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Risk-based inspection and maintenance systems for steam turbines
Kazunari Fujiyamaa,*, Satoshi Nagaia, Yasunari Akikunib, Toshihiro Fujiwarab,Kenichiro Furuyab, Shigeru Matsumotob, Kentaro Takagib, Taro Kawabatac
aPower and Industrial Systems R&D Center, Industrial and Power Systems and Services Company, Toshiba Corporation, Yokohama, JapanbThermal and Hydro Power Division, Industrial and Power Systems and Services Company, Toshiba Corporation, Tokyo/Yokohama, Japan
cKeihin Product Operations, Industrial and Power Systems and Services Company, Toshiba Corporation, Yokohama, Japan
Abstract
The risk-based maintenance (RBM) system has been developed for steam turbine plants coupled with the quick inspection systems.
The RBM system utilizes the field failure and inspection database accumulated over 30 years. The failure modes are determined for each
component of steam turbines and the failure scenarios are described as event trees. The probability of failure is expressed in the form of
unreliability functions of operation hours or start-up cycles through the cumulative hazard function method. The posterior unreliability is
derived from the field data analysis according to the inspection information. Quick inspection can be conducted using air-cooled borescope
and heat resistant ultrasonic sensors even if the turbine is not cooled down sufficiently. Another inspection information comes from
degradation and damage measurement. The probabilistic life assessment using structural analysis and statistical material properties, the latter
is estimated from hardness measurement, replica observation and embrittlement measurement. The risk function is calculated as the sum
product of unreliability functions and expected monetary loss as the consequence of failure along event trees. The optimum maintenance plan
is determined among simulated scenarios described through component breakdown trees, life cycle event trees and risk functions.
Those methods are effective for total condition assessment and economical maintenance for operating plants.
q 2004 Elsevier Ltd. All rights reserved.
Keywords: Risk-based maintenance; Steam turbine; Database; Inspection; Event tree; Unreliability; Life cycle; Failure; Damage
1. Introduction
In Japan, the cost-effective maintenance of power plants
is required under the trend of more competitive power
generation market. Recently, risk-based maintenance
(RBM) has been introduced to fossil power plants for the
solution of utility’s requirements [1]. The object of
introducing RBM is to provide the rational basis of decision
making for life cycle maintenance planning. There are three
categories in the risk assessment, that is, qualitative,
semi-quantitative and quantitative approach. The semi-
quantitative approach is widely used for various plants,
being well known as the risk ranking matrix approach.
The quantitative approach has the advantage to solve the
optimization problem numerically, which enables to apply
various mathematical tools.
0308-0161/$ - see front matter q 2004 Elsevier Ltd. All rights reserved.
doi:10.1016/j.ijpvp.2004.07.005
* Corresponding author.
E-mail address: [email protected] (K. Fujiyama).
The RBM system has been developed to perform the
probabilistic risk analysis coupled with inspection systems.
The RBM system comprises life cycle event trees,
unreliability function analysis for field failure database
and risk-cost analysis for various maintenance scenarios.
Unreliability represents the failure probability here as the
function of operation hours and number of starts. The basis
of unreliability analysis is the statistical database of field
failure and damage related to the operation history.
For global application of the quantitative RBM method,
various ways are considered to compensate for the lack of
statistically meaningful number of data. The RBM system
can be customized to specific users by modifying the unified
master curve for unreliability analysis.
For customizing the system, the inspection information
of specific unit is useful for obtaining posterior unreliability
functions by modification of prior unreliability functions.
To reduce outage time, the air-cooled borescope and the
heat resistant ultrasonic sensors are provided for turbine
inspection before the turbine is not cooled down sufficiently.
International Journal of Pressure Vessels and Piping 81 (2004) 825–835
www.elsevier.com/locate/ijpvp
K. Fujiyama et al. / International Journal of Pressure Vessels and Piping 81 (2004) 825–835826
Life assessment information is also useful for obtaining
probability of creep and fatigue cracking life by stochastic
simulation analysis. With several examples, it is
demonstrated here how the quantitative RBM system
helps the decision making on life cycle plant maintenance
planning and economical management.
2. Basic flow of the risk-based inspection
and maintenance procedure
Fig. 1 shows the basic flow of the risk-based inspection
and maintenance procedure. Each step has the role as
follows:
(1) Component breakdown trees. A steam turbine unit
can be divided into many components. The level of
component breakdown might be decided according to the
level of maintenance action.
(2) Life cycle event trees. Though the event tree is usually
expressed as the sequence of success/fault nodes, it is used
here for describing the chain action of one component
failure leading to another component failure because steam
turbine components are closely assembled each other and
rotating in high speed.
(3) Master field database. The failure, inspection and
repair history database is established for various types units
over 30 years. The database is formed as a relational
database of unit, components, location, event and operation
history.
(4) Unreliability analysis. The failure probability is
defined here as the unreliability. The cumulative hazard
function method is used for deriving the unreliability
functions of operation hours or start-up cycles.
(5) Inspection and life assessment. The unit specific
unreliability functions are obtained as the posterior
unreliability functions after detected event from inspection.
For degradation and damage accumulation phenomena,
probabilistic life assessment is used for simulating future
unreliability.
(6) Risk assessment. The risk is defined here as the sum
product of the unreliability functions and the expected
Fig. 1. Basic flow of risk-based inspection and maintenance procedure.
monetary loss due to the accidents along the scenario of life
cycle event trees.
(7) Maintenance planning. Maintenance scenarios are
planned as the life cycle sequence of failure events and
related preventive actions. The risks and preventive costs
are calculated over the total life cycle for selecting the
optimum maintenance scenario.
3. Damage and failure modes of steam turbines
Fig. 2 shows a component breakdown tree of a steam
turbine unit. Those components show various types of
degradation, damage and failure phenomena according to
temperature, stress, environment and materials.
Fig. 3 shows degradation, damage and failure modes of
steam turbine major components [2,6]. For high- and
intermediate-pressure (HIP) portions, the typical events
are creep induced deformation, thermomechanical fatigue
cracking and steam flow induced erosion. For low pressure
(LP) portion, the typical events are environmental
assisted fatigue cracking and steam flow induced
erosion. The features of events are described as follows
for major components.
(1)
HIP rotor. High centrifugal stress and high temperaturecause creep deformation such as rotor bowing. The rotor
bowing causes vibration and rubbing with bearings and
casings. Creep damage accumulation causes creep void
Fig. 2. Component breakdown tree.
Fig. 3. Degradation, damage and failure modes of steam turbine major
components.
K. Fujiyama et al. / International Journal of Pressure Vessels and Piping 81 (2004) 825–835 827
formation and cracking at highly stressed portions such
as bore and wheel hooks. Thermomechanical fatigue
damage accumulation causes cracking at the wheel
corner portion.
(2)
LP rotor. High centrifugal stress, high vibratory stressand corrosion environment causes corrosion fatigue at
the wheel section.
(3)
HIP moving blade. High centrifugal stress and hightemperature causes creep deformation such as lifting.
Fig. 4. An example of event trees fo
The lifting causes rubbing with casings or nozzles and
finally cracking. Creep damage accumulation causes
creep void formation and cracking at the highly stressed
portion such as dovetail hooks. Oxide scale brought by
steam flow causes erosion. Vibratory stress causes high
cycle fatigue cracking and fretting fatigue at the contact
portion.
(4)
LP moving blade. High centrifugal stress, high vibratorystress and corrosion environment causes corrosion
fatigue cracking. Droplet brought by steam flow causes
erosion.
(5)
HIP nozzle. Oxide scale brought by steam flow causeerosion. Pressure difference at each stage and high
temperature cause downstream deflection of nozzle
diaphragm.
(6)
HIP casing. High pressure stress and high temperaturecause creep deformation. The creep deformation causes
assembling mismatch and steam leak due to stress
relaxation at the flange and the tightening bolt. Creep
and thermomechanical fatigue damage accumulation
causes cracking at the nozzle fit radius and other stress/
strain concentration portions.
(7)
Valve. Creep and thermomechanical damage is the sameas casings. Oxide scale brought by steam flow causes
erosion at the shield plates. Oxidation at the shaft and
valve body contact portion causes valve shaft sticking.
(8)
Pipe. Creep damage accumulation causes creep voidformation and cracking preferably at the weld portion.
Water induction causes thermomechanical or thermal
shock cracking.
Fig. 4 shows the event trees coupled with component
breakdown trees based on the above information. This is the
basis of the following analysis.
r steam turbine unit.
Fig. 5. Cumulative hazard functions for turbine rotor bowing fitted
individually.
Fig. 7. Unified cumulative function for rotor bowing.
K. Fujiyama et al. / International Journal of Pressure Vessels and Piping 81 (2004) 825–835828
4. Unreliability analysis
4.1. Master field database
The master field failure database has the data rows of
plant name, component name, occurrence date, operation
hours, start-up cycles, event contents, event cause and repair
actions. Every event is related to operation hours and start-
up cycles until the events occur. For the events detected at
the scheduled inspection, the estimated hours and cycles are
adopted using reference operation history tables.
4.2. Field data analysis method: Cumulative hazard
function method [3]
The unreliability function is derived through cumulative
hazard function method for the field failure database. The
event data are stacked in the order of time or cycles for the
same mode of failure and the same type of turbines.
Estimated cumulative hazard function is expressed as
follows
HðtkÞ ¼Xk
i¼1
1
n þ 1 K i(1)
Fig. 6. Unreliability functions for turbine rotor bowing fitted individually.
where, tk is event occurrence time at the k-th event, n is total
number of samples including non-failure data.
Regression of cumulative hazard function H(t) is
conducted using the two-parameter Weibull plot expressed
in the following equations.
HðtÞ Z ðt=hÞm (2)
ln HðtÞ Z m ln t Km ln h (2 0 )
where h, m are regression constants.
Unreliability function F(t) is calculated as follows
FðtÞ Z 1 KRðtÞ Z 1 KexpfKHðtÞg (3)
where R(t) is reliability function.
Eqs. (1)–(3) are also applied for cycle N dependent
events using N instead of t. To overcome the lack of
sufficient numbers of data, two approaches are adopted.
One is the unified unreliability function approach and the
other is the empirical unreliability function approach. Those
two approaches are described below.
4.3. Unified unreliability function approach:
example of rotor bowing
If the dominant parameter of an event is known, unified
master curve can be obtained by normalization. Here, rotor
Fig. 8. Unified unreliability function for rotor bowing.
Fig. 11. Machine output class dependence for cycles at 50% unreliability
for nozzle erosion events.Fig. 9. Hours based cumulative hazard functions.
K. Fujiyama et al. / International Journal of Pressure Vessels and Piping 81 (2004) 825–835 829
bowing phenomena is taken as an example though this event
is prevented now due to the improvement of manufacturing
and design.
Figs. 5 and 6 show the cumulative hazard functions and
unreliability functions against operation hours for two types
(A-type and B-type) rotors. The type-B rotor regression is
conducted with only two events. Here, the hazard function
fitting against time (operation hours) is better than that
against number of starts as reported elsewhere [5]. The time
dependence comes from that the rotor bowing is one of the
creep deformation phenomena. It depends on stress,
temperature and material conditions. As the rotor bowing is
one of the creep phenomena, the time is normalized by
creep rupture time, that is, t/tr. Figs. 7 and 8 show the good
unique correlation of cumulative hazard functions and t/tr for
the two types of turbines, expressed by the following
equation.
HðtÞ Zt
trðs; T ; lÞ
� �=hc0
� �mc0
(4)
where hc0, and mc0 are regression constants, s is stress, T is
temperature and l is material strength parameter such as
hardness or tensile strength, etc.
Fig. 10. Cycle based cumulative hazard functions.
Eq. (4) indicates that the unreliability function of the
specific unit can be estimated only by knowing design
conditions or service conditions and material properties.
4.4. Empirical approach: example of nozzle erosion
In the case of nozzle erosion, It is difficult to find the
explicit parameters dominating erosion process. Figs. 9
and 10 show total regression results of cumulative hazard
functions against operation hours and number of starts,
respectively, expressed by the following equations.
HðtÞ Z ðt=ht0Þmt0 (5)
HðNÞ Z ðN=hN0ÞmN0 (6)
where ht0, hN0 and mt0, mN0 are regression constants
Eqs. (5) and (6) fit the whole data well enough but still
indicate discrepancy between the turbine output types at
some extent. Here, we introduce a modifying approach
using hours or cycles at 50% unreliability based on the
unified unreliability function. We show the modification
results for cycle dependent unreliability functions or
cumulative hazard functions.
Fig. 12. Empirical cumulative hazard functions of erosion for various
nozzles.
Fig. 13. Empirical unreliability functions of erosion for various nozzles.
K. Fujiyama et al. / International Journal of Pressure Vessels and Piping 81 (2004) 825–835830
Fig. 11 shows the relationship between number of starts
at 50% unreliability N50 and output class index I that is
proportional to output capacity. N50 shows almost
monotonic decreasing relationship with I, expressed as
follows
N50 Z aIb (7)
where a and b are regression constants.
Fig. 15. Heat resistant UT system (left: application
Fig. 14. Air-cooled borescope v
Modified cumulative function is obtained by using the
modifying coefficient N50/N50,0, where N50,0 is number of
starts at 50% unreliability for the unified curve of Eq. (6).
HðNÞ Z NN50
N50;0
� �=hN0
� �mN0
(8)
Figs. 12 and 13 show the estimation results if the
modifying coefficient approach. The estimation curves fits
actual data reasonably even for the insufficient data.
5. Inspection system and unreliability function
5.1. Quick visual and ultrasonic inspection system
The visual and ultrasonic inspection gives useful
information for adjusting the prior unreliability functions.
To reduce the outage time for inspection, quick inspection
systems have been developed.
Fig. 14 shows an air-cooled borescope inspection system
for nozzle erosion/failure detection. Magnet wheels
attached to the inspection head move along the nozzle
front, and remote observation by CCD camera is easily done
to components; right: the detail of carriage).
isual inspection system.
Fig. 18. Life assessment procedures based on an
Fig. 16. Prior and posterior unreliability functions for moving blade erosion.
Fig. 17. Life assessment system coupled with
K. Fujiyama et al. / International Journal of Pressure Vessels and Piping 81 (2004) 825–835 831
at temperature below 300 8C after machine shutdown.
This may require about a couple of days.
Fig. 15 shows a heat-resistant UT system for casing or
valve defect detection. The moving head contains a
couple of heat resistant UT sensors with the supply
system of high temperature coupling medium to attach
the system to a hot wall of about 300 8C. This system is
used for detecting casing or valve inner defect and bolt
cracking.
Fig. 16 shows the posterior unreliability functions of
moving blade erosion calculated by the prior unreliability
function of nozzle erosion and the prior unreliability of
moving blade erosion. Cycles to erosion event of nozzle is
subtracted from cycles to erosion event of moving blade.
alysis and non-destructive measurement.
non-destructive measurement system.
K. Fujiyama et al. / International Journal of Pressure Vessels and Piping 81 (2004) 825–835832
The cycle difference values and cumulative hazard
function values are coupled and fitted again by Eq. (2).
The obtained posterior unreliability function shows
higher unreliability for small cycles indicating
immediate occurrence of moving blade erosion after
nozzle erosion.
Fig. 20. Cumulative probability of creep rupture life ratio derived from the
unified master curve.
5.2. Degradation/damage measurement and life
assessment system [4,5]
Fig. 17 shows a degradation/damage measurement
and life diagnosis system schematically. Degradation
and damage are measured by the hardness
measurement system, replica observation technique and
embrittlement measurement system. Life assessment
system is programmed to calculate creep and fatigue life
calculation using evaluation master curves and machine
information.
Fig. 18 shows the deterministic life assessment pro-
cedures [7]. Creep and fatigue damage is calculated by
cumulative damage rule using the life assessment master
curves. The feature of the procedure is that life assessment
master curves are derived from material condition data
measured by the hardness measurement system and the
embrittlement measurement system. Creep and fatigue life
evaluation curves are derived from hardness values
measured for post-serviced components. Crack growth
rate and fracture toughness are derived from FATT value
converted from electrochemical polarization parameters
using experimental master curves.
Probabilistic life assessment requires statistical material
properties [5,8]. Fig. 19 shows material creep rupture data
including unused, laboratory aged and service used plotted
Fig. 19. Unified plot and regression of creep rupture for unused, aged and
serviced materials.
using stress/hardness ratio and Larson–Miller parameter.
Fig. 20 shows the unified statistical distribution of
experimental/estimated creep life ratio based on the
whole creep rupture data and the master regression
curve. It can be used as the simulated unreliability
function of creep life of actual component. When
narrower distribution is required, the data for statistical
analysis should be selected carefully according to the
specification of manufacturer.
Fig. 21. An example for the optimization of maintenance interval for rotor
bowing.
Fig. 22. PC based RBM system window view of risk assessment of rotor bowing.
K. Fujiyama et al. / International Journal of Pressure Vessels and Piping 81 (2004) 825–835 833
6. Risk assessment and maintenance planning [5,6]
Risk is defined here as the sum product of unreliability
functions and expected monetary loss for every event in
the event trees. The risk functions are specified by plant
information and inspection information. Monetary loss is
calculated for all expected items related to unscheduled
outage and recovery action. Two ways of optimizing
maintenance planning are presented below, that is, the
optimization of maintenance intervals and the optimization
of life cycle maintenance scenarios.
Fig. 23. Event trees, unreliability functions and risk functions for nozzle
erosion.
6.1. Maintenance interval optimization: example
of rotor bowing
Fig. 21 shows an example of the optimization of
maintenance intervals for rotor bowing. The event tree is
restricted to include typical three events for simplification.
Those three events: (a) rotor bowing; (b) narrow axial
clearance; (c) vibration, have different risk functions. The
total risk function is determined by the sum of the three risk
functions. The maintenance cost index is defined as the total
cost of preventive maintenance action averaged per year for
the subscribed events. The total risk is increasing function of
operation hours and the cost index is proportional to
Fig. 24. The optimization of life cycle maintenance scenario for nozzle erosion.
Fig. 25. Application concept for risk-based engineering.
K. Fujiyama et al. / International Journal of Pressure Vessels and Piping 81 (2004) 825–835834
the reciprocal of maintenance hours-based interval.
The total cost curve is obtained by the sum of risk and
maintenance cost showing a concave curve. If the income by
operation is proportional to operation hours, the shaded area
is recommended to decide the optimum maintenance
intervals. The rotor bowing events are decreasing currently
due to the improvement of manufacturing process, design
and operation.
Fig. 22 shows an example of the personal computer
based RBM system window view of risk assessment of
rotor bowing.
6.2. Maintenance scenario optimization:
example of nozzle erosion
Fig. 23 shows the event tree, the unreliability functions
and risk functions of nozzle erosion event. Nozzle erosion
event [A] shows relatively high unreliability but low cost for
recovery action. The risk function is relatively low. For
other events [B], [C], [D], lower unreliability and high
recovery cost result in the same level risk as event [A].
The total risk is increasing function of operation period.
Here, operation period is taken as operation hours but
number of starts also applicable.
Fig. 24 shows scenario case study for nozzle erosion
events and maintenance action. The scenario 1 comprises
predetermined replace period without preventive repair
action during the service period. It requires no maintenance
cost but runs high risk. The scenario 2 comprises
predetermined replace period with the scheduled preventive
repair actions during the service period. As the repair cost is
relatively low in this case, the sum of risk and cumulative
preventive costs remains low level. The scenario 3
comprises early replacement of erosion resistant upgraded
nozzle and long term use of the upgraded one. It arises
higher cost in the early period but relatively lower
increase in the total cost for long period. The comparison
of total cost gives the optimum maintenance scenario for the
same period.
K. Fujiyama et al. / International Journal of Pressure Vessels and Piping 81 (2004) 825–835 835
7. Concluding remarks
The quantitative RBM method for steam turbines was
presented. Statistical formulation of failure probability as
the function of time or cycles were very effective way to
estimate the risk for various modes of failure and the chain
of successive failure. The RBM system has various features
as follows
(1)
Describe plant maintenance scenario by componentbreakdown trees and life cycle event trees.
(2)
Assign default unreliability function to every event bystatistical analysis of master filed failure database.
(3)
Customize the unreliability functions can be modifiedreflecting the inspection information and probabilistic
life assessment.
(4)
Optimize maintenance intervals using risk functions,cost functions and income functions.
(5)
Optimize maintenance scenario using life cycle eventtrees and total cost analysis.
Those features are useful for wider application,
not restricted to the steam turbine plant. The application
of risk-based engineering is shown in Fig. 25. The
quantitative method provides feedback and optimization
of design, manufacturing and operation parameters. Those
approaches will lead more economical and reliable plant
design, manufacturing and management of plants.
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