sssw3imbrs wd 43 fleet maintenance simulation for unmanned ... · pdf filefleet maintenance...

SimBRS WD 43S S W 3

Fleet Maintenance Simulation for Unmanned Ground Vehicles

Zissimos P. MourelatosMechanical Engineering Department

O kl d U i itOakland University

Matthew P. Castanier, David A. LambUS Army TARDEC

1

SimBRS Program Review Meeting | 26-28 July 2011 | Starkville, MS

UNCLASSIFIED: Dist A. Approved for public release

Report Documentation Page Form ApprovedOMB No. 0704-0188

Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering andmaintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information,including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, ArlingtonVA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if itdoes not display a currently valid OMB control number.

1. REPORT DATE 26 JUL 2011

2. REPORT TYPE Briefing Charts

3. DATES COVERED 26-07-2011 to 26-07-2011

4. TITLE AND SUBTITLE FLEET MAINTENANCE SIMULATION FOR UNMANNED GROUND VEHICLES

5a. CONTRACT NUMBER

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S) Matt Castanier; David Lamb; Zissimos Mourelatos

5d. PROJECT NUMBER

5e. TASK NUMBER

5f. WORK UNIT NUMBER

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Oakland University,Mechanical Engineering Department,Rochester,MI,48309

8. PERFORMING ORGANIZATIONREPORT NUMBER ; #22120

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) U.S. Army TARDEC, 6501 E.11 Mile Rd, Warren, MI, 48397-5000

10. SPONSOR/MONITOR’S ACRONYM(S) TARDEC

11. SPONSOR/MONITOR’S REPORT NUMBER(S) #22120

12. DISTRIBUTION/AVAILABILITY STATEMENT Approved for public release; distribution unlimited

13. SUPPLEMENTARY NOTES SimBRS Program Review Meeting 26-28 July 2011 Starkville, MS

14. ABSTRACT NA

15. SUBJECT TERMS

16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT Same as

Report (SAR)

18. NUMBEROF PAGES

40

19a. NAME OFRESPONSIBLE PERSON

a. REPORT unclassified

b. ABSTRACT unclassified

c. THIS PAGE unclassified

Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18

Overview

What is reliability ?

Basics of reliability methods for repairable and non-repairable systems

Estimation of PDF of Time Between Failures (TBF) using limited, censored datag ,

System reliability and reliability allocation

Fleet Maintenance Simulation (FMS) Tool

Unmanned ground vehicle (UGV) system example

2

g y


What is Reliability?y

Reliability at time t is the probability that the systemReliability at time t is the probability that the system has not failed before time t.

failure

0 T timet

tTPtTPtR 1

3UNCLASSIFIED: Dist A. Approved for public release

Reliability of Non-Repairable Systemsf il

0 T timet

failure

tFtRtTPtTPtR 11 (1)

tTPdtdttTtP

dttTdttTtPt

Fail reFailure Rate

tRtft

tRdttFdttF

(2)

]exp[ t

dttR From (1) and (2) we get :

4

0( ) ( ) g


Reliability of Non-Repairable SystemsNfNf

ilure

s Nf iilu

res Nf i

umbe

r of

fai

Nf i-1

umbe

r of

fai

Nf i-1

m

NN ff

Nu

bint

Nu

bint

i

i1

ff

……1 2 ii -1 m

mileage or time

…∆t

t……1 2 ii -1 m

mileage or time

…∆t

t

i

tNN

NN

fF

fii

i

i

ii

i

j

1

ff

f

1 f11

iHR

i

jji tH

1

5

tNNN jj

j

1

ff1 f

1 iHi eR


Reliability Calculationy

All we need for calculating theAll we need for calculating the reliability of a system (non-repairable

or repairable) is the system PDF ofor repairable) is the system PDF of time to failure (TTF)

We use :

Data to estimate the PDF of TTF for each component

Monte Carlo simulation to estimate the PDF of TTF

6

for the system


Estimation of the PDF of the TTF (TBF) using Limited,

Censored Data

Censored MLE Approach

Censored Data

Censored MLE Approach


Ti B t F ilO i i l d t U d t d d t

Group L1Limited Data / NotationTime Between Failures

(TBF)Original data Updated data

Vehicle# mileage Vehicle# mileage10 741 1 10247 4 5273 2 9044

6027 1738412011 200000

6027

7 6027 2 8977 5 7398 3 13984 6 7495 3 4064 2 9044 4 5273 6027

5984

5373

2 9044 4 5273 1 10247 4 9747 8 12008 5 7398 7 12011 5 7611

Censoring Mileage9 12014 6 7495 10 12074 6 7516 3 13984 7 6027 5 15009 7 59845 15009 7 5984 6 15011 7 5373 4 15020 8 12008 7 17384 9 12014

8

2 18021 10 741 3 18048 10 11333


Observation / Assumption

0,0and,,,,,~d qpBXAqpBAXM iii

0,0,,,,, 1111 qpandBxA,ABxBAxp,q=βqpBAxf qpqp

Beta Distribution

6.0E-05

on

1.2PDF CDF

,,,,,, qpp qβqpf

3.0E-05

4.0E-05

5.0E-05

lity

dens

ity fu

nctio

(PD

F)

0.6

0.8

1

tive

dist

ribut

ion

ctio

n ( C

DF

) A = 0

B = 45,000 miles

0.0E+00

1.0E-05

2.0E-05

0 10000 20000 30000 40000 50000

Prob

abi

0

0.2

0.4C

umul

atfu

ncp = 3, q = 5

9

0 10000 20000 30000 40000 50000

Mileage


Observation / Assumption Beta distribution family is used to model TBF.

A=0, B = 30000

10

0,0and, , ,,,, 1111 qpBxAABxBAxp,q=βqpBAxf qpqp


MLE Approach

Determines parameters (A, B, p, q) of “most likely” Beta di t ib ti i il bl d tdistribution using available data.

# of recorded

Censored MLE

sF N

j

N

i qpBAxFqpBAxfMax ,,,,1,,,,

failures # of survivals

j

ji

iqpBAqpqpf

11,,,,,,,,,,,

Beta PDF Beta CDF


If Only MTBF is Available 0,0,,,,, 1111 qpandBxA ,ABxBAxp,q=βqpBAxf qpqp

MTBF

Beta Distribution

6.0E-05 1.2PDF CDF

MTBF

Assume constant COV

3.0E-05

4.0E-05

5.0E-05

dens

ity fu

nctio

n (P

DF)

0.6

0.8

1

dist

ribut

ion

n ( C

DF

)

PDF CDF Then for:

ABA

AB

and

0 0E 00

1.0E-05

2.0E-05

Prob

abili

ty

0

0.2

0.4

Cum

ulat

ive

func

tio

11

AB ABWe get:

0.0E+000 10000 20000 30000 40000 50000

Mileage

0

111

,112

q

p

12

11 2q


S t R li bilit dSystem Reliability and Reliability Allocationy


PDF

System ReliabilityPDF

MTBF TTFComp. 1

PDFSystem.

.

. System Histogram

System

TTF

. System TTF

g

MTBF TTFComp. n

14

t


System TTF

Histogram System ReliabilityTTF

Monte Carlo

t

Simulation

t

tR 1

1R

2RReliability

dttRMTBF

For System :

2

3Rt

0

dttRMTBF

15

T1t 2t 3tt

0


Reliability Allocation tR 1 1

1R

2R

3R

Reliability

Specify system (vehicle) reliability

T1t 2t 3t

t

0Optimization

Determine required reliability of EACH componenty

This optimization problem DOES NOThave a unique solution


Reliability Allocation

One way to get a unique solution is to trade-off reliability and associated cost

C tiTarget system

CostcompR

min

tRliabilitySystem Res t

g yreliability

RliabilitySystem Res. t.

By varying , we get the so called “Pareto Frontier.”tR


Reliability vs Risk of Failure (Cost)

We want to maximize Reliability and simultaneously minimize Risk of failure (cost)

bilit

y

Utopia

Rel

iab p

PtPareto Front

Feasible Domain

tR

Feasible Domain

18

Cost


Reliability – Cost Pareto Front Calculationx2

12 3 4

5

x2

12 3 4

5Reliability (R)

break(m) = 1x1

1 5domains

ranges

Reliability (R)

break(m) = 1x1

1 5domains

ranges

break(m+1) = paretoU

Rmax

4

5

break(m+1) = paretoU

Rmax

4

5

b k(2)2

3thickness

b k(2)2

3thickness

break(1) = 0

break(2) = paretoLRmin 1

break(1) = 0

break(2) = paretoLRmin 1

19

Cost( )

Cost( )


Reliability-Cost Relation)1MTBF/MTBF(

00 costcost ke : For each component

CN

C

CC

0

1

)1MTBF/MTBF(0 counts) failure1( costCost

ii

ke

For system with Nc componentsUnit CostUnit Cost

For system with Nc components

cost1cost1

cost0cost0

20

MTBF0MTBF0 MTBF1

MTBFMTBF0MTBF0 MTBF1

MTBF


Example : Fifteen ComponentExample : Fifteen-Component System in Series


Component

Input InformationComponent

NumberComp No.

Baseline MTBF in hours (MTBF0)

Coefficient of Variation Bfactor

Baseline cost (Cost0)

k

1 4076 0.3 3 $27,500.00 1

2 15000 0.3 3 $7,000.00 1

3 26510 0.3 3 $3,000.00 1

4 40000 0.3 3 $5,000.00 1

5 18000 0.3 3 $5,000.00 1

6 8000 0.3 3 $500.00 1

7 31809 0.3 3 $22,500.00 1

8 9520 0.3 3 $30,000.00 1

9 9713 0.3 3 $12,500.00 1

10 2330 0.3 3 $20,000.00 1

11 40000 0 3 3 $27 500 00 111 40000 0.3 3 $27,500.00 1

12 8614 0.3 3 $1,000.00 1

13 45000 0.3 3 $30,000.00 1

14 20000 0 3 3 $3 000 00 1

22

14 20000 0.3 3 $3,000.00 1

15 25000 0.3 3 $15,000.00 1


Histogram of System Failures

200es Nf

150

failu

re Nf

100

ber

of

0

50

Num

b

0

066

413

2819

9226

5633

20

3984

4648

5312

5976

6641

Ti (h )

23

Time (hours)


Reliability Comparison between Repairableand Non repairable S stemand Non-repairable System

Reliability

1.0E+00

1.2E+00RFRF1

6.0E-01

8.0E-01

iabi

lity RH

RH1

0 0E 00

2.0E-01

4.0E-01

Rel

i Repairable

0.0E+00

0

1000

2000

3000

4000

5000

6000

7000

8000

Ti (h )Non-repairable

24

Time (hours)p


System Reliability-Cost Pareto Front

8.0E-019.0E-01

5 0E 016.0E-017.0E-018.0E 01

ity

3.0E-014.0E-015.0E-01

elia

bili Pareto front

0 0E+001.0E-012.0E-01R

e

0.0E+002E+05 2E+05 2E+05 2E+05 3E+05 3E+05 3E+05

Cost


Summary: Methodology

A methodology was presented to :

Calculate system reliability using limited data

Perform reliability allocation (determine reliabilities of components) using optimal p ) g ptrade-off between reliability and cost

The methodology was demonstrated with a The methodology was demonstrated with a fifteen-component vehicle system


Fleet Maintenance Simulation (FMS) Tool


Simulation and Optimization - FMS Tool• Developed jointly by TARDEC (CASSI Analytics) and Oakland UniversityDeveloped jointly by TARDEC (CASSI Analytics) and Oakland University• Predicts vehicle maintenance over lifecycle based on component input data• Enables reliability-cost trade/sensitivity/optimization studies for vehicle fleets

0.7500

0.8000

0.8500

ParetoFront

0.6000

0.6500

0.7000

Rel

iabi

lity

Intermediapoints

Pareto front

IntermediatePoints

0.5000

0.5500

$600

$800

1,00

0

1,20

0

1,40

0

1,60

0

1,80

0

Pareto front

FMS Tool used to perform reliability-cost trade study for $1 $1 $1 $1 $1

Cost

28

adding redundant motors and sensors to an unmanned ground vehicle (UGV) manipulator arm

Fault tree in FMS Tool UNCLASSIFIED: Dist A. Approved for public release

Analysis Procedure1.Estimate component probability of failure

vs time or mileage

MTBFPDF

– Focus on cost and repair drivers– Minimum data: mean time between failure (MTBF)

2.Run Monte Carlo simulations to predictTime

Operation Failure Repair

2.Run Monte Carlo simulations to predict fleet reliability, availability, cost

– Vehicle lifetime: user-specifiedNumber of simulated vehicles: user specified– Number of simulated vehicles: user-specified

3.Perform trade/sensitivity/optimization studies

– Tradeoffs among configurations, component changes, maintenance schedules, etc.

– Sensitivity to data uncertainty price changes etc

29

– Sensitivity to data uncertainty, price changes, etc.– Optimization of components, schedules, etc.


Estimation of Component Reliability

Beta Distribution

6.0E-05 1.2PDF CDF

• Beta distribution family is used to model probability of component f il ti il

3 0E 05

4.0E-05

5.0E-05

dens

ity fu

nctio

n PD

F)

0 6

0.8

1

dist

ribut

ion

( C

DF

)

PDF CDFfailure versus time or mileage

• When maintenance records are

1.0E-05

2.0E-05

3.0E-05

Prob

abili

ty d (P

0.2

0.4

0.6

Cum

ulat

ive

dfu

nctio

navailable:– FMS Tool processes raw data

0.0E+000 10000 20000 30000 40000 50000

Mileage

0• For limited, censored data FMS Tool has two options to estimate the distributionthe distribution– Censored Maximum Likelihood

Estimation (MLE)– Bayesian updating approach

30

Bayesian updating approach (“enhances” data with expert opinion)


Example: Unmanned Ground Vehicle ( G )(UGV)

• Focus on robotic arm design• For original design, each joint

and the end effector has:1 motor– 1 motor

– 1 optical encoder (sensor)

• Perform trade study for adding secondary sensors, motors

• Use reliability @ 1000 hours of operation as input dataoperation as input data– Motor: R(1000) = 0.969– Sensor: R(1000) = 0.814


Reliability of UGV Arm – Original Design

Fault Tree for Original Design

j jointd ff tee end effector

m motors sensor


Reliability for One Design Configuration with Redundant ComponentsRedundant Components

Fault Tree with Redundant ComponentsRedundant Components


Reliability vs. Cost Trade Study• Redundant components

provide higher system p g yreliability, but...– At what cost?– Is it worth it?

• Use FMS Tool to– Perform trade study– Find Pareto frontier

Fault Tree Model in FMS Tool

34

au t ee ode S oo


FMS Tool Results: Original Designg g

$995$995Simulation results yield system reliabilityreliabilityR=0.75 @ t=1000 hours

Close to theoretical value

System reliability and cost

of 0.741

35

y y@ 1000 hours of operation


Component Alternatives

Component Input Data

Negative numbers: components that do not have alternatives

36

Negative numbers: components that do not have alternatives


FMS ToolMinCostFMS Tool

Results: Trade Study

MaxR

Knee inTrade Study Knee inthe

curve

Reliability-cost Pareto set @Pareto set @ 1000 hours of operation


Recent and Ongoing Work• Adding system and fleet attributes

– Weight, fuel efficiency/costil bili– Availability

• Enhancing underlying modelsDifferent types of failure modes more probability distributions– Different types of failure modes, more probability distributions

– Scheduled maintenance, preventive maintenance

• Implementing state-of-the-art multi-objective optimizerp g j p– Non-dominated sorting genetic algorithm II (NGSA-II)– Multiple objectives beyond cost and reliability

• Converting software framework from Excel to MATLAB– Improve computational performance– Leverage MATLAB toolkits

38

Leverage MATLAB toolkits– Foster collaborative development (TARDEC, OU, SMART Students)


Summary: FMS ToolSummary: FMS Tool

• Fleet Maintenance Simulation (FMS) Tool has been developed ( ) pto perform trade/sensitivity/optimization studies

• FMS Tool applied to example UGV trade study for validation and demonstration purposes

• Software is under active development by TARDEC and OU to enhance capabilities and improve efficiency


Q & AQ & A


sssw3imbrs wd 43 fleet maintenance simulation for unmanned ... · pdf filefleet maintenance...

Documents