Sensor Management Problems of Nuclear Detection – Layered Defense

1. Sensor Management Problems of Nuclear Detection – Layered Defense Fred S. Roberts Rutgers University

2. Multi-disciplinary, Multi-institutional Project • Based at Rutgers University • Partners at Princeton, Texas State University – San Marcos • Collaborators at LANL, PNNL, Sandia

3. Much of this work takes place at CCICADA Founded 2009 as a DHS University Center of Excellence – the DHS CCI COE based at Rutgers

4. 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.

5. Research Thrusts: Recent Work • Developing Tools for Risk Assessment and Anomaly Detection • 2. Making use of Uncertainty/Randomness in Detection/Prevention Protocols

6. Research Thrusts: Recent Work • Research Thrust 1: Developing Tools for Risk Assessment and Anomaly Detection • Machine Learning Tools • Visualization of Data • Data Sampling Strategies Visualization of Port to Port Shipments

7. Research Thrusts: Recent Work • Research Thrust 1: Developing Tools for Risk Assessment and Anomaly Detection:RecentHighlights • 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

8. 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

9. 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 sensorplacement • Efficient sensor placement with adaptive adversary

10. Target Planning Random Surveillance Locations: Layered Defense Tsvetan Asamov Endre Boros Paul Kantor Fred Roberts Emre Yamangil Rutgers University Milind Tambe University of Southern California

11. 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.

12. 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.

13. 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.

14. 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.

15. Target 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.

16. Target 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?

17. Target 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

18. 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.

19. 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.

20. General Formulation: Outer layer(s) plus inner layer(s) – paths of approach

21. 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.

22. 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 • maximize the illegal flow detected.

23. 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.

24. 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.

25. The Case of Two Layers Dangerous flow captured at outsidesensor j Dangerous flow not captured at outside sensor j that is captured at inside sensor i

26. 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 the problem in our context.

27. 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 avoids the worst part of the computation.

28. Illustration on Some Special Cases Detection network architecture First assumption: linear detection rates both inside and outside

29. Representation of Objective Function Outside resource Rj Inside resource Ri

30. 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 Outside resource

32. Changing the detection rate function

33. Representing the Objective Function

34. 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.

35. 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.

37. A more complicated network: Multiple outside sensors Case of 2 Outside sensors (green and blue) and 1 inside sensor Piecewise linear detection rate functions

38. 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.

40. A more complicated network: Multiple outside and multiple inside sensors

41. 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.

42. 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.

43. 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.

44. The Problem for Two Layers with an Adaptive Adversary

45. The Case of Two Layers with an Adaptive Adversary • We have developed methods that work with • multiple inside sensors and multiple outside sensors

46. 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.

47. Planning Random Surveillance Locations: Layered Defense 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

48. 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?

49. 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

50. 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.