a bayesian approach to estimate failure probability...
TRANSCRIPT
A BAYESIAN APPROACH TO ESTIMATE FAILURE PROBABILITY OF NUCLEAR TURBINE BLADES DUE TO
SEVERAL DEGRADATION MECHANISMS
David Quintanar-Gago, Pamela F. Nelson
Universidad Nacional Autónoma de México, School of Engineering, Department of Energy Systems
Content
• Bayesian networks for diagnosing nuclear turbines • Wear mechanisms • Failure modes
• Optimize maintenance strategies • Future work
• Ageing management • Non-constant failure rates
Wear mechanisms effect = f(stresses, environmental conditions)
Stresses and environmental conditions = f(turbine row)
Conditional probability of having certain wear mechanisms given a specific row
AND
Wear mechanisms = f(presence of other wear mechanisms)
Conditional probability that relates to presence of a wear mechanism given another is present
Conditional relationships among mechanisms, effects and blade location and part
Bayesian net: models relationships of conditional dependent aleatory variables
mech1
mech2
mech3 Turbine spatial variable
Why Bayesian nets?
Reliability DB
There are failure events recorded over the years
(FM, fail location and causes)
Frequency can be calculated as
dependent probabilities
Times that mech1 have been observed given mech2 was too. Times that mech1 have been observed given mech2 wasn’t. Times both previous examples produced in row L-0, or L-1… Kind of failure mode produced having mech1 confirmed, or mech2….
Root cause report
Ideal source of data for conditional tables
Once data is entered into the network tables: - Determine probability of mechanisms to rows, by introducing correct evidence. - Determine typical mechanism combinations that affect a specific row, or blade part. - Simulate cases with available evidence to infer how and where a failure is more
probable - Valuable information to maintenance prioritization.
Why Bayesian nets?
Wear mechanisms in nuclear turbines
Droplet
Resulting roughness decreases stage efficiency.
Excessive degradation can cause weight and shape variations leading to resonance at operating conditions, destroying the piece in few cycles
Blade erosion in convex zone of the airfoil due to a lower tangential velocity of drops compared to the blade
Resulting roughness increases stress intensity factor (K)
Fatigue
Fretting Corrosion Fatigue CF
Pitting
Stress Corrosion Cracking SCC
Wear mechanisms in nuclear turbines (cont.)
Blade Failure Modes Corrosion Failure Mode: from pits developed by chemical action in surfaces.
Engineering judgement could determine that blade is not in conditions to remain in
operation and actions should be performed even if indication of a crack is not found.
Blade could still operate if there is no failure mode manifestation or safety risk.
Erosion Failure Mode: from droplets. Depends on engineering judgement. If FM
is not declared, blade continues operation and could contribute to Fatigue due to stress
concentrations
Cracking Failure Mode. A cracking process is detected with potential safety
implications. A correction is needed. Fragmentation of the piece is also considered in
this FM.
Nuclear vs. fossil turbine row failure distribution
Taken from: EPRI. Survey of Steam Turbine Blade Failures. March 1985. Technical report. CS-3891
Note more complex shape in nuclear distribution
Data Mechanism nodes: Tables were filled simulating cases of failures associated with certain combination of root causes.
Row distribution node from EPRI: Survey of Steam Turbine Blade Failures. march 1985. CS-3891
• Economic values from interviews • Real data can be introduced or even a specialized network could be added to
perform complex economic calculations.
A B C
A: No evidence entered.
B: Forced failure due to airfoil cracks in L-0.
C: Same case but in L-3.
Bayesian Model work flow logic
BASE NET Maintenance module
- Evidence entered for a case
- Some conclusions can be made
Failure distribution and/or part
that had failed
Choose between several actions to be performed over the rows.
Row failure distribution
modified due to maintenance
actions
New levels of wear given new row
distribution
Compare reliability and economic indicators to choose best strategy Evaluate
another strategy
Base Net
Maintenance decision
Distribution states
Maint. Decision nodes
Costs
After Maintenance State
Maintenance actions Repetition Rate (%)
Replace Blades w/ original design or… 40 Machine cracks 77 Weld tie wires 61 Install baffles 38 Replace w/new design or… 38 Install shroud 40 Install tie wire 42 Change grouping 54 Change root 33 Change cover 50
Within a decade
Taken from EPRI Report: Survey of Steam Turbine Blade Failures (CS-3891)
Maintenance actions
M. Cracks L-0
M. Cracks L-1
M. Cracks L-2
M. Cracks L-3
M. Cracks L-4
M. Cracks L-5
Rep. New Design L-0
Rep. Same Des L-1
Rep. Same Des L-2
M. Cracks L-3
Rep. Same Des L-4
M. Cracks L-5
Row_distribution1 Row_distribution2 Row_distribution3 Row_distribution4 Row_distribution5 Row_distribution6
Strategy A
Strategy B
Initial Distribution (from base net) Economic/probability utilities
Final Distribution
B
A
Compare two maintenance strategies
Conclusions
• The model considers a probabilistic relationship between typical wear mechanisms in nuclear steam turbines by blade row and part.
• This is a way to model the turbine, that is usually a super component, for risk analysis.
• A bayesian network approach was choosen as the method to model the
conditional dependence behavior of the mechanisms.
• The most probable causes of failure and its location, based on partial information or evidence available, can be determined.
• The Network was designed to work with reliability data bases and root cause
reports. Statistical failure causes and location are directly used to fill conditional tables
• A task and blade row dependent maintenance model was built as first
approach to create an optimization methodology. • Goal: to evaluate maintenance strategy feasibility by generating the lowest
row dependent economic risk distribution
Maintenance actions
Reliability Levels after maint.
Operation strategy expected
for a period T
Wear level after period T
Again, maintenance simulation to
estimate expected costs
Consider other maintenance efficiency indicators
Future work
Operation strategy in future will also be included
Individual history
Collective history (from population)
Better wear estimation= f(t) at
failure time
Include plant specific history to be combined with the collective history