# Analyzing Air Combat Simulation Results with Dynamic Bayesian Networks

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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.

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.