Sensor Management Problems of
Nuclear Detection – Layered Defense
Fred S. Roberts
Rutgers University
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Multi-disciplinary, Multi-institutional
Project
•Based at Rutgers University
•Partners at Princeton, Texas State
University – San Marcos
•Collaborators at LANL, PNNL, Sandia
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Much of this work takes place at
CCICADA
Founded 2009 as a DHS University Center of Excellence
– the DHS CCI COE based at Rutgers
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Key Underlying Project Themes
•New developments in hardware are
important in nuclear
detection/prevention, but so are new
algorithms, models, and statistical
methods
•Nuclear detection/prevention involves
sorting through massive amounts of
information
•We need ways to make use of as
many sources of information as
possible.
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Research Thrusts: Recent Work
1. Developing Tools for Risk Assessment
and Anomaly Detection
2. Making use of Uncertainty/Randomness in
Detection/Prevention Protocols
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Research Thrusts: Recent Work
Research Thrust 1: Developing Tools for
Risk Assessment and Anomaly Detection
a. Machine Learning Tools
b. Visualization of Data
c. Data Sampling Strategies
Visualization of Port to Port Shipments
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Research Thrusts: Recent Work
Research Thrust 1: Developing Tools for Risk
Assessment and Anomaly Detection: Recent
Highlights
• Higher order machine learning methods
– Extended classification methods to more isotopes
– New preprocessing tools shown to be very useful
• New split and conquer algorithm for our
penalized regression methods for risk scoring
for containers
– Allows add new manifest data without total
recomputation
– Much more efficient & can handle larger data sets 7
Research Thrusts: Recent Work
Research Thrust 2: Making use of Uncertainty/
Randomness in Detection/Prevention Protocols
a. Placing Detectors in Randomly Moving
Vehicles
b. Planning Random Surveillance Routes
c. Planning Random Surveillance
Locations: Layered Defense
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Research Thrusts: Recent Work
Research Thrust 2: Making use of Uncertainty/
Randomness in Detection/Prevention
Protocols: Recent Highlights
• Detectors in randomly moving vehicles
(taxicabs): new methods for multiple classes
of detection and restricted time periods
• New architectures for layered defense and
random location of sensors
– Efficient algorithms for optimal sensor
placement
– Efficient sensor placement with adaptive
adversary
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Planning Random Surveillance
Locations: Layered Defense
Tsvetan Asamov
Endre Boros
Paul Kantor
Fred Roberts
Emre Yamangil
Rutgers University
Milind Tambe
University of Southern
California
Target
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Planning Random Surveillance
Locations: Layered Defense
• A new thrust in our project is a
collaboration with Prof. Milind Tambe
at USC’s CREATE Center.
• Tambe and his team devised ARMOR,
a software tool that uses random
strategies in game theory to locate
surveillance stations.
• His method has been adopted at LAX
Airport and Pittsburgh Airport to
randomly locate inspection stations on
the airport roadway and is in the
process of being adopted nationally.
• The method is also in use by the
Federal Air Marshal Service to
randomly choose international flights to
which to assign air marshals.
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Planning Random Surveillance
Locations: Layered Defense
• We have formulated a model of
how to apply the method to locate
nuclear surveillance in the area
around a facility, e.g., roadways
and walkways approaching sports
stadiums.
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Planning Random Surveillance
Locations: Layered Defense
• This relates to a CCICADA
project in connection with the
National Football League.
• Developing simulation models for
evacuation of stadiums.
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Layered Defense
To develop our ideas, we have formulated a
model of a “perimeter” defense of the target
with several layers of defense:
•Limited budget for surveillance
•How much to invest in each layer?
•Defense at outer layers might be less successful
but could provide useful information to
selectively refine and adapt strategies at inner
layers.
•Arranging defense in layers so decisions can be
made sequentially might significantly reduce
costs and increase chance of success.
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Layered Defense
Abstract model of layered
defense:
• Target in middle
• Threats arrive via 4
inner channels
• Each combines 2 outer
outer flows of vehicles,
persons, etc.
Target
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Layered Defense
Abstract model of layered
defense:
• Fixed budget for outer
layer and for inner layer
defense
• Can choose among
detectors with different
characteristics and costs
• How optimize
probability of
detection?
Target
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Layered Defense
Different models for:
• Flow along different
paths
• Prob. of detection at
different locations
(outer, inner)
• Allowable
modifications of inner
defense strategies based
on outer layer results
Target
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Layered Defense
• Monitoring at outer layer not only hinders an
attacker but can provide information about
current state of threat that can be used to refine
and adapt strategies at inner layers.
• There is a complex tradeoff between
maximizing the cost-effectiveness of each
layer and overall benefits from devoting some
efforts at the outer layer to gathering as much
information as possible to maximize
effectiveness of the inner layer.
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Layered Defense
• We have formulated this as an optimization
problem of maximizing the probability of
detection subject to budget constraints.
• We have developed dynamic programming
methods for solving this problem.
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General Formulation: Outer layer(s)
plus inner layer(s) – paths of approach
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General Formulation: Outer layer(s)
plus inner layer(s) – paths of approach
Model Assumptions: First Model:
•Each incoming path u has a dangerous “flow” Fu
•At each sensor k, the probability of detection is a
function Dk(Rk) of the resources Rk allocated to
that sensor.
•Assume that Dk(Rk) is a concave, piecewise linear
function.
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General Formulation: Outer layer(s)
plus inner layer(s) – paths of approach
Model Assumptions: First Model
Special Case: The Case of Two Layers
•Assume that the outside layers share a limited
resource budget and so do the inside layers.
•More subtle models allow one to make decisions
about how much budget to allocate between
inside and outside.
•Goal: Allocate the total outside resources among
individual sensors and allocate the total inside
resources among individual sensors in order to
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maximize the illegal flow detected.
General Formulation: Outer layer(s)
plus inner layer(s) – paths of approach
Model Assumptions: First Model
Special Case: The Case of Two Layers
•Goal: Allocate the total outside resources
among individual sensors and allocate the total
inside resources among individual sensors in
order to maximize the illegal flow detected.
•Note: So far, this model does not have the
random allocation of resources to sensors that
we ultimately aim for to confuse the attacker.
That will be added later.
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General Formulation: Outer layer(s)
plus inner layer(s) – paths of approach
Model Assumptions: First Model
Special Case: The Case of Two Layers
•Since there are only 2 layers, we can identify
the path name with the outer layer sensor where
it begins.
•Thus, path u is the path beginning at outer
sensor u.
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The Case of Two Layers
Dangerous flow captured at outside sensor j
Dangerous flow not captured
at outside sensor j that is
captured at inside sensor i
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Solving the Optimization Problem
•This formulates the problem as a non-linear
optimization problem.
•A standard approach to such problems is a
brute force approach that fixes a resource
“mesh”size and enumerates all possibilities.
– Discretize the resource space for each
sensor into subintervals
– Examine every possible resource allocation
•That approach is not computationally feasible
for the problem as we have formulated it.
•We have developed a new approach to solving
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the problem in our context.
Solving the Optimization Problem
•We have developed a new approach to solving
the problem in our context.
•Still discretize the resource space for interior
sensors into subintervals and solve that.
•However, we can now find the optimal
configuration for the exterior sensors by solving
a linear programming problem for each
combination of interior and exterior sensors.
•An improvement, but this is still too
computationally intensive.
•However, a dynamic programming variant
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avoids the worst part of the computation.
Illustration on Some Special Cases
Detection network
architecture
First assumption:
linear detection
rates both
inside and outside
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Representation of Objective Function
Inside resource Ri
Outside resource Rj
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Representation of Objective Function
•Because the detection
functions are linear, the
optimal solution is found
at one of the 4 corner
points.
•We only need to
evaluate the objective
function 4 times to find
optimal solution.
•Three of the corners are
in fact optimal solutions.
Inside resource
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Outside resource
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Changing the detection rate function
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Representing the Objective Function
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•Because detection functions are piecewise linear,
we can discretize the feasible region of each
decision variable Ri into Ni subintervals where
Di is linear over the subinterval.
•Same for Rj.
•The problem now
becomes feasible in
this simple case.
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•Our methods for this simple problem as well as
the more complex problems we will describe were
applied on a simple AMD Phenom X4 9550
workstation with 6GB of DDR2 RAM, and
were often solved in a matter of seconds.
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A more complicated network:
Multiple outside sensors
Case of 2
Outside sensors
(green and blue)
and 1 inside
sensor
Piecewise linear
detection rate functions
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•Our methods proceed by looking at
solutions if only use green outside sensor and
inside sensor or if only use blue outside
sensor and inside sensor.
•Then “merge” the results.
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A more complicated network:
Multiple outside and multiple
inside sensors
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•Our methods generalize to this case.
•Even with 4 inside sensors and 2 outside sensors
per inside sensor, solution in < 2 minutes on
modest workstation.
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Solution with 4 inside sensors
and 2 outside sensors per inside sensor
•Solution “tableau” includes10,302 distinct points.
•Solution in < 2 minutes on modest workstation.
•Methods feasible up to 10 inside sensors.
•After that, need approximation methods.
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Case of an Adaptive Adversary
•So far, our model assumed a fixed flow of
dangerous material on each pathway.
•What if we have an adaptive adversary who
recognizes how much of a resource we use for
sensors on each node and then chooses the path
that minimizes the probability of detection?
•To defend against such an adversary we might
seek to assign sensor resources so as to maximize
the minimum detection rate on any path.
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The Problem for Two Layers with
an Adaptive Adversary
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The Case of Two Layers with
an Adaptive Adversary
•We have developed methods that work with
multiple inside sensors and multiple outside sensors
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Solution with 4 inside sensors and
2 outside sensors per inside sensor
•Solution “tableau” had 40,401 distinct points.
•Solution in 3102 seconds (52 minutes) on modest
workstation.
•Hope to be able to speed up so methods feasible
for up to 10 inside sensors.
•After that, need approximation methods.
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Planning Random Surveillance
Locations: Layered Defense
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Next Steps for the Research
Pathways with more than two nodes
Fixed resource limit that the defender can
allocate between inner and outer layers
Probability distributions on the flows Fi
Adaptive redistribution of resources: change
your distribution of resources on inside layer
based on input from outside sensors
Bringing in false positives and false negatives
Randomizing allocation of resources
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Planning Random Surveillance
Locations: Layered Defense
Game theory Approach
• Attacker-defender game (Stackelberg game)
– Defender (security) acts first
– Attacker can observe defender’s strategy and
choose the most beneficial point of attack
• But: can we introduce some randomness to
increase the uncertainty on the part of the
attacker?
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Planning Random Surveillance
Locations: Layered Defense
Game theory Approach
• Bayesian Stackelberg game:
– Randomize defender’s strategy
– Thus, create uncertainties for attacker in choosing its
strategy
– This was used in Tambe’s work at LAX and FAMS
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Planning Random Surveillance
Locations: Layered Defense
• Layered defense makes this into a new kind of
Stackelberg game to analyze, one with two
rounds, one involving the outer layer and one
involving the inner layer based on results at the
outer layer.
• We can look both at nonrandomized and
randomized strategies for the defender.
• This work is just beginning.
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Application to GNDA
There are evident similarities
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Title: Sensor Management Problems of Nuclear Detection
Org/PI: Rutgers University / Fred S. Roberts
Thrust 1: Tools for threat detection and risk assessment
Manifest data
analysis
Data collection
Sensor
data
analysis
Thrust 2: Exploiting randomness in detection protocols
Layered
defense
Opportunistic sensing
Random routing
Technical Merit
 Our project focuses on managing and mitigating uncertainty
for improved collection and interpretation of sensor data
while exploiting randomness for unpredictable surveillance
 Classification methods tailored to radiation sensor data can
reduce nuisance alarms; new methods for analyzing
manifest data and combining sensor and manifest data;
introduced uncertainty into surveillance protocols
Technical Approach
 Optimal learning for data collection; machine learning for
improved detection and risk scoring; layered and
opportunistic surveillance to thwart adversaries
Broader Impact
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Students supported: postdoctoral (1); graduate (7); undergrad (3)
Part of (3) Phd dissertations to date; (3) more nearing completion
More than (10) additional graduate students participating
Developed new undergraduate course on “Optimal Learning” at
Princeton University, with related textbook in progress
Held workshop involving five projects in the DNDO program + Fall
2010 workshop on adversarial decision making
Enhanced relations w/ national labs, incl. (2) summer internships
Many project methods apply to other fields: e.g. machine learning
methods are being applied for police force deployment; optimal
learning methods are being applied in molecule synthesis
(24) papers published/accepted; (11) more under review
Schedule/Cost:
PY01: $486K
 Duration: 48 months
PY02: $491K
44 months (to date)
Major Milestones / Accomplishments
PY03: $494K
PY04: $529K
 Developed machine learning tools for risk scoring and isotope
classification, esp. higher-order methods and preprocessing tools
& new split & conquer algorithm; visualizations to observe
patterns in manifest data; “knowledge gradient” rules for
collecting information under a budget; paradigms for exploiting
randomization in surveillance; novel models of layered defense
Team
 Co-PI: Warren Powell, Princeton University
 Collaborating Universities: Princeton University; Texas State
University – San Marcos
 National Labs interaction: PNNL; LANL; Sandia; LLNL (planned)
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Last updated on: 04/26/11
Project Team
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Rutgers University
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Princeton University
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Fred Roberts
James Abello
Tsvetan Asamov (grad student)
Endre Boros
Jerry Cheng (grad student)
Sid Dalal (RAND Corp, consultant)
Robert Davis (undergrad student)
Emilie Hogan (grad student)
Christopher Janneck (grad student)
Paul Kantor
Adam Marszalek (grad student)
Dimitris Metaxas
Christie Nelson (grad student)
Alantha Newman (postdoc)
Jason Perry (grad student)
Bill Pottenger
Minge Xie
Emre Yamangil (grad student)
Warren Powell
Savas Dayanik
Peter Frazier (grad student)
Ilya Rhyzov (grad student)
Kazutoshi Yamazaki (grad student)
Texas State University – San Marcos
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Nate Dean
Jill Cochran (grad student)
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Project Team: National Lab Partners
(helping with advice, information, data)
• PNNL
– Terence Critchlow
– James Ely
– Cliff Joslyn
• LANL
– Frank Alexander
– Nick Hengartner
• Sandia
– Jon Berry
– Bill Hart
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Thank you
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