & Security
Alta de Waal
Research Group Leader: Socio-Technical Systems
27 February 2006
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Slide 2 © CSIR 2006 www.csir.co.za
Summary
• Modelling of Complex Systems• System-of-systems• Independent research• Lack of whole systems view
• Approach: Causality• Derive causal relationships from combinations of knowledge and
data• Improve understanding of system behaviour
• Causal Inference• Identify sensitive variables in the system• Identify interdependencies between sub-systems• Predict the effects of actions and policies• Evaluate explanations for observed events and scenarios• Support decisions
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Slide 3 © CSIR 2006 www.csir.co.za
Research Case Study: Measure the effectiveness of the FSG Weapon System• Weapon system onboard Corvettes• System-of systems:
• designation radar• tracking radar• electro-optical tracking sensor• combat management system• missile system.
• Define, measure and quantify being effective
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Slide 4 © CSIR 2006 www.csir.co.za
Approach: Causal Modelling
• Cause-and-effect relationships between system variables• Introduce realistic scenario variables such as ‘natural
environment’• Quantify the cause-and-effect relationships• Evaluate the weapon system behaviour and performance
• Graphical Notation: represents causality• Probabilities: represents causal inference
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Slide 5 © CSIR 2006 www.csir.co.za
Bayesian Networks: A marriage of graphs and probabilities
• Causal Graph• Diagonal Acyclic Graph (DAG)
• Nodes (represents variables)• Arrows (represents causal links between variables)
• Causal Inference• Need the joint probability distribution of variables in DAG• Without independence assumption, the joint probability distribution grows
exponentially • Graphs facilitate decomposition of large distribution functions: conditional
independence assumption
),...,( 1 nxxP
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Slide 6 © CSIR 2006 www.csir.co.za
A
B
D
C
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The FSG System Model
A Timeline Approach
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Slide 8 © CSIR 2006 www.csir.co.za
Engagement Timeline
• Utilise causal dependencies along the engagement timeline• Sequence of Events• Measuring Unit: time (seconds) translated to range (km)• Did the intercept happen in-time (or far enough from the ship) not to
endanger the ship?
Firs
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Wea
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Allo
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Per
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to F
ire
Laun
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Inte
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Range (km) from ship
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Slide 9 © CSIR 2006 www.csir.co.za
The Causal Structure
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Slide 10 © CSIR 2006 www.csir.co.za
Quantification of the Model
• Expert Knowledge• Results from Monte Carlo simulations
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Slide 11 © CSIR 2006 www.csir.co.za
The Integrated Model
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Slide 12 © CSIR 2006 www.csir.co.za
Results
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Slide 13 © CSIR 2006 www.csir.co.za
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Slide 14 © CSIR 2006 www.csir.co.za
Conclusions
• Benefits• Tacit Knowledge – Explicit Knowledge• Model that represents the knowledge about the system rather than
the system itself• Shared understanding of the system• What-if capability
• Shortcomings• No feedback loops• Lack of understanding of aggregation of uncertainty