Warranty and Maintenance Decision Making for Gas Turbines

Susan Y. Chao*, Zu-Hsu Lee†, and Alice M. Agogino‡

University of California, Berkeley

Berkeley, CA 94720

*chao@garcia.me.berkeley.edu†leez@ieor.berkeley.edu‡aagogino@euler.me.berkeley.edu

Acknowledgments Many thanks to General Electric

Corporate Research and Development and the University of California MICRO Program.

Special thanks to Louis Schick and Mahesh Morjaria of General Electric Corporate Research and Development for their guidance and intellectual input.

Gas Turbine Basics Complex system: large number of

parts subject to performance degradation, malfunction, or failure.

Turbine, combustion system, hot-gas path equipment, control devices, fuel metering, etc.

Condition information available from operators, sensors, inspections.

Gas Turbine Maintenance Enormous number of candidates for

maintenance, so ideally focus on most cost-effective items.

Maintenance planning (optimized, heuristic, ad hoc) determines: Inspection activities Maintenance activities Intervals between inspection and

maintenance activities.

On-line Statistical AnalysisExpert Subjective ProbabilitiesOn-line Machine LearningKnowledge ExtractionDiagnosis

Maintenance Planning

Sensor Fusion

Sensor Validation

MaintenancePlanning

Repair or Replace PartsOrder Inspections

Sensor ReadingsInspection Results

Gas Turbine Warranty Warranty/service contract for gas

turbine would transfer all necessary maintenance and repair responsibilities to the manufacturer for the life of the warranty.

Fixed warranty period determined by manufacturer.

Gas turbine customer pays fixed price for warranty.

4 Key Issues Types of maintenance and sensing

activities (current focus) Price of a gas turbine and service

contract Length of service contract period Number of gas turbines for consumer

Consumer Profit MaximizationHow many gas turbines should the

customer purchase, if any?

Maximize Rj (nj,w)–(p1 + p2) *nj* -

n (w/* shutdown loss

Producer Profit MaximizationHow much should the manufacturer

charge for a gas turbine engine and warranty?

How long should the warranty period be?

Maximize (p1 + p2 - m) *nj*

p1,p2,w

Subject To m=F0 (xt, s, ts) .

Optimal MaintenanceWhat types of maintenance and sensing

activities should the manufacturer pursue? How often?

Derive an optimal maintenance policy via stochastic dynamic programming to minimize maintenance costs, given a fixed warranty period.

Solve for F0 (xt, s, ts).

Gas Turbine Water Wash Maintenance Focus on a specific area of gas turbine

maintenance: compressor water washing.

Compressor degradation results from contaminants (moisture, oil, dirt, etc.), erosion, and blade damage.

Maintenance activities scheduled to minimize expected maintenance cost while incurring minimum profit loss caused by efficiency degradation.

Compressor Efficiency Motivation: if fuel is 3¢/KWHr, then 1%

loss of efficiency on a 100MW turbine = $30/hr or $263K/yr.

On-line washing with or without detergents (previously nutshells) relatively inexpensive; can improve efficiency ~1%.

Off-line washing more expensive, time consuming; can improve efficiency ~2-3%.

Decision Alternatives

Blade replacement

Major scouring

Do nothing

On-line wash

Do nothing

Off-line wash

Major inspection

Influence Diagram

CurrentEngineState, s´

AverageEfficiency,

xt

Decision,d

TotalMaintenance

Cost, v

LastMeasured

EngineState, s

Stochastic Dynamic Programming Computes minimum expected costs

backwards, period by period. Final solution gives expected

minimum maintenance cost, which can be used to determine appropriate warranty price.

Given engine status information for any period, model chooses optimal decision for that period.

Stochastic Dynamic Programming Assumptions Problem divided into periods, each ending

with a decision. Finite number of possible states associated

with each period. Decision and engine state for any period

determine likelihood of transition to next state.

Given current state, optimal decision for subsequent states does not depend on previous decisions or states.

Other Assumptions Compressor working performance is main

determinant of engine efficiency level. Working efficiency and engine state can

be represented as discrete variables. Current efficiency can be derived from

temperature and pressure statistics. Intra-period efficiency transition

probability depends on maintenance decision and engine state.

Dynamic Program Constraints

c c d P x x s d

P s s t t loss x F x s t

t txs

s t t t s

t1 1 1 1

1 1 1

1

( ) , , )

, ( ) ( , , )

c c d P x x s d

P s s t t loss x F x s t

t txs

s t t t s

t2 2 1 2

1 1 1

1

( ) , , )

, ( ) ( , , )

Dynamic Program Constraints

c c d P s s t t

c dP x x s d

loss x F x s t

ss

d d d d

t t

t t t sx t

3 3

1

1 1 14 5 6 1

( ) ,

min ( ), , )

( ) ( , , ), ,

cP x x s d P s s t t

loss x F x s t

t t s

t t t sxs t

7

1 7

1 1 11

, , ) ,

( ) ( , , )

Dynamic Program Constraints

c c d P s s t t

c dP x x s d

loss x F x s t

ss

d d d d

t t

t t t sx t

3 3

1

1 1 14 5 6 1

( ) ,

min ( ), , )

( ) ( , , ), ,

Ft (xt, s, ts) = min [ c1, c2, c3, c7 ]

cP x x s d P s s t t

loss x F x s t

t t s

t t t sxs t

7

1 7

1 1 11

, , ) ,

( ) ( , , )

Dynamic Program SimulationUser/Other Inputs

Service Contract period Cost of each decision Losses incurred at each

efficiency level Transition probabilities

for state and efficiency changes

Program Outputs

Expected minimum maintenance cost

Optimal action for any period

Turbine Performance Degradation Curves*

*Source: GE

Turbine Performance Degradation Curves*

*Source: GE

Online Water Wash Effects*

*Source: GE

indep1 etac l4ww shown

y = -0.0132x + 562.92

86

86.5

87

87.5

88

88.5

89

89.5

90

8/31/98 0:00 9/5/98 0:00 9/10/98 0:00 9/15/98 0:00 9/20/98 0:000.1

Online Water Wash Effects*

*Source: GE

indep1 flow l4ww shown

800

820

840

860

880

900

920

940

8/31/98 0:00 9/5/98 0:00 9/10/98 0:00 9/15/98 0:00 9/20/98 0:00 9/25/98 0:00

0.1

Efficiency Transition Probabilities

X(t+1)=

1 2 3 4

X(t)=1 >0;

1,2,4,5,6,7

>0;6,7

0 0

2 >0;1,2,4,5

>0;1,2,4,6,7

>0;6,7

0

3 >0;4,5

>0;1,2,4

>0;1,2,4,6,7

>0;6,7

4 >0;4,5

>0;4

>0;1,2,4

>0;1,2,4,6,7

Conclusions Analyzed maintenance and warranty

decision making for gas turbines used in power plants.

Described and modeled economic issues related to warranty.

Developed a dynamic programming approach to optimize maintenance activities and warranty period length suited in particular to compressor maintenance.

Future Research Sensitivity analysis of all user-input

costs . Sensitivity analysis of the efficiency

and state transition probabilities.