Models, Gaming, and Simulation Session 6 - PowerPoint PPT Presentation

1 / 28
About This Presentation
Title:

Models, Gaming, and Simulation Session 6

Description:

Summarize effectiveness in combat with a single scalar measure of combat power for ... Illogical battles can occur (e.g., Arty Bn FPI=80 defeats Tank Co FPI=30) ... – PowerPoint PPT presentation

Number of Views:162
Avg rating:3.0/5.0
Slides: 29
Provided by: classw
Category:

less

Transcript and Presenter's Notes

Title: Models, Gaming, and Simulation Session 6


1
Models, Gaming, and Simulation - Session 6
  • Aggregated Attrition Models -
  • Non-Lanchester Approaches

2
Topics
  • Force Ratio models of attrition
  • Firepower Scores / WEI/WUVs
  • Correlation of Forces
  • Potential-Antipotential Method
  • Hierarchical Attrition Algorithms
  • Next Session Review

3
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
  • Measures can be very subjective, or based on
    summary characteristics of unit equipment, or
    based on a weighted combination of weapon
    firepower, mobility, vulnerability, etc.

4
Force Ratio Approach - Firepower Scores
  • CONCEPT 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 (i1,2,...,n) in
    a unit
  • Si firepower score for each weapon of type i

5
Force Ratio Approach - Limitations of Firepower
Scores
  • Weapon system interactions ("synergisms") are not
    represented
  • FPI is additive across weapon types (e.g.,
    FPI100 derived from 15 tanks, 30 infantry
    fighting vehicles and 6 mortars equals FPI100
    derived from 30 tanks).
  • FPI is linear in the number of weapons - cannot
    directly represent
  • Minimum unit size required for effectiveness.
  • Diminishing returns with large numbers of
    systems.
  • Weapon system types become submerged in the FPI
    formula
  • Illogical battles can occur (e.g., Arty Bn FPI80
    defeats Tank Co FPI30).
  • Validity is suspect because
  • Specification of firepower scores is arbitrary
  • Force-Ratio predictive power is not validated by
    empirical historical research.
  • Then why are we learning about Firepower Scores?
  • Because they match the rule-of-thumb approach
    often used by military planners.
  • Because you need to know enough about them to
    note when they are misused.

6
Force Ratio Approach - Determining Firepower
Scores
  • Alternate Approaches
  • Use historical data about combat performance
    (1950s analysis)
  • Use technical measures of weapon firepower
    (ATLAS)
  • Use situationally-dependent technical firepower
    measures
  • Use weighted combinations of firepower, mobility,
    vulnerability, reliability, etc., where weights
    were assigned by "Delphi" analysis (consensus of
    "experts"). This approach uses the term WEI/WUV
    (pronounced "wee-wuv")
  • WEI Weapon Effectiveness Index
  • Weapon scores are given without regard to
    opposing target types
  • WUV Weighted Unit Value
  • Units are given a base value by summing the WEIs
    of all their weapons
  • Unit values are weighted by subjective ratings
    (e.g., for training, morale, C2 systems)
  • Simple, but very subjective
  • Use a measure of what the weapon can kill
    (potential/antipotential method)

7
Force Ratio Approaches - Correlation of Forces
  • Used primarily in planning, not in combat models
  • Used in Soviet-style operations planning to
    allocate forces to a subordinate for a combat
    mission.
  • Similar approach used in U.S. operations planning
    to estimate whether various parts of a plan are
    feasible.
  • Could be used in a model where attrition is not
    the focus.

8
Force Ratio Attrition Models - U.S. Army
Capability Analysis
  • A base type unit is selected and given the combat
    value 1.0
  • Units are assigned subjective values based on
    their perceived strength compared with base unit
    type, considering
  • Primary type of equipment in unit (e.g., M1A1
    versus M1 versus M60A3),
  • Percent strength authorized, and
  • Modifications subjectively based on intel
    estimate and current status of own unit.
  • Ratio of friendly to enemy estimated combat power
    is used to infer the capabilities of the friendly
    force.
  • Example U.S. Division planning for an operation
    against a threat division using Soviet-style
    equipment and organization.

9
Force Ratio Attrition Models - U.S. Army
Capability Analysis Example
  • U.S. Comparison Values (with respect to a BTR
    Battalion)
  • Maneuver
  • M113 Bn 1.5
  • M2 Bn 2.0
  • M1A1 Bn 3.15
  • M1 Bn 3.0
  • M60A3 Bn 2.25
  • ACR Sqdn 2.75
  • Div Cav Sqdn 1.5
  • Div Cav Sqdn(h) 2.0
  • Atk Hel Bn (AH64) 4.0
  • Atk Hel Bn (AH1) 3.0
  • Artillery
  • MLRS Battery 2.0
  • 155mm SP Bn 2.0

NOTE 1 All units are given an estimated value
with respect to a BTR Battalion NOTE 2 The unit
commander and operations officer are advised to
develop their own table to allow them to take
into consideration local knowledge about the
situation. This table does not contain real
planning data, but only notional data. (Example
taken from US Army CGSC ST 100-9)
10
Force Ratio Attrition Models - U.S. Army
Capability Analysis Example
  • Planning Rules of Thumb for Force Capabilities

11
Force Ratio Attrition Models - U.S. Army
Capability Analysis Example
  • Threat Comparison Values
  • Maneuver
  • BTR Bn 1.0 (Baseline unit)
  • BMP Bn 1.5
  • Tk Bn ITR TR ITB MRR
  • T-80 2.42 1.56 2.0 2.0
  • T-64 2.23 1.44 1.86 .86
  • T-72 1.86 1.20 1.55 1.55
  • T-62 1.24 .80 1.0 1.0
  • T-55 1.0 .64 .83 .83
  • AT Bn 1.0
  • Atk Hel Sqdn 2.0
  • Artillery
  • 122mm or 152mm Bn 2.0
  • MRL Battery 1.0

ITR Independent Tank Regiment TR Tank
Regiment ITB Independant Tank Battalion MRR
Motorized Rifle Regiment
12
Force Ratio Attrition Models - U.S. Army
Capability Analysis Example
  • 53 Mech Division
  • Maneuver
  • TYPE BN VALUE TOTAL
  • M113 4 1.5 6.0
  • M2 1 2.0 2.0
  • M1 2 3.0 6.0
  • M60 3 2.25 6.8
  • Cav 1 1.5 1 .5
  • Atk Hel 1 3.0 3.0
  • TOTAL 25.3
  • X Strength X .9
  • Relative Cbt Power 22.8
  • Ratio for Maneuver 22.8 22.2 11
  • Artillery
  • TYPE BN VALUE TOTAL
  • 155(SP) 3 2.0 6.0
  • MLRS 1 2.0 2.0
  • TOTAL 8.0

27 Gds Motorized Rifle Division
Maneuver TYPE BN VALUE TOTAL BTR
6 x 1.0 6.0 BMP 3
x 1.5 4.5 T64(MRR) 3 x 1.8
5.4 T64 (TR) 3 x 1.4 4.2 T64
(ITB) 1 x 2.0 2.0 Div Recon
1 x 1.6 1.6 AT Bn 1 x 1.0
1.0 Atk Hel 1 x 3.0
3.0 TOTAL 27.7 X Strength
X .8 Relative Cbt Power
22.2 Artillery TYPE BN VALUE
TOTAL 122(SP) 2 x 2.0
4.0 122(T) 4 x 2.0
8.0 152(SP) 1 x 2.0
2.0 MRL Btry 3 x 1.0
3.0 TOTAL 17.0 X Strength
X .8 Relative Cbt Power
13.6
13
Attrition Coefficient Calculation - Potential /
Anti-potential ("Eigenvalue") Method
  • A way to assign firepower scores.
  • Avoids the problem of assigning scores based only
    on weapon's own characteristics, not on opposing
    targets' characteristics.
  • Avoids some problems of subjectivity.
  • CONCEPT Let the value of a weapon system be
    directly proportional to the rate at which it
    destroys the value of enemy weapon systems.
  • NOTE Problem reduces to system of simultaneous
    linear eqns.

14
Attrition Coefficient Calculation - Potential /
Anti-potential Method
  • DEFINITIONS
  • Force X fights Force Y
  • Xi weapons of type i in X force, i 1,2,...,m
  • Yj weapons of type j in Y force, j 1,2,...,n
  • SXi value of one type i weapon in X force
  • SYj value of one type j weapon in Y force
  • Kij rate at which one Xi system kills Yj
    systems
  • i1,2,...,m j1,2,...,n
  • Lji rate at which one Yj system kills Xi
    systems
  • i1,2,...,m j1,2,...,n
  • NOTE Kij and Lji are determined from
    killer-victim scoreboards from a high-resolution
    model. This implies great dependency on the
    high-res scenario, e.g., force structures,
    missions, terrain, etc.
  • So FPIX ?i SXi Xi and FPIY ?j SYj Yj

15
Attrition Coefficient Calculation - Potential /
Anti-potential Method
  • The above concept and definitions lead to a
    system of simultaneous equations
  • for all j, cY ??SYj ?iLji SXi
  • for all i, cX ??SXi ?jKij SYj
  • This is a system of mn equations in mn2
    unknowns, since the two proportionality constants
    cX and cY are not specified.
  • In matrix notation
  • (1) cY ?SY L SX
  • (2) cX ?SX K SY

16
Attrition Coefficient Calculation - Potential /
Anti-potential Method
  • Solving for SY in eqn (1) and substituting in eqn
    (2)
  • cY cX?SX K L SX
  • Similarly for SX
  • cX cY?SY L K SY
  • Let cX cY? ?, then
  • ? SX K L SX (eqn 3)
  • ? SY L K SY (eqn 4)
  • This is a pair of eigenvalue problems for K L
    (mxm) and L K (nxn) where the eigenvalue is ? and
    eigenvectors are SX and SY .

17
Attrition Coefficient Calculation - Potential /
Anti-potential Method
  • Problem Solutions are not unique (mn2
    unknowns, with mn equations). In fact, they are
    only unique to a scaling factors MX for X and MY
    for Y.
  • A Solution Let and set SXi 1.0 for some
    weapon Xi which is a major contributor to killing
    many Yj systems. This can be shown not to change
    the overall Force Ratio as Mx and MY vary, so
    the solution is appealing.

18
Matrix Algebra Review Eigenvalues and
Eigenvectors
  • GIVEN a set of linear equations in unknown
    variables xij such that ? I X A X
    for some constant ?
  • DEFINE ? as an eigenvalue and X as an
    eigenvector.
  • THEOREM due to Frobenius guarantees that
  • 1. There exists a real, non-negative, largest
    eigenvalue ?, and
  • 2. There exist non-negative eigenvectors (SX and
    SY in our formulation) which are unique up to a
    scale factor.

19
Matrix Algebra Review Eigenvalues and
Eigenvectors
  • SOLUTION PROCESS for 2x2 matrix
  • 1. Solve for ?
  • Characteristic polynomial is
  • Let d1 c11c22 and d0 c11c22 - c12c21, then
  • 2. Substitute for ? in equations (3) and (4) and
    solve for Xij.

20
Attrition Coefficient Calculation - Potential /
Anti-potential Example
  • GIVEN
  • X force of 2 systems, strengths X1 200, X2
    150
  • Y force of 2 systems, strengths Y1 75, Y2 100
  • X1 kills Y1 at rate .03, Y1 kills X1 at rate .04
  • X1 kills Y2 at rate .05, Y1 kills X2 at rate .02
  • X2 kills Y1 at rate .03, Y2 kills X1 at rate .04
  • X2 kills Y2 at rate .02, Y2 kills X2 at rate .01
  • So
  • for ?? cX cY , solve for ? in ?SX K L SX

21
Attrition Coefficient Calculation - Potential /
Anti-potential Example
  • d1 .0032 .0008 .004, and
  • d0 (.0032 .0008) - (.0011 .0020)
    .00000036
  • ? .5(.004 sqrt(.0042 - 4 .00000036) )
  • ? max(?1, ?2) .003907878
  • Let SX1 1.0
  • Let
  • Since ? SX K L SX, then
  • ( K L - ??I ) SX 0
  • Since SX1 1.0, we can solve for SX2 in two
    ways
  • -.000707878SX1 .0011SX2 0
  • or .002SX1 - .003107878SX2 0
  • Either way gives SX2 .64353

22
Attrition Coefficient Calculation - Potential /
Anti-potential Example
  • Now solve for SY1 and SY2 using eqn (1) cY SY
    L SX
  • so,
  • Now compute FPIX and FPIY, and then FR
  • Now to assess actual casualties lost by the X and
    Y forces, enter a table indexed by FR (and
    perhaps other factors) to find a percent of force
    lost. Apply this percentage to each weapon type.

23
(No Transcript)
24
Attrition Coefficient Calculation - Potential /
Anti-potential Comments
  • Solutions are scenario-dependent
  • Kill rates must be generated with respect to X
    and Y posture and actions (e.g., X attacking Y in
    a prepared defensive position, versus X delaying
    against Y's attack)
  • Changes in kill rates are hard to understand.
  • In fact, scores sometimes vary greatly with small
    changes to a few inputs, and occasionally the
    score of a major weapon system will be zero.
  • This method has the advantage of automatic
    adjustment of weapon scores, preventing poor
    judgement from influencing the outcome, but the
    related disadvantage is that its computations are
    obscured by the eigenvalue method. But also,
    remember that historical analysis shows little or
    no relation of force ratios to battle outcome.

25
Hierarchical Attrition Algorithms
  • Most combat models have the characteristic that
    higher-resolution models feed them with data.
  • High-resolution models need PH's and PKHs which
    are usually supplied by AMSAA and ARL engineering
    models.
  • Medium and low-resolution models usually depend
    on kill rates from high-resolution models or
    occasionally on engineering models.
  • Some low-resolution models depend on kill rates
    generated by medium-resolution models, e.g.,
    ATCAL (Attrition Calibration) links the
    medium-resolution COSAGE with the low-resolution
    CEM.

26
Hierarchical Attrition Algorithms
  • A hierarchy of ground combat models was proposed
    and partially built by the Army in the 1970s and
    1980s, but never reached completion because of
    enormous technical difficulties
  • The vision was a semi-automated way of getting
    input data for low-res models from high-res
    models, so low-res modelers would not have to
    request special runs from high-res modelers
    (usually in different organizations).
  • Too much variation in scenarios, force
    structures, weapons, and postures meant that
    libraries of high-res results were too hard to
    build.
  • Additionally, organizations resisted getting
    "answers" from "black-box" models they could not
    influence.
  • ATCAL is one of the few examples of an existing
    formal link between models of differing
    resolution for the purpose of generating input
    data from the high-res model for the low-res
    model. Both models were built and are run by the
    same organization, contrary to what was
    envisioned.

27
Hierarchical Attrition Algorithms - ATCAL
  • CONCEPT a set of equations is used to compute
    attrition in a low-res model if a set of input
    parameters are known (provided by a medium-res
    model). The same set of equations can be used
    "backwards" when the medium-res model is run to
    generate the parameters it will provide in
    accordance with its attrition results.
  • For each scenario which the low-res model needs,
    the medium-res model is run in nine different
    "vignettes", or shorter, narrower-scope scenarios
    which fit with the larger scenario. These nine
    vignettes vary the posture of the two opposing
    sides and calculate results for each
  • Blue attack, Red prepared defense
  • Blue attack, Red hasty defense
  • Blue attack, Red delay
  • Meeting engagement
  • Static
  • Red attack, Blue delay
  • Red attack, Blue prep defense
  • Red attack, Blue hasty defense
  • Reserve

28
Hierarchical Attrition Algorithms - ATCAL
  • Medium-resolution model generates three
    parameters (for point fire)
  • Pij Probability of kill of target j by firer i
  • Aij Availability of target j to firer i
  • RATEi shots per unit time by firer i
  • Care must be taken to ensure that all Blue firer
    types have an opportunity to fire at all Red
    target types and vice versa, so that all Pij and
    Aij have values.
Write a Comment
User Comments (0)
About PowerShow.com