warranty
TRANSCRIPT
Warranty and Maintenance Decision Making for Gas Turbines
■Susan Y. Chao*, Zu-Hsu Lee†, and Alice M. Agogino‡
■University of California, BerkeleyBerkeley, CA 94720*[email protected]†[email protected]‡[email protected]
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/µ) * 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) *Σnj*
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.