Vulnerability of Complex Infrastructure Systems

Torbjörn Thedéen

Safety Research, KTH

•HAZARDS

• Nature-Acts of God: Earthquakes, Extreme floods, Thunder storms ...

• Failures of material ...• Human lapses• Organizational errors• Hackers• Terrorism• War

D a t a N e t w o r k

P o w e r N e tF i n a n c e N e t

T r a n s p o r t N e t w o r k

I N F R A S T R U C T U R E S

… … .

Info Stairs

Many dataClassical statistical analysis

Few dataLogical modelReliability methodsPRASubjective

Probabilities

Bayesian methods

Precursors, Incidents

•Research Areas

• Terrorist Groups• Motivation• Religious, political,

social, economic studiesConditional

• Power+possibilities

• Conditional Vulnerability

• Consequences given ´attacks´:

• Dams, transportation, power grids...

Vulnerability USA October 07

Vulnerability of Road Transportation Systems

(Erik Jenelius KTH)

Conditional Vulnerability

• Road systems modelled as a connected graph

• Conditioned of one link is out, the consequences are estimated:

• The increased total traffic time• The unsatisfied demand• The most ´important´ or one link at random

is taken out

Example

• Northern Sweden

• The average traffic is known

• The traffic for a disturbed net can be calculated

Unsatisfied veh/total00 - 0.00050.0005 - 0.00170.0017 - 0.00360.0036 - 0.00840.0084 - 0.024

0 200 400 Kilometers

Figur 6

Vehicles/day0 - 15931594 - 48114812 - 1053310534 - 1958619587 - 35742

0 200 400 Kilometers

Figur 2

Vehicle min/veh0 - 0.020.02 - 0.080.08 - 0.190.19 - 0.450.45 - 1.22

0 200 400 Kilometers

Figur 5

Vulnerability of Power Net

Power Generation

Power Transmission

Power Distribution and Consumption

Power Generation

Dam Safety and Security

Safety analysis OK, but security antagonistic threats??

Nuclear Power Plants. PRA safety OK,

Defense passive?

Power Nets - Vulnerability

• (Statistical Analysis of Collapses) Too few!

• Vulnerability analysis of empirical graph model – partly classisfied!

• Vulnerability analysis of idealized graph model (coupled branching processes)

•

Power law of large consequences, power grid

Power Net – Graph Model

Power stations

Transformers

400 kV

110 kV

220 V Consumers

…………

Powergeneration

Consumers

Branching Process

Limiting result

• One link is removed at random. The proportion of unserved consumers has in the limit a distribution with a right tail of power type exponent – 1.

Vulnerability and Terrorism

Terrorism

Motivation Terrorist groups

Basis Common goal

Cause fear, chaos and deaths!

TERRORISM AND DEFENSE

Enemy infrastructure

Criticalinfrastructure

?Partly known Known

Fighting Terrorism

• Knowledge or qualified guesses about probable terrorist groups, their goals and actions constitutes:

• Basis for our defence of infrastructures ...

• Basis for our actions against terrorist groups

Fight Between Two Networks

• Our critical infrastructures: power, transportation, data, finance, water ...

• KNOWN TO THE ENEMY!

• Enemy infrastructure: terrorist groups

• ALMOST UNKNOWN TO US!

Terrorist Network

Known links and nodesUnknown links and nodes

Sampling Procedures

• Random sampling of nodes/links

• In time or in time periods

• Markov sampling

• Markov sampling with side conditions

Estimates – random sampling

• Link distribution

• Shortest path

• Sampling in many time periods – (N, p):

• ML estimates of p and N (Size of the terrorist population)