Warranty and Maintenance Decision Making for Gas Turbines

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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_at_garcia.me.berkeley.edu leez_at_ieor.berkeley.
  edu aagogino_at_euler.me.berkeley.edu

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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.

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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.

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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.

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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
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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.

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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

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Consumer Profit Maximization

• How many gas turbines should the customer
  purchase, if any?
• Maximize Rj (nj,w)(p1 p2) nj - n (w/m)
  shutdown loss

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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 - m) Snj
• p1,p2,w
• Subject To mF0 (xt, s, ts) .

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Optimal Maintenance

• What 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).

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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.

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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.

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Decision Alternatives
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Influence Diagram
Current Engine State, s
Total Maintenance Cost, v
Decision, d

Average Efficiency, xt
Last Measured Engine State, s
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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.

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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.

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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.

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Dynamic Program Constraints
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Dynamic Program Constraints
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Dynamic Program Constraints

• Ft (xt, s, ts) min c1, c2, c3, c7

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Dynamic Program Simulation

• User/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

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Turbine Performance Degradation Curves
Source GE
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Turbine Performance Degradation Curves
Source GE
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Online Water Wash Effects
Source GE
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Online Water Wash Effects
Source GE
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Efficiency Transition Probabilities
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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.

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Future Research

• Sensitivity analysis of all user-input costs .
• Sensitivity analysis of the efficiency and state
  transition probabilities.