Transcript Or the outcome of AC?

Helsinki University of Technology
Systems Analysis Laboratory
Analyzing Air Combat
Simulation Results with
Dynamic Bayesian Networks
Jirka Poropudas and Kai Virtanen
Systems Analysis Laboratory
Helsinki University of Technology
P.O. Box 1100, 02015 TKK, Finland
http://www.sal.tkk.fi/
[email protected]
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Helsinki University of Technology
Systems Analysis Laboratory
Outline
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Air combat (AC) simulation
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Analysis of simulation results
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Modelling the progress of AC in time
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Dynamic Bayesian network (DBN)
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Modelling AC using DBN
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Summary
Winter Simulation Conference, Washington D.C. 2007
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Helsinki University of Technology
Systems Analysis Laboratory
Analysis of AC Using Simulation

Most cost-efficient and flexible method

Commonly used models based on
discrete event simulation
Objectives for AC simulation study:
 Acquire information on systems performance
 Compare tactics and hardware configurations
 Increase understanding of AC and its progress
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Helsinki University of Technology
Systems Analysis Laboratory
Discrete Event AC Simulation
Simulation input
 Aircraft and
hardware
configurations
Aircraft, weapons,
and hardware models
 Tactics
 Decision making
parameters
Simulation output
 Number of kills
and losses
 Aircraft
trajectories
 AC events
 etc.
Decision making logic
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Helsinki University of Technology
Systems Analysis Laboratory
Traditional Statistical Models Turn AC into a Static Event
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Simulation data has to be analyzed statistically
Statistically reliable AC simulation may require tens of
thousands of simulation replications
Descriptive statistics and empirical distributions for the
simulation output, e.g., kills and losses
Regression models describe the dependence between
simulation input and output
These models do not show the progress of AC in time
or the effect of AC events on AC and its outcome
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Systems Analysis Laboratory
Overwhelming Amount of Simulation Data
How should the progress of AC be analyzed?
How different AC events affect the outcome of the AC?

Not possible, e.g., to watch animations and observe
trends or phenomena in the simulated AC
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Helsinki University of Technology
Systems Analysis Laboratory
Modelling the Progress of AC in Time

State of AC
– Definition depends on, e.g., the goal of analysis and the
simulation model properties

Outcome of AC
– Measure for success in AC?
– Definition depends on, e.g., the goal of analysis

Dynamics of AC must be included
– How does AC state change in time?
– How does a given AC state affect AC outcome?
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Helsinki University of Technology
Systems Analysis Laboratory
Definition for the State of AC
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1 vs. 1 AC, blue and red
Bt and Rt are AC state
variables at time t
State variable values
“Phases” of simulated
pilots
– Are a part of the decision
making model
– Determine behavior and phase
transitions for individual pilots
– Answer the question ”What is
the pilot doing at time t?”
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Example of AC phases in X-Brawler
simulation model
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Helsinki University of Technology
Systems Analysis Laboratory
Outcome of AC
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Outcome Ot is described by a variable with four possible values
–
–
–
–
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Blue advantage: blue is alive, red is shot down
Red advantage: blue is shot down, red is alive
Mutual disadvantage: both sides have been shot down
Neutral: Both sides are alive
Outcome at time t is a function of state variables Bt and Rt
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Helsinki University of Technology
Systems Analysis Laboratory
Probability Distribution of
AC State Changes in Time
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State variables are random
– Probability distribution estimated from
simulation data
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Distributions change in time
= Progress of AC
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What-if analysis
– Conditional distributions are estimated
– Estimation must be repeated for all
analyzed cases, ineffective
Dynamic Bayesian

Network
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Systems Analysis Laboratory
Dynamic Bayesian Network Model for AC
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Dynamic Bayesian network
– Nodes = variables
– Arcs = dependencies
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Dependence between variables
described by
time slice
– Network structure
– Conditional probability tables
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Time instant t presented by
single time slice
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Outcome Ot depends on Bt and Rt
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Helsinki University of Technology
Systems Analysis Laboratory
Dynamic Bayesian Network Is
Fitted to Simulation Data
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Basic structure of DBN is assumed
Additional arcs added to improve fit
Probability tables estimated from
simulation data
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Helsinki University of Technology
Systems Analysis Laboratory
Progress of AC Tracked by DBN
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Continuous probability
curves estimated from
simulation data
DBN model re-produces
probabilities at discrete
times
DBN gives compact and
efficient model for the
progress of AC
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Systems Analysis Laboratory
DBN Enables Effective
What-If Analysis
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Evidence on state of AC fed to DBN
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For example, blue is engaged within
visual range combat at time 125 s
– How does this affect the progress of AC?
– Or the outcome of AC?
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DBN allows fast and efficient
updating of probability distributions
– More efficient what-if analysis
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No need for repeated re-screening
simulation data
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Helsinki University of Technology
Systems Analysis Laboratory
Future Development of Existing Models
 Other definitions for AC state,
e.g., based on geometry and
dynamics of AC
 Extension to n vs. m
scenarios
 Optimized time discretization
– In existing models time
instants have been
distributed uniformly
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Systems Analysis Laboratory
Summary
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Progress of simulated AC studied by estimating
time-varying probability distributions for AC state
Probability distributions presented using
a Dynamic Bayesian network
DBN model approximates the distribution of AC state
– Progress of AC
– Dependencies between state variables
– Dependence between AC events and outcome
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DBN used for effective what-if analysis
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Helsinki University of Technology
Systems Analysis Laboratory
References
» Anon. 2002. The X-Brawler air combat simulator management summary.
Vienna, VA, USA: L-3 Communications Analytics Corporation.
» Feuchter, C.A. 2000. Air force analyst’s handbook: on understanding the nature
of analysis. Kirtland, NM. USA: Office of Aerospace Studies, Air Force Material
Command.
» Jensen, F.V. 2001. Bayesian networks and decision graphs (Information
Science and Statistics). Secaucus, NJ, USA: Springer-Verlag New York, Inc.
» Law, A.M. and W.D. Kelton. 2000. Simulation modelling and analysis. New York,
NY, USA: McGraw-Hill Higher Education.
» Poropudas, J. and K. Virtanen. 2006. Game Theoretic Analysis of Air Combat
Simulation Model. In Proceedings of the 12th International Symposium of
Dynamic Games and Applications. The International Society of Dynamic
Games.
» Virtanen, K., T. Raivio, and R.P. Hämäläinen. 1999. Decision theoretical
approach to pilot simulation. Journal of Aircraft 26 (4):632-641.
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