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Availability Analysis of an Offshore Wind Turbine Subjected to Age-Based Preventive Maintenance by Petri Nets

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This paper analyses the production availability and the associated maintenance costs of an offshore wind turbine with a horizontal axis configuration using Petri Nets modelling with Monte Carlo Simulation. For this purpose, different features are implemented: the reliability and maintainability characteristics of the components; the logistics of the production and maintenance operations, including different types of vessels, the mobilization time, costs and weather window. The maintenance strategies consist of corrective maintenance and age-based imperfect preventive maintenance that depends on the components’ age and age reduction ratio. Thereby, to increase the operating income and to reduce the costs associated with the operation and maintenance activities, the optimal parameters of the age-based preventive maintenance are estimated. As a case study, a generic offshore wind turbine that operates at the Viana do Castelo wind farm in Portugal is adopted. The wind farm is located 18 km off the shore. The turbine’s total exploration life is 25 years.
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Citation: Lotovskyi, E.; Teixeira, A.P.;
Guedes Soares, C. Availability
Analysis of an Offshore Wind Turbine
Subjected to Age-Based Preventive
Maintenance by Petri Nets. J. Mar. Sci.
Eng. 2022,10, 1000. https://doi.org/
10.3390/jmse10071000
Academic Editors: Decheng Wan and
Giuseppe Roberto Tomasicchio
Received: 1 June 2022
Accepted: 19 July 2022
Published: 21 July 2022
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Journal of
Marine Science
and Engineering
Article
Availability Analysis of an Offshore Wind Turbine Subjected to
Age-Based Preventive Maintenance by Petri Nets
Eduard Lotovskyi , Angelo P. Teixeira and C. Guedes Soares *
Centre for Marine Technology and Ocean Engineering (CENTEC), Instituto Superior Técnico,
Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal;
eduard.lotovskyi@centec.tecnico.ulisboa.pt (E.L.); teixeira@centec.tecnico.ulisboa.pt (A.P.T.)
*Correspondence: c.guedes.soares@centec.tecnico.ulisboa.pt
Abstract:
This paper analyses the production availability and the associated maintenance costs
of an offshore wind turbine with a horizontal axis configuration using Petri Nets modelling with
Monte Carlo Simulation. For this purpose, different features are implemented: the reliability and
maintainability characteristics of the components; the logistics of the production and maintenance
operations, including different types of vessels, the mobilization time, costs and weather window.
The maintenance strategies consist of corrective maintenance and age-based imperfect preventive
maintenance that depends on the components’ age and age reduction ratio. Thereby, to increase the
operating income and to reduce the costs associated with the operation and maintenance activities,
the optimal parameters of the age-based preventive maintenance are estimated. As a case study, a
generic offshore wind turbine that operates at the Viana do Castelo wind farm in Portugal is adopted.
The wind farm is located 18 km off the shore. The turbine’s total exploration life is 25 years.
Keywords:
age-based preventive maintenance; Monte Carlo Simulation; offshore wind turbine; Petri
Nets; production availability assessment
1. Introduction
An offshore wind turbine (OWT) is a complex production system that includes various
engineering disciplines. Today, the total offshore wind farm capacity is approximately
18.9 GW and the installation rate has grown in recent years [
1
]. To improve the turbine’s
performance, an availability assessment is required, since it is able to evaluate the impact
of the equipment reliability and maintainability qualities on the system productivity.
The main challenges in the production optimization and in maintenance planning are
the realistic representation of the system’s behaviour main characteristics and the imple-
mentation of the interactions and dependencies among various components of the same
production system [
2
,
3
]. The classical reliability tools, starting from the identification of
failures with Failure Mode and Effect Analysis [
4
,
5
] and including the Reliability Block
Diagram, the Fault Tree and the Event Tree, [
6
,
7
] are not appropriate for analysing indus-
trial production systems, since they do not take into consideration the interdependencies
between the failures, which require other tools [
8
]. The dynamic interactions between oper-
ation and maintenance (O & M) decisions are relevant to be modelled, too [
9
]. The classical
reliability tools use the concept of Boolean algebra, in other words, they are convenient to
assess rare events with serious consequences, while the dependability analyses are able to
assess more likely events but with low effects on the operation [10].
Markov modelling is an effective tool for the mathematical representation of compo-
nent failure interactions and systems with independent failures [
11
13
]. Castanier et al. [
14
]
proposed a Markov decision process to determine the optimal maintenance and operation
policy of an offshore wind farm considering the stochastic wind and weather conditions.
Li et al. [
15
] assessed the reliability of OWT’s Gearbox and formulated the optimal main-
tenance policy by using Markov process. The main limitations of Markov modelling are:
J. Mar. Sci. Eng. 2022,10, 1000. https://doi.org/10.3390/jmse10071000 https://www.mdpi.com/journal/jmse
J. Mar. Sci. Eng. 2022,10, 1000 2 of 24
the state-explosion, because the increasing of the system automatically takes to the high
expansion of the number of states, and the assumption of fixed repair and failure rates, be-
cause this limits its application to simple systems with exponentially distributed events [
13
].
Thus, to represent the complexity of a production system considering all the interactions
and dependencies among the sub-systems, various authors use simulation techniques,
e.g., Bris [16] and Santos et al. [17].
Zio et al. [
18
] proposed a Monte Carlo Simulation (MCS) model for availability as-
sessment of a multi-state and multi-output offshore installation. It was shown that Monte
Carlo simulation can describe the uncertainty of various production system features, such
as: the degradation of the system components, the corrective and preventive maintenance
policies with pre-defined reparation priorities, and the limited number of repair teams.
MCS approach has proven to be an adequate tool to model continuously deteriorating
systems and to determine the “on-condition” maintenance plan that minimises the expected
total system cost over a specified mission period [
19
]. Condition-based maintenance is
becoming increasingly more relevant for this type of equipment [20,21].
Petri Nets (PN) is a tool that combines graphical and mathematical modelling capa-
bilities to simulate and analyse discrete event systems [
22
]. It was developed in 1962 by
Carl Adam Petri in his Ph.D. dissertation [
23
]. The main objective of his study is to find
an efficient way to model several competing or co-operating processes using graphical
representation. Recently, different techniques based on the Stochastic Petri Nets (SPN) have
been developed to improve the modelling of real and complex production systems [
24
,
25
].
Due to the complexity of the stochastic evolution of real systems that is not easily
captured by analytical models [
26
], their application to quantitative analyses of SPN is
rather limited [
27
]. To overcome this difficulty, techniques based on SPN combined with
Monte Carlo simulation have been proposed for modelling and analysing the complex
behaviour of industrial multi-unit systems regarding their reliability, availability and
production efficiency [9,22,24,28].
Santos et al. [
29
] modelled an offshore wind turbine located at the North Sea close to
the German shore combining SPN and MCS in order to assess the operation behaviour and
maintenance policies. The reliability characteristics of OWT’s components were based on
typical onshore reliability data provided by Ding and Tian [
30
]. Using SPN coupled with
MCS, Santos et al. [
31
] presented a parametric study on the availability, operation, and
maintenance costs of OWT.
The effect of age-based preventive maintenance on the availability and maintenance
costs of offshore wind turbines [
32
] and oil and gas production systems [
33
] has also been
assessed through SPN and Monte Carlo simulation. To build the failure models of the
offshore components, the onshore data were used considering an empirical approach based
on stress factors for mechanical systems.
An individual wind turbine is basically a multi-state system composed by several
major components in a series configuration (i.e., Gearbox, Generator, Pitch System, and
Rotor). Many industrial/real systems are characterised by series-parallel structures that
have been widely investigated [
34
]. A production system can be classified as either the
series-parallel (s-p) or the parallel-series (p-s) system [
35
]. In reliability and maintenance
assessments, various industrial and production systems belong to s-p class (e.g., water
supply systems and production lines in manufacturing factories) [
36
,
37
]. Besides, s-p class
is used to represent in simplified mode the main sub-components of the total engineering
system. Kawauchi and Rausand [
38
] and Bris et al. [
39
] provided this approach to estimate
a performance measure (i.e., “production regularity”) of the system, and to minimise the
preventive maintenance cost, respectively.
Usually, the availability assessment of an OWT production system adopts the simpli-
fied maintenance policy. In the implementation of reliability characteristics, it is common
to model only critical failures, considering every equipment as a binary system (i.e., either
as good as new or failed). Besides, in the assessment of age-based preventive maintenance,
the age-reduction ratio and the repair threshold parameters are typically fixed and not opti-
J. Mar. Sci. Eng. 2022,10, 1000 3 of 24
mised. In order to increase the OWT availability, Sobral et al. [
40
] proposed a methodology
to weight the influencing factors, considering operational and maintenance data, distance
to shore, water depth, site accessibility, meteorological and oceanographic factors. Kang
and Guedes Soares [
41
] introduced the conditional-based maintenance strategy based on
the support vector machine algorithm to optimise the maintenance arrangement of OWTs.
According to Nielsen and Sørensen [
42
], the operation and maintenance (O & M) costs
of offshore wind turbines are major contributors to the price of energy and can reach 30% of
it. Castro-Santos et al. [
43
] indicated that in terms of the life-cycle of OWT, the higher
cost corresponds to the exploitation period (i.e., insurance, administration, operation, and
maintenance), followed by the manufacturing and installation periods. The maintenance
and equipment replacements are dependent on the weather windows [
44
]; thus, the correct
planning of O & M activities in advance is important to minimise the expected outlay
over the turbine’s lifetime. Besides, the distance to shore must be also considered, since it
influences the investment, operation, and maintenance costs [
1
]. Castro-Santos et al. [
45
]
assessed the economic feasibility of offshore wind farms based on the meteorological data,
bathymetry, and distances between wind farm-shore, -shipyard, and -port.
To minimise the maintenance costs of offshore wind farms, Kang and Guedes Soares [
41
]
introduced an opportunistic strategy considering imperfect maintenance and the weather
window effects, using the rolling horizon approach. Castro-Santos et al. [
46
] compared
in economic terms the offshore wind farms with other alternatives to harness wind and
wave energies, such as floating offshore wave energy devices, floating offshore co-located
systems, and floating offshore hybrid systems.
The main objective of this paper is to develop a framework capable to assess the effect
of an age-based preventive maintenance on the availability of an OWT with horizontal
axis configuration by Petri Nets and Monte Carlo Simulation. For this purpose, two
variables are highlighted: the equipment age reduction ratio and the time threshold between
maintenance interventions based on the component’s age. The variation of both allows
to visualise the effects of maintenance policy on the production system availability and
associated costs. Besides, it provides the tool capable to identify adequate values that
provide a balance between production availability and costs. As a case study, a singular
OWT that operates at the Viana do Castelo wind farm in Portugal, located 18 km off the
shore, is used. The total exploration life of the turbine is 25 years. The present case study
adopts a parallel-series system (i.e., wind farm, thus, p-s) composed of p subsystems in
parallel (i.e., one wind turbine, thus, p = 1), each of them with s components in series (i.e.,
four degraded components, thus, s = 4). The modelled degraded components (i.e., Rotor,
Gearbox, Generator, and Pitch System) have the higher influence on the total system
availability [47].
Based on empirical offshore reliability data provided by Santos et al. [
32
], the equip-
ment definition is based on the reliability and maintainability stochastic characteristics that
follow non-exponential distributions. In addition to as good as new and failed conditions,
the degraded states of the components are also considered. Thereby, three types of failure
are modelled: incipient (i.e., the transition from as good as new state to degraded one),
degraded (i.e., the transition from degraded state to failed one), and critical failure (i.e., the
transition from as good as new state to failed one). The maintenance policy is divided
into three categories based on [
48
]. These categories differ on the weight of the repaired
equipment and, therefore, the involved logistics.
The Corrective Maintenance (CM) intervention encompasses the manufacture time of
a new component in a factory, the transportation time from the supplier to the port, and
the replacement of the damaged equipment by a new one on the OWT [
48
]. The Preventive
Maintenance (PM) strategy is age-based and imperfect. Each PM activity reduces the
equipment age by a ratio q, and it is performed when the component’s age reaches at least p
×
MTTF hours, where p is a threshold parameter and MTTF is a Mean Time to Failure of the
equipment [
30
,
32
]. Both, q and p are the main input variables that influence the O & M costs.
Thereby, the main PM parameters are optimised to obtain the lower costs and higher income
J. Mar. Sci. Eng. 2022,10, 1000 4 of 24
(i.e., the higher accounting rate of return). Both corrective and preventive maintenance
activities can be subjected to the time delay due to adverse weather conditions [
29
]. All
vessels required for maintenance activities are anchored in Portuguese harbours.
This paper mainly consists of two parts. The first one is Materials and Methods.
This section starts with a brief introduction of the main elements of Petri Nets. Next,
the case study description is presented, explaining in detail the production configuration
and component failure data of OWT’s equipment. A special attention is given to the
maintenance policy delineation with a clear description of CM and PM activities. The
implemented models of costs and weather window are formulated. The PN models of
equipment, total system switch, PM, seasons, and vessels are described step by step. At
the end of the section, the main cost models for economical assessment are presented. The
second part of the paper is Results. In this section the age-based PM parameters are derived
based on economical assessment, availability assessment, and sensitivity analysis. The
obtained results are discussed.
2. Materials and Methods
2.1. Petri Nets
Petri Nets (PN) is a generic name for modelling tools that can represent a complex
production system graphically. PN are divided into three categories [
49
]: the Elementary
Net Systems for small size system representation; the Place/Transition Systems for a more
compact representation of the Elementary Net Systems models; Predicate/Transition Nets
or Coloured Nets for even more compact representations of real applications using algebraic
and logical elements.
In Figure 1, the basic graphic elements of the Place/Transition System (i.e., place,
transition, token, and arc) are presented [50].
Figure 1. Basic elements of Petri Nets.
The place is represented by circles, it models the system’s states or resources. The
transition is represented by rectangles and it is used to model the events (e.g., system
failure) that influence the available resources. The token is a small black dot that represents
the resources. The token is always held inside the places. The arc is represented by directed
arrows that specifies the interconnection between the places and transitions, and indicates
which states are changed by a certain event.
The positioning of the token in the place, called by marking, defines a specific state
of the system. In the case of system state change, the transition moves the tokens to new
places or removes them in accordance with the arcs’ directions. This property enables the
simulation of dynamic systems [
34
]. The Place/Transition net is a bipartite graph, thus,
it is only possible to connect Place-Transition or Transition-Place, meaning that neither
Place-Place nor Transition-Transition are acceptable connections [51].
Another frequently used tool is the Generalized Stochastic Petri Nets (GSPN) with
predicates. This tool has more computing power than conventional Petri Nets and allows
to perform a modular model [
28
]. In the GSPN, the transition is equipped with guards and
assignments. The guards are pre-condition logical functions identified by prefix “??” and
used to enable or inhibit the firing of transitions. The assignments, represented by “!!”, are
J. Mar. Sci. Eng. 2022,10, 1000 5 of 24
the post-condition messages that update the variables used in the model. To learn more
about Petri Nets, studies [
50
,
51
] are recommended; a comprehensive overview of GSPN is
provided in [52].
2.2. Case Study Description
For case study analysis, a generic OWT with Horizontal Axis Wind Turbine (HAWT)
configuration is considered. The OWT is a multi-unit and multi-state system with complex
dependencies between components. In this paper, only the equipment that most influence
the system availability is considered, namely: Rotor (RT), Gearbox (GB), Generator (GT),
and Pitch System (PS).
The case study is defined based on various sources of information. The reliability
parameters of the OWT’s components are based on empirical offshore reliability data
provided in [
32
]. The corrective and preventive maintenance policies are based on [
30
,
32
,
48
].
The weather window is adopted from [29].
The case study OWT is located at the Portuguese wind farm close to Viana do Castelo.
The wind farm area is located 18 km off the shore, that is, close to the global average of
distance to the shoreline, i.e., 18.8 km [
1
]. The wind resource at the location is given in [
53
],
while the wave conditions are indicated in [
54
]. The total exploration life of OWT is 25 years
with a capacity factor of 50.8% per year [
55
]. The electric power is 5 MW. The tariff for wind
energy produced by OWT in Portugal is considered to be 0.1544 EUR/kWh [56].
2.2.1. Production Configuration
The OWT system can be divided into eight main subsystems, namely: support struc-
tures, pitch and hydraulic system, gearbox, generator, speed train, electronic components,
blades system, and yaw system [
6
]. All of them are installed in a series configuration. Thus,
any subsystem failure of OWT can undermine the total production. Hence, the critical
or degraded failure of RT, GB, GT, or PS leads to the total production stop. Besides, the
Place/Transition Petri Nets has a limitation: different events cannot occur simultaneously
(i.e., the firing of the differently enabled transitions is sequential). Thereby, the defining of
equipment sequence switch is needed. To shut down the OWT production, the equipment
sequence switch is: RT
GB
GT
PS. To start up the wind turbine production, the
equipment sequence switch consists of: PS
RT
GB
GT. The Pitch System controls
the blade pitch to follow a predetermined speed ramp during startup and shutdown of the
turbine. Thus, the PS is the last one in the first sequence and the first one in the second
one. In the case of failure of one of the pieces of equipment presented in the sequences,
the order in which the subsystems are switched off is preserved, giving priority to the
damaged equipment.
2.2.2. Component Failure Data
In this case study, only the failures of the RT, GB, GT, and PS are considered. The
component failure data is given in Table 1.
The non-perfect systems can be in three different states: “As good as new”, “Degraded”
and “Failed”. “As good as new” state is a component in normal operation. “Failed” state
corresponds to a non-functioning component. “Degraded” state means that the function
of a component is maintained, but the system has a higher probability of failure. The
equipment can be repaired in “Failed” or in “Degraded” states.
The incipient and critical failures are described by the Weibull Truncated distribution,
which accounts the equipment’s age. The shape parameters,
β
, chosen for the transitions
are 2 and 3, respectively [
30
,
32
]. Both are larger than 1, representing the equipment in
the wear-out period of life. In this period, the larger the shape parameter, the higher
degradation effect.
The degraded failure is described by the exponential distribution, with the failure rate,
λ, due to the failure being independent from the equipment’s age.
J. Mar. Sci. Eng. 2022,10, 1000 6 of 24
Table 1. Component failure data.
Component Failure Distribution β1MTTF 2
(h)
λ3
(h1)
Rotor Incipient Weibull Truncated 3 19,948 -
(RT) Critical Weibull Truncated 3 22,164 -
Degraded Exponential - - 4.51 ×104
Gearbox Incipient Weibull Truncated 3 15,952 -
(GB) Critical Weibull Truncated 3 17,724 -
Degraded Exponential - - 5.64 ×104
Generator Incipient Weibull Truncated 2 17,215 -
(GT) Critical Weibull Truncated 2 19,128 -
Degraded Exponential - - 5.23 ×104
Pitch System Incipient Weibull Truncated 3 12,355 -
(PS) Critical Weibull Truncated 3 13,728 -
Degraded Exponential - - 7.28 ×104
1Shape parameter. 2Mean Time to Failure. 3Failure rate.
2.3. Maintenance Policy
The case study OWT with four degraded components is subjected to corrective main-
tenance (CM) when necessary and to age-based preventive maintenance (PM) only in
the summer. To keep the functioning of the OWT system, three different maintenance
categories are used [
48
]. Each of them depends on the weight of the component being
replaced (CM) or repaired (PM), thus according to the vessel involved:
Jack-Up vessel (JU)—is used in CM activities to replace the Rotor (its weight is between
90 t and 150 t).
Crane Barge (CB)—is used in CM activities to replace the Generator (up to 20 t) or the
Gearbox (up to 65 t).
Supply Vessel (SV)—is used in CM activities to replace the Pitch System and to support
the CM operations of the larger vessels. Moreover, SV is used in all PM activities.
The technical specifications of each vessel and the summary of maintenance categories
are presented in Tables 2and 3, respectively. The SV is the only one docked at the nearest
available port to the OWT, in Viana do Castelo; whereas the JU and CB are docked in Porto
and Aveiro, respectively, see Table 4.
Table 2. Technical specifications of the vessels.
Categories (Vessels) Draught (m) Service Speed (Knots)
Jack-Up (JU) 5.8 12
Crane Barge (CB) 3.8 7
Supply Vessel (SV) 3.8 7
Table 3. Maintenance categories.
Categories
(Vessels)
Turbine’s Components
RT GB GT PS
JU CM
CB CM CM
SV CM & PM CM & PM CM & PM CM & PM
J. Mar. Sci. Eng. 2022,10, 1000 7 of 24
Table 4. Principal constraints of Portuguese harbours.
Harbour Terminal Draught
(m)
Distance to OWT
(km)
Viana do Castelo Commercial port 8 19.48
Porto (Leixões) General cargo I 10 63.51
General cargo II 11 63.51
Aveiro Multipurpose 12 124.77
The Supply Vessel is used to transport a unique maintenance crew of 4 technicians
and spares for the Pitch System. The maintenance crew is considered as always available.
Moreover, it can start at any time of the day as long as all the logistics are concluded and
there is a weather window available. It is worth noting that the Supply Vessel is set to arrive
at the turbine at the same time with the Jack-Up (or the crane vessel), so the maintenance
team can start working immediately upon arrival.
2.3.1. Corrective Maintenance
CM activity consists of replacing the damaged equipment by a new one including all
the operation steps from the production of equipment in a factory to its commissioning on
the turbine. The component manufacture in a factory and the equipment transportation
from the supplier to the port constitute the vessels’ logistic time, see Table 5[
48
]. It is
worth noting that the SV is available 24 h per day to depart to an OWT immediately, and
only in the case of PS’s corrective repair, the Supply Vessel possesses a logistic time, since
the arrival of the new Pitch System takes 2 days (i.e., 48 h). The logistic time follows a
Log-normal distribution with a coefficient of variation of 30%.
Table 5. Vessels’ logistic times.
Categories (Vessels) Logistic Time (h) SD 1(h)
JU 504 151.2
CB 160 48
SV 48 14.4
1Standard Deviation.
The time spent on transportation of the new component from the port to the OWT
is estimated from the vessels’ service speed and the travelled distance. Additionally, the
sailing time follows a Log-normal distribution with a coefficient of variation of 20%. Please
note, the manoeuvres and the transit time in port are neglected.
Table 6contains the information regarding the mean duration of component replace-
ment and the respective standard deviation (SD). This time depends on both the equipment
type and the production state (i.e., degraded or failed). The time of CM activities follows a
Log-normal distribution with coefficient of variation of 20%.
Table 6. Corrective maintenance data (replacement phase) by equipment.
Transition RT GB GT PS
Failed As good as new Mean (h) 40 50 50 10
SD 1(h) 8 10 10 2
Degraded As good as new Mean (h) 52 65 65 13
SD 1(h) 10.4 13 13 2.6
1Standard Deviation.
J. Mar. Sci. Eng. 2022,10, 1000 8 of 24
2.3.2. Preventive Maintenance
The RT, GB, GT, and PS are subjected to imperfect age-based PM. This maintenance
action can start whether the equipment is in the perfect state or the component is stopped,
but not damaged. Please note, once a PM begins, it must be concluded, even if a critical or
degraded failure occurs in another component. PM is performed by the same maintenance
team as the CM, which is located on the Supply Vessel.
PM tasks are performed based on age reduction ratio,
q
(0 <
q
< 1). Thus, after repair
activity, the component is
q
younger (i.e., the age is reduced by
q
percent). After PM activity,
the age is defined by [30]:
Agei=Ageacc
i×(1q)Agei=(titi1+Agei1)×(1q)(1)
where,
Agei
and
Agei1
are the component’s consecutive ages after
ith
and
(i1)th
main-
tenance tasks, respectively;
Ageacc
i
is the age at the beginning of the
ith
maintenance action,
accumulated from the
(i1)th
maintenance task;
ti
and
ti1
are the calendar times at the
beginning of the
ith
and at the end of the
(i1)th
maintenance actions, respectively. It is
worth noting that after corrective maintenance activity, the component is new, so its age is
Agei=0.
PM is carried out only in the summer season, and when the age of a component is at
least equal to p×MTTF hours [17]:
(titi1+Agei1)p×MTTF,where 0p1 (2)
where,
p
, is a preventive repair threshold parameter which is the same for all components.
In this case study, four different PM activities are considered and presented in Table 7.
The frequency of the maintenance depends on the equipment’s age and it is assumed to be
Delta Dirac distributed. The duration of PM depends on the age reduction ratio,
q
, and
on the Mean Time to Repair (MTTR) of critical failure. The Log-normal distribution with
coefficient of variation of 30% is used to describe the duration of PM.
Table 7. Preventive maintenance models of individual component.
Component Period (h) Duration (h) Recovered Age (%)
RT p×MTT FRT q×MTT RRT
q×100
GB p×MTTFGB q×MTT RG B
GT p×MTTFGT q×MTT RG T
PS p×MTTFPS q×MTTRPS
2.4. Costs
In Table 8, the approximate costs for the new turbine’s components are presented.
These values are based on an offshore wind farm guide from [
57
]. Please note, the trans-
portation outlay of a new equipment from the manufacturer to the port is included in the
overall price of the component.
Table 8. Overall cost of the turbine’s components.
Component Cost/Unit (EUR)
RT 1,849,000
GB 863,000
GT 247,000
PS 123,300
The costs related to the vessels and technicians, Table 9, are approximate values based
on [48], where the hourly rate of a technician is EUR 70 by person.
J. Mar. Sci. Eng. 2022,10, 1000 9 of 24
Table 9. Hourly rates and mobilization costs.
Service Hourly Rate (EUR) Mobilization (EUR)
JU 6250 57,000
CB 6250 45,000
SV 600 0
Technician 70 0
The cost of the imperfect PM,
Cp
, depends on the age reduction ratio,
q
. According
to [30], it is given by:
Cp=(q2×Cpv +Cp f , 0 <q1
0, q=0(3)
where,
Cpv
is the preventive component replacement cost;
Cp f
is a fixed maintenance cost.
Since the PM is stochastically driven,
Cp f
, is not considered in this paper, thereby,
Cpv
comprises the total replacement cost of a new component. After the simulation, the number
of occurred PM activities per component is obtained. Then, this number is multiplied by
the component’s cost/unit (see Table 8). Hence,
Cpv
per turbine’s component is calculated.
The cost of PM considers neither hourly rates of SV nor technician crew. The hourly rates
and the mobilization costs are calculated separately considering the expenses of CM and
PM activities together.
2.5. Weather Window
The corrective and preventive maintenances are only performed when the weather
window (WW) is available (i.e., the wind speed and the significant wave height are within
the operational limits of the marine operation for a period long enough due to safety
reasons). The probability of favourable WW, Pw, and the time delay due to bad weather
conditions, Tw, are presented in Table 10 [
17
]. Please note that these values are merely
illustrative. The probabilities of the available WWs are conservative based on the typical
behaviour of each season. So, the increase of probability of available WW corresponds to
the decrease of waiting time for a WW. More realistic correlations can be obtained from
available weather data at the offshore wind farm.
Table 10. Availability of weather window and waiting time.
Season Availability of WW
(Pw)
Availability
Random Number
Waiting Time for a WW
(Tw) (h)
Winter 0.3 [0, 0.3] 240
Autumn 0.5 [0, 0.5] 168
Spring 0.6 [0, 0.6] 120
Summer 0.8 [0, 0.8] 48
The WW must be available when a maintenance activity (i.e., CM or PM) is to be
performed. As a result, as soon as the ships and the maintenance team are in port, the
model randomly generates a number between 0 and 1. If this value is less than or equal
to the seasonal Pw, a WW is available and the maintenance activity can start, otherwise a
waiting time, Tw, for a weather window is set. When the waiting period expires, a WW
becomes available.
Due to the relatively small distances between the ports, the available WW is required
only for the first departure ship by maintenance activity.
2.6. System Modelling by Petri Nets
The case study OWT is modelled by GSPN with predicates and the production avail-
ability and maintenance costs are obtained from Monte Carlo simulation. At the initial
instant, the PN model of turbine has all components of offshore production plant in op-
J. Mar. Sci. Eng. 2022,10, 1000 10 of 24
eration with initial age equal to zero (i.e., all equipment components are as good as new),
the maintenance team and the Supply Vessel are localised in Viana do Castelo, the Jack-Up
vessel is anchored in Porto, while the Crane Barge is anchored in Aveiro.
2.6.1. Equipment
Each component of OWT is schematised using the same type of PN model, consisting
of a sequence of events, which includes the simulation of failure and of the repair process.
To avoid a too extensive description, only the simplified model of Rotor (RT) is presented
(see Figure 2).
Figure 2. PN model of equipment (Rotor).
To ensure a logical sequence, the PN model of the equipment is accompanied by
various variables. Thus, the variable RT_Work is used to determine whether the equipment
fulfils its technical mission (i.e., RT_Work == true), or not (i.e., RT_Work == false). The
variable RT_Degradation is used to determine whether the equipment is degraded and
available or not degraded. Moreover, due to the PM activity, the model is complemented
by: RT_Age and RT_LastCM. The first registers the equipment’s age in hours; the second
records the time of the completion of the last corrective repair. These variables are used in
calendarization of the preventive maintenances. After every CM, RT_Age is set to zero.
When the place RT_Work is marked, Rotor is in operation and the variable RT_Work
is true. While RT_Work is marked, RT can fail (i.e., critical failure) or degrade (i.e., incip-
ient failure). RT fails when the transition RT_Failure_AGAN-F is enabled. Please note,
AGAN means As-Good-As-New and F means Failure. Through the firing rule, RT_Work is
unmarked, the token moves to the place RT_Failed and the variable RT_Work changes to
false. The token stays at RT_Failed place until RT_StartRepair2 becomes enabled, in other
words, until a repair team and both Supply Vessel (SV) and Jack-Up vessel (JU) arrive to
the offshore installation (i.e., SV_OnBoard == true and JU_OnBoard == true). During the
repair activity, RT_Repair2 place is marked. The duration of CM activity is introduced in
the delay of RT_FinishRepair2. When this transition is enabled, it means the conclusion of
CM repair, thus the token moves to RT_Work, the variable RT_Work changes to true, the
variable RT_Age turns to zero, and the variable RT_LastCM records the time of completion
of corrective repair.
J. Mar. Sci. Eng. 2022,10, 1000 11 of 24
The incipient failure occurs when the transition RT_Failure_AGAN-D is enabled. Through
the firing rule, RT_Work is unmarked, and the token moves to the place RT_Degraded, the
variable RT_Degraded changes to true, and the variable RT_Work remains true. When the
Rotor is degraded, both transitions RT_StartRepair1 and RT_Failure_D-F can fire, depending
on the failure history of the component, because the first failure is repaired if it is degraded
or critical and the next failure only if it is critical. Thus, if the Rotor is degraded and
the previous failure was critical, RT_StartRepair1 is enabled, the token moves to the place
RT_Repair1 and the corrective maintenance team is reserved. Moreover, if the Rotor is
degraded and the previous failure was degraded, the transition RT_Failure_D-F is enabled,
the token moves to the place RT_Failed, and the variable RT_Degraded turns false.
2.6.2. Total System Switch
Stochastic Petri Nets cannot simulate different operations at the same time. All actions
must be sequential. Therefore, all components of the OWT are impossible to switch
off simultaneously. Hence, the total system switch includes four different fail scenarios.
Each scenario has the same order of equipment turning-off, starting with the unavailable
component. The PN model of total system switch is presented in Figure 3.
Figure 3. Total system switch.
J. Mar. Sci. Eng. 2022,10, 1000 12 of 24
Total system switch has two objectives: to calculate the availability of the total system,
through the Boolean variable OWT_Availability, and to turn off offshore processing plant
equipment when at least one important production component (i.e., RT, GB, GT, and
PS) is not available, through the Boolean variable Equipment Abbreviation_Off. If the
system is available, OWT_Availability is true, in the unavailable state, it is false. Equipment
Abbreviation_Off is true only when the system component is shut down due to failure of
another component.
2.6.3. Preventive Maintenance
The preventive maintenance is a scheduled activity. Regardless of the type, the generic
PN model of PM repair is the same for every equipment. As an example, the simplified PN
model of preventive maintenance activity of the RT is shown in Figure 4.
Figure 4. PN model of PM activity (Rotor).
The PN sub-model for PM activity is accompanied by variables: RT_PM_Reservation
and RT_LastPM.RT_PM_Reservation is a Boolean variable that identifies with the true
condition (i.e., RT_PM_Reservation == true) that the Rotor reserves the PM team for itself.
RT_LastPM records the time of the completion of the last preventive repair.
When the place RT_PM_Free is marked, the equipment is waiting for preventive
maintenance, thus, the variable RT_PM_Reservation is false. The main objective of the
transition RT_PM_Verification is the validating of PM conditions. Namely, it must be a
summer, the component’s age must be more than
p×MTTFrotor
, and the equipment must
be functional.
J. Mar. Sci. Eng. 2022,10, 1000 13 of 24
When the RT_PM_Verification is satisfied, the transition fires and the token moves to
the place RT_PM_Queue. The variable RT_PM_Reservation turns true. At this instant, to
proceed with the PM activity, the simulation verifies another two conditions. The first
condition is represented by the transition RT_PM_Start, which is enabled only when the
PM team arrives to the wind. The second condition (i.e., the transition RT_PM_Cancel)
verifies whether the Rotor is still functional, while the turbine is waiting for the Supply
Vessel coming. In the case of unexpected Rotor’s fail, the variable RT_Work becomes false
(i.e., RT_Work == false), therefore, the transition RT_PM_Cancel enables, and the PM is
cancelled (i.e., RT_PM_Reservation == false).
When the first mentioned condition is met, the transition RT_PM_Start is enabled,
the token moves from the place RT_PM_Queue to RT_PM. When the PM is concluded,
the transition RT_PM_Finish is enabled, and the token moves to RT_PM_Free. After the
transition enabling, the component’s age is updated (i.e., RT_Age = RT_Age
×
q), the variable
RT_LastPM changes the registered time, and the Boolean variables return their values to
the initial ones.
2.6.4. Seasons
Figure 5shows the simplified PN model that identifies the seasons. The transitions
between the seasons follow the Delta Dirac distribution. The delay of each transition
corresponds to the time of three months, considering 30 days in each one. The simulation
starts on the 1 December.
Figure 5. PN model for seasons.
2.6.5. Vessels
The maintenance policy of the OWT system consists of three different maintenance
categories according to the vessel involved: Jack-Up vessel, Crane Barge, and Supply
Vessel. In order to avoid an extensive description, only the simplified model of JU vessel is
presented (see Figure 6).
To ensure a logical sequence, the PN model of JU vessel is accompanied by variables:
JU_Availability and JU_OnBoard. JU_Availability is a binary variable. When
JU_Availability == true
,
it identifies the time under which the Jack-Up vessel is localised at the port with no
reservation order. Thus, while JU vessel is waiting for an available weather window,
JU_Availability is equal to false, since the vessel is already reserved for a specific corrective
maintenance task. JU_OnBoard is a binary variable, too. JU_OnBoard is used to identify the
time interval when the JU vessel is localised at the OWT (i.e., JU_OnBoard == true).
J. Mar. Sci. Eng. 2022,10, 1000 14 of 24
Figure 6. PN model of Jack-up vessel.
When the place JU_Porto is marked, the Jack-Up vessel is available at the port of
Porto. Moreover, from the transition firing rule, the transition JU_StartCM_RT is enabled
when both the place #68 (i.e., a new Rotor arrived at the port) and the place JU_Porto are
marked. The main objective of this transition is to give a start for the CM activity. When
the transition JU_StartCM_RT fires, the place JU_Porto is unmarked. Thus, from the firing
rule, the place JU_StartVoyage is marked. Further, the variable JU_Availability turns false.
When the vessel is available to start the voyage (i.e., the place JU_StartVoyage is
marked), the weather window must be validated. For this purpose, two transitions are used,
namely: JU_WW_NonAvailable and JU_WW_Available. If the WW is available, the transition
JU_WW_Available fires and the token moves from the place JU_StartVoyage to the place
JU_Voyage. In the case of a non-available weather window, the token moves from the place
JU_StartVoyage to the place JU_WW_Waiting. The token preserves at the new place until the
enabling of the transition JU_WW_WaitingTime. After the enabling of JU_WW_WaitingTime,
the token moves from the place JU_WW_Waiting to the place JU_Voyage.
The voyage time of the JU vessel is defined by the time delay of the transition
JU_FinishVoyage. When the transition JU_FinishVoyage fires, the token moves from the
place JU_Voyage to the place JU_OWT, changing the variable JU_OnBoard to true. When
the CM activity is concluded, the variable JU_OnBoard is false, hence, the transition
JU_StartReturnVoyage fires and the token moves from the place JU_OWT to the place
JU_ReturnVoyage. The token at the place JU_ReturnVoyage means that the JU is in return-
J. Mar. Sci. Eng. 2022,10, 1000 15 of 24
ing voyage. The duration of the voyage is defined by the time delay of the transition
JU_FinishReturnVoyage. After the enabling of JU_FinishReturnVoyage, the token moves from
the place JU_ReturnVoyage to the place JU_Porto. Moreover, the variable JU_Availability
changes to true.
2.7. Economical Assessment
The efficiency of an age-based imperfect PM depends on two parameters: an age
reduction ratio,
q
, and a repair threshold parameter,
p
. To assess optimal values of
q
and
p
,
it is necessary to determine the lower related costs for the higher possible profit.
The O & M costs (
CO&M
) correspond to the sum of different features, such as: a
new turbine’s component cost, hourly rates, mobilization costs, and the cost of PM. To
determine the operation and maintenance expenses (OME), the sojourn times and the
number of triggers obtained from the implemented PN model are used. The sojourn time
corresponds to the time during which the token is located at the place ## throughout the
simulation time. Through the sojourn time, the identifying of the number of hours of each
vessel (i.e., JU, CB, and SV) dispatched to the O & M activities and the PM duration record
of each OWT’s component (i.e., RT, GB, GT, and PS) are possible. The number of triggers
corresponds to the total number of transition fires. Through the number of triggers, it is
possible to identify the number of failures of each component, the number of mobilizations
of each vessel, and the number of realised PM activities.
The variation of
q
and
p
influences the
CO&M
and the total system availability (
Asystem
),
which in turn influences the revenue or Gross Income (GI):
GI =Asystem ×P×η×Tsimulation ×CPT (4)
where,
P
is an electric power in MW,
η
is a capacity factor of OWT,
Tsimulation
is a total
simulation time in hours, and
CPT
is a cost for wind energy produced by OWT in Portugal
in EUR/MWh.
Knowing the value of
CO&M
and
GI
, the profit or Operating Income (
OI
) is possible
to determine:
OI =G I CO&M(5)
To assess an optimal value for
q
and
p
, it is necessary to minimise
CO&M
and to max-
imise
OI
. Hereupon, the optimum
q
and
p
correspond to the highest value of Accounting
Rate of Return (ARR):
ARR =OI
CO&M
(6)
3. Results
To perform the availability analysis of an OWT, the GRIF (Graphical Interface for
reliability Forecasting) analysis software is used [
58
]. To simulate the PN model, GRIF uses
MOCA-RP computation engine based on Monte Carlo simulation.
The simulated time of the base model is defined by iterations from instant 0 to instant
219,000 h (i.e., 25 years) with a step of 100 h for 1000 different scenarios (i.e., histories).
The average error related to the 90% CI (Confidence Interval) of the model outcomes
corresponding to the number of simulated histories is less than 0.04%.
3.1. Age-Based PM Parameters’ Decision Based on Economical Assessment
To obtain the optimal values of
q
and
p
, variations 0
<q<
1 and 0
<p
1 in steps
of 0.1 are considered. Table 11 and Figure 7present the availability of the total system for
different
q
and
p
values. As can be observed, the higher the values of
q
and
p
, the greater
the availability. Furthermore, the increase of
q
is more notable for low values of
p
. Thus, as
expected, in terms of availability, the qo pti mal is 0.9 and the po ptimal is 0.1.
J. Mar. Sci. Eng. 2022,10, 1000 16 of 24
Table 11. Availability of the total system for different qand p(in MEUR). Matrix representation.
p
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
q
0.1 0.80 0.81 0.82 0.82 0.83 0.83 0.84 0.84 0.84 0.85
0.2 0.81 0.81 0.82 0.82 0.83 0.83 0.84 0.84 0.84 0.85
0.3 0.81 0.82 0.82 0.83 0.83 0.83 0.84 0.84 0.84 0.84
0.4 0.82 0.83 0.83 0.83 0.83 0.84 0.84 0.84 0.84 0.85
0.5 0.83 0.84 0.84 0.84 0.84 0.84 0.84 0.84 0.85 0.85
0.6 0.84 0.84 0.84 0.85 0.85 0.84 0.85 0.85 0.85 0.85
0.7 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85
0.8 0.86 0.86 0.86 0.86 0.86 0.85 0.85 0.85 0.85 0.85
0.9 0.87 0.87 0.87 0.87 0.86 0.86 0.86 0.85 0.85 0.85
Figure 7. Availability of the total system for different qand p. Graphic representation.
Table 12 and Figure 8show the O & M costs for different
q
and
p
values, considering
the cost structure described in Section 2.4 and the results of sojourn times and of number of
triggers obtained from PN model. Comparing the results from Table 11 with Table 12, it is
concluded that the greater the availability, the greater the operation and maintenance costs.
Table 12. O & M costs for different qand p(in MEUR). Matrix representation.
p
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
q
0.1 57.3 57.4 57.6 58.1 58.6 57.9 59.5 59.4 59.7 59.8
0.2 56.5 56.8 57.1 57.6 58.1 58.1 59.2 59.3 59.5 59.8
0.3 57.1 57 56.9 57.4 58 58.4 58.9 59.4 59.5 59.9
0.4 58.9 58.2 57.9 57.8 58.2 58.7 59.2 59.6 59.6 59.7
0.5 61.7 60.3 59.8 59.2 59 59.2 59.4 59.8 59.8 59.8
0.6 66.0 63.9 62.4 61.5 60.8 60.3 60.1 59.9 60.0 60.3
0.7 72.7 69.9 67.2 65.7 63.6 61.9 60.8 60.4 60.3 60.2
0.8 81.7 78.1 74.3 71.3 66.8 63.2 61.7 61.1 60.5 60.2
0.9 94.3 89.9 83.5 77.9 68.7 64.5 62.8 61.7 61.0 60.4
J. Mar. Sci. Eng. 2022,10, 1000 17 of 24
J. Mar. Sci. Eng. 2022, 10, x FOR PEER REVIEW 17 of 25
Figure 7. Availability of the total system for different 𝑞 and 𝑝. Graphic representation.
Table 12 and Figure 8 show the O & M costs for different 𝑞 and 𝑝 values,
considering the cost structure described in Section 2.4 and the results of sojourn times and
of number of triggers obtained from PN model. Comparing the results from Table 11 with
Table 12, it is concluded that the greater the availability, the greater the operation and
maintenance costs.
Table 12. O & M costs for different 𝑞 and 𝑝 (in MEUR). Matrix representation.
𝒑
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
𝒒
0.1 57.3 57.4 57.6 58.1 58.6 57.9 59.5 59.4 59.7 59.8
0.2 56.5 56.8 57.1 57.6 58.1 58.1 59.2 59.3 59.5 59.8
0.3 57.1 57 56.9 57.4 58 58.4 58.9 59.4 59.5 59.9
0.4 58.9 58.2 57.9 57.8 58.2 58.7 59.2 59.6 59.6 59.7
0.5 61.7 60.3 59.8 59.2 59 59.2 59.4 59.8 59.8 59.8
0.6 66.0 63.9 62.4 61.5 60.8 60.3 60.1 59.9 60.0 60.3
0.7 72.7 69.9 67.2 65.7 63.6 61.9 60.8 60.4 60.3 60.2
0.8 81.7 78.1 74.3 71.3 66.8 63.2 61.7 61.1 60.5 60.2
0.9 94.3 89.9 83.5 77.9 68.7 64.5 62.8 61.7 61.0 60.4
Figure 8. O & M costs for different 𝑞 and 𝑝 (in MEUR). Graphic representation.
0.80
0.82
0.84
0.86
0.88
0.1 0.3 0.5 0.7 0.9
Availability
q
p = 0.1
p = 0.2
p = 0.3
p = 0.4
p = 0.5
p = 0.6
p = 0.7
p = 0.8
p = 0.9
p = 1.0
55.0
70.0
85.0
100.0
0.1 0.3 0.5 0.7 0.9
O & M costs (in MEUR)
q
p = 0.1
p = 0.2
p = 0.3
p = 0.4
p = 0.5
p = 0.6
p = 0.7
p = 0.8
p = 0.9
p = 1.0
Figure 8. O & M costs for different qand p(in MEUR). Graphic representation.
Table 13 and Figure 9show an Operating Income (OI) for different
q
and
p
values
calculated by Equation (5). For
q
> 0.7, the operating income represents the financial
loss. This means that the O & M costs are higher than the profit for high values of age
reduction values. Despite the lower values of availability, the values of
q
0.7 lead to more
profitable scenarios.
Table 13. Operating income for different qand p(in MEUR). Matrix representation.
p
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
q
0.1 11.9 12.1 12.6 12.5 12.3 13.6 12.4 12.7 12.6 12.9
0.2 13.1 13.2 13.3 13.2 13.2 13.5 12.7 13.0 12.9 13.0
0.3 12.8 13.4 13.9 13.8 13.5 13.2 13.1 12.8 13.0 12.7
0.4 11.6 12.9 13.2 13.7 13.4 13.2 13.1 12.8 12.9 13.0
0.5 9.7 11.5 12.1 12.8 13.0 13.0 12.8 12.5 12.9 13.0
0.6 6.1 8.4 9.8 11.1 11.9 12.3 12.5 12.9 12.6 12.5
0.7 0.3 3.3 5.9 7.7 9.4 11.1 12.0 12.4 12.5 12.9
0.8 8.0 4.2 0.5 2.6 6.8 10.1 11.4 12.0 12.6 12.8
0.9 19.7 15.1 9.1 3.5 5.3 9.3 10.6 11.5 12.1 12.7
Figure 9. Operating income for different qand p(in MEUR). Graphic representation.
J. Mar. Sci. Eng. 2022,10, 1000 18 of 24
Finally, Table 14 and Figure 10 show the Accounting Rate of Return (ARR) calculated
for different
q
and
p
values by dividing the operation income by the O & M costs. The
higher
ARRs
are within 0.2
q
0.4 and 0.2
p
0.6, where the maximum
ARR =
0.244
corresponds to the optimal values of
q
and
p
. Hence, the lower related costs for the higher
possible profit corresponds to qoptimal =0.3 and po pti mal =0.3.
Table 14. Accounting rate of return for different qand p. Matrix representation.
p
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
q
0.1 0.207 0.21 0.218 0.216 0.21 0.235 0.209 0.214 0.211 0.216
0.2 0.232 0.232 0.232 0.229 0.226 0.232 0.214 0.219 0.216 0.217
0.3 0.225 0.235 0.244 0.240 0.232 0.226 0.222 0.215 0.219 0.212
0.4 0.196 0.222 0.228 0.237 0.231 0.224 0.222 0.216 0.216 0.218
0.5 0.158 0.191 0.202 0.216 0.22 0.22 0.216 0.209 0.215 0.217
0.6 0.093 0.131 0.157 0.180 0.196 0.204 0.208 0.215 0.209 0.208
0.7 0.004 0.048 0.088 0.117 0.148 0.180 0.197 0.205 0.208 0.214
0.8 0.098 0.054 0.007 0.036 0.102 0.160 0.184 0.197 0.209 0.213
0.9 0.209 0.168 0.109 0.045 0.077 0.143 0.169 0.187 0.199 0.210
Figure 10. Accounting rate of return for different qand p. Graphic representation.
In Table 15, to validate the optimal values of
q
and
p
, the main system results for
two maintenance strategies are presented, namely: CM only and age-based PM. As can
be observed, the introduction of PM reduces the total system availability from 84.9% to
82.5%. However, from the economical point of view, the OWT production with PM is more
profitable, as ARRCM only <ARRoptimum ageb ased P M .
Table 15. Main system results for CM and optimum age-based PM.
Results CM Only Age-Based PM with
q= 0.3 and p= 0.3
Asystem 84.9% 82.5%
OME (MEUR) 59.9 56.9
OI (MEUR) 12.9 13.9
ARR 0.216 0.244
J. Mar. Sci. Eng. 2022,10, 1000 19 of 24
3.2. Sensitivity Analysis: OWT Availability
A sensitivity analysis is conducted to identify the parameters (i.e., input values) that
significantly impact the production availability of the OWT. For this purpose, an elasticity
factor is used, as:
Exi=yj
|xi|(7)
where, xiis the input value, and yjis the output result.
The elasticity factor is a nondimensional measure defined by the ratio of the variation
of OWT availability by 10% increase of input variable. The elasticity analysis is applied to
the optimal scenario (i.e.,
qoptimal =
0.3 and
poptimal =
0.3). Each input value is analyzed
separately. The analyzed input parameters are the component failure data described in
Table 1(i.e., shape parameters, MTTF, and failure rate); the voyage time of SB, JU, and SV
vessels obtained from Tables 2and 4; the logistic time carried out as a part of corrective
maintenance summarized in Table 5and the duration of replacement phase in Table 6; the
duration of PM activity, Table 7; the availability of WW and the waiting time for a WW
given in Table 10. The output is the OWT availability resulted from the input value change.
Figure 11 shows, in decreasing order of importance, the input parameters with the
highest elasticity factor. In Table 16, the description of each parameter is presented. The
obtained results show that the ranking of the input parameters on OWT availability are the
failure rates of RT, GT, PS; probability of available weather window, the voyage time of SV
and JU; shape parameter of RT.
Figure 11. Elasticity factors of input parameters in terms of availability.
Table 16. Description of the input parameters.
Input Parameter Description
MTTF_RT_D_F Failure rate of Rotor from the degraded state to the failure
MTTF_GT_D_F Failure rate of Generator from the degraded state to the failure
MTTF_PS_D_F Failure rate of Pitch System from the degraded state to the failure
P_WW_summer Probability of the weather window to be favorable in summer
P_WW_winter Probability of the weather window to be favorable in winter
P_WW_spring Probability of the weather window to be favorable in spring
P_WW_autumn Probability of the weather window to be favorable in autumn
VoyageTime_SV Total voyage time of Supply Vessel
beta_RT_AGAN_F Shape parameter of Rotor from the as good as new state to the failure
beta_RT_AGAN_D
Shape parameter of Rotor from the as good as new state to the degraded
VoyageTime_JU Total voyage time of Jack-Up vessel
J. Mar. Sci. Eng. 2022,10, 1000 20 of 24
3.3. Sensitivity Analysis: Accounting Rate of Return
A sensitivity analysis is also conducted to understand how the operational costs may
affect the financial aspect of production. For this case, the elasticity factor is defined by
the ratio of the variation of accounting rate of return by 10% increase of input costs. The
elasticity analysis is applied to the optimal scenario (i.e.,
qoptimal =
0.3 and
poptimal =
0.3).
Each input cost is analysed separately. The analysed input parameters are the cost of a new
turbine’s components (Table 8), the hourly rate of technician and vessel rental (Table 9),
and the mobilization costs (Table 9).
Figure 12 shows in decreasing order of importance, the operation and maintenance
expenses input parameters. The obtained results show that the most influential costs on
ARR are the hourly rates of technician and vessel rental.
Figure 12. Elasticity factors of input parameters in terms of accounting rate of return.
3.4. Discussion on the Availability Assessment
Considering the logistics, the operation and maintenance activities presented in Sec-
tion 2, an age reduction ratio,
q=
0.3, and a repair threshold parameter,
p=
0.3, the
availability of the OWT system is 82.5%, which compares favourably with those obtained
by other studies. Pfaffel et al. [
59
] showed that the availability of the onshore wind farm is
around 95%, while of the offshore wind farm, it is around 88%. Scheu et al. [
60
] determined
that the mean availability of a wind farm constituted by 80 OWT is 91%. In the SPARTA
project, the availability is 93%, in the OWEZ wind farm, it is 80%, in the Stratch-off wind
farm, it is 84% [
61
]. As one can see, some studies show that the production availability
can be higher than 90%, however, it is important to note that these values refer to the
availability of the wind farm with several wind turbines. This means that in the case of the
critical failure at one wind turbine, the availability of that turbine will decrease, while the
total availability of the system will not be significantly affected as the rest of the turbines
are working. Moreover, the logistic of the maintenance activity for a single wind turbine
is different from the entire offshore wind farm. In the case of wind farm, it is possible to
combine different maintenance activities, thus, reducing the logistic and voyage time of a
repair team. Hence, it is expected that the availability of the single wind turbine be slightly
lower than of the wind farm.
The obtained 82.5% availability also reflects some conservative modelling assumptions
that can be relaxed. The main reasons for low availabilities of OWT are: the low reliability
values, the overestimation of restrictions for maintenance activities, and the non-availability
of technical support vessels [
62
]. From the effectuated sensitivity assessment, it is possible
to see that the MTTF of PS, GT, and RT represent the highest sensitivity factors. This means
that the availability of OWT can increase for more recent and reliable components. In this
J. Mar. Sci. Eng. 2022,10, 1000 21 of 24
study, the reliability parameters are based on empirical offshore reliability data from 2014.
The second factor that decreases the availability is the underestimation of the probability
of an available weather window. Due to the lack of WW data for Viana do Castelo wind
farm, the conservative values were used. From the sensitivity analysis, the availability of
WW in summer is the most influential factor if comparing with other seasons. However,
the increase of WW availability in winter and spring can positively influence the OWT
availability, too. The voyage time of technical support vessels (i.e., JU and SV) is also
important to production availability increase.
Among the support vessels, the higher availability is provided by Jack-Up vessel
(i.e., 97.5%)
, as JU is used only to transport the new Rotor from port to the OWT. From
the base model results, the JU vessel is used 9.8 times in 25 years. The Crane Barge vessel
has slightly lower availability (i.e., 92.6%). CB vessel is used to support the replacement
of the Generator and Gearbox. From the base model results, the CB vessel is used 27.1
times in 25 years. The lowest availability belongs to the Supply Vessel (i.e., 82.9%). SV is a
unique vessel that is used in all maintenance activities. Over 25 years, this vessel is used
105.8 times.
It is worthwhile to note that the repair maintenance team is unique and is used in both
CM and PM actions. Moreover, the repair team always uses the Supply Vessel, thus, the
availability of the repair team is equal to the availability of the Supply Vessel.
4. Conclusions
The main objective of this paper is to analyse the availability of an offshore wind
turbine system subjected to an age-based preventive maintenance, considering the optimal
age reduction ratio,
q
, and repair threshold parameter,
p
. For this purpose, the Generalized
Stochastic Petri Nets with predicates coupled with the Monte Carlo Simulation method
are used.
An economical assessment of the production availability and maintenance costs of
the offshore wind turbine is performed to estimate the optimal values for
q
and
p
. The
influence of
q
and
p
on the availability, O & M costs, operating income, and accounting
rate of return are assessed. The higher availability occurs at the high values of
q
and at the
low values of p. However, at this range of qand p, the O & M costs are very high, leading
to negative incomes. Using the results obtained from the accounting rate of return, the
optimal values for
q
and
p
are obtained. Hence,
q=
0.3 and
p=
0.3 correspond to the
lower O & M costs and provide the higher possible profit.
A sensitivity analysis is conducted to identify the parameters (i.e., input values) that
significantly impact the production availability of the OWT. The obtained results show that
the ranking of the input parameters on OWT availability are the failure rates of RT, GT,
PS; probability of available weather window, the voyage time of SV, and JU, and shape
parameter of RT. Another sensitivity analysis is also conducted to understand how the
operational costs may affect the financial aspect of production. The obtained results show
that the most influential costs on accounting rate of return are the hourly rates of technician
and vessel rental.
The simulation results show that the availability of the OWT is 0.825, which reflects
some conservative model parameters, but is in line with the values obtained by other
studies for offshore wind farms. The Jack-Up shows the higher availability between vessels:
0.975. The availability of Crane Barge vessel is 0.926, while the availability of Supply
Vessel is 0.829.
The availability analysis of the OWT adopted a Simple Place/Transition
PN. This tool becomes difficult to read graphically as the complexity of the production
system increases. Hence, it is recommended to use Coloured PN in further works, which
facilitates the graphical representation.
To obtain more accurate estimates from the O & M model, real weather data for
weather window implementation is recommended. Knowing the wind speed and the wave
height at the OWT location, and specific operational limits of the different vessels, it is
possible to calculate their availability more precisely. Moreover, real wind data together
J. Mar. Sci. Eng. 2022,10, 1000 22 of 24
with the power performance curve of the OWT allows the assessment of the real power
output of the system.
Author Contributions:
Conceptualization, A.P.T. and C.G.S.; methodology, E.L. and A.P.T.; software,
E.L.; validation, E.L.; formal analysis, E.L. and A.P.T.; investigation, E.L.; resources, A.P.T. and C.G.S.;
data curation, A.P.T.; writing—original draft preparation, E.L.; writing—review and editing, A.P.T.
and C.G.S.; visualization, E.L.; supervision, A.P.T. and C.G.S.; project administration, C.G.S.; funding
acquisition, C.G.S. All authors have read and agreed to the published version of the manuscript.
Funding:
This study was completed within the project ARCWIND—Adaptation and implementa-
tion of floating wind energy conversion technology for the Atlantic region, which is co-financed by
the European Regional Development Fund through the Interreg Atlantic Area Programme under
contract EAPA 344/2016. This work contributes to the Strategic Research Plan of the Centre for
Marine Technology and Ocean Engineering (CENTEC), which is financed by the Portuguese Foun-
dation for Science and Technology (Fundação para a Ciência e Tecnologia—FCT) under contract
UIDB/UIDP/00134/2020.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Conflicts of Interest: The authors declare no conflict of interest.
Abbreviations/Nomenclature
ARR Accounting Rate of Return
CB Crane Barge
CI Confidence Interval
CM Corrective Maintenance
GB Gearbox
GI Gross Income
GRIF Graphical Interface for reliability Forecasting
GSPN Generalized Stochastic Petri Nets
GT Generator
HAWT Horizontal Axis Wind Turbine
JU Jack-Up vessel
MCS Monte Carlo Simulation
MTTF Mean Time to Failure
MTTR Mean Time to Repair
O & M Operation and Maintenance
OI Operating Income
OME Operation and Maintenance Expenses
OWT Offshore Wind Turbine
PM Preventive Maintenance
PN Petri Nets
PS Pitch System
RT Rotor
SD Standard Deviation
SPN Stochastic Petri Nets
SV Supply Vessel
WW Weather window
References
1.
Díaz, H.; Guedes Soares, C. Review of the current status, technology and future trends of offshore wind farms. Ocean Eng.
2020
,
209, 107381. [CrossRef]
2.
Guedes Soares, C.; Caldeira Duarte, J.; Garbatov, Y.; Zio, E.; Sorensen, J.D. Framework for Maintenance Planning. In Safety and
Reliability of Industrial Products, Systems and Structures; Guedes Soares, C., Ed.; Taylor & Francis Group: Chippenham, UK, 2010;
pp. 33–52.
3.
Zio, E.; Baraldi, P.; Patelli, E. Assessment of the availability of an offshore installation by Monte Carlo simulation. Int. J. Press.
Vessel. Pip. 2006,83, 312–320. [CrossRef]
J. Mar. Sci. Eng. 2022,10, 1000 23 of 24
4.
Li, H.; Teixeira, A.P.; Guedes Soares, C. A two-stage Failure Mode and Effect Analysis of offshore wind turbines. Renew. Energy
2020,162, 1438–1461. [CrossRef]
5.
Li, H.; Diaz, H.; Guedes Soares, C. A developed failure mode and effect analysis for floating offshore wind turbine support
structures. Renew. Energy 2021,164, 133–145. [CrossRef]
6.
Li, H.; Guedes Soares, C.; Huang, H.-Z. Reliability analysis of a floating offshore wind turbine using Bayesian Networks. Ocean
Eng. 2020,217, 107827. [CrossRef]
7.
Dutuit, Y.; Châtelet, E.; Signoret, J.-P.; Thomas, P. Dependability modelling and evaluation by using stochastic Petri nets:
Application to two test cases. Reliab. Eng. Syst. Saf. 1997,55, 117–124. [CrossRef]
8.
Kang, J.; Sun, L.; Guedes Soares, C. Fault Tree Analysis of floating offshore wind turbines. Renew. Energy
2019
,133, 1455–1467.
[CrossRef]
9. Zio, E. Reliability engineering: Old problems and new challenges. Reliab. Eng. Syst. Saf. 2009,94, 125–141. [CrossRef]
10.
Signoret, J.-P. Production Availability. In Safety and Reliability of Industrial Products, Systems and Structures, 1st ed.;
Guedes Soares, C., Ed.; Taylor & Francis Group: London, UK, 2010; pp. 331–345.
11.
Byon, E.; Ntaimo, L.; Ding, Y. Optimal Maintenance Strategies for Wind Turbine Systems under Stochastic Weather Conditions.
IEEE Trans. Reliab. 2010,59, 393–404. [CrossRef]
12. Lewis, E. Introduction to Reliability Engineering, 2nd ed.; John Wiley & Sons: New York, NY, USA, 1994.
13.
Signoret, J.-P. Availability of petroleum installations using Markov processes and Petri net modelling. In Risk and Reliability in
Marine Technology; Guedes Soares, C., Ed.; Balkema: Rotterdam, The Netherlands, 1986; pp. 455–472.
14.
Castanier, B.; Pehlivan, C.; Yeung, T.G. Optimization of maintenance and operational policies of an offshore wind farm subject
to stochastic wind conditions. In Safety and Reliability: Methodology and Applications, 1st ed.; Nowakowski, T., Mlynczak, M.,
Jodejko-Pietruczuk, A., Werbinska-Wojciechowska, S., Eds.; Taylor & Francis Group: London, UK, 2014; pp. 1141–1146.
15.
Li, M.; Kang, J.; Sun, L.; Wang, M. Development of Optimal Maintenance Policies for Offshore Wind Turbine Gearboxes Based on
the Non-homogeneous Continuous-Time Markov Process. J. Mar. Sci. Appl. 2019,18, 93–98. [CrossRef]
16.
Bris, R. Evaluation of the production availability of an offshore installation by stochastic Petri nets modeling. Int. Conf. Digit.
Technol. 2013, 147–155. [CrossRef]
17.
Santos, F.; Teixeira, A.P.; Guedes Soares, C. Modelling and simulation of the operation and maintenance of offshore wind turbines.
Proc. Inst. Mech. Eng. Part O J. Risk Reliab. 2015,229, 385–393. [CrossRef]
18.
Zio, E.; Marella, M.; Podofillini, L. A Monte Carlo simulation approach to the availability assessment of multi-state systems with
operational dependencies. Reliab. Eng. Syst. Saf. 2007,92, 871–882. [CrossRef]
19.
Barata, J.; Guedes Soares, C.; Marseguerra, M.; Zio, E. Simulation modelling of repairable multi-component deteriorating systems
for ‘on condition’ maintenance optimisation. Reliab. Eng. Syst. Saf. 2002,76, 255–264. [CrossRef]
20.
Kang, J.; Sobral, J.; Guedes Soares, C. Review of Condition-Based Maintenance Strategies for Offshore Wind Energy. J. Mar. Sci.
Appl. 2019,18, 1–16. [CrossRef]
21.
Kang, J.; Wang, Z.; Guedes Soares, C. Condition-Based Maintenance for Offshore Wind Turbines Based on Support Vector
Machine. Energies 2020,13, 3518. [CrossRef]
22.
Santos, F.; Teixeira, A.P.; Guedes Soares, C. Production regularity assessment using stochastic Petri nets with predicates. In
Maritime Engineering and Technology, 1st ed.; Guedes Soares, C., Garbatov, Y., Sutulo, S., Santos, T., Eds.; Taylor & Francis Group:
London, UK, 2012; pp. 441–450.
23.
Petri, C.A. Kommunikation mit Automaten. Doctors der Naturwissenschaften, Universität Bonn, Bonn. 20 June 1962. Available
online: http://edoc.sub.uni-hamburg.de/informatik/volltexte/2011/160/ (accessed on 28 April 2022).
24.
Boiteau, M.; Dutuit, Y.; Rauzy, A.; Signoret, J.-P. The AltaRica data-flow language in use: Modeling of production availability of a
multi-state system. Reliab. Eng. Syst. Saf. 2006,91, 747–755. [CrossRef]
25.
Signoret, J.-P.; Dutuit, Y.; Cacheux, P.-J.; Folleau, C.; Collas, S.; Thomas, P. Make your Petri nets understandable: Reliability block
diagrams driven Petri nets. Reliab. Eng. Syst. Saf. 2013,113, 61–75. [CrossRef]
26.
Marseguerra, M.; Zio, E. Basics of the Monte Carlo Method with Application to System Reliability. Automatisierungstechnik
2002
,
51, 242.
27. Rausand, M. Risk Assessment: Theory, Methods, and Applications; John Wiley & Sons: Hoboken, NJ, USA, 2011.
28.
Dutuit, Y.; Innal, F.; Rauzy, A.; Signoret, J.-P. Probabilistic assessments in relationship with safety integrity levels by using Fault
Trees. Reliab. Eng. Syst. Saf. 2008,93, 1867–1876. [CrossRef]
29.
Santos, F.; Teixeira, A.P.; Guedes Soares, C. Maintenance Planning of an Offshore Wind Turbine Using Stochastic Petri Nets With
Predicates. J. Offshore Mech. Arct. Eng. 2018,140, 021904. [CrossRef]
30.
Ding, F.; Tian, Z. Opportunistic maintenance for wind farms considering multi-level imperfect maintenance thresholds. Renew.
Energy 2012,45, 175–182. [CrossRef]
31.
Santos, F.; Teixeira, A.P.; Guedes Soares, C. Influence of logistic strategies on the availability and maintenance costs of an offshore
wind turbine. In Safety, Reliability and Risk Analysis; Taylor & Francis Group: London, UK, 2013; pp. 791–799. [CrossRef]
32.
Santos, F.; Teixeira, A.P.; Guedes Soares, C. An age-based preventive maintenance for offshore wind turbines. In Safety and Relia-
bility: Methodology and Applications; Nowakowski, T., Mlynczak, M., Jodejko-Pietruczuk, A.,
Werbinska-Wojciechowska, S., Eds.;
Taylor & Francis Group: London, UK, 2014; pp. 1147–1155.
J. Mar. Sci. Eng. 2022,10, 1000 24 of 24
33.
Lotovskyi, E.; Teixeira, A.P.; Guedes Soares, C. Availability analysis of an offshore oil and gas production system subjected to
age-based preventive maintenance by Petri Nets. Eksploat. Niezawodn. Maint. Reliab. 2020,22, 627–637. [CrossRef]
34.
Santos, F.; Teixeira, A.P.; Guedes Soares, C. Modeling, simulation and optimization of maintenance cost aspects on multi-unit
systems by stochastic Petri nets with predicates. Simulation 2018,95, 461–478. [CrossRef]
35.
Levitin, G.; Xing, L.; Dai, Y. Optimal loading of series parallel systems with arbitrary element time-to-failure and time-to-repair
distributions. Reliab. Eng. Syst. Saf. 2017,164, 34–44. [CrossRef]
36.
Zhou, Y.; Zhang, Z.; Lin, T.R.; Ma, L. Maintenance optimisation of a multi-state series–parallel system considering economic
dependence and state-dependent inspection intervals. Reliab. Eng. Syst. Saf. 2013,111, 248–259. [CrossRef]
37.
Zhou, Y.; Lin, T.R.; Sun, Y.; Bian, Y.; Ma, L. An effective approach to reducing strategy space for maintenance optimization of
multistate series-parallel systems. Reliab. Eng. Syst. Saf. 2015,138, 40–53. [CrossRef]
38.
Kawauchi, Y.; Rausand, M. A new approach to production regularity assessment in the oil and chemical industries. Reliab. Eng.
Syst. Saf. 2002,75, 379–388. [CrossRef]
39.
Bris, R.; Châtelet, E.; Yalaoui, F. New method to minimize the preventive maintenance cost of series–parallel systems. Reliab. Eng.
Syst. Saf. 2003,82, 247–255. [CrossRef]
40.
Sobral, J.; Kang, J.C.; Guedes Soares, C. Weighting the influencing factors on offshore wind farms availability. In Advances in
Renewable Energies Offshore; Guedes Soares, C., Ed.; Taylor & Francis Group: London, UK, 2019; pp. 761–769.
41.
Kang, J.; Guedes Soares, C. An opportunistic maintenance policy for offshore wind farms. Ocean Eng.
2020
,216, 108075. [CrossRef]
42.
Nielsen, J.J.; Sørensen, J.D. On risk-based operation and maintenance of offshore wind turbine components. Reliab. Eng. Syst. Saf.
2011,96, 218–229. [CrossRef]
43.
Castro-Santos, L.; Martins, E.; Guedes Soares, C. Methodology to Calculate the Costs of a Floating Offshore Renewable Energy
Farm. Energies 2016,9, 324. [CrossRef]
44.
Martins, D.; Gangadharan, M.; Guedes Soares, C. Analysis on weather windows conditioned by significant wave height and
wind speed. In Renewable Energies Offshore; Guedes Soares, C., Ed.; Taylor & Francis Group: London, UK, 2015; pp. 91–98.
45.
Castro-Santos, L.; Silva, D.; Bento, A.R.; Salvação, N.; Guedes Soares, C. Economic feasibility of floating offshore wind farms in
Portugal. Ocean Eng. 2020,207, 107393. [CrossRef]
46.
Castro-Santos, L.; Martins, E.; Guedes Soares, C. Economic comparison of technological alternatives to harness offshore wind and
wave energies. Energy 2017,140, 1121–1130. [CrossRef]
47.
Kang, J.C.; Sun, L.P.; Lu, Y.; Sobral, J. An opportunistic condition-based maintenance policy for offshore wind farm. In Advances
in Renewable Energies Offshore; Guedes Soares, C., Ed.; Taylor & Francis Group: London, UK, 2019; pp. 753–760.
48.
Rademakers, L.; Braam, H. O&M Aspects of the 500 MW Offshore Wind Farm at NL7 (80
×
6 MW Turbines)—Baseline
Configuration. Report for Dutch Offshore Wind Energy Converter (DOWEC). Report no. 10080 rev 2. 2002. Available online:
https://www.researchgate.net/publication/265084960_OM_aspects_of_the_500_MW_offshore_wind_farm_at_NL7 (accessed on
30 May 2022).
49. Reisig, W.; Rozenberg, G. Lectures on Petri Nets: Advances in Petri Nets; Springer: Berlin/Heidelberg, Germany, 1998.
50. Murata, T. Petri Nets: Properties, Analysis and Applications. Proc. IEEE. 1989,77, 541–580. [CrossRef]
51. Peterson, J.L. Petri Net Theory and the Modeling of Systems; Prentice-Hall: Englewood Cliffs, NJ, USA, 1981.
52.
Marsan, M.A.; Balbo, G.; Conte, G.; Donatelli, S.; Franceschinis, G. Modelling with Generalized Stochastic Petri Nets, 1st ed.; John
Wiley & Sons, inc.: New York, USA, 1995.
53.
Salvação, N.; Guedes Soares, C. Wind resource assessment offshore the Atlantic Iberian coast with the WRF model. Energy
2017
,
145, 276–287. [CrossRef]
54.
Silva, D.; Bento, A.R.; Martinho, P.; Guedes Soares, C. High resolution local wave energy modelling in the Iberian Peninsula.
Energy 2015,91, 1099–1112. [CrossRef]
55. Official Site of Lindo Offshore Renewables Center (LORC). Available online: http://www.lorc.dk/ (accessed on 28 April 2022).
56. Official Site of EDP Renováveis. Available online: https://www.edpr.com/en (accessed on 28 April 2022).
57. BVG Associates. Guide to an Offshore Wind Farm; The Crown Estate: London, UK, 2019.
58.
TOTAL. GRIF 2021. Petri Nets with Predicates. 2018. Available online: https://file.team9.satodev.fr/public/COM/GRIF2021/
Doc/grif-2021-doc-en- petri12.pdf (accessed on 28 April 2022).
59. Pfaffel, S.; Faulstich, S.; Rohrig, K. Performance and Reliability of Wind Turbines: A Review. Energies 2017,10, 1904. [CrossRef]
60.
Scheu, M.N.; Kolios, A.; Fischer, T.; Brennan, F. Influence of statistical uncertainty of component reliability estimations on offshore
wind farm availability. Reliab. Eng. Syst. Saf. 2017,168, 28–39. [CrossRef]
61.
Cevasco, D.; Koukoura, S.; Kolios, A.J. Reliability, availability, maintainability data review for the identification of trends in
offshore wind energy applications. Renew. Sustain. Energy Rev. 2021,136, 110414. [CrossRef]
62.
Koukoura, S.; Scheu, M.N.; Kolios, A. Influence of extended potential-to-functional failure intervals through condition monitoring
systems on offshore wind turbine availability. Reliab. Eng. Syst. Saf. 2021,208, 107404. [CrossRef]
... The accuracy of the results provided by MCS is influenced by the number of simulation histories used (Lotovskyi et al., 2022). To determine the appropriate number of histories, the error related to the Confidence Interval (CI) can be estimated using Equation 3. ...
... Long-term, continuous, representative wind gust observations form the basis for risk assessments and wind gust forecasting. Estimating return levels of wind gust maxima in the scale of decades or even centuries are needed for construction planning, but they are also of interest to O&M strategies [56][57][58]. For wind energy, information on wind extremes is needed in the planning phase to ensure the strength of the turbine structure [8]. ...
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This paper proposes a two-stage Failure Mode and Effect Analysis (FMEA) technique as a basis for implementing the failure analysis of offshore wind turbines. At the first stage, critical failure causes and failure modes of each component of offshore wind turbines are identified. In the next stage, critical components and systems of offshore wind turbines are ascertained by a cost-and-risk-based index that considers both risk priority and failure costs of components. The objective is to overcome some weaknesses of the traditional FMEAs including: (i) Risk-based FMEA ignores practical information extracted in the operation stage of offshore wind turbines such as failure cost and, (ii) Cost-based FMEA addresses mainly failures of components and systems and cannot deepen to failure modes and failure causes of offshore wind turbines. A methodology towards conducting uncertainty analysis of FMEA results is developed to provide a new insight into a good understanding of FMEAs and their results. The developed uncertainty analysis methodology reveals that the proposed two-stage FMEA technique is adequate to reduce the uncertainty of FMEA results and is superior in failure analysis of offshore wind turbines. The application of the methodology can provide recommendations toward corrective actions and condition-based maintenance implementations.
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