EFFICIENT PROBABILISTIC METHODS FOR TIME-DOMAIN PIPELINE...

OPT 2015 1 Madeley et. al. 2015

EFFICIENT PROBABILISTIC METHODS FOR TIME-DOMAIN PIPELINE ANALYSIS

Chris Madeley, Gavin Coombes & Adam Czajko Subsea Engineering Associates

Perth, WA, Australia

ABSTRACT

Free-spans that evolve due to seabed scour beneath pipelines

may be temporary in nature if the seabed continues to be

mobile. Traditional deterministic approaches assume

persistence of the span for the pipeline’s remaining life are

therefore overconservative. This may lead to unnecessary

intervention of these spans. In 2013 the MOBILEspan JIP

was established to improve the assessment of transient free-

spans. Scour, response and fatigue models have been

combined in a probabilistic framework to better quantify the

integrity of the free-spanning sections.

The free-span assessment requires simulation of a pipeline

segment in the time domain for its design lifetime. To

ensure the system meets nominal reliability targets, the

analysis must be repeated for up to 107 iterations. Hence the

scale of the computational problem becomes onerous. Two

strategies have been used to approach this problem.

Bayesian methods have been applied to refine the

probabilistic approach; quantifying the uncertainty in the

result allows for a reduced number of trials to be performed.

Secondly, the analysis procedure has adapted to fit a

MapReduce framework, taking advantage of scalable

computational capacity in a cloud environment to achieve

acceptable runtimes. Combined, these two approaches can

achieve up to 400x calculation speedup. This paper details

these approaches to show how free-span integrity

assessment has been achieved efficiently despite appearing

computationally prohibitive.

INTRODUCTION

BACKGROUND

When left unmanaged, pipeline freespans have the potential

to pose a serious risk to pipeline integrity. To manage this

risk significant research has been performed to better

characterise the response and loading of freespans to prevent

fatigue or ultimate failure. When the integrity of a pipeline

freespan cannot be assured offshore intervention is required,

which can often be a costly exercise.

Pipeline freespans can generally be classified into two

groups: stationary and mobile. Stationary spans do not

change in time throughout the pipeline lifetime. These spans

typically arise due to the uneven pre-lay seabed profile and

only change due to changes in a pipeline’s operating

conditions. Conversely, mobile freespans constantly evolve

throughout a pipelines lifetime, due to morphological

changes in the seabed around the pipeline. Changes in the

seabed profile may be due to local flow changes causing

seabed erosion near the pipeline, i.e. scour, or due to larger

scale bedform activities, e.g. sand waves.

Although the industry best practice for freespan assessment,

DNV-RP-F105, acknowledges the occurrence of mobile

spans, the guidance on how to assess these spans is brief and

very conservative. Specifically, the RP states:

In the case of scour induced spans, where no detailed

information is available on the maximum expected span

length, gap ratio and exposure time, the following apply:

— Where uniform conditions exist and no large-scale

mobile bed-forms are present the maximum span length

may be taken as the length resulting in a static mid span

deflection equal to one external diameter (including any

coating).

— The exposure time may be taken as the remaining

operational lifetime or the time duration until possible

intervention works will take place. All previous damage

accumulation must be included.


In 2013 the MOBILEspan JIP was established with the aim

of producing a tool for the probabilistic assessment of

pipeline free spans on mobile, scouring seabeds. In contrast

to the above passage, free spans on mobile seabeds are

typically transient in nature. The spans form due to scouring

of the seabed beneath the pipeline, and disappear as the

pipeline self-buries due to shoulder collapse or touchdown

inside the scourhole. The MOBILEspan appoach aims to

reduce over-conservatism inherent in the current

methodology, which was developed for stationary free

spans, by combining a pipeline scour model with a Monte

Carlo based probabilistic assessment. This would allow

operators to reduce their intervention costs by more

accurately quantifying the risk of failure by using a more

detailed and accurate analysis of the span behaviour.

The scour process and pipeline fatigue damage

accumulation are coupled through their common

dependence on environmental conditions. Because of this

interdependence a single, conservative analysis case is

difficult to define. To overcome this limitation, and better

quantify the integrity of a pipeline, the entire analysis

procedure has been wrapped in a probabilistic framework; a

Monte Carlo analysis. This advance in engineering analysis

is only possible due to the recent availability of on-demand,

large scale computational power on the cloud, billions of

analysis cases can be analysed within a reasonable

timeframe at an affordable cost.

APPLICATION OF PROBABILISTIC METHODS

The use of probabilistic techniques in structural reliability

analyses of fatigue in offshore structures has been in

existence for many years; nearly 40 years ago Vughts &

Kinra (1976) published a study into the probabilistic fatigue

analysis of fixed offshore structures. This study used

probabilistic techniques to determine local stress histories of

each member for a given sea state, and then used Miner’s

cumulative damage law to evaluate the local fatigue

damage. Whilst the computational methods used may have

advanced since then, the underlying mathematical procedure

is still the core of a structural reliability analysis.

In the context of subsea pipelines, structural reliability

analyses using probabilistic methods are recognised in

DNV-OS-F101 (2013) as an alternative to the DNV-OS-

F101 design format. Section 2 C500 of DNV-OS-F101

states:

As an alternative to the specific LRFD (and ASD) format, a

recognised structural reliability analysis (SRA) based design method may be applied provided that:

the method complies with DNV Classification Note

no. 30.6 “Structural reliability analysis of marine

structures”

the approach is demonstrated to provide adequate

safety for familiar cases, as indicated by this standard.

As far as possible, nominal target failure probability levels

shall be calibrated against identical or similar pipeline

designs that are known to have adequate safety on the basis

of this standard. If this is not feasible, the nominal target

failure probability level shall be based on the failure type and safety class as given in Table 2-5.

For a pipeline freespan in a production pipeline a nominal

target failure probability of 10-5 is appropriate. Note that

these nominal failure probabilities are not a realistic

illustration of pipeline failure probability (Palmer 2012),

however they do provide a basis to design a consistent level

of inherent resilience into each pipeline (Agrell and

Collberg 2014).

DNV Classification Note 30.6 (1992) describes a rule of

thumb for basic Monte Carlo methods that in order to

calculate an estimated reliability level with a known

variance of 10%, the number of iterations required is 100/Pf,

where Pf is the target failure probability. Therefore a

minimum of 107 Monte Carlo iterations are required to

demonstrate compliance with the code. Since each of these

ten-million iterations is a complete time-domain fatigue

assessment of free spanning sections of a pipeline, the

probabilistic MOBILEspan methodology presents a massive

computational challenge that far exceeds that of

conventional methods.

PROBABILISTIC FREESPAN ASSESSMENT

Probabilistic methods have been used to assess pipeline

integrity in previously published studies.

Bruschi et al. (1997) proposed a probabilistic method to

assess the structural integrity of scour induced free spans in

their summary of pipeline interaction with erodible seabeds.

A probabilistic method is used to capture uncertainty in the

distribution of span lengths and exposure to hydrodynamic

loading due to random nature of the environmental

conditions. A first order reliability method (FORM) was

used to estimate the probability of failure. It is noted that a

more complete reliability analysis requires detailed

distributions of all of the basic variables involved and

FORM is sometimes infeasible. Bruschi et al. recommended

that simpler alternatives, such as the Monte Carlo method,

were needed for practical engineering.

Esplin and Stappenbelt (2011) utilised a Monte Carlo

approach based on DNV-RP-F105 (2006) to demonstrate

that traditional deterministic assessments of free spans are

overly conservative, and this conservatism can be reduced

by adopting a probabilistic analysis. Rather than using the

computationally demanding basic Monte Carlo method, they

use an approximate method where Monte Carlo simulations


are performed to determine the mean value of fatigue

damage, with the error is estimated using the central limit

theorem. This approach can reduce the number of iterations

in the Monte Carlo simulation but requires subjective

measures to judge convergence and has poorly defined error

bounds due to the error estimation. Because their method

calculates the mean fatigue damage rather than individual

values of fatigue damage accumulation to determine the

failure probability, it does not capture the extreme events of

fatigue damage.

A Monte Carlo simulation methodology for a reliability

assessment of free spanning pipeline systems subjected to

random wave-induced hydrodynamic forces is presented by

Gazis (2012). A pipeline free span is modelled as a multi-

degree of freedom system and the wave loading is modelled

as a random process generated from a wave spectrum. The

study uses a Monte Carlo method to generate a large number

of sample functions from the wave spectrum that drive the

pipeline response. The pipeline stress response is used to

estimate the pipeline fatigue life. The study by Gazis (2012)

demonstrates that Monte Carlo methods can be applied to

the probabilistic assessment of pipeline free spans, and that

such an approach can provide greater insights into the

response of the system.

All previous probabilistic approaches to time-domain

freespan assessments have indicated the potential gains in

design life where the methodology has been applied.

However the number of Monte Carlo iterations required to

prove structural reliability has been unachievably high.

Combined with the normal amounts of computational power

available running the simulation on a single machine leads

to unpractically long runtimes, which cannot be achieved

within a standard project timeframe.

PROPOSED APPROACH

The use of probabilistic methods for structural integrity

assessment of pipeline freespans in the time domain is

unfeasibly difficult if existing methods are applied. To

overcome these challenges there are two approaches

available to reduce the magnitude of the task: reduce the

number of iterations required, or run more iterations

simultaneously to speed up analyses. For the MOBILEspan

JIP, both approaches have been used and combined together

to realise maximum benefit.

For cases with very low failure rates, it is intuitive that all

iterations of a Monte Carlo analysis need to be performed

when no failures are observed after a significant number of

trials. At its simplest level, each iteration of the Monte Carlo

procedure will either pass or fail the limit state checks.

Hence each iteration can be considered to be a Bernoulli

trial, with probability of failure θ. The realisation of many

Bernoulli trials follow a binomial distribution. Because we

expect the number of calculated failures to be very low,

even lower than 10-5, we may find that there are almost no

observation failures after 106 iterations of the Monte Carlo

analysis.

Figure 1 shows the cumulative probability of seeing

increasing numbers of failure observations, calculated using

the binomial distribution, given 106 iterations when the

probability of failure is 10-5. If the probability of failure is

10-5, the chance of observing 3 or fewer failures when 106

iterations have been analysed is less than 1%. Hence, in

cases where the number of failure observations are

extremely low it is highly unlikely that the actual probability

of failure is greater than 10-5, and there is a possibility that

the analysis could be truncated instead of running the

expensive, long full analysis. The certainty of the underlying

failure rate being acceptable is calculated using Bayesian

probability, discussed in the following section.

Figure 1 – Cumulative binomial distribution

The second strategy to improve runtimes is to perform many

calculations simultaneously. In the past it would be

prohibitively expensive to gain access to sufficiently large

computing clusters to enable effective distributed

computing. However the rise of cloud computing has

enabled easy and affordable access to large scale computing

power, available on demand. The MapReduce framework,

described later, it a widespread and popular programming

approach for efficient, distributed computation. By shaping

the Monte Carlo problem to fit within this framework it is

possible to perform calculations simultaneously across

hundreds of cores, significantly improving runtime.


BAYESIAN PROBABILITY

Although it is useful to know what the chances are that the

marginal case would produce a given number of failures

after 106 iterations, of more interest is the reverse question:

after observing i failures in n iterations, how confident are

we that the actual probability of failure is less than 10-5?

Assuming the failure cases are binomially distributed, we

can answer this question using a Bayesian approach. The

fundamental principal of Bayesian probability theory is that

the outcome probability of a Bernoulli trial is only known to

a certain degree of certainty. The certainty one can have in

the value of the underlying success rate is a function of the

number of trial observations made prior to the current trial,

i.e. as more trials are performed there is more certainty

about the true success rate. Hence, the success rate of a

Bernoulli trial, in this paper denoted as θ, can itself be

described by a probability density function (PDF).

An introduction to the Bayesian approach is provided in the

following subsections, although a more detailed treatment of

the subject can be found in chapter 5 of Kruschke (2011) or

a similar text.

Through answering the above question, and quantifying the

uncertainty of the random process, the results of a Monte

Carlo process can be compared against the required

certainty implied by the DNV codes for probabilistic

analysis. Hence, a proper understanding of the uncertainty in

the results will enable fewer iterations of the Monte Carlo

analysis to be performed to demonstrate the structural

integrity of the system.

THE BETA DISTRIBUTION

A beta distribution has two parameters, α and β controlling

its shape, and x represents a probability of an event.

𝑓(𝑥; 𝛼, 𝛽) =𝑥𝛼−1(1 − 𝑥)𝛽−1

𝐵(𝛼, 𝛽) (1)

One application of the beta distribution is for calculating

posterior distributions, i.e. the PDF of the failure rate given

a history of trial outcomes. Specifically if n trials have been

performed with a failures and b successes, the probability

distribution of the underlying failure rate for the experiment,

θ can be described using the beta distribution as follows:

𝑝(𝜃|𝑎, 𝑏) = 𝑓(𝜃; 𝑎 + 1, 𝑏 + 1) (2)

Additionally, we can extend this to find the likelihood that θ

is less than a given value by taking the cumulative density

function of f.

ILLUSTRATIVE EXAMPLES

The application of the beta distribution for estimating the

failure rate in a binomial distribution can be applied to any

experiment where there are two mutually exclusive

outcomes. The archetype example is to estimate the bias of a

coin given a certain number of tosses.

Consider the case where a coin is thrown two times for one

head and one tails. For this case we would think it is most

likely that the coin is most likely going to return heads with

0.5 probability, however it can’t be ruled out that the coin is

biased and has a probability greater or less than 0.6.

However it is known the probability of θ being 0 or 1 is nil,

since a head and a tail has already been observed. The

distribution for the failure probability is plotted using the

beta function in Figure 2, and is consistent with

expectations.

Figure 2 – Failure probability distribution for 1 failure

in two trials

As more cases are observed, if exactly half of our coin

tosses are heads then the underlying probability distribution

for the coin returning heads remains centred on 0.5, but we

get increasing confidence about that true value of θ. This

increasing confidence with successive tosses is illustrated in

Figure 3.


Figure 3 – Outcome PDF for increasing trial count

Finally, the probability distribution of θ for a biased set of

results is considered. Shown in Figure 4 is the probability

distribution for θ after 100 trials for an increasing number of

heads being observed. As expected, the mode of the

distribution shifts to match the observed failure rate in each

case.

Figure 4 – Outcome probability distribution for

increasing numbers of heads

APPLICATION TO DNV TARGETS

For the MOBILEspan analysis, our target probability of

failure is 10-5. DNV Classification note for the Structural

Reliability Analysis of Marine Structures (DNV-CN-30.6)

clause 3.4.3 states:

Reliability estimates by simulation methods are

considered as verified if a sufficient number of

simulations are carried out. Simulations by

indicator-based Monte Carlo methods should be

carried out with a number of simulations samples not

less than 100/PF, where PF denotes the failure

probability. Simulations by other methods should be

carried out such that the estimate of PF has a

coefficient of variation less than 10%.

For the case of a pipeline freespan, the threshold case for

structural acceptability is 100 failures in 107 trials. The

probability distribution for the underlying failure rate, using

the posterior distribution, is shown in Figure 5.

Figure 5 – Failure probability distribution for DNV

threshold case

Additionally, for this threshold case the distribution

properties have also been calculated to find the coefficient

of variation, presented in Table 1. Reassuringly, we observe

from the above analysis that the coefficient of variation is

10%, hence the two methods proposed in the Classification

Note are consistent. This supports the validity of the Beta

method.


Table 1 – Threshold case distribution properties

Distribution Properties for 100 failures in 1e7 trials

Mean 1.01e-05

Standard Deviation 1e-06

Coefficient of Variation 9.95%

Now consider an alternative case, where 106 trials have been

performed with 3 observed failures. When the PDF for θ is

plotted, shown in Figure 6, it is clear that although broader,

it is further to the left. The interpretation of this plot is that

the observation of 3 failures in 106 trials is far more likely to

have a lower underlying failure rate than when 100 failures

are observed in 107 cases.

Figure 6 – Failure probability distribution for two

Monte Carlo outcomes

However despite the underlying failure rate clearly being

superior in the case with only three failures, when we

calculate the coefficient of variation for this distribution it is

actually far higher than the 10% required by DNV-CN-30.6.

Table 2 – Threshold case distribution properties

Distribution Properties 100 failures

in 107 trials

3 failures in

106 trials

Mean 1.01e-05 3.00e-06

Standard Deviation 1.00e-06 1.73e-06

Coefficient of Variation 9.95% 57.73%

It appears from the above results that although the

requirement of 100 failures in 107 iterations will provide

sufficient information about failure rates to enable a robust

design, but also shorter length trials may also demonstrate

sufficiently safe designs when there are very few observed

failures.

CONFIDENCE CURVES

To extend the ideas above a concept named 'confidence

curves'. The idea for the confidence curve is as follows:

Given I've had Y failures in Z trials, what is the

chance that the actual underlying probability of

failure is greater than X?

The ‘underlying probability of failure' is plotted on the X

axis, and the chance that the actual probability of failure is

greater than X is on the Y axis. A curve exists for each

combination of Y failures in Z trials.

For the current DNV GL requirement, we need to satisfy

100 failures in 107 trials, the confidence curve is shown in

Figure 7, referred to as the 'base case'.


Figure 7 – Confidence curve for DNV base case

From this curve it can derived that after observing 100

failures in 107 trials there is 52.6% chance that the

underlying probability of failure (PoF) ≥ 1.0e-5, a 18.3%

chance that the PoF ≥ 1.1e-5, and 3.5% chance

PoF ≥ 1.2e-5.

Consider a case where only 106 trials are performed and

observe 10 failures in this time. The confidence curve for

this case has been compared against the base case in Figure

8. In this figure the curve is has a shallower gradient,

indicating less certainty about the underlying failure rate.

This is symptomatic of there being less information

available about the failure rate given fewer trials have been

analysed. The confidence that the actual probability of

failure being greater than 1e-5 is actually lower, but the

confidence of the actual probability of failure being less than

1.4e-5 is much greater than the base case.

Figure 8 – Confidence curve comparison for reduced

trial length

This problem could instead be approached from another

direction. Instead of saying that 100 failures in 107 trials

implies that the estimated PoF is 1.0e-5, it would be better to

instead say that probability of failure is less than 1.26e-5

with 99% certainty. So if only 106 trials were to be ran, what

would be the maximum number of failures allowable to

have the same level of confidence?

Figure 9 shows confidence curves for 106 trials with various

failure counts, for comparison against the base case shown

previously. Note that that a logarithmic scale has been used

for the y-axis to allow for high levels of certainty to be

examined; the however the base case confidence curve is the

same as Figure 7.


Figure 9 – Confidence curve comparison for different

numbers of observed failures

From the previous plot we can see that we are 99%

confident that θ is less than 1.26e-5. Note that if 4 or fewer

failures are observed in 106 iterations that there is even

greater confidence of θ being better than the base case at this

level of confidence. If the threshold is raised even higher, to

the 99.99% confidence level, the corresponding value for θ

is 1.43e-5. This level of confidence is exceeded if there are 2

or fewer observations after 106 iterations.

It is also worth noting that all of the above curves indicate a

higher level of certainty that θ is less than the nominal

reliability target of 10-5 than the base case.

It is asserted that if a reduced number of trials has been

performed, and the number of failures is sufficiently low to

allow us to determine that θ is better than the base case at

the 99% confidence level that this is acceptable in

demonstrating that the system meets the nominal safety

target prescribed by DNV-OS-F101. Based on the

observations to that point it is highly unlikely that more than

100 failures in 107 evaluations occurred if the analysis were

to continue.

MINIMUM NUMBER OF TRIALS

Based on the above analyses, the minimum number of trials

required to have 99% confidence in the PoF being better

than the base case, for a given number of failures, have been

calculated and plotted in Figure 10. It is proposed that

during a Monte Carlo simulation if at any point the number

of trials exceeds the minimum number for the failures

observed, that sufficient analysis has been performed on the

system to demonstrate its reliability.

Figure 10 – Required iterations vs. number of observed

failures

Finally, it is worth noting that the proposed acceptable

threshold for reducing the number of analysis iterations

requires a significantly lower observed failure rate than the

10-5 required as the nominal failure rate. For example, a

nominal failure rate of 10-5 would imply 10 failures in 10

million trials. However the proposed method would require

fewer than 5 failures in 1 million trials to remain 99%

certain that the system is as reliable as the DNV base case.

This is reflective of the increased uncertainty in lower trial

counts, hence there is a mathematically inherent 'buffer' to

the nominal failure probability is required to attain 99%

confidence in the outcome, demonstrated in Figure 11.


Figure 11 – Maximum allowable failure rate vs. number

of iterations

SCALED CLOUD COMPUTING

Since the target analysis times for the project could not be

achieved with changes to the probabilistic approach alone,

extra speed was found through procuring extra

computational power and parallelising the calculation.

Monte Carlo problems are ideally suited to parallelisation

due to the near-complete independence of threads. To

maximise the advantage of parallelising the problem, the

calculation has been restructured to allow execution in the

cloud.

Distributed computing in the cloud is a very attractive

solution for calculations that are ‘pleasingly parallel’

because large clusters of machines can be procured, used

and released quickly and at comparatively low costs

compared to using local resources. By renting computational

power on the cloud an organisation can quickly and easily

access far more computational power than may otherwise be

possible.

LINEAR VS PARALLEL

Traditional approaches to computing distribute a job across

the resources on one computer. The simplest calculations

run on a single thread, i.e. only one instruction can be

processed at a time. Modern processors typically include

multiple logical cores, and clear performance improvements

can be found if multiple threads are executed at once.

However this increases programming complexity, as the

workload needs to be managed and balanced across multiple

threads. With increased complexity, work can be distributed

even further, across multiple computers on a network.

The decision to parallelise calculation depends on a handful

of key factors: the current runtime, the potential

performance gain of the calculation, and the complexity of

implementation. The amount of potential gains in

parallelising a calculation depends greatly on the proportion

of the code that can be executed in parallel. This is

highlighted in Figure 12, which illustrates the diminishing

returns of added extra cores in partially parallelisable

problems. Monte Carlo problems are ‘pleasingly parallel’,

with almost no linear code, allowing for almost linear

scaling across many processors.

Figure 12 – Maximum gains through parallelisation

MAPREDUCE ARCHITECTURE

Despite the ‘pleasingly parallel’ nature of Monte Carlo

problems, a time-domain style simulation performed for

millions of cases generates a wealth of results and output

data, and the compilation and post-processing of results can

become a significant portion of the work. If not managed

correctly this can place an upper bound on the maximum job

speed that can be attained.

To mitigate this problem for the MOBILEspan calculation

software, the amount of linear code in the Monte Carlo

analysis has been minimised by performing the calculation

within a MapReduce framework. MapReduce is a


framework for distributed calculations across a cluster of

computers, where a large job is split across multiple nodes

which work on the problem simultaneously and

asynchronously. The key advantage of this framework is

that it allows results processing to also be executed on

parallel cores, instead of it being performed as a linear task

at the end of the job.

The basic components of the MapReduce procedure are

illustrated in Figure 13. The components of the above

framework, and how they are used in a Monte Carlo analysis

are as follows:

Split The job is split to be distributed across multiple

nodes. In this case, different samples are

distributed for the Monte Carlo analysis.

Map Calculations are performed on the pieces of the

job, processed one at a time. Results from the

calculations are emitted from the mapper. For

MOBILEspan, the mapper performs the time-

domain simulation of pipeline scour and fatigue.

Shuffle The results emitted from the mapper are shuffled

and sent to the appropriate nodes, where they will

be reduced and summarised.

Reduce Different results from each mapper are all

handled separately on different reducers. This

allows for the large volume of results to be

processed simultaneously and quickly. For

MOBILEspan the reducers derive the important

statistical results from the analysis.

Figure 13 – Outline of the MapReduce framework

IMPLEMENTATION AND CHALLENGES

Usage of the MapReduce procedure across a range of

problems is becoming increasingly common, and multiple

packages implementing this approach are now publicly

available. For MOBILEspan an existing framework was

adopted, chosen for its track record, flexibility and its ability

to scale the analysis across a cluster of many machines on

the cloud.

Deploying the calculation on the cloud has allowed for

much faster runtimes at a cheaper cost. During calculation,

the demand for computational resources is very high,

however it would be economically impractical to purchase

the number of computers required to achieve fast runtimes,

when these machines would otherwise sit idle. To illustrate

the difference in costs required, a fast multiprocessing

workstation with dual 8 core Xeon processors has an initial

cost of approximately US$10000, plus ongoing

maintenance. By comparison, a similarly powered virtual

machine can be rented for $2.12/hr on-demand, or as little as

$0.32/hr at off-peak times, with no ongoing maintenance or

replacement costs.

Additionally, many of these machines can be rented

simultaneously for effective job division and significant

runtime improvements, with only a marginal increase in the

total job cost. For MOBILEspan, clusters of 20 machines

have been provisioned, which represents a 16x speedup

compared to running a single local workstation. Maximum

available speedups across large cloud-based clusters also

become limited due to new overhead processes that are

introduced to establish the cloud computing environment.

For example, the provision and setup of computational

nodes can take up to 30 minutes alone at the start of an

analysis.

However running analyses distributed on the cloud is not

without drawbacks. Programming complexity increases

significantly compared to local parallelisation of code,

which can mean that there may only be a benefit when large

computational capacity is necessity. Such complexity arises

due to the necessity to provision and setup remote

calculation environments, and also handle and monitor

multiple remote nodes. Complexity may also be introduced

into the calculation procedure if it is not a natural fit for

distributed computing, and instead the calculation had to be

moulded to fit into the chosen framework. Complex code is

not only difficult to write, but also difficult to maintain, and

therefore the suitability may depend on the availability and

retention of the correct skill sets within an organisation.

CONCLUSIONS

Although at first performing time-domain Monte-Carlo

simulations for free-spanning pipelines on a scouring seabed

appeared unachievable, the combination of Bayesian


statistics and distributed cloud computing has made this

analysis possible. Separately, the use of Bayesian statistics

and distributed computing have provided speed multipliers

of up to 27x and 16x respectively, for a combined gain of

over 400x. This has dramatically improved the feasibility of

probabilistic analysis in this case, making the entire project

viable.

The use of Bayesian statistics allows the uncertainty of

Monte Carlo results to be quantified. This provides an

improved understanding of the nominal reliability of a

system compared to standard methods. Using this method it

can be demonstrated that the confidence in the underlying

failure rate of a system meets code requirements even when

fewer iterations have been performed than recommended.

Analysis speed was also significantly improved through

using cloud computing infrastructure to distribute the Monte

Carlo calculation across hundreds of processing cores. The

flexible, scalable nature of cloud computing, where

resources can be provisioned and released rapidly, has

enabled access to huge speed improvements at a much lower

cost than using traditional approaches.

The combination of these two approaches creates new

opportunities for the use of probabilistic techniques across

multiple engineering areas. This will allow for better

understanding of the behaviour of these systems, and

consequently reduce unnecessary conservatism in design. In

the context of the MOBILEspan JIP, it allows for time-

domain simulation of pipeline scour and fatigue to reduce

the number of free-span interventions required, representing

a significant saving in operational costs for operators.

ACKNOWLEDGEMENTS

This research has been performed as part of the broader

activities of the MOBILEspan JIP currently being executed

by Subsea Engineering Associates. The authors would like

to thank the contributions made by the JIP partners in

providing survey data, funding and guidance throughout the

duration of the project. Additionally the authors would like

to recognise the work of Stuart Saare during the initial

project phases, and thank Prof. Liang Cheng from the

University of Western Australia, and Prof. Andrew Palmer

from National University Singapore, for their ongoing input,

advice and support for the project.

REFERENCES

Agrell, C & Collberg, L 2014, ‘What the ridiculously small

failure probability targets really are’, Offshore Pipeline

Technology, Amsterdam, Netherlands, February 26-27,

2014.

Bruschi, R, Drago, M, Venturi, M, Jiao, G & Sotberg, T

1997, ‘Pipeline reliability across erodible/active seabeds’

Proceedings of the 1997 Offshore Technology

Conference, Houston, Texas, 5-8 May 1997, pp. 11-20.

DNV-OS-F101 2010, ‘Submarine Pipeline Systems’, DNV

Offshore Standard DNV-OS-F101, Det Norske Veritas,

October 2010

DNV-RP-F105 2006, ‘Free Spanning Pipelines’, DNV

Recommended Practice DNV-RP-F105, Det Norske

Veritas, February 2006.

DNV Classification Notes No. 30.6 1992, ‘Structural

Reliability Analysis of Marine Structures’, Det Norske

Veritas, July 1992.

Esplin, G & Stappenbelt, B 2011, ‘Reducing conservatism

in free spanning pipeline vortex-induced vibration fatigue

analysis’, Australian Journal of Mechanical Engineering,

vol. 8, pp. 11-20.

Gazis, N 2012, ‘A Probabilistic Approach for Reliability

Assessment and Fatigue Analysis of Subsea Free

Spanning Pipelines’, Proceedings of the Twenty-second

(2012) International Offshore and Polar Engineering

Conference, Rhodes, Greece, June 17-22, 2012.

Kruschke, JK 2014, ‘Doing Bayesian Data Analysis’,

Academic Press, 1st edition.

Palmer, A 2012, ‘10-6 and all that: what do failure

probabilities mean?’, Journal of Pipeline Engineering,

vol. 12, pp. 269-271.

Vughts, JH & Kinra, RK 1976, ‘Probabilistic fatigue

analysis of fixed offshore structures’, Proceedings of

Eighth (1976) Annual Offshore Technology Conference,

Houston, Texas, USA, May 3-6, 1976, pp. 889-906.

EFFICIENT PROBABILISTIC METHODS FOR TIME-DOMAIN PIPELINE...

Documents

Transcript of EFFICIENT PROBABILISTIC METHODS FOR TIME-DOMAIN PIPELINE...