I/ITSEC2009 Best Tutorial

63
Approved for Public Release 09-MDA-4814 (2 SEPT 09) 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.

Transcript of I/ITSEC2009 Best Tutorial

Page 1: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09)

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 1

Mathematical and

Heuristic Models of Combat with

ExamplesJeffrey Strickland, Ph.D., CMSP

Missile Defense Agency

DISTRIBUTION STATEMENT A. Approved for

public release; distribution is unlimited.

Page 2: I/ITSEC2009 Best Tutorial

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

Page 3: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 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

Page 4: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09)

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

Page 5: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 5

Level of Detail

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

Air Combat Terrain Ground Combat Terrain

Page 6: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 6

Component

Models

Environmental

State

Behavior

Models

Environmental

Models

Synthetic Natural Environment

Behaviors (e.g.)

• Maneuver

• Sustainment

• Force

Protection

• Intelligence

• Command &

Control

• Fires

Military System Model

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

Conceptual Reference Model

SOURCE: Paul A. Birkel, "SNE Conceptual Reference Model", 1999 Fall SIW Conference, September 1999.

http://www.sisostds.org/siw/98Fall/view-papers.htm

Page 7: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 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

Page 8: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 8

Storing Environmental Data

Triangulated Irregular Network (TIN)

Data point correlation

Surface tiled with hexagons

Page 9: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 9

Static Environment

Trafficability

Terrain Type

Visibility

Page 10: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 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

Page 11: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 11

Classic Problems in Interpretation

1

2

3a 3b

1

2a 2b

Terrain Points Building Corners

Page 12: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 12

Environmental Standardization

Page 13: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 13

Physical Modeling

Detect/Acquire

Engage(other major

combat functions)

Communicate

Move

Start Cycle Here

Page 14: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09)

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

Page 15: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 15

Movement Points Movement

2

3

6

1

2 6 2

1

Movement

Points =

20

Movement

Points

Remaining =

20 – 11 = 9

Page 16: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 16

Bald Earth Movement

Set heading, speed, start time

Rate*Time = Distance

20 km/hr * 30 min = 10 km

Page 17: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 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

Page 18: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09)

Proportional Force

Calculation

Resistive Force

Calculation

Braking Force

Calculation

main force calculations

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

Page 19: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 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

Page 20: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 20

Topology Smart

Set Objective: Position or Vector

Movement model selects path from topological map

Maintain objective

Route traveled is function of topology

Page 21: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 21

Grid Registration

Grid 14 → V71, V109, V1212, V10101

Vehicles registered into geographic grid during movement

Improve LOS, sensor, and interaction performance

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 46 4745

Page 22: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 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

Pitch

Yaw

Roll

Page 23: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 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

b

e

d

Prediction Horizon

Observe Ghost prediction

Insertion Horizon

Measure Ghost fitness t =

τ

(Now

) Ghost time τ

c

Real-World

Entity

Avatar

Ghosts

1nRThreat

nn

nnn

DistGNest

TargetGTargetRF

Page 24: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09)

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

Page 25: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 25

Perfect Detection

Every object knows the true location of every other

object.

There are no models of sensors or processors.

Page 26: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 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%

Page 27: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 27

Detection Range

Complete circle—no field of view/field of regard

Terrain line-of-sight (LOS) is separate

Page 28: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 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

sin2

sin

sin2

2sin

2

sin

sinsin

0

sin2

sin

sin2

2sin

sin

sinsin

0

d

dN

a

a

II

d

dN

a

a

Page 29: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 29

Target Acquisition

Glimpse models

Intermittent glimpses: E[N] = Σn np(n)

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

Factors

Sensor

characteristics

Target characteristics

Line-of-sight

Glance/

Glimpse

Target

Found?

No

Yes

tg tg tg

Pacq Pacq Pacq

Page 30: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 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.

Page 31: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 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

Page 32: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 32

Line-of-Sight Models

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

. . . . . . . . . . . . . . . . .Primary Direction of

view (white)

Max Range

of view

LOS does not

exist

LOS exists

Orange lines

Left Limit

of View (white)

Right Limit

of View (white)

Page 33: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09)

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

Page 34: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 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

Evaluate Target's Intent

Evaluate Target's Geometry

Recognize Target

Update Target's Knowledge

Notify Knowledge Processing

Activity Diagram: Process Info Use Case

Process Info

Get Data from Fire

Control Sensor

Get Data from

Target Sensor

Get Info from Data

Processing

Page 35: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 35

Perfect Communications

Targets

~~~~~

Orders

~~~~~

Reports

~~~~~

Shared information, no representation of comms

Software-to-software message delivery

Page 36: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 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.

… …

Page 37: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 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

etc.…

…Success

Lost

Degraded

Delayed

Page 38: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09)

Physics-Based Communication Networks

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

Page 39: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 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

kr r

r

CITACS interacts with Joint Theater Level Simulation (JTLS)

Page 40: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09)

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

Page 41: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 41

Point System

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]

18

4

20

8

Weapon Power

Path Degradation(range, shelters, obstructions)

Health

Armor

Page 42: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 42

Markov Pk Table

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

Ta

rge

t

Phit is rolled into the overall Pkill

Damage = 1, where Random Number <= Pk

= 0, where Random Number > Pk

Page 43: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 43

Random Numbers

Generated by a recursive function

Evenly distributed between 0 and 1 ~ Unif(0,1)

Perfect for Pk evaluations0.002589 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

Page 44: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 44

Pk’s and Random Numbers

Kill Area No-Kill Area

0% 75% 100%

Random Number = 0.63

Pk = 75% = 0.75

Page 45: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 45

Precision Engagements

Round Impact Point

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).

Actual Target Location

Doctrinal Aim Point

Aim Point

“Bias” : Systematic Errors

“Dispersion” : Round-to-Round

Independent Errors

Perceived Doctrinal

Aim Point

Perceived Target Location

Page 46: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 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 =

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).

x

p(x)

25 m

Page 47: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 47

Assume no systematic error.

2126.03937.06063.0 zzPSSH

NOTE: “” is available in

tabular form in any Statistics

text: see Normal Distribution.

Single-Shot Accuracy1D Target Example 1

3937.00644.37010

6064.00644.37010

then,m, 10 m, 0664.376745.025 0,

z

z

x

PSSH

0

-z +z

Page 48: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 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

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

x

y

p(y)

p(x)

Page 49: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 49

P(destruction of a point target) = P(hit within a circle of radius R), i.e., Pd = P.

When x0 = y0 = 0 and x2 = y2 = 2,

If R0 is the radius of a circle for which

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.

Circular Target Phit

2

2

2exp1

RRPd

2

1

2exp1

2

2

00

RRP

Target

Simplified Vehicle

Assembly Area

Cluster of Soldiers

Page 50: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 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

Page 51: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 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.

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).

2

1 44

3

0.6

1.6

1.0

1.4 2.6

0.6

Page 52: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 52

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

3) Determine the Y coordinate of the impact point (using RN .2287):

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=−0.37154) Round hits area 4, so no kill is assessed.

2

1 44

3

0.6

1.6

1.0

1.4 2.6

0.6

Y

X

−0.3715

. 53

Direct-Fire Accuracy Example (2)

Page 53: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09)

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

Page 54: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 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.

The solution to these equations as functions of x(t)

and y(t) provide insights about battle outcome.

dx

dtf x y

dy

dtf x y 1 2, ,... , ,...

aydt

dx

bxdt

dy

Page 55: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 55

Aggregated Combat Groups

Contiguous pistons

Aggregated force

attrition

Distance from

middle affects

power and attrition

Units accumulate

as piston moves

Explicit withdrawal

required

Page 56: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 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

unit ofindex firepower FPI1

n

i

iisx

battle ain forceFPI

FPIFR

defender

attacker

Page 57: I/ITSEC2009 Best Tutorial

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) 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

aTa

aT

gaT

gg

dTd

dT

tt

tt

ttWW

tWtW

11

1

11

11 max

Page 58: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09)

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 58

Scenarios

Elements of a Scenario

Scenario Development

Scenario Generation Tools

Page 59: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 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.

Page 60: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 60

Scenario Development

Resolution (high or low)

Aggregated-disaggregated

Terrain data

Weapon/Sensor data

Virtual or constructive

Interfaces

Distributed/federated

Page 61: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 61

Provide users the ability to:

• Create, modify, and verify

scenario files.

• Specify entities,

tactical overlays,

and environment

parameters.

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

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 (SGTs)

Page 62: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 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.

Page 63: I/ITSEC2009 Best Tutorial

Approved for Public Release

09-MDA-4814 (2 SEPT 09) 63

ReferencesAncker, 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.