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Helsinki University of Technology Systems Analysis Laboratory
Analyzing Air Combat Analyzing Air Combat Simulation Results with Simulation Results with
Dynamic Bayesian Networks Dynamic Bayesian Networks
Jirka Poropudas and Kai VirtanenSystems Analysis Laboratory
Helsinki University of TechnologyP.O. Box 1100, 02015 TKK, Finland
http://www.sal.tkk.fi/forename.surname@tkk.fi
Helsinki University of Technology Systems Analysis Laboratory
2Winter Simulation Conference, Washington D.C. 2007
OutlineOutline Air combat (AC) simulation Analysis of simulation results Modelling the progress of AC in time Dynamic Bayesian network (DBN) Modelling AC using DBN Summary
Helsinki University of Technology Systems Analysis Laboratory
3Winter Simulation Conference, Washington D.C. 2007
Analysis of AC Using SimulationAnalysis 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
Helsinki University of Technology Systems Analysis Laboratory
4Winter Simulation Conference, Washington D.C. 2007
Discrete Event AC SimulationDiscrete Event AC Simulation
Simulation input Aircraft and
hardware configurations
Tactics Decision making
parameters
Simulation output Number of kills
and losses Aircraft
trajectories AC events etc.
Decision making logic
Aircraft, weapons, and hardware models
Helsinki University of Technology Systems Analysis Laboratory
5Winter Simulation Conference, Washington D.C. 2007
Traditional Statistical Models Turn AC into a Static EventTraditional 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 timeor the effect of AC events on AC and its outcome
Helsinki University of Technology Systems Analysis Laboratory
6Winter Simulation Conference, Washington D.C. 2007
Overwhelming Amount of Simulation DataOverwhelming 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
7Winter Simulation Conference, Washington D.C. 2007
Modelling the Progress of AC in TimeModelling 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?
Helsinki University of Technology Systems Analysis Laboratory
8Winter Simulation Conference, Washington D.C. 2007
Definition for the State of ACDefinition for the State of AC 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?”
Example of AC phases in X-Brawlersimulation model
Helsinki University of Technology Systems Analysis Laboratory
9Winter Simulation Conference, Washington D.C. 2007
Outcome of ACOutcome 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
10Winter Simulation Conference, Washington D.C. 2007
Probability Distribution of Probability Distribution of AC State Changes in TimeAC 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
Helsinki University of Technology Systems Analysis Laboratory
11Winter Simulation Conference, Washington D.C. 2007
Dynamic Bayesian Network Model for ACDynamic 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 Ot depends on Bt and Rt
time slice
Helsinki University of Technology Systems Analysis Laboratory
12Winter Simulation Conference, Washington D.C. 2007
Dynamic Bayesian Network Is Dynamic Bayesian Network Is Fitted to Simulation DataFitted to Simulation Data
Basic structure of DBN is assumed Additional arcs added to improve fit Probability tables estimated from
simulation data
Helsinki University of Technology Systems Analysis Laboratory
13Winter 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 DBNProgress of AC Tracked by DBN
Helsinki University of Technology Systems Analysis Laboratory
14Winter Simulation Conference, Washington D.C. 2007
DBN Enables Effective DBN Enables Effective What-If AnalysisWhat-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
Helsinki University of Technology Systems Analysis Laboratory
15Winter Simulation Conference, Washington D.C. 2007
Future Development of Existing ModelsFuture 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
Helsinki University of Technology Systems Analysis Laboratory
16Winter Simulation Conference, Washington D.C. 2007
SummarySummary 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
Helsinki University of Technology Systems Analysis Laboratory
17Winter Simulation Conference, Washington D.C. 2007
References 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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