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Tidal stream device reliability comparison modelsT M Delorm*, D Zappala, and P J Tavner

School of Engineering and Computing Sciences, Durham University, Durham, UK

The manuscript was received on 6 February 2011 and was accepted after revision for publication on 16 August 2011.

DOI: 10.1177/1748006X11422620

Abstract: Tidal stream devices are a new technology for extracting renewable energy from thesea. Various tidal stream device models have been proposed and, if they are installed at cho-sen high tidal stream velocity sites, they may face extreme climatic, current, and wave loadconditions. As they contain complex mechanical, electrical, control, and structural systems,reliability and survivability will be a challenge. Data on their reliability have been scarce, asonly a few prototypes have been built and operated. However, reliability prediction of newdevices could minimize risk in prototype work. A practicable tidal stream device reliabilityprediction method could assist the development of cost-effective and viable future options.The present study proposes such a method and derives system reliability models for four gen-eric-design, horizontal-axis, tidal stream devices, all rated 1–2 MW. Historical reliability datafrom similarly rated wind turbines and other relevant marine databases were used to populatethe devised reliability models. The work shows that tidal stream devices can expect to have alower reliability than wind turbines of comparable size and that failure rates increase withcomplexity. The work also shows that with these predictions, few devices can expect to survivemore than a year in the water. This suggests that either predicted failure rates must bereduced dramatically or that methods for raising reliability – by the use of twin axes orimproving maintenance access by unmooring or the use of a seabed pile and turbine raising –will be needed to achieve better survivor rates. The purpose of this work is not to predict defi-nitive individual device failure rates but to provide a comparison between the reliabilities of anumber of different device concepts.

Keywords: tidal stream device, reliability prediction model, reliability block diagram,

environmental adjustment factor, surrogate data sources, wind turbine failure rate, failure

rate, comparison

1 INTRODUCTION

Tidal stream devices (TSDs) are an emerging tech-

nology. Permanently installed at selected tidal sites,

they may endure extreme climatic, current, and

wave load conditions, and their mechanical and

electrical control systems are complex. Therefore

their reliability and survivability will be an engineer-

ing challenge, although this could be mitigated by

selecting benign tidal sites.

Probabilistic reliability modelling is a proven

methodology for assessing probability of system

success or failure [1, 2] at the conceptual design

stage. The present paper reports the conceptual

development of generic reliability prediction models

to quantify reliability and make life-cycle predic-

tions for specific TSD types. Surrogate reliability

data from the wind turbine (WT), marine, and con-

ventional electric power generation industries are

used to predict device failure rates and survivor

functions. The purpose of this work is to provide a

means of comparing relative concept reliabilities,

rather than to derive definitive device failure rates.

The paper is organized as follows: Section 2 is an

overview of current TSD technology and problems

*Corresponding author: School of Engineering and Computing

Sciences, Durham University, South Road, Durham DH1 3LE,

UK.

email: [email protected]

SPECIAL ISSUE PAPER 1

Proc. IMechE Vol. 000 Part O: J. Risk and Reliability



with reliability predictions. Section 3 presents a

methodology for deriving non-repairable prediction

models for single- and twin-axis turbine devices

with a ‘mission time’ of 1 year and an overview of

acceptable surrogate source data sources for use in

those models. Section 4 presents results and a dis-

cussion of applications for comparison of reliability

model results. Section 5 presents conclusions and

recommendations for the future on the basis of this

methodology and its results.

2 BACKGROUND STATE OF THE ART

2.1 Tidal stream technology specifics and

uncertainties

TSDs can be constructed as modules, installed

incrementally in arrays, with minimal environmen-

tal intrusion, unlike barrages, which require large-

scale civil engineering [3]. They can be horizontal or

vertical turbines or oscillating hydrofoils. More than

60 TSD technologies have been identified [4] and

some examples are shown in Fig. 1.

Horizontal-axis turbine devices can be further

sub-categorized by their seabed fixing and position

in the water column; Fig. 2 illustrates generic

designs currently being considered. Horizontal-axis

devices experience a strong drag and need to be

grounded to the seabed; the arrangements for this

depend upon differing environments [5].

Device designs are presently in the research and

development stage, with only a few, first-stage pro-

totypes being deployed. Technology data have not

been released to the public, so equipment defini-

tion, particularly for auxiliary systems, can only be

researched in generic terms. Devices will also have

to overcome the problems of fouling, tethering, and

power take-off described by Boyle [3], where more

investigation and evaluation will be needed in the

future.

2.2 Problems with reliability predictions

Two definitive studies exist for wave power device

reliability [6, 7] but are rather dated. A methodology

for the analysis of offshore devices was proposed in

reference [8] and developed in reference [9]. In ref-

erence [10] this developed analysis was applied in

the Supergen Marine project to a wave device, using

surrogate data as proposed in the present paper, but

the method did not propose an overall methodol-

ogy, as suggested here. Complementary work has

also been done in the Supergen Marine project

in reference [11], analysing the reliability of tidal

device components based upon their specific

design, rather than comparing between concepts, as

proposed here. It will become important to compare

the results of the present work with reference [11] to

gain tidal device reliability experience, and with ref-

erence [10] to learn common lessons between wave

and tidal power.

References [8] and [9] focused on problems of

system reliability and total system unavailability,

showing that assembly and subassembly reliability

starts by recognizing sequential failure processes,

through a risk-based framework for system life

cycle, using a reliability estimation method.

The reliability methodology in reference [8] has

not yet been applied to tidal energy, nor has a

comparison been made between different tidal

technologies. The literature surveyed did not reveal

a well-defined reliability model needed for such

reliability predictions. Concerns have been

expressed that reliability data are not yet available

from tidal devices, but core TSD technologies are

very similar to those used in current WTs of similar

power.

Fig. 1 Types of TSD [4]: (a) horizontal-axis turbine; (b) vertical-axis turbine; (c) oscillating hydro-foil; (d) vertical-axis cup turbine

2 T M Delorm, D Zappala, and P J Tavner




3 TSD RELIABILITY PREDICTIONS MODEL,CASE STUDY

3.1 TSDs considered

The present study aims to formulate a reliability

prediction model based on an assembly/subassem-

bly approach for analysing and comparing four hor-

izontal-axis devices, with taxonomies similar to

WTs, illustrated in Fig. 2 and listed below.

1. TSD1: floating tethered, semi-submerged deep-

water application, induction generator, single-

axis turbine, rated power 1.2 MW.

2. TSD2: seabed pile-mounted, shallow-water

application, induction generator, twin-axis tur-

bine, rated power 2 3 0.6 MW = 1.2 MW.

3. TSD3: seabed bottom-mounted, gravity base,

shallow- or deep-water application, permanent

magnet generator, single-axis ducted turbine,

rated power 1.0 MW.

4. TSD4: floating tethered, deep-water application,

permanent magnet generator, twin-axis turbine,

rated power 2 3 0.6 MW = 1.2 MW.

Based on naming standards [12, 13] the authors

have established a general taxonomy suitable for

all devices. For brevity, the case of only one device,

TSD1, is presented in detail in the paper, but

reliability models for all four devices were

developed and analysed, and are summarized gra-

phically here.

3.2 Modelling methodology used

Reliability modelling and prediction (RMP) [1, 2]

was chosen as an appropriate quantitative method

because:

(a) TSDs are a new technology in an early stage of

design and development;

(b) RMP is applicable to both the mechanical and

electrical subassemblies incorporated in these

TSDs.

A reliability model presents a visual representa-

tion of functional interdependencies and a frame-

work for prediction analysis, which applies

assembly/subassembly-based interdependencies

and failure rates to the modelled assembly in the

following sequence.

1. Classify subassemblies using robust methods

[12, 13].

2. Establish a schematic diagram for each device.

3. Derive a functional block diagram (FBD) from

that schematic diagram, showing the functional

interdependencies between assemblies and sub-

assemblies, constituting a reliability block dia-

gram (RBD).

4. Collect reliability data from surrogate sources,

using them to allocate failure rates for each FBD

subassembly.

5. In the unknown environment without historical

reliability data, establish lower- and upper-bound

Fig. 2 Types of horizontal-axis TSD [5]

Tidal stream device reliability comparison models 3




failure rates, kGi_min and kGi_max, for each sub-

assembly from surrogate data and use the upper

bound as the more conservative value.

6. Adjust surrogate failure rate data to the tidal

environment using two failure rate estimate

approaches.

7. Calculate predicted tidal environment failure

rates.

8. Evaluate the total device reliability, using the

parts count reliability prediction technique [14,

15], assuming that subassembly times-to-failure

are exponential, i.e. hazard rates are the result of

random failures.

3.3 Reliability data collected from surrogate

sources

Data are vital to new technology reliability predic-

tion. However, when no historical information is

available, surrogate data can be used [1] and in the

present case were available from the following pub-

lic databases.

1. European onshore WT databases summarized in

Fig. 3, from reference [16]:

(a) WMEP (Wissenschaftlichen Mess- und

Evaluierungsprogramm) database [17] con-

taining data on failure rates of fixed- and

variable-speed WTs with geared or direct

drives over 15 years of operation from

15 400 WT-years;

(b) LWK (Landwirtschaftskammer Schleswig-

Holstein) database [18] containing data on

failure rates of fixed- and variable-speed

WTs with geared or direct drives over 11

years of operation from 5800 WT-years.

2. Petrochemical industry database OREDA

(Offshore Reliability Data) [19] containing relia-

bility data from a wide range of equipment used

in oil and gas exploration and production for

topside and subsea equipment.

3. Generic databases:

(a) NPRD-95 (Nonelectronic Parts Reliability

Data) [20] containing failure rates for

25 000 mechanical, electromechanical, and

discrete electronic subassemblies used in

military and commercial applications.

(b) MIL-HDBK-217F (Military Handbook 217F)

[14] containing empirical failure rates data

of electrical subassemblies used in military

and commercial applications.

Because no reliability data are yet available from

tidal turbines these surrogate data were used as the

backbone of the present study, thereby benefitting

from the similarity of WT core technologies to TSDs,

including their most vital subassemblies: gearbox,

generator, and power electronics.

3.4 Subassembly predicted failure rate in tidalenvironment

The main question mark over this approach is the

relevance of these data to the device environment;

the environments from which the surrogate data

came are summarized in Table 1.

Further treatment is therefore needed to apply

the surrogate data to a marine environment, for

example by the use of environmental adjustment

Fig. 3 Summary of WT failure rates and downtimes from the large WMEP and LWK surveys [16]





factors. Three different operational environments

found in tidal devices were to be applied as pre-

sented in Table 2.

1. GF – ground, fixed: severe environment.

2. NS – naval, sheltered: normal environment.

3. NU – naval, unsheltered: severe environment.

In general, WTs and electrical equipment are in the

GF environment, whereas TSDs are in the NS or

NU environment. Tidal environment subassembly

failure rates could be predicted using surrogate

data by applying a GF to NU or NS adjustment

factor.

Environmental conversion factors for electrical

and electronic components from MIL-HDBK-217F

[14] are tabulated in Table 6.4.1-2 of reference [2].

These data must be modified for the present study,

which considers component failure rates, ki,

because MIL-HDBK-217F multipliers were intended

for mean time between failures (MTBF). The modi-

fied data are presented in Table 2 and environmen-

tal definitions are described in references [14]

and [21].

Applying appropriate environmental adjustment

factors will reduce errors in the subsequent predic-

tions. The authors were unable to find a previously

defined rationale for this approach, so they propose

the use of two failure rate estimates set out in

Table 3:

(a) a conservative failure rate estimate without

adjustment, FREcon;

(b) an environmentally adjusted conservative fail-

ure rate estimate, FREenv.

In the particular case of OREDA data, where the

tidal environment differs from the oil and gas

environment, the authors have used OREDA failure

rates at the upper limit of the 90 per cent confi-

dence interval, to ensure the most conservative

estimate.

3.5 Reliability prediction model calculations

Individual subassembly failure rates were combined

into a total failure rate for two alternative operating

constraints, as follows:

Table 1 Environments of surrogate data sources used in the model

Surrogate data source Naval, unsheltered:severe environment NU

Naval, sheltered: normalenvironment NS

Ground, fixed: severeenvironment GF

LWK, WMEP – – XOREDA X X XNPRD-95 X X XMIL-HDBK-217F X X X

Table 2 Environmental adjustment factors, pE

To that environmentMIL-HDBK-217F [14]

GB GF GM NS NU

SD-18 [21]

Protected – – Normal Severe

From this environment GB Protected – 2.0 5.0 3.3 10.0GF – 0.5 X 0.4 1.7 3.3GM – 0.2 0.4 X 0.7 1.4NS Normal 0.3 0.6 1.4 X 2.0NU Severe 0.1 0.3 0.6 0.5 X

Environments are defined in the Notation.

Table 3 Failure rate estimates

Failure rate estimate Method using surrogate data Limitations

Conservative:FREcon

No environmental adjustment appliedkðbÞi ¼ kGi max

Represents a conservative failurerate for a branch, b, butneglects environmentalconditions

Environmentally adjustedconservative: FREenv

Multiplied by an environmental factor, pEi

kðbÞi ¼ kGi max3pEi For mechanical components: pEi=1For electrical/electronic components: pEi as defined in Table 2

Represents a conservative failurerate for a branch, b, but takesaccount of environment





1. Predicted total failure rates based on the

assumption of a non-repairable series assembly

of independent subassemblies operating up to

full 100 per cent of device power output for

TSD1 to TSD4 for one calendar year.

2. The same but operating up to full 100 per cent of

device power output for TSD1 to TSD4, or 50 per

cent of device power output for TSD2 and TSD4,

which incorporate twin-axis turbines and there-

fore have implicit redundancy.

To evaluate assembly reliabilities the parts count

reliability prediction technique was used whereby

the FBD was simplified to a series model, reducing

any redundant subassemblies to an equivalent sin-

gle branch, b, then using subassembly failure rates

to calculate the predicted failure rate for the ith gen-

eric unit according to Table 3, either

k(b)i = kGi max(failures=year) (1)

or

k(b)i = kGi max3pEi(failures=year) (2)

The predicted assembly failure rate models are as

follows:

1. Series network: For a TSD with all subassemblies

in series, the device will fail if any one of the

subassemblies fails. For a series reliability model

of independent subassemblies with constant

failure rates, the reliability model forms and

total failure rate are expressed as

ktot Ns =XNs

b = 1

SNb

i = 1k(b)i (3)

2. Series parallel network: For a device with Ns sub-

assemblies in series and Np assemblies with two

identical branches in parallel with constant fail-

ure rates, for example TSD2 and TSD4 with

twin-axis drive trains up to 50 per cent power

production (DT), an uninterrupted electrical

assembly (B), a redundant ancillary assembly

(XA), and twin-axis nacelle structures (U), and

so on for other similarly redundant subassem-

blies with two identical branches in parallel, the

reliability model forms and total failure rate are

expressed as

ktot = ktot Ns +2

3ktot Np

(4)

ktot Np = kDT + kB + kXA + kU + � � � (5)

ktot =XNs

b = 1

SNb

i = 1k(b)i +

2

3kDT + kB + kXA + kU + � � �ð Þ

(6)

where

kDT =XNDT

i = 1

k(DT)i (7)

is the total failure rate of a drive train (DT), equal

to the sum of the failure rates of the single-

branch DT subassemblies, and

kB =XNB

i = 1

k(B)i (8)

is the total failure rate of an uninterrupted elec-

trical assembly (B), single branch of a twin-axis

assembly, and

kXA =XNXA

i = 1

k(XA)i (9)

is the total failure rate of an ancillary assembly

(XA), single branch of a twin-axis redundant

assembly, and

kU =XNU

i = 1

k(U)i (10)

is the failure rate of a single-branch twin-axis

nacelle or support structures (U).

Therefore, the device reliability survivor function

R(t) can be calculated as follows:

For series network

R(t) = e�ktot Nst (11)

For series/parallel network

R(t) = e�ktot t (12)

where R(t) is the reliability survivor function and t

(years) is the device total time offshore.

The paper uses a standard formula for assemblies

with twin-axis redundant DT branches to

represent a single reliability parameter curve.

The method can be extended to more complex

assemblies using standard reliability equations

[1].





3.6 Example of development of reliability

prediction model for TSD1

A schematic diagram was developed for TSD1, see

Fig. 4. A taxonomy of critical subassemblies was

then derived to form an FBD, see Fig. 5. The subas-

semblies were arranged in a table, using the classifi-

cation system [12], to produce a reliability model,

which was populated with surrogate failure rate

data. For brevity, Table 4 shows only the DT ele-

ment of that model.

The FBD in Fig. 5 shows the functional interdepen-

dencies and Table 4 shows the method for deriving

quantitative total system reliability. The FBD reveals

system dependencies that will eventually require more

advanced reliability modelling methods.

This study used the upper-bound failure rate,

kGi_max, for each subassembly, giving a conservative

prediction for a novel technology. The failure

rates were calculated using equations (1) to (10),

assuming each subassembly was independent of

others and that all operated in a single environment.

Device reliability can be analysed as series/parallel

subassemblies or decomposed to series subassem-

blies using the RBD.

Results predicted for the tidal environment based

on Table 3 are summarized for the DT of TSD1 in

Table 4. Again for brevity only the critical subassem-

blies contributing directly to TSD1 power produc-

tion are presented in Table 4, but the whole

structure for all devices has been analysed.

Predicted reliability characteristics of TSD1 com-

pared with the other three devices are shown in

Fig. 6 and discussed in section 3.7.

3.7 Reliability comparison of the four device

models

The parts count reliability prediction technique was

applied to calculate the average number of failures

Fig. 4 TSD1 schematic diagram





per year. It was assumed that assembly-redundant

subassemblies are individual blocks. It is acknowl-

edged that this approach can lead to error [22],

which could be as much as 20 per cent of the resul-

tant failure rate; however, again this will lead to a

conservative result. The reliability results for the

four devices are summarized in Figs 6 and 7, which

show a failure and survivor rate comparison

between models to assess their architectures. In par-

ticular, Fig. 6 compares the predicted failure rates

with the total number of subassemblies in the

device, allowing comparison to be made between

failure rate and complexity.

4 RESULTS AND DISCUSSION

4.1 Wind versus tidal stream turbines: model

validation

Given the absence of TSD reliability data, it is useful

initially to compare predicted reliability values

obtained from the four TSDs in this study with

Fig. 5 TSD1 functional block diagram

Table 4 TSD1 drive train element of the reliability model, according to equations (1) to (3)

Reliability characteristics for: Surrogate failure rates(failures/year)

Failure rate estimate(failures/year)

Branch b i Code Subassemblies Data source kGi_min – kGi_max FREconv pEi FREenv

Drive train (MD&MK) 1 MDA10 Rotor blades, pitch electronics [17], [18] 0.115 – 0.230 0.230 3.3 0.7592 MDA20, MDC10, MDC10P001 Hub, pitch system, pitch

bearing[17], [18] 0.083 – 0.177 0.177 1.0 0.177

3 MDK10, MDK10 UP001,MDK40

Main shaft, bearing, couplings [17], [18] 0.031 – 0.055 0.055 1.0 0.055

4 MDK11 Shaft seal [20] 0.061 0.061 1.0 0.0615 MDK20, MDV10 Gearbox, lubrication & cooling [17], [18] 0.101 – 0.134 0.134 1.0 0.1346 MDK30 Electric brakes [20] 0.031 0.031 1.0 0.0317 MKA10 Generator water cooled [17], [18] 0.106 – 0.139 0.139 1.7 0.2368 MKY10, MKY11 Converter, AC/AC; converter

controller[17], [18] 0.239 – 0.430 0.430 1.7 0.731

9 MKC10 Generator circuit-breaker [14] 0.020 – 0.175 0.175 1.0 0.175Drive train estimated total failure rate, kDT (failures/year) 1.433 2.360





measured reliabilities of onshore WTs of similar size

[18]; this is done in Fig. 8. The similarities of subas-

semblies used in the power trains of these two tech-

nologies make this comparison interesting.

From Fig. 8 the predicted failure rates for the four

devices show that they are less reliable than onshore

WTs of similar power output: the predicted TSD fail-

ure rates range from 150 to 200 per cent of wind tur-

bine failure rates. This is to be expected, bearing in

mind that the TSD technology is in its infancy and

operating in a harsher environment, but suggests

that these predicted TSD failure rates are represen-

tative and that the industry either needs to reduce

them in some radical way or provide more accessi-

ble methods of repair.

Significant failure rate improvements for devices

are clearly possible with time, bearing in mind

Fig. 6, where failure rates can be improved if subas-

sembly counts are reduced. Moreover, the data in

Fig. 8 were obtained from WTs undergoing regular

service at least twice per annum, controlling WT

failure rates which can be maintained at any time,

compared with an offshore device for which the

shortest practical maintenance interval is likely to

be one year [8]. Considerable experience is being

gained of offshore WTs and reference [23] gives a

good summary of UK Round 1 offshore wind farm

operations. However, WT failure rates in these cir-

cumstances are not being released due to

confidentiality.

A further interesting comparison can be made

between wave device reliability, predicted in refer-

ence [10], and that of devices considered in this

paper. This shows that the TSDs have broadly simi-

lar predicted reliabilities to that of the analysed

wave device.

4.2 Failure rate and complexity

Figure 6 clearly shows that the TSDs with more sub-

assemblies have a higher failure rate. This is compli-

cated by the twin-axis devices TSD2 and TSD4,

which also have some intrinsic redundancy, the

effect of which is visible in their higher failure rates

when 100 per cent power is expected but lower fail-

ure rates when only 50 per cent power is required.

4.3 Impact of maintenance on reliabilityestimation

Assuming non-repairable operation for all devices of

1 year, the percentage of survivors after 1 year in the

water has been predicted in Fig. 7 to be less than

two devices in 100. This is very low and would

be commercially unacceptable, suggesting that

Fig. 6 Comparison of predicted failure rates for TSD1to TSD4 and the number of subassemblies

Fig. 7 Predicted survivor functions for TSD1 to TSD4after 1 year in the water

Fig. 8 Comparison of failure rates. The histogramshows the predicted failure rates for each of thefour devices. The horizontal band representsthe range of measured failure rates of onshoreWTs of similar rating [18]





predicted failure rates must be reduced or the

annual maintenance concept is simply untenable.

This could also suggest that fixed devices, without

maintenance access, will suffer poor survivor rates

unless failure rates are reduced dramatically,

whereas devices with maintenance access, either by

unmooring or the use of a seabed pile and turbine

raising, may achieve much better survivor rates.

4.4 Limitations

Dynamic and peak-stress effects, such as wave-slam

or exceptional tidal ranges, were not considered in

the process and it is unlikely that this kind of

approach could reasonably consider such dynamic

effects. Issues of fouling were also not dealt with in

the process, but all of these issues could be included

if the appropriate adjustment factors were available.

5 CONCLUSIONS

A methodology for analysing and comparing TSD

reliabilities in the early design phase, using surro-

gate data, has produced informative results. The

methodology has obtained predicted failure rates

which show the following.

1. Predicted TSD failure rates increase with

increasing device complexity, as expected.

2. These failure rates, based on the conservative

FREenv estimate, range from 150 to 200 per cent

of the failure rates of WTs of similar size. This is

so when WTs are a mature technology while

TSDs are a new technology, suggesting that

these predicted TSD failure rates are

representative.

3. TSD3, with a seabed bottom-mounted, ducted

single-axis turbine, has the lowest failure rate

because of its simple technology and low Ntot.

4. Ntot increases for twin-axis TSD2 and TSD4 and

therefore so too do failure rates.

5. However, TSD2 and TSD4 show improved fail-

ure rates when only 50 per cent power is

required because of the implicit redundancy of

the twin-axis technology.

6. TSD2, when operating at 50 per cent power, has

a failure rate almost as low as TSD3, because it

is utilizing the subassemblies of only one drive

train.

7. TSD4 has a higher predicted failure rate than

TSD2 because it is more complex and

Ntot,TSD4 . Ntot,TSD2.

8. Predicted failure rates for TSDs are worse than

measured failure rates for WTs of similar rating,

as expected, because of the infancy of tidal com-

pared with wind technology and because predic-

tions were adjusted for the more arduous

marine environment.

9. However, the necessary significant failure rate

improvements for tidal devices are clearly possible.

The methodology has obtained predicted device

survivor rates and predicted failure rates which

show the following:

1. Assuming non-repairable operation for a year,

the device predicted failure rates show the per-

centage surviving in the water after 1 year will

be small.

2. This suggests that:

(a) either device failure rates must be dramati-

cally reduced;

(b) or fixed devices without maintenance access

must suffer poor survivor rates;

(c) whereas devices with maintenance access,

either by unmooring or the use of a seabed

pile and turbine raising, must achieve bet-

ter survivor rates.

The proposed methodology has the following

limitations.

1. Surrogate data were derived from repairable

sources, representing different population sizes

and failure mechanisms in environments differ-

ent from those that may arise for tidal devices.

2. An appropriate rationale for the use of surrogate

data and their adjustment for the tidal environ-

ment are not yet agreed, so the authors pro-

posed the use of two failure rate estimates.

3. This reliability prediction analysis, suitable for

the early design stage, considered main subas-

semblies only, as shown in the FBD, and did not

drill-down to all components.

4. ‘Naval, sheltered’ and ‘naval, unsheltered’ envir-

onments were considered closest to the tidal

environment where the devices will operate.

5. Dynamic and peak-stress effects, such as wave-

slam or exceptional tidal ranges, and fouling

were not considered in the process.

The failure and survivor rate results derived in the

present paper are an approximation to reality and

cannot be treated as definitive. Differences between

predicted device failure rates were not large and

also should not be treated as absolute, rather for

technology comparison. However, the methodology

and use of surrogate data have been shown to be





useful for predicting device reliability and for mak-

ing these comparisons. These predictions are only

as good as the constructed model and data and can

only be used in the early stages of device design,

after which more detailed analyses, such as pro-

posed in reference [11], are needed.

The proposed method needs to be applied to a

wider range of tidal devices to develop the methodol-

ogy and raise confidence. Comparison should also be

made to similar analyses being made on offshore

WTs [23] and wave devices [10], for the same rea-

sons. It is recommended that the failure rate estima-

tion approach should be used for further early-stage

TSD design analysis, using surrogate data adjusted to

the tidal environment. It is proposed to initiate a

project with developers for using this surrogate data

with the restricted model approach. More investiga-

tion is needed of system simulation of these models

to evaluate the impact on the reliability of the more

complex device systems, such as their controls.

FUNDING

This work was supported by the Engineering and

Physical Sciences Research Council under the

Supergen Marine Doctoral Programme [grant num-

ber EP/E040136/1].

ACKNOWLEDGEMENTS

The authors acknowledge the funding support and

the advice of Dr P. Fraenkel, Dr F. J. Franklin, Dr D.

Nicholls, and G. Mackie.

� University of Durham 2011

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APPENDIX

Notation

B uninterrupted electrical assembly

DT drive train

FBD functional block diagram

FRE failure rate estimate

FREcon conservative failure rate estimate

without adjustment

FREenv environmentally adjusted conserva-

tive failure rate estimate

GB ground benign: protected

environment

GF ground fixed: severe environment

GM ground mobile environment

LWK Landwirtschaftskammer Schleswig-

Holstein

MIL-HDBK Military Handbook

MTBF mean time between failure

Nb number of sub-assemblies in series

in one branch b of an assembly

Np number of subassemblies in series

within an identical parallel branch

Ns number of subassemblies in series

with none in parallel

Ntot total number of device

subassemblies

NPRD Nonelectronic Parts Reliability Data

NS naval sheltered: normal environment

NU naval unsheltered: severe

environment

OREDA Offshore Reliability Data

R(t) reliability survivor function

RBD reliability block diagram

RMP reliability modelling and prediction

t device total time offshore

TSD tidal stream device

U support structure

WMEP Wissenschaftlichen Mess- und

Evaluierungsprogramm

WT wind turbine

XA ancillary assembly

k(t) failure intensity function

kB uninterrupted electrical assembly

single-branch total failure rate

kDT drive train single-branch total failure

rate

kGi_max maximum generic failure rate for ith

subassembly

kGi_min minimum generic failure rate for ith

subassembly

kðbÞipredicted failure rate of ith sub-

assembly in branch b

ktot series/parallel network total pre-

dicted failure rate

ktot_Np parallel network single-branch total

predicted failure rate

ktot_Ns series network total predicted failure

rate

kU support structure single-branch total

failure rate

kXA ancillary assembly single-branch

total failure rate

pE environmental adjustment factor





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