SystemsofSystems Analysis of Ballistic Missile Defense Architecture Effectiveness through Surrogate

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Systems-of-Systems Analysis of Ballistic Missile
Defense Architecture Effectiveness through
Surrogate Modeling and Simulation
SysCon 2008 IEEE International Systems
Conference Montreal, Canada April 710, 2008
Paul Miceli, W. Dale Blair, Phil West Georgia
Tech Research Institute Georgia Institute of
Technology Atlanta, Georgia 30332-0801

• Tommer Ender, Ryan Leurck,
• Brian Weaver, Dimitri Mavris
• Aerospace Systems Design Laboratory
• School of Aerospace Engineering
• Georgia Institute of Technology
• Atlanta, GA 30332-0150

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Introduction

• Realizing an effective BMD system has been a goal
  of U.S. military planners since the first German
  V-2 rockets began falling on London during WWII
• Emergence of new nuclear threats
• North Korean ballistic missile tests in summer of
  2006
• Suspected ongoing nuclear weapons development
  program in Iran

An integrated, layered Ballistic Missile Defense
System to defend the United States, its deployed
forces, allies and friends from ballistic
missiles of all ranges and in all phases of
flight. -MDA
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Challenges

• No historical database of working BMD systems
  from which designers can generate trends or
  rules of thumb to help reduce design cycle time
• Scope of the problem limits physical testing
• Full-scale test of realistic threat scenario
  expensive
• Modeling and simulation (MS) required
• Modeling of entire BMD scenario too
  computationally expensive to be useful in
  earliest stages of design

Emerging techniques for quickly evaluating the
performance of complex systems-of-systems can be
used to study BMD
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Architecture Diagram
Analysis codes for each component are extremely
complex
Even if all tools could be successfully
integrated, runtime would be prohibitive
www.mda.mil
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Systems-of-Systems Architecture Analysis

• Systems-of-Systems
• Elements that are operationally and managerially
  independent 2
• Collaborating only through information exchange
• Capability of the integrated whole to produce
  results greater than sum of the individual
  components

BMD is an SoS problem targets, interceptors,
radars, and launch platforms evolve independent
of one another

• Architecture Analysis
• SoS architecture acts as a framework that directs
  the interaction of components with their
  environment, data management, communication, and
  resource allocation 3
• The system-of-systems architecture defines the
  interfaces and composition which guides its
  implementation and evolution ?4

Allocation of functionality to components and
inter-component interaction, rather than the
internal workings of individual components
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Current Approaches for BMD Architecture Analysis

• Wilkening BMD effectiveness determined by
  modeling the integrated system as a series of
  Bernoulli trials 5
• Required numbers of interceptors needed as a
  function of key parameters, target properties and
  rules of engagement
• Ben-Asher applying SoS design principles when
  defining architecture enhances the probability of
  creating successful BMD systems 6
• Limited to defining responsibility sharing rules
  and interfaces between system level components
• Parnell methods should enable interaction
  between decision makers, operators, and
  developers, through real-time what-if scenarios
  7

Common Issue Rapid architecture analysis of the
entire BMD problem sacrifices MS accuracy
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Functional Decomposition
Search/Scan

• A series of battle management elements that
  execute in a serial process
• Comparable to standard kill chain
• Execution of any element is conditional on the
  success of the previous element

Detect
Report
Locate
Track
Develop track
Report
Associate
Sensor Fusion
Fuse
BMD Battle Management
Report
Prioritize Threats
Fire Control
Identify Candidate Platforms
Develop Fire Control Solution
Launch
Update target/track
Engage
Fly to intercept
Activate seeker
Discriminate target
Endgame
Kill Assessment
NOTE No claim is made that the complete BMD
problem is represented in this study
Determine Kill
Report
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Proof-of-Concept Scenario

• Used to scope the elements of the problem
  decomposition that are necessary to be studied in
  detail

• 4 Threats
• Launched near simultaneously
• 2 Ships
• Stationed within an operational area
• Sensor/shooter platforms
• 1 Land Based Interceptor
• Fixed location
• Sensor/shooter platform

Four near-simultaneous Threat Launches
Operational Area for two battleships
Land Based Interceptor
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Surrogate Models

• Surrogate models enable rapid manipulation of
  any modeling and simulation tools
• Equation based regressions of complex codes
• Negligible loss in accuracy of original tools
• Can be executed in fractions of a second instead
  of hours or days
• On-the-fly tradeoffs yield results that otherwise
  may not have been discovered
• Enables decision making across a
  systems-of-systems hierarchy

Bringing Modeling Simulation Forward in the
Decision Making Process
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Neural Network Surrogate Models

• Any regression model must make assumptions as to
  the behavior of a measured response and accept a
  certain amount of error
• i.e. Response Y roughly varies linearly with
  variables X1 and X2
• Polynomial based Response Surface methods are
  proven
• How does one create regressions in which a
  functional form behavior assumption is not
  possible?

Design Space Behavior
Regression Functional Form
How do we fit this?
Equation Form
Solve for
Y mxb
m, b
Y ax2bxc
a, b, c
Y ax3 bx2 cx d
a, b, c, d
Neural Network
Linear Fit
Quadratic Fit
Cubic Fit
Neural Networks are emerging as a useful way of
creating highly nonlinear regression models
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Neural Network Surrogate Models
Neural Network Structure

• A Neural Network is a computational
  architecture based on the design of the
  interconnections of neurons in our brains
• The elements of Neural Networks were inspired by
  biological nervous systems, in which the
  connections between elements determines the
  network function
• It is a set of nonlinear equations that predict
  output variables from a set of given input
  variables using layers of linear regressions and
  S-shaped logistic functions

Input Layer
Hidden Layer
Output Layer
H1
X1
H2
X2
H3
Y1
H4
X3
Single Response

H5

Xn
Pattern of Connections Found by Training
Hn
of Hidden Nodes Defined by Optimization
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Modeling and Simulation (MS)

• Goal of BMD simulation is to model protection of
  some area from incoming targets by engaging them
  with interceptors
• Consider MS of all elements within the kill
  chain

Interceptors
Scenarios
Sensors
Tracking
Sensor Fusion
Battle Management
Sensor 1
T 1
Sensor 2
T 2
EVALUATE Intercept. Success
.
.
.
.
.
.
Sensor n
T n
Performance Metrics

• Defended Area
• Leakers / Interceptors . .

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Computational Complexity of BMD Modeling and
Simulation
Due to computational complexity BMD simulation is
very computationally intensive and time consuming

• Run Time Example
• Consider 9 TBM Threats, 16 Sensors all in fixed
  locations 1 set of Monte Carlo (MC) runs 10
  Hours
• Parameter Variation
• Hold launch points constant, vary impact among 5
  different locations
• Move each radar though 6 locations
• Corresponding Run Time
• 10hrs 59 166 3.3x1015 hrs gt 37,000,000
  years
• (if run on 1,000 parallel machines)
• Many other system parameters of interest remain
  

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Target Detection and Tracking

• Due to computational complexity most tools for
  studying BMD system performance are either
• Truth Based
• Any target in a systems field of view (FOV) if
  presumed to be under track
• Ignores reality, since the BMD system performance
  is highly dependent on ability of system to
  detect and track targets
• Performance Prediction Based
• Based on sensor and tracking parameters, however
• Do not require Monte Carlo Simulations
• Have fast run times
• Typically make many assumptions

Performance Prediction Target Detection
Tracking Techniques are Used for this Study
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Sensor Model

• Two Phased Array Radars
• Notional ground based X-band radar
• Notional ship based S-band radar with four array
  faces
• Assumptions
• Perfect resolution so that merged measurements
  not an issue
• No false alarms
• Probability of detection is 1 given a sufficient
  signal-to-noise ratio

• Sensor Parameters
• Sensor / Target Geometry

• Monopulse Parameters
• Sensor / Target Geometry
• Off bore-sight steer angle

Local Tracker Performance Prediction
Compute Measurement Covariance
Compute SNR
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Local Tracker Performance Prediction

• Based on a measurement covariance and track
  filter parameters, tracker performance is
  expressed as a noise only covariance and maneuver
  lag
• Assumptions
• Perfect measurement to track association
• Steady State
• Constant update rate
• Critical in the future to relax assumption of
  perfect measurement to track association
• Closely spaced objects a BIG deal in BMD

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System Track Performance Prediction

• Centralized Multi-Sensor Track Fusion
• Fuse all local tracks at a centralized location
• Performance prediction techniques used to assess
  the quality of the fused tracks
• Reporting Responsibility
• System track selected as the best of all local
  tracks for a given object under tracks
• Used in Link-16
• Architecture level effects?

Two network level tracking schemes considered
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Engagement Planner Analysis

• Define the battle space as the set of all
  possible launch solutions
• Computed for each interceptor and target pair for
  all times at which, target is presumed to be in
  coast phase

Predicted Intercept Point 1
Predict target trajectory using ballistic
extrapolation
X
Predicted Intercept Point N
X
Fly-out fan trajectory
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Engagement Planner Analysis

• For each possible intercept as determined by
  fly-out fans
• Compare the maneuverability of the interceptor to
  a critical threshold
• Threshold a function of predicted system track
  accuracy
• Compare at three key decision points
• Interceptor Launch Time
• Interceptor Burnout Time
• Interceptor Seeker Activation
• A launch solution is possible if key decision
  points pass
• Compute Probability of Kill (PK)

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Probability of Kill
Pib
PK is a function of track covariance and
interceptor seeker field of view (FOV)
Align track covariance with interceptor body frame
Pecef
U
V
W
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Probability of Kill
Pib
Compute distance in each cross range coordinate
DcrV
V
Area under curve is Gaussian CDF
f Seeker Field of View
W
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Fire Control

• Single engagement manager supervising
  interceptor-target assignments over all platforms
• Utilized a shoot early strategy
• Threats were engaged when a shot was available
  with a Pk exceeded a threshold
• Time dependent threshold used to instill
  confidence in each chosen shot while being more
  accepting of low Pk as the threat nears
• Shots constrained by
• Availability of platforms
• Interceptors currently engaging threat
• Pk for a given shot

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Results Placement Trade

• Surrogate models of MS used for Monte Carlo
  system performance assessment of ship operational
  area
• 10,000 Ship/Sensor2 (S2) locations are considered
  for a given single Ship/Sensor 1 (S1) location
• Ground Based Interceptor/Sensor (S3) fixed all
  times
• System performance, probability of zero leakers
  (P0L), provides operational contours

Expanded Operational Area
New S1 Location
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Results Tracking Method Trade

• With the current Reporting Responsibility
  architecture, it is not possible to get a high
  confidence of success
• Holding the interceptor and fire control systems
  constant, surrogates are used to explore
  different sensor architectures

Reporting Responsibility
Track Fusion
P0L Results Min 0.00 Max 0.60 Avg 0.11
P0L Results Min 0.53 Max 0.87 Avg 0.79
Track fusion vastly improves P0L in terms of
capability and robustness
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Results Number of Sensors Trade

• Track fusion results show the system performance
  is not sensitive to S2 location
• Surrogates are used to explore the number of
  sensors used

• Models were generated with the forward deployed
  land based sensor removed

• Two ship track fusion architecture yields
• Sizeable operational area
• Improved confidence over three platform reporting
  responsibility
• Note Two ship track fusion requires more
  communications bandwidth and different processing

Probability of Zero Leakers (P0L)
2 Platform Track Fusion 0.00 0.83 0.20
3 Platform Report. Responsibility 0.00 0.60 0.11
Min Max Avg
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Conclusions

• Surrogate models used to greatly improve runtime
  of large system-of-systems simulation with
  negligible loss in fidelity
• Enabled real-time system-of-systems level
  architectural trade studies utilizing accuracy of
  high-fidelity MS tools
• Asset placement trade
• Tracking method trade
• Number of sensors trade
• Plan to increase fidelity of various modeling and
  simulation of current BMD elements

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• Supporting Slides

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Engagement Planner Analysis
Condition 1 for launch
Position Covariance
Track covariance extrapolated to predicted
intercept
Track covariance at interceptor launch
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Engagement Planner Analysis
Condition 2 for launch
Position Covariance
Track covariance at interceptor burnout
Track covariance extrapolated to predicted
intercept
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Engagement Planner Analysis
Condition 3 for launch
Position Covariance
Track covariance extrapolated to predicted
intercept
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