a bayesian approach to estimate failure probability...

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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 [email protected] [email protected]

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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

[email protected] [email protected]

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

Base Net

Dependency of row and blade part (SPATIAL DEPENDENCY)

Wear mechanisms, FMs and location

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