May 31, 2009 Industrial Engineering Research Conference - 2009 Slide 1 Scheduling Radar Warning...

May 31, 2009 Industrial Engineering Research Conference - 2009 Slide 1

Scheduling Radar Warning Receivers (RWRs)

Scott R. Schultz Mercer University / Mercer Engineering Research

CenterF.M. Barron

Paul MacNeilEric Mullenax


About the Speaker

Dr. Scott Schultz – associate professor Mercer University, and consultant at Mercer Engineering Research Center.Industry Experience:• 13 years automotive experience – Ford Motor Company.• 2 years furniture experience – Furniture Manufacturing Management center.• Consulting – manufacturing and militaryTeaching Experience:• 6 years as Industrial Engineer – Mercer Univ. • Simulation• Production, scheduling, inventory control• Operations Research• others…


Problem Statement

Develop an RWR scheduler that minimizes the time to detect multiple threats across multiple frequency bands.


RWR Scheduling Definitions

Pulse Width (PW)

Revisit Time (RT)

IlluminationTime (IT)

Pulse RepetitionInterval (PRI)

Beam Width (BW)

Definitions:

Revisit Time (RT) – time to rotate 360 degrees (rotating radar)

Illumination Time (IT) – function of RT and BW

Pulse Width (PW) – length of time while target is energized

Pulse Repetition Interval (PRI) – time between pulses

Time


Example RWR Schedule

RWR Schedule – a series of dwells on different frequency bands: sequence and length


RWR Scheduling Problem

Objective – detect all threats as fast as possible (protect the pilot)

How to sequence dwells?How to determine dwell length?How to evaluate / score schedules?

Meta-Heuristics

Simulation


RWR Scheduling Approach

Meta-Heuristics: Simulated Annealing (SA)

SA Components:• Solution representation• Neighborhood generation scheme • Solution evaluation/score



RWR SA Solution Representation:

Assumptions: • Unit Time• Idle Time fills space from end of last dwell to total cycle time.

Schedule 1 Total Cycle Time: 30

Dwell Frequency Band Start Time Width Retune Dwell

1 1 0 7 1

2 2 8 10 1

3 3 19 5 1



RWR SA Neighborhood generation scheme:

Two Examples:

Add or Subtract a Unit of Time Split a Dwell


Solution Evaluation: Simulation Approach:Given that the offset for each threat pulse train is unknown.

Determine: MTDAT - expected time to detect all threats, MaxDAT - maximum time to detect all threats

Threat 1Band 2

Band 1

Band 2

Band 3

Band 1

Band 2

Band 3

Band 1

Band 2

Band 3

Threat 1Band 2

300 360 390 420 450 480 510 540 ......

Time (milliseconds)

RWR Schedule

Threat

Band 1

Band 2

Band 3

Band 1

Band 2

Band 3

Band 1

Band 2

Band 3

Threat 1Band 2

Threat 1Band 2

300 360 390 420 450 480 510 540 ......

Time (milliseconds)

RWR Schedule

Threat

Note different offsets

Threat detected in

cycle 1

Threat detected in

cycle 2



n = 1

i = 1

Generate offset for threat i ~ U(0,RTi)

Determine time when RWR schedule

coincides with threat i

i = i + 1

i < I

Objective: Evaluate / Score a single RWR schedule.

N – number of iterations

I – number of threatsn = n + 1

Update MTDAT, MaxDAT

n < N

Done

Yes

Yes

NoNo



When does the MTDAT running average begin to converge?

Running Average - 3 Threats

760

780

800

820

840

860

0 10000 20000 30000 40000 50000 60000

Number of Iterations

MTD

AT

MTDAT running average: 3 threats


4400

4500

4600

4700

4800

4900

5000

5100

0 10000 20000 30000 40000 50000 60000

Number of Iterations

MTD

AT


16000

16400

16800

17200

17600

18000

0 10000 20000 30000 40000 50000 60000

Number of IterationsM

TDA

T





Compare SA to Simple Heuristic:

Experimental Design

Pre-determined Cycle Time Heuristic:• Set the number of dwells equal to the number of frequency bands, • Set the dwell time as calculated below:

dwell time = int((RWR cycle time – retune time * number of bands )/ number of bands)

• Any time left over is assumed idle time and placed at the end of the schedule


Problem Parameters:

Retune Time: 1 Time Unit (sec)RWR Cycle Times: Evaluate from 40 to 90 (sec)Threat List: 5 Enemy Radars

Experimental Design

Frequency Band RT (sec) IT (sec) IT/RT

1 277 40 0.14

2 352 30 0.08

3 427 40 0.09

4 321 10 0.03

5 307 25 0.08


Results:

Note: MTDAT approaching infinity for pre-determined cycle time heuristic at some cycle times due to synchronization.

Results

Pre-determined Cycle Time -vs- SA

02000400060008000

40 60 80 100

Initial Cycle Time

MT

DA

T Pre-determined CycleTime Heuristic

After SA


ResultsStarting Cycle Time 40 41 42 43 44 45 46 47 48 49 50Threat Revisit Time

277 6.9250 6.7561 6.5952 6.4419 6.2955 6.1556 6.0217 5.8936 5.7708 5.6531 5.5400352 8.8000 8.5854 8.3810 8.1860 8.0000 7.8222 7.6522 7.4894 7.3333 7.1837 7.0400427 10.6750 10.4146 10.1667 9.9302 9.7045 9.4889 9.2826 9.0851 8.8958 8.7143 8.5400321 8.0250 7.8293 7.6429 7.4651 7.2955 7.1333 6.9783 6.8298 6.6875 6.5510 6.4200307 7.6750 7.4878 7.3095 7.1395 6.9773 6.8222 6.6739 6.5319 6.3958 6.2653 6.1400

Init Cycle Time 40 41 42 43 44 45 46 47 48 49 50RWR Dwell Band

1 7 7 7 7 7 8 8 8 8 8 92 7 7 7 7 7 8 8 8 8 8 93 7 7 7 7 7 8 8 8 8 8 94 7 7 7 7 7 8 8 8 8 8 95 7 7 7 7 7 8 8 8 8 8 9

Retune Time 5 5 5 5 5 5 5 5 5 5 5Idle Time 0 1 2 3 4 0 1 2 3 4 0MTDAT 5562 2522 2080 2299 99999 2112 6579 3362 2418 2327 2462

Starting Cycle Time 40 41 42 43 44 45 46 47 48 49 50RWR Dwell Band

1 7 7 7 7 7 7 7 7 7 7 72 7 7 7 7 7 10 8 7 7 7 73 7 8 7 7 7 7 9 7 7 7 84 9 7 7 7 20 21 20 20 20 20 195 7 7 7 7 7 7 7 9 8 7 11

MTDAT 1758 1912 1976 2123 987 940 977 981 982 997 958Retune Time 5 5 5 5 5 5 5 5 5 5 5Idle Time 0 1 2 3 4 0 1 2 3 4 0Final Cycle 42 42 42 43 57 57 57 57 57 57 57

Schedule using pre-determined cycle time heuristic

Schedule after Simmulated Annealing

Ratio of threat revisit time / RWR cycle time


Conclusions

• SA outperforms simple heuristic • SA approach presented for developing RWR schedules using the performance measure “mean time to detect all threats”, MTDAT. • SA will converge on an RWR schedule having a particular cycle time, however this is dependent on the initial cycle time and bounded by cycle times which are synchronized with a threat’s revisit time. • Synchronization poses an interesting challenge compared to many SA applications of discrete optimization problems which converge to a global optimal solution independent of the starting solution.


RWR Research - Status

Future:

Investigate alternative means of generating scores to avoid costly simulation • Research literature identified• Compare to enhanced evaluator (simulator)

Assess impact of multiple radars in RWR platform• Replace single radar with one monitoring high frequencies and one monitoring lower frequencies

Math Model?


Research Sponsor

Sponsors:• RAPCEval - collaborative Air Force and university education and research program to support advances in electronic combat technology. The RAPCEval program is overseen by a steering committee of scientists and engineers from the Air Force Research Laboratory at Wright Patterson AFB, the Warner Robins Air Logistics Center at Robins AFB, Mercer University, Mercer Engineering Research Center (MERC), Wright State University, and Rose-Hulman Institute of Technology who are charged with ensuring that student research is of sufficient interest to the USAF and also of high academic quality.

• Mercer Engineering Research Center – located in Warner Robins, Georgia, a non profit operating unit of Mercer University. MERC employs over 150 engineers, scientists, and support staff. Engineering, Logistics, management, and educational services are provided to a wide range of government and commercial customers

May 31, 2009 Industrial Engineering Research Conference - 2009 Slide 1 Scheduling Radar Warning...

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