• date post

04-Feb-2016
• Category

## Documents

• view

69

0

Embed Size (px)

description

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] Analyzing Air Combat Simulation Results with Dynamic Bayesian Networks. Outline. Air combat (AC) simulation - PowerPoint PPT Presentation

### Transcript of Analyzing Air Combat Simulation Results with Dynamic Bayesian Networks

Selecting forest sites for voluntary conservation in FinlandAnalyzing Air Combat
Simulation Results with
Dynamic Bayesian Networks
Systems Analysis Laboratory
http://www.sal.tkk.fi/
[email protected]
*
Outline
Dynamic Bayesian network (DBN)
Modelling AC using DBN
*
Analysis of AC Using Simulation
Most cost-efficient and flexible method
Commonly used models based on
discrete event simulation
Increase understanding of AC and its progress
Helsinki University of Technology Systems Analysis Laboratory
*
Discrete Event AC Simulation
Aircraft trajectories
AC events
*
Traditional Statistical Models Turn AC into a Static Event
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
Helsinki University of Technology Systems Analysis Laboratory
*
Overwhelming Amount of Simulation Data
Not possible, e.g., to watch animations and observe trends or phenomena in the simulated AC
How should the progress of AC be analyzed?
How different AC events affect the outcome of the AC?
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
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?
Helsinki University of Technology Systems Analysis Laboratory
*
1 vs. 1 AC, blue and red
Bt and Rt are AC state
variables at time t
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?”
Example of AC phases in X-Brawler
simulation model
*
Outcome of AC
Outcome Ot is described by a variable with four possible values
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
Helsinki University of Technology Systems Analysis Laboratory
*
Probability Distribution of
State variables are random
Distributions change in time
Dynamic Bayesian Network
*
Dynamic Bayesian network
Network structure
single time slice
time slice
*
Dynamic Bayesian Network Is
Fitted to Simulation Data
Helsinki University of Technology Systems Analysis Laboratory
*
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
Helsinki University of Technology Systems Analysis Laboratory
*
DBN Enables Effective
Evidence on state of AC fed to DBN
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?
DBN allows fast and efficient updating of probability distributions
More efficient what-if analysis
*
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
Helsinki University of Technology Systems Analysis Laboratory
*
Summary
time-varying probability distributions for AC state
Probability distributions presented using
a Dynamic Bayesian network
Progress of AC
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.