1. 1 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/ forename.surname@tkk.fi

2. Helsinki University of Technology Systems Analysis Laboratory 2 Winter Simulation Conference, Washington D.C. 2007 Outline n Air combat (AC) simulation n Analysis of simulation results n Modelling the progress of AC in time n Dynamic Bayesian network (DBN) n Modelling AC using DBN n Summary

3. Helsinki University of Technology Systems Analysis Laboratory 3 Winter Simulation Conference, Washington D.C. 2007 Analysis of AC Using Simulation Most cost-efficient and flexible method Commonly used models based on discrete event simulation Objectives for AC simulation study: Ÿ Acquire information on systems performance Ÿ Compare tactics and hardware configurations Ÿ Increase understanding of AC and its progress

4. Helsinki University of Technology Systems Analysis Laboratory 4 Winter Simulation Conference, Washington D.C. 2007 Discrete Event AC Simulation Simulation input n Aircraft and hardware configurations n Tactics n Decision making parameters Simulation output n Number of kills and losses n Aircraft trajectories n AC events n etc. Decision making logic Aircraft, weapons, and hardware models

5. Helsinki University of Technology Systems Analysis Laboratory 5 Winter Simulation Conference, Washington D.C. 2007 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

6. Helsinki University of Technology Systems Analysis Laboratory 6 Winter Simulation Conference, Washington D.C. 2007 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?

7. Helsinki University of Technology Systems Analysis Laboratory 7 Winter Simulation Conference, Washington D.C. 2007 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?

8. Helsinki University of Technology Systems Analysis Laboratory 8 Winter Simulation Conference, Washington D.C. 2007 Definition for the State of AC 1 vs. 1 AC, blue and red B t and R t 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?” Example of AC phases in X-Brawler simulation model

9. Helsinki University of Technology Systems Analysis Laboratory 9 Winter Simulation Conference, Washington D.C. 2007 Outcome of AC Outcome O t 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 B t and R t

10. Helsinki University of Technology Systems Analysis Laboratory 10 Winter Simulation Conference, Washington D.C. 2007 Probability Distribution of AC State Changes in Time State variables are random –Probability distribution estimated from simulation data Distributions change in time = Progress of AC What-if analysis –Conditional distributions are estimated –Estimation must be repeated for all analyzed cases, ineffective Dynamic Bayesian Network 

11. Helsinki University of Technology Systems Analysis Laboratory 11 Winter Simulation Conference, Washington D.C. 2007 Dynamic Bayesian Network Model for AC Dynamic Bayesian network –Nodes = variables –Arcs = dependencies Dependence between variables described by –Network structure –Conditional probability tables Time instant t presented by single time slice Outcome O t depends on B t and R t time slice

12. Helsinki University of Technology Systems Analysis Laboratory 12 Winter Simulation Conference, Washington D.C. 2007 Dynamic Bayesian Network Is Fitted to Simulation Data Basic structure of DBN is assumed Additional arcs added to improve fit Probability tables estimated from simulation data

13. Helsinki University of Technology Systems Analysis Laboratory 13 Winter Simulation Conference, Washington D.C. 2007 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 Progress of AC Tracked by DBN

14. Helsinki University of Technology Systems Analysis Laboratory 14 Winter Simulation Conference, Washington D.C. 2007 DBN Enables Effective What-If Analysis 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 No need for repeated re-screening simulation data

15. Helsinki University of Technology Systems Analysis Laboratory 15 Winter Simulation Conference, Washington D.C. 2007 Future Development of Existing Models n Other definitions for AC state, e.g., based on geometry and dynamics of AC n Extension to n vs. m scenarios n Optimized time discretization –In existing models time instants have been distributed uniformly

16. Helsinki University of Technology Systems Analysis Laboratory 16 Winter Simulation Conference, Washington D.C. 2007 Summary 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 DBN used for effective what-if analysis

17. Helsinki University of Technology Systems Analysis Laboratory 17 Winter Simulation Conference, Washington D.C. 2007 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.