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 2

 Infeasibility of electromagnetic sensors  A type of sensor called SONAR (SO SOund NA NAvigation and Ranging) is used  Sonars work based on sound waves 3

 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 6

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 , a characteristicvalueof cell i j ij  p detection probabilityof asonar  c budget for placing sonars  n numberof cellsasonarcancover  NC set of neighboring cellsof i, j that a sonar ij positioned at celli, j cancoverincluding i, jitself  1 , if a sonaris placed at celli j  x ij  0 otherwise  1 if celli, j iscovered by a sonar  y ij  0 otherwise

Objective   (1 . ) Min a p y Function ij ij i j   . (1) n x y ij kl Placement  , k l NC ij Constraints   (2) y x ij kl  , k l NC ij Cost   (3) c x b Constraint ij i j   Decision y  , 0,1 x ij ij Variables

  (1 . ) Min a p y ij ij i j This objective function minimizes a risk-like measure according to cell coverage and also the importance of cells (a ij 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 13

        {1 [((1 ) ) ]} Min a t dp y t dp max ij ij n ijn ij i j n     : , , , St d x y i j m n mn ijm kln Placement  ( , ) k l N ijmn Constraints     , , y x i j n ijn klm  ( , ) m k l N ijmn Cost    c x b Constraint m ijm i j m      1 , y M t i j Multiple ijn ij n Coverage  Constraints     (1 ) 2 , M t y i j ij ijn n   Decision t  , , 0,1 x y ijm ijn ij Variables 14

 1 ( , ) if a sonar of type m is placed incell i j  x ijm  0 otherwise  1 ( ) if cell i, j iscovered bycoveragetype n  y ijn  0 otherwise  1 ( , ) if cell i j iscoverd by morethanonesonar  t ij  0 otherwise 15

Te Test st Case se New w Yo York Ha Harbor bor (as an example) 16

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Thank you! 22