I/ITSEC2009 Best Tutorial
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The document discusses mathematical and heuristic models of combat, detailing their scope, types, and examples, as well as the process of creating combat scenarios. It covers various modeling aspects including environmental and physical modeling, data processing, and communication systems. The objective is to enhance understanding of combat dynamics through simulation and visualization techniques.
![Target Acquisition
Glance/
Glimpse
No
tg tg tg
Pacq Pacq Pacq
Glimpse models
Target
Found?
Yes
Intermittent glimpses: E[N] = Σn np(n)
Factors
Sensor
characteristics
Target characteristics
Line-of-sight
Continuous looking model = PROBDETECT in time t = 1 - e-Dt
DYNTACS curve fit model = D = PFOV (α/(β + t(δ + ζR2 – ξVc)))
NVEOL acquisition algorithm
Approved for Public Release
09-MDA-4814 (2 SEPT 09) 29](https://image.slidesharecdn.com/907-141108183007-conversion-gate02/85/I-ITSEC2009-Best-Tutorial-29-320.jpg)
![Point System
18
4
20
8
Weapon Power
Path Degradation
(range, shelters, obstructions)
Health
Armor
New Health = (Health + Armor) – (Weapon Power – Path Degrade)
New Health = (18 + 8) – (20 – 4) = 10
New Armor = Armor – ABS[( Weapon Power – Path Degrade) *0.25]
Approved for Public Release
09-MDA-4814 (2 SEPT 09) 41](https://image.slidesharecdn.com/907-141108183007-conversion-gate02/85/I-ITSEC2009-Best-Tutorial-41-320.jpg)
I/ITSEC2009 Best Tutorial
- 1. Approved for Public Release 09-MDA-4814 (2 SEPT 09) 1 Mathematical and Heuristic Models of Combat with Examples Jeffrey Strickland, Ph.D., CMSP Missile Defense Agency DISTRIBUTION STATEMENT A. Approved for public release; distribution is unlimited.
- 2. Approved for Public Release 09-MDA-4814 (2 SEPT 09) Learning Objectives 1. Describe the scope of mathematical and heuristic combat models. 2. Compare and contrast different representations of combat phenomenon. 3. List combat behaviors that can be represented by mathematical & heuristic models. 4. State the various types of mathematical and heuristic combat models. 5. Identify examples of mathematical and heuristic combat models. 2
- 3. Tutorial Outline Environmental modeling how to model the environment level of detail entity interaction Physical modeling how to move how to sense or detect how to shoot (or create other effects) how to communicate Simulation scenario development what are the elements of a scenario how to develop scenarios Approved for Public Release 09-MDA-4814 (2 SEPT 09) 3
- 4. Approved for Public Release 09-MDA-4814 (2 SEPT 09) 4 Environment Modeling Level of Detail Conceptual Reference Model Data Collection Data Processing Static Environment Dynamic Environment Standardization
- 5. Level of Detail Air Combat Terrain Ground Combat Terrain Perceived details bitmaps over data points hills, trees, rivers, rocks No interaction simulated system does not interact directly with terrain details. Visual detail polygon color & lighting bit mapped surfaces hard surfaces Modeling detail surface trafficability foliage density tree trunk diameter Approved for Public Release 09-MDA-4814 (2 SEPT 09) 5
- 6. Conceptual Reference Model Component Models Environmental State Behavior Models Environmental Models Synthetic Natural Environment Military System Model Behaviors (e.g.) • Maneuver • Sustainment • Force Protection • Intelligence • Command & Control • Fires Effects (e.g.) • Attenuation • Propagation • Mobility Internal Dynamics Impacts (e.g.) • Obscurants/ Energy (smoke, chaff, spectral,..) • Damage (engrg, craters,..) Data (e.g.) • Terrain (surface, hydro,..) • Atmosphere (aerosols, clouds,..) • Ocean (sea state, SVP,..) • Space (particle flux,..) • Cultural (roads, structures,..) • Military (engrg. works,..) Passive Sensors Active Sensors Weapons & Countermeasures Units/Platforms SOURCE: Paul A. Birkel, "SNE Conceptual Reference Model", 1999 Fall SIW Conference, September 1999. http://www.sisostds.org/siw/98Fall/view-papers.htm Approved for Public Release 09-MDA-4814 (2 SEPT 09) 6
- 7. Data Processing Collection survey the environment (satellite, maps, etc.) store the results vector, grid, and model data Cleaning remove collection process discontinuities synchronize vector and grid data Organizing index and archive Integration merge vector, grid, model generate terrain skin with embedded features and surface data Transmission move data to the host system Compilation create performance-optimized runtime databases cut into sheets Approved for Public Release 09-MDA-4814 (2 SEPT 09) 7
- 8. Storing Environmental Data Triangulated Irregular Network (TIN) Surface tiled with hexagons Data point correlation Approved for Public Release 09-MDA-4814 (2 SEPT 09) 8
- 9. Static Environment Trafficability Terrain Type Visibility Approved for Public Release 09-MDA-4814 (2 SEPT 09) 9
- 10. Dynamic Environment Independent weather movement – clouds, rain, wind sea state – storms, daily tide daylight – sunrise, sunset, dark smoke & dust – clouds, raising, dispersing Interaction holes – artillery craters, engineering artifacts tank treads – tracks, destruction terrain morphing – engineering, construction feature modification – building damage, trees burned Approved for Public Release 09-MDA-4814 (2 SEPT 09) 10
- 11. Classic Problems in Interpretation 1 2 Terrain Points Building Corners 3a 3b 1 2a 2b Approved for Public Release 09-MDA-4814 (2 SEPT 09) 11
- 12. Environmental Standardization Approved for Public Release 09-MDA-4814 (2 SEPT 09) 12
- 13. Physical Modeling Detect/Acquire Engage (other major combat functions) Move Start Cycle Here Communicate Approved for Public Release 09-MDA-4814 (2 SEPT 09) 13
- 14. Approved for Public Release 09-MDA-4814 (2 SEPT 09) 14 Movement Modeling Movement Points Movement Bald Earth Movement Terrain and Feature Movement Physics-based Movement Automated Route Planning A* Search Topology Smart Grid Registration Behavioral
- 15. Movement Points Movement 2 3 6 1 2 6 2 1 Movement Points = 20 Movement Points Remaining = 20 – 11 = 9 Approved for Public Release 09-MDA-4814 (2 SEPT 09) 15
- 16. Bald Earth Movement Set heading, speed, start time Rate*Time = Distance 20 km/hr * 30 min = 10 km Approved for Public Release 09-MDA-4814 (2 SEPT 09) 16
- 17. Terrain and Feature Movement Set Objective: position or vector Terrain & features modify instantaneous heading & speed Speed = min(order_speed, max_speed*trafficability*slope_factor)* weather_factor*lighting_factor*fatigue_factor*supression_factor Approved for Public Release 09-MDA-4814 (2 SEPT 09) 17
- 18. Approved for Public Release 09-MDA-4814 (2 SEPT 09) main force calculations Proportional Force Calculation Resistive Force Calculation Braking Force Calculation Dynamic Equation Calculations net force new vehicle state (pos, vel, acc) Vehicle type, terrain type, slope, controls, current platform state Physics-based Movement • The CCTT ground vehicle mobility model is based on a general first-principle dynamics model. • The model integrates explicit driver inputs (e.g., throttle, brake) with vehicle class-specific velocity, resistance force, and deceleration pre-computed curves. Simple View of a Dynamic Movement Model CCTT Vehicle Dynamics Block Diagram 18
- 19. Automatic Route Planning CONCEPT: provide an algorithm by which units can automatically find their own routes. allows the analyst to focus on higher issues such as the overall scheme of maneuver reduces the intrusion of the analyst into C2 units can still be given explicit routes if desired, or closely grouped intermediate objectives ALGORITHMS: based on graph theory could be a satisfying algorithm (not guaranteed to find an optimal route) might be an optimal algorithm “optimal" may mean fastest, or shortest, or safest, etc. EXAMPLES A* search, Johnson’s algorithm, Dijkstra's algorithm, hill climbing Approved for Public Release 09-MDA-4814 (2 SEPT 09) 19
- 20. Topology Smart Set Objective: Position or Vector Movement model selects path from topological map Maintain objective Route traveled is function of topology Approved for Public Release 09-MDA-4814 (2 SEPT 09) 20
- 21. Grid Registration 11 12 13 14 15 16 17 21 22 23 24 25 26 27 31 32 33 34 35 36 37 41 42 43 44 45 46 47 Grid 14 → V71, V109, V1212, V10101 Vehicles registered into geographic grid during movement Improve LOS, sensor, and interaction performance Approved for Public Release 09-MDA-4814 (2 SEPT 09) 21
- 22. Beyond 2-D Movement 3 Dimensional—aircraft rotation axes yaw - vertical axis rotation roll - longitudinal axis rotation pitch- lateral axis rotation 3-D Mathematics Euler angles axis angle rotation matrices quaternions Other degrees of freedom: 3+3 DOF, 6 DOF Yaw Pitch Roll Approved for Public Release 09-MDA-4814 (2 SEPT 09) 22
- 23. Behavioral—Agent Based Behavioral evolution and extrapolation Each avatar generates (a) a stream of ghosts samples the personality space of its entity. They evolve (b, c) against the entity’s recent observed behavior. The fittest ghosts run into the future (d), and the avatar analyzes their behavior (e) to generate predictions. a c Ghosts b Real-World e Entity d Prediction Horizon Ghost time τ Observe Ghost prediction Avatar Insertion Horizon Measure Ghost fitness t = τ (Now) RTarget GTarget n n RThreatn 1 GNest Dist n n F n Approved for Public Release 09-MDA-4814 (2 SEPT 09) 23
- 24. Approved for Public Release 09-MDA-4814 (2 SEPT 09) 24 Detection Modeling Perfect Detection Gridded Probability Areas Detection Range 3D Detection Range Target Acquisition Process Sensor & Target Characteristics Line-of-Sight NVEOL Model
- 25. Perfect Detection Every object knows the true location of every other object. There are no models of sensors or processors. Approved for Public Release 09-MDA-4814 (2 SEPT 09) 25
- 26. Gridded Probability Areas Perfect detection within the same grid area (Pdet = 1.0) Probability of detection within adjacent areas Adjacent Pdet =F(terrain) Non-Adjacent Pdet = 0.0 60% 30% 100% 0% Approved for Public Release 09-MDA-4814 (2 SEPT 09) 26
- 27. Detection Range Complete circle—no field of view/field of regard Terrain line-of-sight (LOS) is separate Approved for Public Release 09-MDA-4814 (2 SEPT 09) 27
- 28. 3D Detection Range Probability of detection based on range of spheres Concentric areas Different Pdet for each ring For some sensors, Pdet of inner ring is 0.00 2 sin N d sin sin N d sin 2 2 2 2 2 sin sin 2 sin sin 2 sin sin 0 sin sin sin 0 sin Approved for Public Release 09-MDA-4814 (2 SEPT 09) 28 d a a I I d a a
- 29. Target Acquisition Glance/ Glimpse No tg tg tg Pacq Pacq Pacq Glimpse models Target Found? Yes Intermittent glimpses: E[N] = Σn np(n) Factors Sensor characteristics Target characteristics Line-of-sight Continuous looking model = PROBDETECT in time t = 1 - e-Dt DYNTACS curve fit model = D = PFOV (α/(β + t(δ + ζR2 – ξVc))) NVEOL acquisition algorithm Approved for Public Release 09-MDA-4814 (2 SEPT 09) 29
- 30. NVEOL Acquisition Algorithm Joint Conflicts And Tactical Simulation Developed by US Army's Night Vision and Electro-Optical Laboratories In Time-Stepped Model: PROBDETECT in time T = PINF (1 - e -CT) Use this as success probability for a Bernoulli trial. In Event-Stepped Model: Compute PINF and draw a random number to determine if detection would occur in infinite amount of time Sample from an exponential distribution with mean C to determine time till detection given that a detection will occur. Approved for Public Release 09-MDA-4814 (2 SEPT 09) 30
- 31. Sensor & Target Characteristics Sensor characteristics Maximum range Sensor footprint Frequency, pulse rate EO, IR, RF, mag, sonar Geometry Range Off-set angle Terrain & weather effects Line-of-sight (LOS) Obscurants Earth curvature Target characteristics Camouflage Color & pattern Radar cross section IR signature Movement Cavitations Magnetic mass Obscurants Earth curvature Approved for Public Release 09-MDA-4814 (2 SEPT 09) 31
- 32. Line-of-Sight Models Max Range of view LOS does not exist Left Limit of View (white) . . . . . . . . . . . . . . . . .Primary Direction of view (white) LOS exists Orange lines Right Limit of View (white) EXPLICIT: combat model stores a terrain representation and uses it to compute line-of-sight Grid: covers the battlefield with regular polygonal grid, each grid having associated terrain attributes (e.g., elevation, vegetation, etc.) Look at intervening grids between observer and target to see if any grid is higher than the line between them. Discontinuity is a disadvantage in high-res models. Simplicity and speed are advantages. Surface Triangulate the terrain data grids, then interpolate for a point between grid points. Greater accuracy is an advantage in high-res models. IMPLICIT: combat model stores expected results of line-of-sight and looks up the result when required probability of LOS intervisibility segment length Approved for Public Release 09-MDA-4814 (2 SEPT 09) 32
- 33. Approved for Public Release 09-MDA-4814 (2 SEPT 09) 33 Communications Modeling Comms Model Effects Perfect Communications Direct Message Passing Broadcast Messages Virtual Cell Layout Physics Modeling
- 34. Comms Model Effects Information exchange process info process data Intelligence collection ISR sensors target sensors fire control sensors Comms system overload network, sender, receiver Interference environment, electronic warfare Time delay Activity Diagram: Process Info Use Case Process Info Get Data from Target Sensor Evaluate Target's Intent Evaluate Target's Geometry Recognize Target Notify Knowledge Processing Update Target's Knowledge Get Data from Fire Control Sensor Get Info from Data Processing Approved for Public Release 09-MDA-4814 (2 SEPT 09) 34
- 35. Perfect Communications Targets ~~~~~ Orders ~~~~~ Reports ~~~~~ Shared information, no representation of comms Software-to-software message delivery Approved for Public Release 09-MDA-4814 (2 SEPT 09) 35
- 36. Direct Message Passing Consult command status If sender and receiver are alive, then pass message. If sender health is degraded, add error to target location. … … Approved for Public Release 09-MDA-4814 (2 SEPT 09) 36
- 37. Broadcast Messages Receiver determines whether signal is accessible to them based on range terrain degradation earth curvature jamming environment communications contention quality of receipt Success … Lost Degraded Delayed etc. … Approved for Public Release 09-MDA-4814 (2 SEPT 09) 37
- 38. Physics-Based Communication Networks Approved for Public Release 09-MDA-4814 (2 SEPT 09) 38 Packet-based model: network traffic flow: model packets in flow # sources, data rates increase, so too does simulation workload Fluid-based model: network traffic flow: continuous fluid rate changes at discrete points in time rate constant between changes can modulate rate at different time scales single modeling paradigm for many time scales abstract out fine-grained details: simulation efficiency
- 39. Virtual Cell Layout (VCL) The real cells are mobile and created by the mobile base stations, which are either: radio access points (RAPs) or cluster head man packed radios (MPRs). Computer aided exercise interacted tactical communications simulation (CITACS) A scenario with 153 units are simulated over an area of 115 km × 170 km Location manager deployed 77 RAPs and 18529 MPRs for this scenario based on the unit types and sizes. kr r kr r CITACS interacts with Joint Theater Level Simulation (JTLS) Approved for Public Release 09-MDA-4814 (2 SEPT 09) 39
- 40. Approved for Public Release 09-MDA-4814 (2 SEPT 09) 40 Engagement Modeling – Entity Level Point System Markov Pk Tables Random Numbers Pk’s and Random Numbers Precision Engagements Linear Target Phit Rectangular Target Phit Circular Target Phit Kill Categories
- 41. Point System 18 4 20 8 Weapon Power Path Degradation (range, shelters, obstructions) Health Armor New Health = (Health + Armor) – (Weapon Power – Path Degrade) New Health = (18 + 8) – (20 – 4) = 10 New Armor = Armor – ABS[( Weapon Power – Path Degrade) *0.25] Approved for Public Release 09-MDA-4814 (2 SEPT 09) 41
- 42. Markov Pk Table Damage = 1, where Random Number <= Pk Pk = 0, where Random Number > Pk Weapon W1 W2 W3 W4 … T1 0.5 0.7 0.8 0.92 T2 0.4 0.45 0.76 0.99 T3 0.31 0.34 0.56 0.85 T4 0.27 0.55 0.67 0.81 Target … Phit is rolled into the overall Pkill Approved for Public Release 09-MDA-4814 (2 SEPT 09) 42
- 43. Random Numbers Generated by a recursive function Evenly distributed between 0 and 1 ~ Unif(0,1) Perfect for Pk evaluations 0.002589 0.709121 0.688907 0.23241 0.248291 0.279792 0.099733 0.672374 0.177176 0.5124 0.253238 0.885889 0.08127 0.337699 0.967582 0.11894 0.917944 0.691778 0.377643 0.167685 0.23337 0.821207 0.775446 0.94055 0.916313 0.342373 0.494679 0.83171 0.76565 0.300179 0.081692 0.212297 0.323383 0.088898 0.976731 0.826355 0.633324 0.390983 0.559808 0.032313 0.337002 0.429531 0.284963 0.978167 0.177686 0.39425 0.729517 0.196937 0.053272 0.537055 0.753125 0.189256 0.790979 0.437795 0.757163 0.953741 0.714325 0.899821 0.139968 0.139168 0.803138 0.274158 0.226658 0.151101 0.555232 0.533085 0.327454 0.753654 0.268759 0.307099 0.21175 0.644434 0.011707 0.809213 0.3742 0.38085 0.412449 0.425525 0.346873 0.490443 0.397201 0.114504 0.831309 0.291209 0.157902 0.994106 0.22623 0.215775 0.503133 0.544428 0.05825 0.173804 0.322742 0.984154 0.512732 0.340096 0.626067 0.746717 0.391907 0.168648 0.606554 0.280939 0.804009 0.290058 0.550802 0.743599 0.108666 0.557355 0.850634 0.908114 0.209818 0.600702 0.682586 0.265387 0.792137 0.241523 0.077536 0.282332 0.244388 0.688018 0.607142 0.296545 0.583956 0.652407 0.773843 0.801856 0.037354 0.516678 0.27669 0.360097 0.700107 0.821834 0.912564 0.914889 0.18311 0.164431 0.880446 0.527801 0.887302 0.209683 Approved for Public Release 09-MDA-4814 (2 SEPT 09) 43
- 44. Pk’s and Random Numbers Pk = 75% = 0.75 0% 75% 100% Kill Area No-Kill Area Random Number = 0.63 Approved for Public Release 09-MDA-4814 (2 SEPT 09) 44
- 45. Precision Engagements PROBLEM: Find point of impact (if any) of round on its target. ASSUMPTION: The projectile impact point is a random variable with a normal probability distribution (empirically shown to be a good assumption). “Bias” : Systematic Errors “Dispersion” : Round-to-Round Independent Errors Round Impact Point Actual Target Location Doctrinal Aim Point Aim Point Perceived Doctrinal Aim Point Perceived Target Location Approved for Public Release 09-MDA-4814 (2 SEPT 09) 45
- 46. Linear Target Phit Normal parameters for 1D target: “Front view" (i.e., direct-fire weapon) Deflection error "Top view" (i.e., indirect-fire weapon) Range error DEFINE: Bias = Dispersion = x p(x) 25 m Error Probable - distance in deflection (for x) within which half of rounds will land. Linear Error Probable (LEP) - linear distance from aim point within which half of rounds will land, based on the error probable (details to follow). Approved for Public Release 09-MDA-4814 (2 SEPT 09) 46
- 47. Single-Shot Accuracy 1D Target Example 1 Assume no systematic error. x 0, 25 0.6745 37.0664 m, 10 m, then, 10 0 37.0644 0.3937 z 10 0 37.0644 0.6064 z PSSH -z +z 0 P zz0.60630.39370.2126 SSH NOTE: “” is available in tabular form in any Statistics text: see Normal Distribution. Approved for Public Release 09-MDA-4814 (2 SEPT 09) 47
- 48. Rectangular Target Phit Normal parameters for 2D target: "Side view" (i.e., direct-fire weapon) Elevation error Deflection error "Top view" (i.e., indirect-fire weapon) Range error Deflection error DEFINE: Bias = x , y Dispersion = x , y x y p(y) p(x) Range Error Probable (REP) – linear distance from aim point within which half of rounds will land, x-coordinate Cross-range Error Probable (CREP) – linear distance from aim point within which half of rounds will land, y-coordinate Approved for Public Release 09-MDA-4814 (2 SEPT 09) 48
- 49. Circular Target Phit P(destruction of a point target) = P(hit within a circle of radius R), i.e., P= P. d When x= y= 0 and x= y= , 0 0 2 2 2 If Ris the radius of a circle for which 0 R R 1 exp 2 2 Pd 1 2 2 0 R 0 1 exp 2 2 P R then 50% of all impacts points for the probability distribution P(r) will fall within this radius r ≤ R0. R0 is called the circular error probable (CEP), and R0 = 1.1774. 2 Target Simplified Vehicle Assembly Area Cluster of Soldiers Approved for Public Release 09-MDA-4814 (2 SEPT 09) 49
- 50. Kill Categories K-Kill: catastrophic kill F-Kill: firepower kill M-Kill: mobility kill MF-Kill: mobility & firepower kill, usually => K-Kill P-Kill: personnel kill (crew and passengers) No-Kill: no damage due to hit. ranx = random(seed) if (ranx < PkN) {No Kill} else if (ranx < PkN + PkM) {Mobility Kill} else if (ranx < PkN + PkM + PkF) {Firepower Kill} else if (ranx < PkN + PkM + PkF + PkMF) {Mobility & Firepower Kill} else {Catastrophic Kill} Single random number draw can result in more than just “Miss/Hit” Engagement outcome has at least 5 states Approved for Public Release 09-MDA-4814 (2 SEPT 09) 50
- 51. Direct-Fire Accuracy Example (1) An infantry fighting vehicle (IFV) has the following frontal profile: A hit in area 1 will produce a firepower kill. A hit in area 2 will produce a catastrophic kill. A hit in area 3 will produce a mobility kill. A hit in other areas will produce no permanent effect. 1.6 1.0 2 4 1 4 3 0.6 1.4 2.6 0.6 Assess the IFV’s vulnerability when engaged with a frontal shot whose impact point is modeled as a random variable pair (X,Y) ~ BVN(0,0,.5,.5,0). Using the below list of pseudo random numbers as needed, simulate the first round to determine which type of kill, if any, occurs (.8554, .2287, .6659, .8243, .6840, .0430, .8598, .2381, .5035, .2723). Approved for Public Release 09-MDA-4814 (2 SEPT 09) 51
- 52. Direct-Fire Accuracy Example (2) 1) Do a Monte Carlo simulation of impact point with origin centered on the target, then compare impact point with target profile to calculate where it hit. 2) Determine X coordinate of impact point: Enter the Normal Table with 0.8554 Find Z-1 = 1.06 Note that Z-1 = ((x − x)/x Solve for x in 1.06 = (x − 0)/0.5 x = 0.53 1.6 2 . 53 1.0 Y 4 1 4 3 3) Determine the Y coordinate of the impact point (using RN .2287): 0.6 1.4 2.6 0.6 Normal Table goes from 0.5000 to 0.9999, but Normal Dist. is symmetric, so compute 1.0 − 0.2287 = 0.7713, and change sign of resulting Y coordinate. Interpolating between 0.75 and 0.74, gives Z-1 = 0.743. Solve for y in −0.743=(y − 0)/0.5 gives y=−0.3715 4) Round hits area 4, so no kill is assessed. X −0.3715 Approved for Public Release 09-MDA-4814 (2 SEPT 09) 52
- 53. Approved for Public Release 09-MDA-4814 (2 SEPT 09) 53 Engagement Modeling – Aggregate Level Lanchester Equations Aggregated Combat Groups Epstein’s Equations Quantified Judgment Model (QJM) Force Ratio Approach
- 54. Lanchester Equations CONCEPT: describe the rate at which a force loses systems as a function of the size of the force and the size of the enemy force. This results in a system of differential equations in force sizes x and y. dx f 1 x , y ,... dy f x , y ,... 2 dt dt The solution to these equations as functions of x(t) and y(t) provide insights about battle outcome. ay dx dt bx dy dt Approved for Public Release 09-MDA-4814 (2 SEPT 09) 54
- 55. Aggregated Combat Groups Contiguous pistons Aggregated force attrition Distance from middle affects power and attrition Units accumulate as piston moves Explicit withdrawal required Approved for Public Release 09-MDA-4814 (2 SEPT 09) 55
- 56. Force Ratio Attrition Models CONCEPT: Summarize effectiveness in combat with a single scalar measure of combat power for each unit. When combat occurs, use the ratio of attacker's to defender's measures to determine the outcome. Assign a firepower score to each weapon system and sum these scores for each weapon system on hand in a unit. DEFINITIONS: n = number of distinct types of weapon systems in a unit Xi = number of systems of type i (I =1,2,...,n) in a unit Si = firepower score for each weapon of type i n FPI firepower index of unit 1 i i i x s force in a battle FPI attacker FPI FR defender Approved for Public Release 09-MDA-4814 (2 SEPT 09) 56
- 57. Approved for Public Release 09-MDA-4814 (2 SEPT 09) Other Aggregated Models Epstein equations Defender’s withdrawal rate: Attacker’s Prosecution rate: Quantified Judgment Model (QJM) aT g T.N. Dupuy created the QJM to transform Clausewitz’s Law of Number to a combat power formula. Multi-agent models The environment takes the form of a distributed network of place agents. Aggregate state-space models Represented by aggregate state variables, rather than the locations and current behaviors of individual entities 57 a aT aT g g d dT dT t t t t t W W t W t W t 1 1 1 1 1 1 1 max
- 58. Approved for Public Release 09-MDA-4814 (2 SEPT 09) 58 Scenarios Elements of a Scenario Scenario Development Scenario Generation Tools
- 59. Elements of a Scenario Settings environment, terrain, etc. Actors Blue/Red forces, weapons, sensors, etc. Task Goals missions, objectives, etc. Plans overlays, control measures, etc. Actions move, shoot, communicate, etc. Events contact, engagements, etc. Approved for Public Release 09-MDA-4814 (2 SEPT 09) 59
- 60. Scenario Development Resolution (high or low) Aggregated-disaggregated Terrain data Weapon/Sensor data Virtual or constructive Interfaces Distributed/federated Approved for Public Release 09-MDA-4814 (2 SEPT 09) 60
- 61. Scenario Generation Tools (SGTs) Provide users the ability to: • Create, modify, and verify scenario files. • Specify entities, tactical overlays, and environment parameters. Ability to translate legacy scenario files into the new scenario file format & able to translate the new scenario files back into the legacy format Simulation System Scenario Generation Tools are typically developed to be utilized as an off-line pre-runtime tool that can be run on a laptop and provide a modular scenario development environment Approved for Public Release 09-MDA-4814 (2 SEPT 09) 61
- 62. Summary The are several types of combat models driving simulations for combat training, research & development, and advanced concepts requirements: Environmental models Physical models (engagement, target acquisition, communications, etc.) Behavioral models In addition, simulations require some means of scenario development, and these are often separate components. Understanding the underlying concepts and methods of combat models embedded in simulations, enhances our ability to choose the right simulations for our training or analysis requirements. Approved for Public Release 09-MDA-4814 (2 SEPT 09) 62
- 63. References Ancker, C.J., Jr. and Gafarian, A.V., Modern Combat Models: A Critique of Their Foundations, Operations Research Society of America, 1992. Birkel, P. A., "SNE Conceptual Reference Model", 1999 Fall SIW Conference, September 1999. http://www.sisostds.org/siw/98Fall/view-papers.htm Bracken, J., Kress, M. and Rosenthal, R.E., Eds., Warfare Modeling, MORS, 1995. Caldwell, B, Hartman, J., Parry, S., Washburn, A., and Youngren, M., Aggregated Combat Models. NPS ORD, 2000. Davis, P.K., Aggregation, Disaggregation, and the 3:1 Rule in Ground Combat. MR-638 DuBois, E.L., Hughes, W.P., Jr., Low, L.J., A Concise Theory of Combat, Institute for Joint Warfare Analysis, NPS, 2000. Dupuy, T.N., Understanding War: History and Theory of Combat, Falls Church, VA.: Nova 1987. Epstein, J.M., The Calculus of Conventional War: Dynamic Analysis without Lanchester Theory, Washington, D.C., Brookings Institute, 1985. Fowler, B.W., De Physica Beli: An Introduction to Lanchestrial Attrition Mechanics, 3 Vols. IIT Research Institute/DMSTTIAC, Rept. SOAR 96-03, Sep. 1996. Hillestad, R.J., and Moore, L., The Theater-Level Campaign Model: A New Research Prototype for a New Generation of Combat Analysis Model, RAND, 1996. MR-388 Koopman, B.O., Search and Screening, MORS, 1999. Reece, D.A., Movement behavior for soldier agents on a virtual battlefield, Teleoperators and Virtual Environments , Volume 12 , Issue 4 (August 2003). MIT Press Cambridge, MA, USA Smith, R. Military Simulation, http://www.modelbenders.com/ Strickland, J.S., Fundamentals of Combat Modeling with Microsoft Excel, USALMC, 2004. Taylor, J.G., Lanchester Models of Warfare, 2 Vols, Defense Technological Information Center (DTIC), ADA090843 (Naval Post Graduate School, Monterey, CA), October 1980. Taylor, J.G., Force-on-Force Attrition Modeling, Operations Research Society of America, Military Applications Section, 1981. Washburn, A.R., Search and Detection, 4th Ed., Operations Research Section, INFORMS, Baltimore, MD, 2002. Washburn, A., Lanchester Systems, NPS, April 2000. Volluz, R.J. and Volluz, R.M., The Anatomy of Combat, 17th ISMOR Symposium, 28 Aug – 1 Sep 2000. Approved for Public Release 09-MDA-4814 (2 SEPT 09) 63