Spada_IDRC_Presentation

Wir schaffen Wissen – heute für morgen
Paul Scherrer Institut
Matteo Spada and Peter Burgherr
Towards Extreme Consequence Accidents in Energy
Sector: Are they expected based on historical
observations?
IDRC 2014, Davos, Switzerland, 24-28 August 2014

• Motivation
• Method
• Application to the Energy Sector:
• ENSAD database
• Likelihood Function
• Bayesian Model
• Results
• Conclusions
Outline
IDRC 2014, Davos, Switzerland, 24-28 August 2014 Seite 2

Motivation
Digital Globe, Fukushima I, 2011 BABS and EBP, Risk Report for Switzerland, 2013
• Extreme events are the cause of most of the consequences in the total historical observation
• It is of great interest to assess the probability level of such events in the context of risk assessment
• Frequencies and consequence in risk matrixes can be based upon subjective, qualitative judgments
or may be determined through quantitative modeling
• Is an extreme event (happened or expected by experts) statistically likely given the historical
observations?

Method
Historical
Observa ons
Threshold Analysis
(if possible)
Severe
Accidents
Bayesian
Analysis
• Fully Probabilistic Approach: Bayesian Analysis
• Bayesian Analysis intrinsically account for:
• Aleatory Uncertainty
• Epistemic Uncertainty
• Model a certain quantile of interest (e.g., 99%)
based on historical observation
Maximum
Consequence
Event
Maximum
Consequence Event
within uncertainty
NO YES
range of the
Expecta on at 1%
of the Accidents?
Sta s cally likely
Maximum
Consequence
Event
Sta s cally
unlikely
Maximum
Consequence
Event

μL(y;q )p(q ) By applying Markov
Chain Monte-Carlo
(MCMC) algorithms
Seite 5
Method: An Overview to Bayesian Analysis
Prior
Bayes
Theorem
Posterior
Data
Bayes Theorem:
p(q | y) =
L(y;q )p(q )
ò L(y;q )p(q )dq
Posterior: Conditional probability that is assigned after the relevant evidence is taken into
account. Thus, it expresses our updated knowledge about parameters after observing data
Prior: expresses what is known about the parameters before
observing the data. Prior describes epistemic uncertainty.
Likelihood Function: Likelihood describes the process giving rise to data y in
terms of unknown parameters θ. Likelihood describes aleatory uncertainty.
Marginal Likelihood: Normalization constant in order to let the posterior
distribution to be “proper”. That is, the posterior should converge to 1.

Coal mine explosion Deepwater Horizon (US)
LNG facility (Algeria)
Gas Refinery pipeline Tapped oil pipeline (Nigeria)
Seite 6
Test the Method: Accidents in the Energy Sector

ENSAD database
Seite 7
ENergy related Severe Accident Database (ENSAD)
- Comprehensive, worldwide coverage of energy-related severe accidents, 1970-2008 covered
- Covers entire energy chains (the risk to society and environment occur not only during the actual
energy generation)
- Updated from a variety of sources
Coal (incl. Lignite)
Exploration
Mining & Preparation
Transport
Conversion
Transport
Power/Heating Plant
Waste Treatment & Disposal
Natural Gas
Exploration
Extraction & Processing
Transport
Power/Heating Plant
Oil
Exploration
Extraction
Transport
Refining
Transport
Power/Heating Plant
Waste Treatment & Disposal

ENSAD database
Seite 8
ENergy related Severe Accident Database (ENSAD)
- Comprehensive, worldwide coverage of energy-related severe accidents, 1970-2008 covered
- Covers entire energy chains (the risk to society and environment occur not only during the actual
energy generation)
- Updated from a variety of sources
- ENSAD definition of severe accidents: ≥5 fatalities, ≥10 injured, ≥5 Mio $, etc.
Risk description Impact Category ENSAD severity threshold Consequence indicator
Human health Fatalities
Injuries
≥ 5
≥ 10
Fatalities per GWeyr
Injured per GWeyr
Societal Evacuees
Food consumption ban
≥ 200
yes
Evacuees per GWeyr
Nominal scale
Environmental Release of hydrocarbons
Land/water contamination
≥ 10’000 t
≥ 25 km2
Ton per GWeyr
km2 per GWeyr
Economic Economic loss ≥ 5 Mio USD (2000) USD per GWeyr

Datasets

Datasets
Seite 10
• Identify and exclude the maximum consequence event
• Check if the maximum consequence event is expected (at the
level of 1% of the accidents) based on the remaining historical
observations

Likelihood Function for the Bayesian Analysis
Bayesian Theorem:
Seite 11
Tail distribution - Which Distribution:
- Generalize Pareto
- Lognormal
- ?
p(q | y)μL(y;q )p(q )

Likelihood Function for the Bayesian Analysis
Bayesian Theorem:
Find the model that best fit the data, in terms of
goodness of fit:
Where BIC is the Bayesian Information Criterion, k
is the number of parameters to be estimated, n is
the number of observations and L is the likelihood.
Lower the BIC score, better the model fit the data.
Seite 12
Tail distribution - Which Distribution:
- Generalize Pareto
- Lognormal
- ?
BIC = k ln(n)-2ln(L)
p(q | y)μL(y;q )p(q )

Seite 13
Likelihood Function: BIC Score
- In all cases the best fitting model, according to the BIC score, is the Log-Normal distribution;
- Followed by the Weibull distribution in Coal OECD and Natural Gas non-OECD;
- Followed by the Generalized Pareto distribution in Oil non-OECD.

Bayesian Model
Bayesian Theorem:
Seite 14
m = N(m = 0,s = 0.01) s ~U(a = 0.001,b =1000)
Log - Normal =
1
xs 2 2p
Severity
e
-
(ln x-m )2
2s 2
• A priori distributions: uninformative and weak
• Parameter of interest: 99% Quantile
• Markov Chain Monte Carlo Method (MCMC):
x
=
- Model fit performed using a Gibbs sampling algorithm (JAGS)
- 100000 generations, 10000 burn-in (the parameter converged after 30000 generations)
- 10000 generations to adapt the model to the data
a priori distributions
Likelihood function
Posterior distributions

Results
Seite 15
• Fatalities exceeded in 1% of Accidents. Maximum observed consequences not inside the
uncertainty range at this probability level are considered as not expected based on the historical
data.
• Results are shown for the following country groups:
• Oil non-OECD
• Natural Gas non-OECD
• Coal OECD
• All results include uncertainty level: 5% - 95%

Results

Results
Very unlike event:
Crash between a Tanker
and a Ferry Boat in the
Philippines in 1987

Results

Conclusions
• Fully Probabilistic approach, which counts for both aleatory and epistemic uncertainty, is defined in
order to test the expectation of a given catastrophic event with respect to the historical information
• The methodology could be used to prove the expectation of an event based on expert judgement,
commonly used in risk assessment analysis
• For the energy sector, with respect to the historical observation:
• Coal OECD and Natural Gas non-OECD extreme events are expected at 1% of the accidents
• Oil non-OECD extreme event is not expected at 1% of the accidents
• Oil non-OECD extreme event is expected at 0.1% of the accidents

Thank You! Questions?
matteo.spada@psi.ch
www.psi.ch/ta/mspada

QQ Plots
5 10 20 50 100
5 10 20 50 100 200
QQ plot with outliers, Method I
lognormal distribution, R2 = 0.9526
Predicted
Observed
NG non-OECD
5 10 20 50 100
5 10 20 50 100 200
Predicted
Observed
Coal OECD
5 10 20 50 100 200 500
5 10 20 50 100 200 500 1000 5000
Predicted
Observed
Oil non-OECD

Marginal Likelihood: MCMC with Gibbs Sampler
• The Gibbs sampler is a generic method to sample from a high dimensional distribution.
• Consider two parameters of interest: θ1 and θ2
• Target: p(θ1, θ2 | y)
• Suppose we can sample from p(θ1 | θ2,y) and p(θ2 |θ1,y).
• Starting at the point (θ1(0) , θ2(0)) in parameter space, generate a random walk, a sequence (θ1(k),
θ2(k)) as follows:
For k=1,...,n, define θ1(k) ~p(θ1 | θ2(k-1),y), θ2(k) ~ p (θ2 | θ1( k ) , y )
• The values at the (k+1)th step depend only on the values at the k-th step and are independent of
previous values.
• The Markov chain will in general tend to a stationary distribution, and the stationary distribution will be
the desired p(θ1, θ2 | y)

Convergence – 1 - Autocorrelation
NG non-OECD Coal OECD
Oil non-OECD

Convergence – 2
NG non-OECD Coal OECD
Oil non-OECD

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