Renewable Energy 162 (2020) 1438e1461

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Renewable Energy
journal homepage: www.elsevier.com/locate/renene

A two-stage Failure Mode and Effect Analysis of offshore wind

turbines
He Li a, b, Angelo P. Teixeira a, C. Guedes Soares a, *
a
Centre for Marine Technology and Ocean Engineering (CENTEC), Instituto Superior, T
ecnico, Universidade de Lisboa, Lisbon, Portugal
b
Center for System Reliability and Safety, University of Electronic Science and Technology of China, Chengdu, Sichuan, 611731, PR China

a r t i c l e i n f o a b s t r a c t

Article history: This paper proposes a two-stage Failure Mode and Effect Analysis (FMEA) technique as a basis for
Received 10 May 2020 implementing the failure analysis of offshore wind turbines. At the first stage, critical failure causes and
Received in revised form failure modes of each component of offshore wind turbines are identified. In the next stage, critical
16 July 2020
components and systems of offshore wind turbines are ascertained by a cost-and-risk-based index that
Accepted 1 August 2020
Available online 17 August 2020
considers both risk priority and failure costs of components. The objective is to overcome some weak-
nesses 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
Keywords:
Failure mode and effect analysis
mainly failures of components and systems and cannot deepen to failure modes and failure causes of
Failure analysis offshore wind turbines. A methodology towards conducting uncertainty analysis of FMEA results is
Offshore wind turbine developed to provide a new insight into a good understanding of FMEAs and their results. The developed
Uncertainty analysis 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.
© 2020 Elsevier Ltd. All rights reserved.

1. Introduction similar configuration [14]. Hence, improving energy efficiency

and cutting down maintenance costs call for better mainte-
Onshore and offshore are two complementary sectors of the nance activities for offshore wind turbines [15e19].
wind energy industry. The onshore wind energy emerged Time-based maintenance (TBM), failure-based maintenance
earlier and has a much larger number of installations. The (FBM), and condition-based maintenance (CBM) are different
offshore sector is more recent but is growing fast [1]. Inspired maintenance strategies for offshore wind turbines [14,20e23].
by advantages, such as higher and more stable wind profiles, TBM performs maintenance obeying a predetermined time
pollution-free, and higher electricity generation, offshore wind interval. FBM carries out maintenance after the occurrence of
energy is becoming more attractive among decision-makers failures. Both strategies, however, lead to higher maintenance
and stakeholders in the renewable energy field [2,3]. costs [8,24]. Specifically, FBM performs the maintenance
Offshore wind farms are typically located 10e40 km from considerably late even for simple failures as a consequence of
the coast [4]. The transportation delays due to weather win- that they may turn into catastrophic failures. TBM may be an
dows [5,6] lead to increased downtimes and the higher failure either too late (failures have occurred) or too early (resulting in
rates [7e11] and subsequently increase the maintenance cost of long downtimes) choice for the maintenance of offshore wind
offshore wind turbines [12,13]. For instance, a 2 MW offshore turbines [25,26].
wind turbine would cost £47.25/MWh for maintenance The CBM, in the scope of preventive maintenance, includes
compared with £10/MWh of an onshore wind turbine with a actions like the assessment of physical conditions, analysis of
possibilities of failures, and performing the maintenance
[27e29]. CBM has the potential of reducing operating costs of
* Corresponding author. offshore wind turbines since failures can be predicted,
E-mail address: c.guedes.soares@centec.tecnico.ulisboa.pt (C. Guedes Soares).

https://doi.org/10.1016/j.renene.2020.08.001
0960-1481/© 2020 Elsevier Ltd. All rights reserved.
H. Li, A.P. Teixeira, C. Guedes Soares et al. Renewable Energy 162 (2020) 1438e1461

reported, and repaired in advance [30]. However, CBM is much overwhelming efforts are required when the modeling
more complex in implementation than TBM and FBM as it re- becomes more detailed.
quires failure databases, analysis tools, and sensors [14,31,32].
Failure databases are created to categorize and store failure Subjective results of FMEAs, generally, result from the index
features e.g. signals of vibration, sound, and temperature scale definition, experts’ opinion employed, and the calculation
[33e35]. Analysis tools are typical software developed to of RPNs. Efforts have been made to remove the uncertainty of
analyze and predict potential failures according to what failures FMEA results. For instance, objective indices like failure prob-
have been recorded in failure databases. Sensors are installed to ability, detection probability, and failure cost are introduced to
extract failure information from operating offshore wind tur- create a Cost Priority Number (CPN) as a substitution of an RPN
bines [36,37]. Before the implementation of CBM, however, [35,38e40]. Accordingly, the aforementioned drawbacks (1)
some details should be addressed [38,39]: (i) Components need and (2) of existing FMEAs have been partly removed. CPNs are
to be monitored; (ii) Failures should be observed; (iii) Failure comparable and have clear physical meanings. FMEAs
signals need to be extracted which should be already read-in to employing RPNs are risk-based methods. Nevertheless, FMEAs
failure databases. generating CPNs are cost-based approaches. Publications
The mentioned premises of the implementing CBM call for a related to FMEAs/FMECAs of wind turbines are shown in
thorough failure analysis of offshore wind turbines. Failure Table 1.
analysis is the first step of understanding the inherent failure However, the risk-based FMEA and its extensions are not
behaviors of systems and is the precondition of implementa- able to remove the uncertainty of results of failure analysis.
tion of CBM. Specifically, the failure analysis of offshore wind Moreover, restrictions of cost-based FMEA are obvious. Firstly,
turbines is to recognize their critical failure items (failure cau- input data for generating CPNs (e.g. failure costs and failure
ses, failure modes, etc.). Accordingly, preventive actions can be probabilities) are difficult to be obtained especially at the
implemented in advance of the occurrence of critical failures design stage of wind energy projects. Secondly, the cost-based
[40,41]. FMEA addresses mainly failures of components and systems
Failure analysis includes qualitative (e.g. checklist), quanti- and cannot deepen to failure modes and failure causes of
tative (e.g. Markov analysis), and semi-quantitative (e.g. Failure offshore wind turbines since failure costs are estimated ac-
Mode and Effect Analysis, FMEA) methods [1]. However, due to cording to failures of components. Hence, the purposes of this
their properties such as the highly hierarchical structure, un- article are as follows:
derstandability, and easy-to-construct, FMEA and its upgraded
methodology namely Failure Modes, Effects and Criticality (1) To develop a two-stage FMEA technique for failure analysis of
Analysis (FMECA) have been extensively employed in failure offshore wind turbines. The method analyses in detail fail-
analysis of onshore and offshore wind turbines, see ures of offshore wind turbines by using a risk-based FMEA
approach to identify critical failure modes and failure causes
Ref. [14,39,42e49].
(the first stage) and uses a cost-based FMEA approach to
FMEA is a systemic process of ascertaining critical failure
ascertain critical components and systems of offshore wind
items (e.g. failure modes, failure causes, components, sub-
turbines (the second stage).
systems) of a system [50e52]. It assesses the Risk Priority
(2) To propose a relative-weight method for pretreatment of
Number (RPN) of a failure item as the product of three
input data of FMEA as a basis to reduce the uncertainty of
indices: severity, occurrence, and detection. Severity repre- FMEA results of offshore wind turbines.
sents the consequence of a failure. Occurrence denotes a (3) To put forward an uncertainty estimation method for FMEA
failure’s likelihood. Detection reflects the ability of a failure to results.
be observed.
However, FMEAs are criticized for their weaknesses when The rest of this paper is organized as follows: Section 2
applying to the offshore wind turbine sector [39,44,46e48]: presents the two-stage FMEA approach with the uncertainty
assessment methodology. Section 3 introduces the offshore
(1) Subjective input data and results. The values of severity, wind turbine considered in this study. The case study is
occurrence, and detection of failure items are estimated by implemented in Section 4. Conclusions are provided in Section
specialists based on their knowledge in the field. The sub-
5.
jective input data makes FMEA results subjective;
(2) Uninformative RPNs. The RPNs lack physical meanings and
2. Proposed two-stage FMEA approach with uncertainty
are not possible to be compared with others computed on
assessment methodology
different offshore wind turbines;
(3) Arguable results. Various combinations of severity, occur-
2.1. Two-stage FMEA approach
rence, and detection may result in the same RPN and the
hidden meaning of each could be completely different.
In this section, a two-stage FMEA technique is developed
Assign the same importance to severity, occurrence, and
detection; Discrete values of severity, occurrence, and
to remove the drawbacks of traditional FMEAs, including: (i)
detection makes the RPNs to be distributed mainly at the Risk-based FMEA ignores practical information extracted in
bottom of the scale and some certain values; the operation stage of offshore wind turbines such as failure
(4) Defective calculation. FMEAs generally consider three fac- cost and, (ii) Cost-based FMEA addresses mainly failures of
tors (severity, occurrence, and detection), and other as- components and systems and cannot deepen to failure modes
pects such as failure cost are ignored. Moreover, traditional and failure causes of offshore wind turbines. In the first stage,
FMEA considers independent failure causes and instead of adopting absolute values of severity, occurrence,
and detection of each failure cause, a relative-weight method
is proposed beneath the aim of reducing the uncertainty of
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H. Li, A.P. Teixeira, C. Guedes Soares et al. Renewable Energy 162 (2020) 1438e1461

Table 1
Publications related to failure analysis of wind turbines using FMEAs/FMECAs.

Risk-Based FMEAs/FMECAs Cost-Based FMEAs/FMECAs

Publication Applied Indices Publication Applied Indices

[14] Severity, Occurrence, Detection [44] Failure Cost, Occurrence, Detectability

[39] Severity, Occurrence, b-factor [47] Profit Loss, Failure Rate, Undetected Possibility
[42] Severity, Occurrence, Detection [48] Failure Cost, Failure Rate
[45] Probability Rating, Consequences Rating [49] Failure Cost, Failure Rate

Fig. 1. The comparison between the proposed method and traditional FMEAs.

FMEA results. In the second stage, costs of components’ (3) Data collection. Collect data from the target offshore wind
failures are introduced into the proposed FMEA. Accordingly, turbine (if the information was sufficient) or from similar
Cost-and-Risk-based Priority Numbers (CRPNs) are con- offshore wind turbines (if the information was
structed to seek critical components and systems of offshore insufficient).
wind turbines. The actionable steps of the proposed two- (4) Definition of scales for indices. Define scales of severity,
stage FMEA are listed as follows. A comparison between the occurrence, and detection (from one to ten in this study).
proposed methodology and the traditional technique is (5) Severity. Assign a value (within the scale defined in step (4))
to each failure mode according to its consequence.
shown in Fig. 1.
(6) Occurrence and detection. Estimate the likelihood of each
failure cause and the difficulties of observation its occur-
(1) Identification of the offshore wind turbine. Determine the
rence, assign values to occurrence and detection of each
offshore wind turbine to be analyzed.
failure cause in the scope of scales defined in step (4).
(2) Decomposition of the offshore wind turbine. Decompose the
(7) Rank RPNs of failure causes and failure modes. Calculate
offshore wind turbine into systems, components, failure
(using Eq. (5)) and rank (decreasingly) the RPNs of failure
modes, and failure causes, record the hierarchical
causes based on the proposed relative-weight method and
relationship.

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rank (decreasingly) the RPNs of failure modes (the summa-

tion of RPN(s) of their corresponding failure cause(s)). bij
kjik ¼ (3)
(8) Rank CRPNs of components and systems. Calculate (using Eq. bkj
(7)) and rank CRPNs of components and systems (the sum-
mation of CRPN(s) of corresponding component(s)). The hi- Then the normalized value (fij ) of index j of the failure cause
erarchical relationship of the offshore wind turbine refers to i is computed as:
that what had been concluded in step (2).
P
n
(9) Recommendations for corrections. Identify the failure modes kjik
with higher RPNs then find out actions to avoid the occur- fij ¼ k¼1
(4)
rence of their causes. P
m P n
kjik
(10) Recommendations for CBM. Determine components and i¼1 k¼1
systems with higher CRPNs, review their failure modes and
causes and develop measures to implement CBM Hence, the RPN of failure cause i can be calculated as:
accordingly.
Y
m
RPNi ¼ fij (5)
Overall, the proposed two-stage FMEA is applicable for all j¼1
economy-critical systems. In general, these systems require the
careful consideration of economic performance such as cost, On this basis, the RPN of the failure mode w defined as
income, and loss of revenue [3,13,53]. The proposed two-stage summation of all RPNs of its causes, which can be represented
FMEA divides the failure analysis into two stages. At the first as:
stage, the complex calculation is the biggest concern because of X
FM
RPNw ¼ RPNi (6)
the implementation of the relative-weight method. It should be
noted that the computational complexity of the proposed In the second stage of the two-stage FMEA technique, the
methodology increases exponentially with respect to the in- failure costs of components are considered. CRPNs of compo-
crease in number of failure causes. At the second stage, failure nents (CRPN COMP ) and systems (CRPN S ) can be computed as:
costs of components are real concerns for practitioners as such
X
information is hard to be estimated. CRPNhCOMP ¼ RPNiFM
Ch (7)
In the Two-Stage FMEA approach, the relative-weight method
is proposed to reduce the uncertainty of results. The relative- X
weight method has a similar logic as the Analytic Hierarchy CRPNgS ¼ CRPNhCOMP (8)
Process (AHP) which analyses the importance of its elements by In Eqs. (7) and (8), Ch reflects the failure cost of the
their relative values [54e56]. Mathematically, the relative- component h of the offshore wind turbine.
weight method considers n failure causes with m indices (e.g.
severity, occurrence, detection, etc.). Define a matrix b as:
2.2. Uncertainty assessment methodology for results of FMEAs

2 3
b11 b12 … b1j … b1m In this section, an uncertainty assessment methodology for
6 b21 b21 … b2j … b2m 7 FMEA results is developed. The global uncertainty of FMEA
6 7
6 « « « « 7 results mainly introduced by: (i) data source; (ii) indices scales;
bn
m ¼ 6
6
7
6 bi1 bi2 … bij … bim 7
7 (iii) data and calculation, which is mathematically expressed
4 « « « 1 « 5
by:
bn1 bn2 … bnj … bnm
  ~
¼ b1 b2 … bj … bm (1) S1 þ ~
S ¼ TS
ð~ S2 Þ þ ~
S3 (9)

where, bij denotes the value of index j of the failure cause i, bj ¼ where, ~
S refers to the global uncertainty of FMEA results, ~
S1 is the
  uncertainty introduced by the data source, ~ S expresses the un-
b1j b2j / bij / bnj T presents values of index j for all 2

failure causes. certainty that comes from indices scales, and ~ S3 denotes the un-
For bj, define a matrix U as: certainty resulting from data and calculation. TS reflects the type of
input data. It should be either objective data extracted from the
field (e.g. failure costs) or subjective data collected from experts’
2 3 experience (e.g. values of severity, detection, and occurrence). The
6 7 type of input data (TS) is mathematically expressed by:
6 kj11 kj12 … kj1k … kj1n 7
6 7 
6 7 0 ; Input data is objective
6 kj21 kj22 … kj2k … kj2n 7 TS ¼ (10)
6 7 1 ; Input data is subjective
6 7
6 « « « « 7
Um
n ¼ 6
6
7
7 (2) Specifically, is defined as the reciprocal of total years of ex-
6 kji1 kji2 … kjik … kjin 7
6 7 perts working in the field, which is expressed as:
6 7
6 « « « 1 « 7
6 7 1
6 7 ~
6 … 7 S1 ¼ (11)
4 kjm1 kjm2 kjmk … kjmn 5 P
n
YoWi
i¼1

where in which, YoWi is the working experience of the expert i (by years),
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~
S1 is the inverse proportion concerning the entire working expe- each index, as in Eq. (16).
P
rience ( ni¼1 YoWi ). However, employing experts is costly. Hence,
the number of employed experts should be balanced with the k ¼ ½k1 ; k2 ; /; ki ; /; km  (16)
benefit of uncertainty reduction. Therefore, maxfDRPNg can be computed by the designed
This study assumes that the more detailed design of indices algorithm in Table 2.
rating (for instance, design the scale of severity, occurrence,
and detection from one to ten other than one to four) the less
uncertainty introduced to the results of failure analysis, under
the expectation that experts can correctly select a right state for 3. Offshore wind turbine case study
each index. On this basis, the uncertainty of FMEA results
introduced by the design of index scales is defined as: Offshore wind turbines are complex systems with an array
of components [19,57,58]. Systemic failure analysis is based on
~ 1 decomposing the offshore wind turbine into four levels: sys-
S2 ¼ (12)
P
m tems, components, failure modes, and failure causes.
RSLi
i¼1 The system level comprises an energy receiving system, an
energy producing system, an energy transforming system, a
where support structure, and an auxiliary system. Specifically, the
energy receiving system consists of blades and a hub. It con-
RSLi ¼ maxfRSi g  minfRSi g (13) verts the kinetic energy of the wind into mechanical power of
In Eqs. (12) and (13), RSLi denotes the rating scale length of the main shaft. The energy producing system is an integration
the index i, maxfRSi g and minfRSi g are the maximum and the of a main bearing, a main shaft, a generator, and a gearbox. It
minimum values of the rating scale of index i, respectively. transforms mechanical energy into electricity. The energy
transforming system adjusts the frequency and voltage of
The ~S denotes the uncertainty introduced by data and
3
generated electricity to match the requirements of the grid. The
calculation, which is represented by the maximum percentage
support structure provides support to the nacelle including
of RPN variation in terms of the variation of indices, see Eq. (14).
mooring facilities and a tower. The auxiliary system does not
~ maxfDRPNg get involved in electricity generation and transmission directly.
S3 ¼ (14) It is designed to improve the efficiency of electricity generation.
Y
m Y
m
maxfRSi g  minfRSi g The auxiliary system is an integration of a pitch subsystem, a
i¼1 i¼1 yaw subsystem, as well as controller and electrical facilities.
This paper decomposes the offshore wind turbines into 5
where, maxfDRPNg is the maximum RPN variation concerning the
systems, 13 components, and 32 failure modes with 53 failure
Y
m Y
m
variation of values of indices. maxfRSi g  minfRSi g is the causes. A comparison of components between the offshore
i¼1 i¼1 wind turbine in this paper and others already published is
RPN scale. carried out in Appendix A. The comparison indicates that this
To calculate maxfDRPNg, define a data block for all possible paper covers most components of offshore wind turbines.
values of indices as: Failure modes together with their effects and causes are listed
in Appendix B. A four-element-coding technique (system-
RS11 RS12 … RS1j … RS1k1 component-failure mode-failure cause) is introduced below to
RS21 RS22 … RS2j / RS2k2
encode each item of the FMEA.
« « « «
(15)
RSi1 RSi2 … RSij … RSiki
« « (i) At the failure mode and the failure cause levels. Overall, 32
« «
failure modes of 13 components are encoded from FM1 to
RSm1 RSm2 … RSmj … RSmkm
FM32. Failure causes are encoded from #1 to #53 according
Define a vector k to count the number of possible values of to the sequence of failure modes.

Table 2
Designed algorithm for computing.maxfDRPNg

Algorithm: Computation of maxfDRPNg.

INPUT:
1 Definition of variables and parameters
2 Definition of the RPN function: C ¼ CðRSi1 ; …; RSij ; …; RSik Þ.
3 Initial point: maxfDRPNg ¼ CðRS11 ; …; RS1j ; …; RS1k Þ  CðRS12 ; …; RS1j ; …; RS1k Þ.
4 Initialization of boundary vector.
BODY
5 for i ¼ 1:m
6 for j ¼ 1:ki
7 Seek the maxfDRPNg within the value space of index i under the determined values of other indexes that been given by experts.
8 end
9 Seek the maxfDRPNg of all indices.
10 end
OUTPUT
11 maxfDRPNg.

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Fig. 2. The hierarchical structure of the offshore wind turbine/Physical meanings of FMs and # are listed in Appendix B.

(ii) At system and component levels. The systems and compo-  Wear and fatigue (AS-PS-FM26-#47; EP-GB-FM15-#25; SS-MF-
nents of the offshore wind turbine considered in this paper FM23-#42).
are shown in Fig. 2 and in Appendix B.  Dirty or low quality of lubrication (EP-MB-FM7-#7).
(iii) Welding defects, for instance, as a cause of cracks of the  Iron core corrosion (ET-TR-FM21-#38).
generator in the energy producing system are represented as  Harsh environment (SS-TO-FM24-#45).
EP-MS-FM8-#8, see Fig. 2.  Insufficient lightning protection (ER-BL-FM2-#2; AS-CE-FM32-
#53).
Data in this study, that is, values of the severity of failure  Invert power input fault (ET-CV-FM19-#33).
modes, values of occurrence and detection of each failure cause  Excessive vibration (AS-PS-FM27-#48).
as well as the costs of components’ failures are taken from
literature, including [14,39,42e49], as indicated in Appendix C The mentioned failure causes are divided into four cate-
and Fig. 6. The scales of severity, occurrence, and detection are gories: material degradation, design errors, manufacturing er-
designed to be integers from one to ten. The scale of occurrence rors, and operational errors (see Fig. 4). Failure causes related to
in Ref. [45] is from one to five, hence, their values were doubled harsh environmental conditions are regarded as design errors
before the use in this study. under the assumption that it is the defective design that leads
to the system fails to stand up to harsh environmental condi-
tions. Material degradation mainly due to fatigue and corrosion
4. Results, discussion, and comparisons occupies a considerable proportion among the top 16 failure
causes. Design errors, e.g. insufficient protection of moisture
4.1. Proposed two-stage FMEA
penetration and inadequate heat dissipation design, result in
overheating of electrical components. Besides, manufacturing
Overall, 5 systems, 13 components, 32 failure modes with 53
and operational errors are nonnegligible, especially the
root failure causes were analyzed by the proposed two-stage
manufacturing errors of blades occupy the first place of the RPN
FMEA. The hierarchical configuration of the offshore wind
rank of failure causes.
turbine is illustrated in Fig. 2 in section 3. The graphic expres-
sion of the relative-weight method (from Eqs. (1)e(4)) is
plotted in Fig. 3, under the expectation of providing a deep 4.1.2. Results at failure mode level
understanding of the method presented. In this study, 32 failure modes from 13 components of the
offshore wind turbine are investigated, as indicated in Fig. 5.
4.1.1. Results at the failure cause level The top 8 failure modes are winding failure of the generator,
About 55% of the entire RPN are due to the following top 16 converter open circuit, blades cracks, deformation of generator
failure causes (see Appendixes B and C): bearings, transformer open circuit, the collapse of the tower,
fractured gear teeth, and seized gears of the gearbox, since the
 Manufacturing error (ER-BL-FM1-#1; ER-HB-FM4-#4). RPNs of these failure modes are remarkably higher than others.
 Sudden shock exceeds limitation (EP-GB-FM14-#23). Failures of the electrical components such as defective
 Overheat (ET-CV-FM19-#31; ET-TR-FM21-#36). windings of the generator as well as open circuits of the con-
 Moisture penetration (AS-CE-FM31-#52). verter and the transformer are critical. Lightning strikes, the
 Winding corrosion (EP-GE-FM12-#20). overload of the circuits, and long-term vibrations introduce

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Fig. 3. Flowchart of the computational process of the relative-weight method.

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(EP-GE-FM12), as well as max CRPNs of the component (BL)

and the system (EP) are displayed in Appendix E. It is expected
that such details can provide clear guidance of the RPN/CRPN
calculations of the proposed methodology.

4.1.5. Recommendations to corrections and CBM

FMEA is a bottom-up approach (from failure causes to
systems). Failure identification and maintenance strategies
planning, however, follow the reverse order. With the results,
the energy producing system and the energy receiving system
are the two most critical systems. Specifically, the gearbox and
the main bearing are top components that lead to malfunc-
Fig. 4. The top 16 critical failure causes of the offshore wind turbine, see Appendixes B
tions of the energy producing system. Seized gears, fractured
and C. gear teeth, and shaft crack are crucial failure modes of the
gearbox. These failure modes are mostly caused by fatigue.
Bearings vibration as a consequence of the dirty or low quality
of lubrication is the main failure mode of the main bearing.
Accordingly, structural reliability analysis methods are
additional vulnerability to electrical facilities of the offshore required to determine the most dangerous part of the fatigue-
wind turbine. Moreover, bearing deformation (generator) and prone area for gear assemblies within the gearbox. Measures
gear fracture (gearbox) are two main mechanical failure modes to prevent gears from fatigue e.g. enforce contact fatigue
of the offshore wind turbine as well. strength should be considered. Besides, periodical inspections
of lubrication of the main bearing are recommended. Crack
4.1.3. Results at the component level and delamination of blades caused mainly by manufacturing
The RPN ranks of components of the offshore wind turbine errors and insufficient lightning protections are remarkable
calculated by risk-based RPN (the conventional method) as critical failure modes for the offshore wind turbine. The failure
well as CRPN (the proposed method) are listed in Table 3. cost of blades is higher than other components due to their
Generally, the failure costs of components vary a lot con- large size and difficulties in maintenance. Hence, harsh envi-
cerning the locations of offshore wind farms, maintenance ronmental conditions such as lightning strikes should be
strategies, and transportation approaches. The failure costs of noticed in the design stage of the blades of the offshore wind
components in this study are the same as those have been turbine.
used in Ref. [44,47], and [48], see in Fig. 6. The cost of mooring Furthermore, open circuits of the converter and trans-
facilities, however, are unavailable in published references. former are consequences of overheat, iron core corrosion,
Hence, a failure cost of 2000V was assumed for each failure of and overcurrent. Such failures require larger safety allow-
mooring facilities. ances and better heat dissipation designs to the converter
Table 3 indicates that blades are the most critical compo- and the transformer as a basis of that to ensure electrical
nents of the offshore wind turbine, followed by the pitch sub- components would survive from the high operational
system, the generator and the converter. The CRPN ranks of temperature.
blades, the main bearing, the main shift, the tower, the pitch Technological advancements on sensors, data analysis, and
subsystem, and the yaw subsystem are increased compared fault diagnosis make online monitoring and diagnosis of po-
with the RPN ranks computed by the conventional method. tential failures possible for offshore wind turbines. Monitoring
Contrarily, the CRPN ranks for the hub, the generator, the and diagnosis of potential failures are promising techniques for
gearbox, the transformer, mooring facilities, as well as discovering failures before their occurrences. This analysis
controller and electrical facilities are decreased. In general, suggests that the vibration signals of the gearbox and the main
CRPNs are more informative than RPNs concerning mainte- bearing as well as the temperature of the converter and the
nance planning and operational cost saving. transformer should be read-in to the failure databases for the
implementation of the CBM of offshore wind turbines. Vibra-
4.1.4. Results at the system level tion monitoring sensors should be set on the gearbox and the
The results of the failure analysis of the offshore wind main bearing to collect their vibration signals. Temperature
turbine at the system level are shown in Fig. 6. The energy sensors should be installed for monitoring the temperature of
producing subsystem (the CRPN of which is 4.3) is the most the converter and the transformer. Subsequently, failure anal-
critical system, followed by the energy receiving system (3.09), ysis software can compare signals collected in the operating
the auxiliary system (2.67), the energy transformer system offshore wind turbine with that what has been read-in to the
(1.95), and the support structure (1.42). The CRPN rank of CBM database and judge working state of the offshore wind
systems of the offshore wind turbine strongly in line with the turbine accordingly.
complexity of systems. Generally, a system with complex The proposed relative-weight approach preserves the
functions and structures is more critical than other systems. importance of indices, that is, an index with a higher value will
The reason is that complex systems tend to fail more in fre- remain higher than others after applying the relative-weight
quency than simple ones and maintenance costs of which are approach, see Appendix D-1 to D-3 and D-7 to D-9. Accord-
higher. ingly, the criticality ranks of failure causes obtained by the
Detailed algorithms and examples for computing the max conventional FMEA and the relative-weight approach (the first
RPNs of the failure cause (ER-BL-FM1-#1) and the failure mode stage of the proposed methodology) are the same (see
1445
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Fig. 5. Results of failure modes analysis of the offshore wind turbine. The sequence of the legend of each component is ordered by the RPN rank of failure modes.

1446
H. Li, A.P. Teixeira, C. Guedes Soares et al. Renewable Energy 162 (2020) 1438e1461

Fig. 6. The results of failure analysis at the system level and failure costs of components of the offshore wind turbine/CE: Controller and electrical facilities.

Appendix C), which validated the correctness of the relative- Disagreements among literature are the differences of RPN/
weight approach. But the relative-weight method has merits CRPNs’ percentages (the contribution of RPN/CRPN of a specific
in reducing the uncertainty of FMEA results, see Section 4.2.2. component to the total) of the main bearing, the pitch sub-
On the other hand, at the second stage of the two-stage FMEA, system, controller and electrical facilities, and auxiliary com-
failure costs of components are introduced to extend the failure ponents, see Fig. 7(b). The CRPNs of the main bearing and the
analysis of the offshore wind turbine from risk domain to pitch subsystem are higher than that from other publications.
economy (cost) field. The results of this study, in general, are The reason is that other FMEAs either ignored these compo-
more practical to operations of offshore wind turbines. nents or excluded the economic factor (failure cost) in their
failure analysis. Meanwhile, failure costs of the controller and
electrical facilities are lower compared to other assemblies, as a
4.1.6. Comparison
consequence, disagreement of RPN/CRPN percentages of these
A comparison of the proposed FMEA and others available in
facilities between this study and the selected literature appears.
published literature at the components level is conducted to
From Fig. 7(b), RPN/CPN/CRPN percentages of components
clarify the differences and similarities of the results, see Fig. 7.
vary considerably in different FMEAs. The evidence is insuffi-
Some components in different literature are integrated into one
cient to judge the result computed in each study as credible or
for comparison purposes. For instance, the blades failure rep-
not. However, according to the authors’ experience and
resents both blades failure and blades bearing failure (if any) in
knowledge in the offshore wind energy sector, huge assemblies
some literature. An auxiliary component is introduced to
with complex maintenance processes may result in consider-
denote several components that were not mentioned in this
ably high downtime and higher costs of transportation and
study, details of integrations of components are listed in
maintenance. The existing FMEAs either focus on risk e.g.
Table 4.
Ref. [14,42,43] or cost e.g. Ref. [44,47e49]. This is one of the
A big agreement among literature is that the criticality of the
main factors that motivated this study, that is, to combine cost
hub and mooring facilities are low and most literature even
and risk factors to carry out failure analysis of the offshore wind
ignored these components in their failure analysis. Another
turbine.
agreement is that the gearbox, the generator, the tower, and
Cumulative RPN/CRPN of the entire 9 FMEAs related to
blades have higher criticalities than other components, as
offshore wind turbines is shown in Fig. 7(a). Fig. 7 provides an
combined consequences of the complexity in maintenance,
outlook of failures of offshore wind turbines by accumulated
longer downtime, and higher failure costs.

1447
 H. Li, A.P. Teixeira, C. Guedes Soares et al.
Table 3
RPN and CRPN ranks of components of the offshore wind turbine.

Components Risk-based RPN Rank Risk-and-Cost-based RPN Rank Changes

Cost Rank CRPN Rank Amount In/de-crease

Blades 3 4 1 2

Hub 11 11 12 1

Main Bearing 8 2 5 3

Main Shift 12 8 10 2

Generator 1 9 7 6
1448

Gearbox 2 7 3 1

Converter 4 6 4 0 d
Transformer 5 10 8 3

Mooring Facilities 10 13 13 3

Tower 9 3 6 3

Pitch System 6 1 2 4

Yaw System 13 5 9 4

Controller and Electrical Facilities 7 12 11 4

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H. Li, A.P. Teixeira, C. Guedes Soares et al. Renewable Energy 162 (2020) 1438e1461

Fig. 7. Comparison of FMEA results of this study and others available in the literature.

RPN/CPN/CRPN, despite those wind turbines in literature are higher failure frequencies e.g. controller and electrical
from different wind farms located in United Kingdom, Ger- components.
many, and China. Fig. 7(a) demonstrates that, in general, gen-
erators are the key assemblies of offshore wind turbines, 4.2. Uncertainty assessment methodology
followed by gearboxes, blades, controller and electrical com-
ponents, towers, etc. These components should be designed 4.2.1. Analysis of the method
and be operated carefully either for their higher failure costs Data source (~
S1 ), indices scales (~
S2 ), and data and calculation
e.g. gearboxes, blades, towers, and generators or for their
(~
S3 ) are three sources of the uncertainty of FMEA results.

Table 4
Details of components integration in literature.

Literature Components Integration

Controller and Electrical Facilities Auxiliary Components

[34] Controls; Electrical Components Brake; Hydraulic Subsystem; Other Subsystem

[35] e Brake; Main Frame; Screws; Nacelle Housing; Other Subsystem
[38] Electrical Components; Electronic Components; Sensors Hydraulic Subsystem; Brake
[39] Controllers; Electrical Components Hydraulic Subsystem, Brake; Other Subsystem
[40] Combined Controls; Circuit; Sensors; Electrical Components; Safety Facilities; Service Items Heaters/Coolers; Oil; Other Components

Fig. 8. ~S1 with respect to experts’ experience.

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H. Li, A.P. Teixeira, C. Guedes Soares et al. Renewable Energy 162 (2020) 1438e1461

Fig. 9. ~S2 in terms of the number of indices state.

According to the definitions of Eqs. (11) and (12), ~ S1 in respect are a burden to experts. On the other hand, in the uncertainty
of experts’ working experience and ~ S2 in terms of the number reduction perspective, the benefit of introducing more experts
of states of indices are plotted in Figs. 8 and 9, respectively. or more states of indices turn out to be quite low when the
~ decreases as experts’ experience increases, existing evidence is sizable according to gradient lines in Figs. 8
Theoretically, S 1
and 9.
see Fig. 8. This indicates that involving more experts or
Up to now, no consensus has been reached about deter-
replacing an inexperienced specialist by an experienced one
mining the number of experts and numbers of index states for
will be benefic for the uncertainty reduction of FMEA results
failure analysis do be adopted in FMEAs/FMECAs in the offshore
introduced by the data source. Similarly, designing more states
energy sector. For instance, Shafiee and Dinmohammadi [44]
of indices will pull down the value of ~
S , see Fig. 9. However, the
2 employed four specialists, while Scheu et al. [39] adopted 40 to
marginal benefit will diminish as the progressive increase of carry out FMEAs of offshore wind turbines. The reality, how-
experts’ experience and the number of indices states. On one ever, is that employing a large number of experts is unfeasible
hand, introducing more experts is costly and sorting of indices

Fig. 10. Uncertainty assessment of the gearbox of the offshore wind turbine.

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Table 5
Details of selected FMEAs applied to offshore wind turbines’ failure analysis.

Literature Type of Information Experts’ Information Scales of Indices

Subj. Obj. Number AWY Type Scale

This paper √ √ 1 4 CT/DT S(1-10); O(1-10); D(1-10)

[14] √ 1 4 DT S(1-8); O(1-8); D(1-8)
[43] √ 1 4 DT S(1-4); O(1-10); D(1-10)
[44] √ 4 6 DT S(1-4); O(1,2,3,5); D(1,4,7,10)
[45] √ 1 4 DT S(1-4); O(1-10)
[46] √ 1 4 DT S(1-4); O(1-10); D(1-10)

S: Severity; O: Occurrence; D: Detection; CT: Continuous type; AWY: Average working years; DT: Discrete type; Subj.: Subjective; Obj.: Objective.

for some projects with limited funding. 2%). A comprehensive comparison between the proposed FMEA
Another practical case is that no publication shows the and the other 5 published FMEAs of offshore wind turbines is
investigation on how many states of indices of FMEA/FMECA conducted, see Table 5 and Fig. 11. The comparison is to validate
should be designed for failure analysis of offshore wind tur- the performance of the proposed FMEA technique and to verify
bines. For instance, 3 (severity and occurrence in Ref. [39], the availability of the developed uncertainty estimation
severity in Refs. [46]), 4 (occurrence and detection in Ref. [14]), method. For studies that the information on involved experts is
and 10 (severity, occurrence, and detection in Ref. [44], occur- not given, a fictitious expert with 4 years of working experience
rence and detection in Ref. [46]) states were designed. is assumed (including this study).
This study suggests these parameters from an uncertainty According to Fig. 11, the uncertainty of the proposed two-
estimation perspective. According to Fig. 8, 4 years’ experience stage FMEA results is the lowest. Specifically, S~ and ~ S of the
2 3
in total is recommended, as the marginal benefit is low when proposed FMEA technique are the bottommost. ~ S1 in most
introducing more experienced specialists. But at least special- studies (including this study) are equal to 0.25, mainly due to
ists working in mechanical and in electrical domains should be the imaginary expert with four years working experience
employed according to the knowledge of authors towards designed. In terms of the uncertainty from indices scales, the
offshore wind turbines. According to Figs. 9 and 20 states of all differences among studies are not distinguished but the pro-
indices are recommended since the marginal benefit (the un- posed method is the lowest. Contributors to the uncertainty of
certainty reduction) of introducing an additional state is not selected studies are listed in Table 6, which proves that the
significant. proposed two-stage FMEA technique is good at reducing the
The calculation of ~S is associated with all failure indices of
3 uncertainty introduced by data and calculation.
the offshore wind turbine. To plot ~ S3 visibly, the gearbox in-
cludes 6 failure modes with 10 failure causes (EP-GB-FM13-#21
to EP-GB-FM18-#30, see Appendixes B and C) has been selected 5. Conclusions
and displayed in Fig. 10. Fig. 10 suggests that the proposed
FMEA has the advantage of reducing the uncertainty of FMEA This paper proposes a two-stage FMEA technique for failure
results introduced by the data and calculation. analysis of offshore wind turbines. In the first stage, consider-
ations of severity, occurrence, and detection are employed to
carry out failure analysis at the failure cause and the failure
4.2.2. Comparison of results mode levels using the proposed relative-weight FMEA method.
The entire uncertainty of the FMEA results in this study is In the second stage, failure costs are included in the failure
about 0.29. The data source (~ S1 , 0.25, 87% of the total) con- analysis at the component and system levels of offshore wind
tributes the most uncertainty to the total followed by indices turbines.
scales (~
S , 0.033, 11%) as well as data and calculation (~
2 S , 0.006, 3 The proposed technique overcomes the limitation of risk-

Fig. 11. Results of uncertainty analysis of selected FMEAs/: The proposed method.

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Table 6
Comparison of contributors to the uncertainty of FMECAs results.

References This paper [14] [43]

AV P AV P AV P

Uncertainty ~
S1 0.250 87% 0.250 70% 0.250 66%
~
S 0.033 11% 0.042 12% 0.042 11%
2
~
S3 0.006 2% 0.063 18% 0.088 23%
In total 0.289 100% 0.355 100% 0.380 100%
Share of Uncertainty

References [44] [45] [46]

AV P AV P AV P
Uncertainty ~
S1 0.040 13% 0.250 45% 0.250 55%
~
S 0.083 28% 0.071 13% 0.042 9%
2
~
S3 0.176 59% 0.231 42% 0.160 36%
In total 0.299 100% 0.552 100% 0.452 100%
Share of Uncertainty

based FMEAs that ignores operational information of failure CRediT authorship contribution statement
analysis of offshore wind turbines and removes the restriction
that cost-based FMEAs only applies at the component and the He Li: Methodology, Formal analysis, Visualization, Writing -
system levels of offshore wind turbines. This study concludes original draft. Angelo P. Teixeira: Writing - review & editing,
that: Supervision. C. Guedes Soares: Writing - review & editing,
Supervision.
(1) The energy producing system and the energy receiving sys-
tem are the two most critical systems of the offshore wind
turbine when considering both subjective concerns (severity, Declaration of competing interest
occurrence, and detection) and objective concerns (costs of
components’ failures). The authors declare that they have no known competing
(2) Blades, pitch subsystems, and gearboxes are the top critical financial interests or personal relationships that could have
components of offshore wind turbines. These components appeared to influence the work reported in this paper.
call for extensive tests and inspections than nowadays.
(3) Mechanical failures (e.g. blades cracks and bearing defor-
mation of the generator) are more critical than electrical Acknowledgment
failures (e.g. open circuit of the transformer) from a statistical
point of view. This study was completed within the project ARCWIND -
(4) Most failures of offshore wind turbines are the consequence Adaptation and implementation of floating wind energy con-
of the following aspects: (i) Design errors such as insufficient version technology for the Atlantic region, which is co-financed
lightning protection of the blades and overheat of the con- by the European Regional Development Fund through the
verter and the transformer. (ii) Material degradations like Interreg Atlantic Area Programme under contract EAPA 344/
fatigue, corrosion of winding (mechanical components), 2016. The first author has been supported by the scholarship
corrosion iron core (electrical components), and wear.
from China Scholarship Council (CSC) under Grant No.
(5) Recommendations to corrections and CBM include: (i)
201806070048. This work contributes to the Strategic Research
Improve surface contact strength of gears in the gearbox. (ii)
Plan of the Centre for Marine Technology and Ocean Engi-
Set sensors to monitoring vibration of the gearbox and the
neering (CENTEC), which is financed by the Portuguese Foun-
main bearing. (iii) Set thermodynamic sensors to report the
dation for Science and Technology (Fundaça ~o para a Cie
^ncia e
temperature of the converter and the transformer.
Tecnologia - FCT) under contract UIDB/UIDP/00134/2020.
The paper also develops a methodology to analyze FMEA
results from an uncertainty estimation point of view. The re-
Appendix A. Components considered in FMEAs/FMECAs of
sults validated the advantage of the proposed two-stage FMEA
offshore wind turbines
technique that it is good at reducing the uncertainty of results
of failure analysis.

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 H. Li, A.P. Teixeira, C. Guedes Soares et al.
Literature This Paper [14] [39] [42] [43] [44] [45] [46] [47] [48] [49]

FMs, FCs, and Comp. numbers 13 Comps. with 53 FCs 1 Comp. with 53 FCs 10 Comps. with 337 FMs 11 Comps. with 25 FCs 13 16 16 Comps. with 28 FMs 4 Comps. with 46 FCs 12 12 19
Comps. Comps. Comps. Comps. Comps.
Blade ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓
Pitch System ✓ ✓ ✓ ✓ ✓ ✓ ✓
Main Shift and/or Coupling ✓ ✓ ✓ ✓ ✓ ✓ ✓
Gearbox ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓
Generator ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓
Transformer ✓ ✓ ✓ ✓ ✓
1453

Yaw System ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓
Converter ✓ ✓ ✓ ✓ ✓ ✓ ✓
Support Structure and Nacelle ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓
Hydraulics ✓ ✓ ✓ ✓ ✓ ✓
Electrical or Cooling System ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓
Brake ✓ ✓ ✓ ✓ ✓ ✓
Hub ✓ ✓ ✓ ✓ ✓
Main or Blades’ Bearings ✓ ✓ ✓ ✓
Power, Sensor, Motor System ✓ ✓ ✓
Controller ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓
Other Parts ✓ ✓ ✓ ✓
FM: Failure Modes; FC: Failure Causes; Comps.: Components.

Renewable Energy 162 (2020) 1438e1461

H. Li, A.P. Teixeira, C. Guedes Soares et al. Renewable Energy 162 (2020) 1438e1461

Appendix B. Failure modes and causes of the considered

offshore wind turbine

Failure Mode Level Failure Cause Level

Code Failure Modes End Effects Code Failure Causes

ER-BL-FM1 Blades cracks Wind turbine stop working #1 Manufacturing error

ER-BL-FM2 Delamination Wind turbine stop working #2 Insufficient lightning protection
ER-BL-FM3 Gear teeth slip Blades fail to attack wind properly #3 Wear, fatigue, etc.
ER-HB-FM4 Fracture in the shell Rotor break #4 Manufacturing error
ER-HB-FM5 Error in positioning Blades break away from the hub #5 Manufacturing error and or fitting error
EP-MB-FM6 Bearing damage Wind turbine stop working #6 Wear, fatigue, etc.
EP-MB-FM7 Bearing vibration Abnormal working condition #7 Dirty or low quality of lubrication
EP-MS-FM8 Cracks The collapse of the wind turbine #8 Welding defects
EP-MS-FM9 Fracture The collapse of the wind turbine #9 Fatigue
EP-GE-FM10 Bearing deformation No, abnormal or unbalanced electricity generation #10 Improper grease
#11 Over tighten
#12 Electric corrosion of rollaway nest
#13 Shaft wear deformation
EP-GE-FM11 Overheat (GE) Offshore wind turbine shutdown #14 Turbine overload
#15 Cooling system failure
#16 Partial short circuit on stator winding
EP-GE-FM12 Winding failure No, abnormal or unbalanced electricity generation #17 Cable insulation failure
#18 Connecting plug fall off
#19 Interturn short circuit
#20 Winding corrosion
EP-GB-FM13 Wear gears Exceeded vibration or unstable electricity output #21 Wear, fatigue
#22 Dirty or lacking lubrication
EP-GB-FM14 Seized gears No electricity output #23 Sudden shock exceeds the limitation
EP-GB-FM15 Fractured gear teeth Exceeded vibration or unstable electricity output #24 Sudden shock exceeds the limitation
#25 Fatigue
EP-GB-FM16 Wear bearing Exceeded vibration #26 Fatigue
EP-GB-FM17 Overheat (GB) Offshore wind turbine shutdown #27 Wear
#28 Lubrication dried out
#29 Leaking
EP-GB-FM18 Shift crack Offshore wind turbine shutdown #30 Fatigue
ET-CV-FM19 Converter shutdown #31 Overheat
ET-CV-FM20 Disconnect to grid #32 Load mutation
#33 Invert power input fault
#34 Overload
#35 Cooling system fault
ET-TR-FM21 Short circuit Transformer shutdown #36 Overheat
ET-TR-FM22 Open circuit Disconnect to grid #37 Constant overload
#38 Iron core corrosion
#39 Overcurrent
#40 Overvoltage
SS-MF-FM23 Mooring lines fracture Offshore wind turbine shutdown #41 Extreme marine environment
#42 Fatigue damage
#43 Improper anchor installation
SS-TO-FM24 Collapse Offshore wind turbine damage #44 Unsafe structure integrity
#45 Harsh environment
AS-PS-FM25 Wrong pitch angle The decrease in electricity output #46 Poor calibration
AS-PS-FM26 Pitting Gears Vibration increase #47 Wear, fatigue
AS-PS-FM27 Misalignment bearings The decrease in electricity output #48 Wear, excessive vibration
AS-YS-FM28 Seizure bearings Overheat #49 Poor lubrication
AS-YS-FM29 Corrosions Pitting of raceways #50 Presence of corrosive substances
AS-YS-FM30 Hydraulic leakage Rotor fails to stop #51 Wear or degradation on hydraulic lines
AS-CE-FM31 Short circuit Offshore wind turbine shutdown #52 Moisture penetration
AS-CE-FM32 Open circuit Offshore wind turbine shutdown #53 Lightning strike

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H. Li, A.P. Teixeira, C. Guedes Soares et al. Renewable Energy 162 (2020) 1438e1461

Appendix C. Results comparison of the relative-weighted

technique (the first stage of the proposed method) and the
conventional FMECA for failure causes

Appendix D-1. Original values of the severity of failure causes

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H. Li, A.P. Teixeira, C. Guedes Soares et al. Renewable Energy 162 (2020) 1438e1461

Appendix D-2. Original values of the occurrence of failure

causes

Appendix D-3. Original values of the detection of failure

causes

Appendix D-4. Relative values of severity

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H. Li, A.P. Teixeira, C. Guedes Soares et al. Renewable Energy 162 (2020) 1438e1461

Appendix D-5. Relative values of occurrence

Appendix D-6. Relative values of detection

Appendix D-7. Relative-weights of severity (fij )

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H. Li, A.P. Teixeira, C. Guedes Soares et al. Renewable Energy 162 (2020) 1438e1461

Appendix D-8. Relative-weights of occurrence (fij )

Appendix D-9. Relative-weights of detection (fij )

Appendix E. The detailed algorithm for computing the max

RPNs/CRPNs O ¼ ½8 8 6 6 4 4 4 4 3 7 6 5 7 5 5 7 8 7 6 8 3 1 7 2 3 3 1 3 1
2 6 6 7 8 7 6 6 8 7 7 4 6 4 2 3 8 7 6 3 2 5 7 5
(1) The algorithm for computing the RPN of the failure cause ER-BL-
FM1-#1
D ¼ ½7 3 6 4 4 4 6 7 7 5 5 5 3 5 3 5 5 4 4 7 7 6 7 7 8 6 6 3 3 8 7
Step 1: Arrange the value matrix of severity, occurrence, and 6 8 6 4 6 4 8 4 3 3 8 2 7 7 7 7 7 4 4 4 6 6
detection as:

b¼½S O D (E.1)
Step 2: calculate the matrix U of severity, occurrence, and
where detection as:
h i
S ¼ ½8 7 4 7 4 8 8 3 4 4 4 4 4 3 3 3 4 4 4 4 5 5 6 8 8 5 4 4 4 8 6 U ¼ kjiS kjiO kjiD (E.2)
3 3 3 3 6 3 3 3 3 4 4 4 9 9 2 4 4 2 2 2 6 6
where


8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8
kjiS ¼
8 7 4 7 4 8 8 3 4 4 4 4 4 3 3 3 4 4 4 4 5 5 6 8 8 5 4 4 4 8 6 3 3 3 3 6 3 3 3 3 4 4 4 9

8 8 8 8 8 8 8 8 8
9 2 4 4 2 2 2 6 6

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H. Li, A.P. Teixeira, C. Guedes Soares et al. Renewable Energy 162 (2020) 1438e1461


8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8
kjiO ¼
8 8 6 6 4 4 4 4 3 7 6 5 7 5 5 7 8 7 6 8 3 1 7 2 3 3 1 3 1 2 6 6 7 8 7 6 6 8 7 7 4 6 4

8 8 8 8 8 8 8 8 8 8
2 3 8 7 6 3 2 5 7 5


8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8
kjiD ¼
7 3 6 4 4 4 6 7 7 5 5 5 3 5 3 5 5 4 4 7 7 6 7 7 8 6 6 3 3 8 7 6 8 6 4 6 4 8 4 3 3 8 2

8 8 8 8 8 8 8 8 8 8
7 7 7 7 7 4 4 4 6 6

Hence, the weighted values of severity, occurrence, and detec-

tion are computed as. ¼ 2:3252
105 þ 8:720
106 þ 7:474
106 ¼ 3:9446
105
(E.6)
88 = 88 = 87
=
fijS ¼ P ¼ 0:033; fijO ¼ P ¼ 0:029; fijD ¼ P ¼ 0:024
kjiS kjiS kjiS Step 2: calculate the CRPN of blades as:
(E.3)
CRPNðER  BLÞ ¼ RPNðER  BLÞ
CBL ¼ 3:9446
105
7:7

104 z3:04
Step 3: calculate the RPN of the failure cause ER-BL-FM1-#1, as:
(E.7)
RPNðER  BL  FM1  #1Þ ¼ 0:033
0:029
0:024 ¼ 2:2968 Similarly, CRPNs of other components can be computed.

105
(E.4) (4) The algorithm for computing the CRPN of the energy producing
system
Similarly, RPNs of other failure causes can be computed.
Step 1: calculate the CRPN of the energy producing system as the
summation of its components:
(2) The algorithm for computing the RPN of the failure mode EP-GE-
FM12 CRPNðEPÞ ¼
CRPNðEP  MBÞ þ CRPNðEP  MSÞ þ CRPNðEP  GEÞ (E.8)
Step 1: calculate the RPN of failure mode EP-GE-FM12 as the þCRPNðEP  GBÞ ¼ 4:3
summation of its failure causes:
Similarly, CRPNs of other systems can be computed.
X
20
RPNðEP  GE  FM12Þ ¼ RPNðEP  GE  FM12  #iÞ References
i¼17
[1] M. Leimeister, A. Kolios, A review of reliability-based methods for risk
¼ 8:304
106 þ 5:813
106 þ 4:983
106 þ 1:1626 analysis and their application in the offshore wind industry, Renew.

105 ¼ 3:0726
105 Sustain. Energy Rev. 91 (2018) 1065e1076.
[2] J. Carroll, A. McDonald, D. McMillan, Failure rate, repair time and un-
(E.5) scheduled O&M cost analysis of offshore wind turbines, Wind Energy 19
(2016) 1107e1119.
Similarly, RPNs of other failure modes can be computed. [3] A.S. Bahaj, M. Mahdy, A.S. Alghamdi, D.J. Richards, New approach to
determine the Importance Index for developing offshore wind energy
potential sites: supported by UK and Arabian Peninsula case studies,
Renew. Energy 152 (2020) 441e457.
(3) The algorithm for computing the CRPN of blades [4] H.M. Diaz, C. Guedes Soares, Review of the current status, technology and
future trends of offshore wind farms, Ocean. Eng. 209 (2020), 107381.
Step 1: calculate the summation of RPNs of failure modes of [5] D. Martins, G. Muraleedharan, C. Guedes Soares, Weather window anal-
ysis of a site off Portugal, in: C. Guedes Soares, T.A. Santos (Eds.), Maritime
blades as: Technology and Engineering, Taylor & Francis Group, London, UK, 2015,
pp. 1329e1338.
X
3 [6] D. Martins, M. Gangadharan, C. Guedes Soares, Analysis on weather
RPNðER  BLÞ ¼ RPNðER  BL FMiÞ windows conditioned by significant wave height and wind speed, in:
i¼1 C. Guedes Soares (Ed.), Renewable Energies Offshore, Taylor & Francis
Group, London, UK, 2015, pp. 91e98.

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H. Li, A.P. Teixeira, C. Guedes Soares et al. Renewable Energy 162 (2020) 1438e1461

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rez, M. Papaelias, Condition moni-
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