Poto?nik P. (Ed.) Natural Gas

Risk assessment of marine LNG operations 581

Fig. 5. Risk model showing most severe scenario 'fires on open deck', corresponding to

minimum total expected utility

Fig. 6. Sensitivity analysis on 'occasional probability'.

5.3 Fuzzy Risk Assessment Results

5.3.1 Determination of Membership Functions and Rule Base

In order to adopt this approach for risk assessment, probabilities of accident scenarios as

well as accident consequences are modeled as fuzzy sets. In doing so, it is implied that

probabilities/consequences are by themselves uncertain or at least a degree of uncertainty is

associated with their values. Several approaches for building and adapting membership

functions exist (Zhou et al., 1997). In this work, a fixed center-based membership function

approach using the symmetric Gaussian membership function was adopted. One

membership function is assigned to each value of the fuzzy variable. The Gaussian

membership function depends on two parameters and is given by:

݂

ሺ

ݔǡ ߪǡ ܿ

ሻ

ൌ ݁

షሺೣష೎ሻ

మ

మ഑

మ

(6)

W

h

ce

n

Fo

av

c=

0

fu

n

m

i

(Z

h

m

o

oc

c

ar

e

fr

e

fu

z

T

a

10

re

p

‘i

m

’

m

‘

m

th

e

Fi

g

Ta

h

ere c is the m

e

n

tered, each at t

h

r example for 'r

e

era

g

e value of

t

0

.00275, as sho

w

n

ctions were ch

i

nimum and ma

x

h

ou et al., 1997)

.

o

re than two fu

z

c

urrence and co

n

e

represented b

y

e

quenc

y

ran

g

es

s

z

y

sets whose r

a

ble 2. Figure 8 s

h

was adopted to

r

p

resentation of l

i

m

probable’ for li

k

m

a

j

or’, ’critical’

a

m

edium’ and ‘hi

gh

e

developed fuzz

g

. 7. Membership

ble 6. Membersh

i

e

an value and



h

e mid-value of t

h

e

mote probabilit

y

t

he interval (0.0

w

n in Table 6. T

h

osen such that

x

imum points o

f

.

With these me

m

z

y

sets. Fig. 7

s

n

sequences respe

c

y

fuzz

y

sets wh

o

s

hown in Table

1

an

g

es are chose

n

h

ows the membe

r

epresent output

i

n

g

uistic terms,

s

k

elihoods. Cons

e

a

nd ‘catastrophi

c

h

’. Table 6 sum

m

y

inference s

y

ste

m

functions for pr

o

i

p t

y

pe and para

m



is the standar

d

h

e numeric inter

v

y

' the Gaussian

m

05-0.0005) whic

h

e standard de

v

membership fu

n

the interval ass

o

m

bership functi

o

s

hows the mem

b

c

tivel

y

modeled

a

o

se ran

g

es are

c

1

. Similarl

y

, acc

i

n

to coincide wit

h

r

ship functions f

o

t

risk values. As

c

s

uch as ‘frequen

t

e

quences are als

o

c

’. Finall

y

outp

u

m

arizes the mem

b

m

FIS.

o

babilit

y

of occu

r

m

eters in the fuz

z

d

deviation. Me

m

v

al associated w

i

m

embership func

t

h

would corres

p

v

iation paramete

r

n

ction curves a

r

o

ciated with eac

h

o

ns each input

v

b

ership function

s

a

s fuzz

y

sets. Pr

o

c

hosen to coinci

d

i

dent consequen

c

h

the indicative s

e

o

r the resultin

g

ri

s

c

an be seen, the

u

t

’, ‘probable’, ‘o

c

o

represented li

n

u

t risk values

a

b

ership t

y

pe and

r

rence and conse

q

zy

inference s

y

st

e

m

bership functio

i

th each fuzz

y

v

a

t

ions is centered

p

ond to a mean

r

s  for the G

a

r

e completed w

i

h

of the fuzz

y

va

r

v

alue will belon

g

s

for the probab

i

o

babilities of occ

u

d

e with the ind

c

es are represen

t

e

verit

y

levels sh

o

s

k value. A scale

u

se of fuzzy sets

c

casional’, ‘remo

t

ng

uisticall

y

as ‘

m

a

re denoted as

parameters ado

p

q

uence severit

y

l

e

m.

ns are

a

riable.

on the

value

a

ussian

i

th the

r

iables

g

to no

i

lit

y

of

u

rrence

icative

t

ed b

y

o

wn in

of 1 to

allows

t

e’ and

m

inor’,

‘low’,

p

ted in

e

vels

Natural Gas582

P

C

R

Fi

g

T

h

us

e

ca

n

co

n

ris

ru

l

R

u

R

u

R

u

R

u

R

u

R

u

R

u

Var

i

P

robability –' frequ

e

P

robability – 'prob

a

P

robability – 'occas

i

P

robability- 'remot

e

P

robability- 'impro

b

C

onsequence- 'cata

s

C

onsequence- 'criti

c

C

onsequence- 'maj

o

C

onsequence- 'min

o

R

isk – 'high'

R

isk – 'medium'

R

isk – 'low'

g

. 8. Membership

h

e mappin

g

betw

e

of fuzz

y

if-the

n

be used in the

f

n

sequence and t

h

k assessor when

l

es of the develo

p

u

le 1: if (Probab

i

u

le 2: if (Probab

i

u

le 3: if (Probab

i

u

le 4: if (Probab

i

u

le 5: if (Probab

i

u

le 6: if (Probab

i

u

le 7: if (Probab

i

able

e

nt'

a

ble'

i

onal'

e

'

b

able'

s

trophic'

c

al'

o

r'

o

r'

functions for ris

k

e

en probabilit

y

,

c

n

rules. For a sin

g

f

uzz

y

inference

s

h

e computed ris

k

usin

g

the qualit

p

ed s

y

stem are li

s

i

lit

y

is Frequent)

i

lit

y

is Frequent)

i

lit

y

is Frequent)

i

lit

y

is Frequent)

i

lit

y

is Probable)

i

lit

y

is Probable)

i

lit

y

is Probable)

Value/Rang

e

> 0.5

0.5-0.05

0.05-0.005

0.005 -0.000

5

 0.0005

4

3

2

1

10

5.5

1

k

values

c

onsequences an

d

g

le attribute risk

sy

stem FIS to pr

o

k

value. The rule

s

ative risk matri

x

s

ted below

.

and (Consequen

c

and (Consequen

c

and (Consequen

c

and (Consequen

c

and (Consequen

c

and (Consequen

c

and (Consequen

c

e

Membership

Type

Gauss

5

Gauss

d

final risk value

problem, a tota

l

o

vide the mappi

n

s

are desi

g

ned t

o

approach outli

n

c

e is Minor) then

c

e is Ma

j

or) then

c

e is Critical) the

n

c

e is Catastrophi

c

e is Minor) then

c

e is Ma

j

or) then

c

e is Critical) the

n

Membersh

i

parameters (



(0.11,0.75)

(0.19,0.275

)

(0.09,0.027

5

(0.009,0.002

7

(0.0009,0.000

2

(0.4247,4)

(0.4247,3)

(0.4247,2)

(0.4247,1)

(1.911,10)

(1.911,5.5)

(1.911,1)

is accomplished

l

of twent

y

if-the

n

ng

between prob

a

o

follow the lo

g

ic

n

ed earlier. First

t

Risk is Medium.

Risk is High.

n

Risk is High.

c

) then Risk is Hi

Risk is Medium.

n

Risk is High.

i

p



,c)

)

5

)

7

5)

2

75)

b

y

the

n

rules

a

bilit

y

,

of the

t

welve

g

h.

Rule 8: if (Probability is Probable) and (Consequence is Catastrophic) then Risk is High.

Rule 9: if (Probability is Occasional) and (Consequence is Minor) then Risk is Low.

Rule 10: if (Probability is Occasional) and (Consequence is Major) then Risk is Medium.

Rule 11: if (Probability is Occasional) and (Consequence is Critical) then Risk is Medium

Rule 12: if (Probability is Occasional) and (Consequence is Catastrophic) then Risk is High.

As can be seen, the first four rules represent the first row in the qualitative risk matrix given

in Table 3. The second row in the matrix is represented by the next four rules i.e. rules 5-8

and so on. For the qualitative risk matrix given in Table 3, (Skramstad & Musaeus, 2000), the

numbers of rows is five and the number of columns is four, i.e. a total of twenty rules are

needed for modeling the logic embedded in this matrix. As such, the total number of rules

needed to construct the fuzzy inference engine can be expressed as:

� � ��



�� (7)

where N = number of fuzzy if-then rules

m = number of rows in qualitative risk matrix.

n = number of columns in qualitative risk matrix.

These rules provide the mapping for each hazardous scenario for only one consequence

attribute.

5.3.2 Application to Hazardous Scenarios

Often LNG risk assessment problems involve multiple consequence attributes for each

hazardous scenario, such as material assets, human life and/or environmental pollution.

These consequences are combined to provide an overall risk value for each accident

scenario. In this work, a fuzzy risk index FRI is used to combine the various consequence

attribute risks into a unified risk measure. The fuzzy risk index FRI value is an average

aggregation operator for each accident scenario can be calculated by (Yager, 1988)

��

�

∑

��

�

��

�

��

�

��

∑

�

��

(8)

where N = number of consequences.

k

i

= weight factor for each consequence.

Risk

i

= calculated fuzzy risk value for each consequence attribute.

The weighting factors k

i

reflects the attribute's relative importance. Fig. 9 shows the

structural hierarchy and information storage for the fuzzy inference system used. The FIS

structure contains various substructures which in turn contain variable names, membership

function definitions and computation method

.

Risk assessment of marine LNG operations 583

P

C

R

Fi

g

T

h

us

e

ca

n

co

n

ris

ru

l

R

u

R

u

R

u

R

u

R

u

R

u

R

u

Var

i

P

robability –' frequ

e

P

robability – 'prob

a

P

robability – 'occas

i

P

robability- 'remot

e

P

robability- 'impro

b

C

onsequence- 'cata

s

C

onsequence- 'criti

c

C

onsequence- 'maj

o

C

onsequence- 'min

o

R

isk – 'high'

R

isk – 'medium'

R

isk – 'low'

g

. 8. Membership

h

e mappin

g

betw

e

of fuzz

y

if-the

n

be used in the

f

n

sequence and t

h

k assessor when

l

es of the develo

p

u

le 1: if (Probab

i

u

le 2: if (Probab

i

u

le 3: if (Probab

i

u

le 4: if (Probab

i

u

le 5: if (Probab

i

u

le 6: if (Probab

i

u

le 7: if (Probab

i

able

e

nt'

a

ble'

i

onal'

e

'

b

able'

s

trophic'

c

al'

o

r'

o

r'

functions for ris

k

e

en probabilit

y

,

c

n

rules. For a sin

g

f

uzz

y

inference

s

h

e computed ris

k

usin

g

the qualit

p

ed s

y

stem are li

s

i

lit

y

is Frequent)

i

lit

y

is Frequent)

i

lit

y

is Frequent)

i

lit

y

is Frequent)

i

lit

y

is Probable)

i

lit

y

is Probable)

i

lit

y

is Probable)

Value/Rang

e

> 0.5

0.5-0.05

0.05-0.005

0.005 -0.000

5



0.0005