Advisor: Tayfur Altiok, Professor, Rutgers University, NJ - - PowerPoint PPT Presentation

Presented by:

Amir Ghafoori, PhD Student, Rutgers University, NJ

Advisor:

Tayfur Altiok, Professor, Rutgers University, NJ

CAIT-DIMACS Laboratory for Port Security

 Divers  AUV’s  Hull mounted objects

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 Infeasibility of electromagnetic sensors  A type of sensor called SONAR (SO

SOund NA NAvigation and Ranging) is used

 Sonars work based on sound waves

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 Electromagnetic waves get stuck in sea water  Sound waves can travel in sea water even for

tens of miles

 Active  Passive

 A Risk Minimization problem, with integer (binary)

decision variables

 With:

• Multiple coverage
• Detection probability reduces by distance from the sonar
• Various properties of sonars
• Different sonar types

Are considered in the model.

 Discretization

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,

ij

a characteristicvalueof cell i j 

p detection probabilityof asonar 

1 ,

ij

if a sonaris placed at celli j x

• therwise

   1

ij

if celli, j iscovered by a sonar y

• therwise

   c budget for placing sonars  n numberof cellsasonarcancover 

ij

NC set of neighboring cellsof i, j that a sonar positioned at celli, j cancoverincluding i, jitself 

(1 . )

ij ij i j

Min a p y 



,

. (1)

ij

ij kl k l NC

n x y



 

,

(2)

ij

ij kl k l NC

y x



  (3)

ij i j

c x b 



 

, 0,1

ij ij

x y 

Placement Constraints Cost Constraint Decision Variables Objective Function

(1 . )

ij ij i j

Min a p y 



This objective function minimizes a risk-like measure according to cell coverage and also the importance of cells (aij values)

[ ] [ | ] ( ) [ | ] ( | ) ( ) R E C E C Successful Attack P Successful Attack E C Successful Attack P Successful Attack Attack Happens P Attack Happens C V T         

 Featuring

• Multiple detection of sonars
• Range dependent detection probability
• Various types of sonars

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max

{1 [((1 ) ) ]}

ij ij n ijn ij i j n

Min a t dp y t dp      

 

( , )

, , ,

ijmn

mn ijm kln k l N

d x y i j m n



  



1 ,

ijn ij n

y M t i j    



(1 ) 2 ,

ij ijn n

M t y i j    



 

, , 0,1

ijm ijn ij

x y t 

: St

m ijm i j m

c x b  



( , )

, ,

ijmn

ijn klm m k l N

y x i j n



 

 

Placement Constraints Cost Constraint Multiple Coverage Constraints Decision Variables

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1 ( , )

ijm

if a sonar of type m is placed incell i j x

• therwise

   1 ( )

ijn

if cell i, j iscovered bycoveragetype n y

• therwise

   1 ( , )

ij

if cell i j iscoverd by morethanonesonar t

• therwise

  

Te Test st Case se New w Yo York Ha Harbor bor

(as an example)

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Thank you!

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