Toward An Approach To Probabilistic Resilience Analysis Of Networked Infrastructure

Toward
an
Approach
to
Probabilistic
Resilience
Analysis
of
Networked
Infrastructure Yan
Cao
([email protected]),
William
L.
McGill
([email protected]) College
of
Information
Sciences
and
Technology,
the
Pennsylvania
State
University,
USA

Abstract



Methodology
(con.nued)



Results:
Under
threats
(con.nued)

•
Parameter
defini.on

The
measurement
of
system
resilience
is
an


•
Other
resilience
exceedence
curves

important
element
of
risk
analysis
for
infrastructure


•
Capacity
loss
happens
on
link
AC

protec4on.

Yet,
to
date,
few
authors
offered
useful


1.05

measures
of
resilience
that
can
be
integrated
into
a


0.9

larger‐scale
risk
analy4c
framework.

The
problem
is


100% 90%

0.8

to
admit
that
any
expression
of
resilience
is
highly


()'""*"&'"+,-./0/$%$12

even
more
acute
when
one
forces
himself/herself
 •
Op.miza.on
model

uncertain
due
to
the
typically
complex
and
dynamic


80%

0.7

70% 60% 50% 40% 30%

0.6 0.5

20% 10%

0.4

No loss

0.3

structure
of
most
networked
systems.

This
work


0.2

aims
to
make
progress
toward
a
probabilis4c


0.1 0

expression
of
resilience
that
fits
within
a
larger


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

!"#$%$"&'"

framework
for
infrastructure
risk
analysis.

We


•
Capacity
loss
happens
on
link
BD

consider
in
our
study
a
simple
network
loosely


1.05

•
Data

modeled
aCer
a
por4on
of
the
global
undersea


30%, 20%, 10%, 0 loss

0.9

telecommunica4ons
infrastructure
to
construct


0.8 ()'""*"&'"+,-./0/$%$12

resilience‐exceedence
curves
based
on
data
for
 uncertain
nodal
informa4on
demand,
which
we
 then
combine
with
the
probability
of
various
link
 capacity‐reducing
events
to
make
statements
about


0.7 0.6

40%

0.5

50% 60%

0.4 70% 0.3

80% 90%

0.2

risk.

Direc4ons
for
future
work
will
be
offered.

100% 0.1 0

0

0.1

0.2

0.3

0.4

•
Incorpora.on
of
uncertainty




Introduc.on

0.5

0.6

0.7

0.8

0.9

1

!"#$%$"&'"

•
Each
demand
is
independent

•
Network
methodology



Probabilis.c
Resilience
Study:

•
Truncated
normal
distribu4on

•
Risk
analysis

•
Assump.ons:

•
Global
telecommunica.on
infrastructure •
Convergence
check



Background
Concept

0.9715

0.045 0.0445

0.971

0.044 0.0435

%&'()'*)+,-."'&"/(+/0+1-2"3"-(4-

•
Incorpora.on
of
uncertainty

%&'()*'+,&)-.)/&0","&(1&

•
Resilience,
vulnerability,
risk

0.9705

0.97

0.9695

0.969

•
Bayes’
equa.on

0.043 0.0425 0.042 0.0415 0.041 0.0405 0.04 0.0395 0.039

0.9685

0.038

0.968

50

100

150

200

250

300

350

400

450

0

500

50

100

150

200

250

300

350

400

450

500

!"#$

!"#$

•
Our
equa.on



Results:
Under
threats •
Types
of
threats

•
Capacity
loss
happens
on
link
AB •
Resilience
exceedence
curves:

•
Sources
of
threats

1.05

•
How
to
response
to
specific
threats



Methodology

0.8

()'""*"&'"+,-./0/$%$12

•
How
to
integrate

0.9 NO loss

0.7 100%

0.6

•
Risk
curve
of
the
system


90%

0.5

80%

0.4

10% 1

70% 0.3

•
Network
construc.on




Result:
Probabilis.c
Resilience:

60% 50%

0.2

0.9

20% 40%

0.1 0

0.8

30%

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

!"#$%$"&'"

•
Fragility
curves:

0/,,)"1$""2"%$")2+,&#+3-&+/%

•
Items
to
be
considered

•
Equa.on
for
the
example

0.7 0.6 0.5 0.4 0.3

1.05 0.2

0.9 80%

!#/0'0+1+&2)/3)"4$""*"%$"

0.8

•
Simplified
network
to
be
studied

0.1

90% 100%

0

70% 0.7

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

!"#$"%&'(")*+,#-.&+/%

60% 50%

0.6

•
Future
direc.ons:

40%

0.5 30% 0.4

•
DATA!

20% 10%

0.3

•
Residue
capacity

NO loss

0.2 0.1 0

0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

!"#$"%&'(")*+,#-.&+/%

•
Probability
box •
Time
dependence

College
of Information
Sciences
and
Technology Sponsored
by:
The
Center
for
Network‐Centric
Cogni.on
and
Informa.on
Fusion