Transcript Warranty and Maintenance Decision Making for Gas Turbines

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

*[email protected]
†[email protected]
‡[email protected]
Acknowledgments
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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
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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
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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.
Maintenance Planning
On-line Statistical Analysis
Expert Subjective Probabilities
On-line Machine Learning
Knowledge Extraction
Diagnosis
Sensor Fusion
Maintenance
Planning
Sensor Validation
Sensor Readings
Inspection Results
Repair or Replace Parts
Order Inspections
Gas Turbine
Warranty
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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
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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
Maximization
How many gas turbines should the
customer purchase, if any?
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Maximize Rj (nj,w)–(p1 + p2) *nj* n
(w/m) * shutdown loss
Producer Profit
Maximization
How much should the manufacturer
charge for a gas turbine engine and
warranty?
How long should the warranty period be?

Maximize
p1,p2,w
Subject To
(p1 + p2 - m) *Snj*
m=F0 (xt, s, ts) .
Optimal Maintenance
What types of maintenance and sensing
activities should the manufacturer
pursue? How often?
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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
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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
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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
On-line wash
Off-line wash
Major scouring
Major inspection
Blade replacement
Do nothing
Do nothing
Influence Diagram
Total
Maintenance
Cost, v
Current
Engine
State, s´
Decision,
d
Last
Measured
Engine
State, s
Average
Efficiency,
xt
Stochastic Dynamic
Programming
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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
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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
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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
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c1  c(d1 )    P xt 1 xt , s , d1 )

s x t 1
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 P s  s, t  t s  loss( xt 1 )  Ft 1 ( xt 1 , s, t s )


c2  c(d 2 )    P xt 1 xt , s , d 2 ) 

s x t 1

P s  s, t  t s  loss( xt 1 )  Ft 1 ( xt 1 , s, t s )

Dynamic Program
Constraints
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
c3  c(d 3 )   P s  s, t  t s 
s
min
d  d 4 ,d5 ,d 6
c( d )  
x t 1



P x t 1 x t , s  , d ) 
loss( x
t 1
)  Ft 1 ( x t 1 , s , t s )
 
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 P x t 1 x t , s , d 7 )  P s  s, t  t s 

c7    

s  xt  1 loss( x
t 1 )  Ft 1 ( x t 1 , s, t s )

Dynamic Program
Constraints


c3  c(d 3 )   P s  s, t  t s 
s
min
d  d 4 ,d5 ,d 6
c( d )  
x t 1



P x t 1 x t , s  , d ) 
loss( x
t 1
)  Ft 1 ( x t 1 , s , t s )
 

 P x t 1 x t , s , d 7 )  P s  s, t  t s 

c7    

s  xt  1 loss( x
t 1 )  Ft 1 ( x t 1 , s, t s )

Ft (xt, s, ts) = min [ c1, c2, c3, c7 ]
Dynamic Program
Simulation
User/Other Inputs
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Service Contract period
Cost of each decision
Losses incurred at each
efficiency level
Transition probabilities
for state and efficiency
changes
Program Outputs
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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*
indep1 etac l4ww shown
90
89.5
89
88.5
88
y = -0.0132x + 562.92
87.5
87
86.5
86
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
*Source: GE
Online Water Wash
Effects*
indep1 flow l4ww shown
940
920
900
880
860
840
820
800
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9/5/98 0:00
9/10/98 0:00
9/15/98 0:00
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0.1
9/25/98 0:00
*Source: GE
Efficiency Transition
Probabilities
X(t+1)
=
X(t)=
1
2
1
2
3
4
>0;
1,2,4,
5,6,7
>0;
1,2,4,5
>0;
6,7
0
0
>0;
6,7
0
>0;
1,2,4,
6,7
>0;
1,2,4
>0;
6,7
3
>0;
4,5
>0;
1,2,4,
6,7
>0;
1,2,4
4
>0;
4,5
>0;
4
>0;
1,2,4,
6,7
Conclusions
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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
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Sensitivity analysis of all user-input
costs .
Sensitivity analysis of the efficiency
and state transition probabilities.