Bayesian Networks for Modeling and Managing Risks of ... · 09.09.2010 3 Bayesian network in a nutshell • Probabilistic models based on directed acyclic graphsdirected acyclic graphs

09.09.2010

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[National Telford Institute and Scottish Informatics and Computer Science Alliance, Glasgow University, Sept 8, 2010 ]

Bayesian Networks for Modeling and Managing Risks of Natural Hazards

Daniel StraubEngineering Risk Analysis GroupTU München

Decisions in complex systems under conditions of uncertainty

Aging of the infrastructuresystem:‐Monitoring & Inspection‐MaintenanceR l t / d i

Natural hazards in the system„built environment“‐ Prevention‐ Emergency responseR h bilit ti

Safety in the system „society“‐ Target reliability‐ Prescriptive limits‐ Service life duration

‐ Replacement / redesign ‐ Rehabilitation

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Vision

• Decision support systems which:– Provide accurate assessments of system state at all timesProvide accurate assessments of system state at all times– Include state-of-the-art models– Account for past observations– Use near-real-time observation– Suggest optimal decisions

3Bensi M.T. (2010). PhD thesis, UC Berkeley.

What to expect

• Part A: Bayesian network in a nutshell– Exemplified with EQ risk management examplesExemplified with EQ risk management examples

• Part B: Applications of Bayesian networks (ongoing)– Avalanche risk assessment– Wildfire risk– Flood detection– Deterioration

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Deterioration– Earthquake

• Part C: Discussion

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Bayesian network in a nutshell

• Probabilistic models based on directed acyclic graphsdirected acyclic graphs

• Models the joint probability distribution of a set of variables

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• Efficient factoring of the joint probability distribution intoprobability distribution into conditional (local) distributions given the parents

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General:


• Facilitates Bayesian updating when additional information (evidence)additional information (evidence) is available

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• Tsunami warning example:

Bayesian network is a powerful modeling tool

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Computational benefits through conditional independence assumptions

Straub D., (2010). Lecture notes. TU München

Modelling with BN: System dependence through common factors

• Performance of an electrical substation during an EQ

0.5

0.6

0.7

0.8

0.9

1

agili

ty

10

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.1

0.2

0.3

0.4

0.5

PGA [g]

Fra

gi

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System fragility

• Redundant system:(parallel system with 100 Parallel system TR 1

5 components)

10− 4

10− 3

10− 2

10− 1

Syst

em fr

agili

ty

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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.910− 6

10− 5

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PGA [g]

Including dependenceNeglecting dependence

Straub D., Der Kiureghian A. (2008). Structural Safety, 30(4), pp. 320‐366.

Modelling complex systems using BN:Object-oriented BN

• Principles of object-oriented programming can be applied.

14Straub D., Der Kiureghian A., (2010). Journal of Engineering Mechanics, in print

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Bayesian networks can be extended to decision graphs as a tool for optimizing decisions

• Example: EQ emergency response:Seismic demand

Bridge condition

Observable condition

15Bensi M.T. (2010). PhD thesis, UC Berkeley.

• Two types of information:– Data obtained from previous projects and investigations

How do we use information updating?

Data obtained from previous projects and investigations– Observations made during the actual application

• Model Y = g(X,A)– A: Model parameters– X: Observables

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Data



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PastPresent/future

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• Optimizedecisions:

Decision

Consequences

What to expect

• Part A: Bayesian network in a nutshell– Exemplified with EQ risk management examplesExemplified with EQ risk management examples

• Part B: Applications of Bayesian networks (ongoing)– Avalanche risk assessment– Wildfire risk– Flood detection– Deterioration

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Deterioration– Earthquake

• Part C: Discussion

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Avalanche riskassessment

• Where is it safe to build?• Where should protection• Where should protection

measures beimplemented?

• When should roads beclosed / buildings beevacuated?

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Source: Kt. St. Gallen, Switzerland

Bayesian networks for avalanche risk assessment

23Grêt‐Regamey A., Straub D. (2006). Natural Hazards and Earth System Sciences, 6(6), pp. 911‐926.

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Avalanche risk assessment

• Observationsavailable(here 50 years)

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Avalanche risk analysis – Information updating

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Avalanche risk analysis

26Straub D., Grêt‐Regamey A. (2006). Cold Regions Science and Technology, 46(3) , pp. 192‐203.

Bayesian networks for avalanche risk assessment


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Implementation of the BN modelsin software is straightforward

• Implementation in a GIS environmentGIS environment

• Regional risk analysis


BN for wildfire risk management

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Weather Stationx

Case study: Rhodes

Municipality

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BN model

Geography

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HumanPopulationdensity

Land Cover

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BN input is obtained from GIS

• E.g. elevation

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Automatic flood detection from satelite images

Flooded

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Flooded

PossiblyTrafficable

Trafficable

FloodedTrafficable

with Daniel Frey, Chair of Remote Sensing, TUM


• BN: Combining the flood model (elevation) with satelite data

Elelvationwith satelite data

Visibleobject

Clouds Flooded

e

35with Daniel Frey, Chair of Remote Sensing, TUM

Grey channels

e

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Detection of flooded objects using GIS andremote sensing data

θ2θ1θ θT…

d2d1 dT…d0

U1 V2 XT

θ3

d3

W3


U,V,W,X: observations from different sensorsθ: Altitude from DEMd: damage index (flooded or not flooded)

Detection of flooded objects using GIS andremote sensing data – including damage models

θk : altitude of object

States:

[θ1, … θk]θ

n: number of bands

[flooded,not flooded]

[c1, c1, …cm]

[c c c ]

object

c

d

i: number of pixels in object

c: classes(i.e. water, forest, road …)

m: number of classes

g: grayvalues


…g2 gn …g1 g2 gn …g1 g2 gn

pixel 1 pixel 2 pixel i

c [c1, c1, …cm]

[0 … 255]

pixel

c c

…g1

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Flooded

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Flooded

PossiblyTrafficable

Trafficable

FloodedTrafficable

with Daniel Frey, Chair of Remote Sensing, TUM

Managing deterioration through inspection and monitoring

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DBN model for deterioration modeling

m m1 m2 m3 mTC

q1 q2

a0 a1 a2

q3

a3

qT

aT

qS

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Inspection

Failure/survival E1

Z1

E2

Z2

E3

Z3

ET

ZT

Straub D. (2009). Journal of Engineering Mechanics, 135(10), pp. 1089‐1099

Calculations are robust AND efficient

41Straub D. (2009). Journal of Engineering Mechanics, 135(10), pp. 1089‐1099

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Performance of buildings subject to hazards:Combining continuous and discrete random variables

Measurements

Structural model:

R1

R2 R3 R4

R5

H

V

5m

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1 5

5m 5m

Straub D., Der Kiureghian A., (2010). Journal of Engineering Mechanics, in print

Performance

Combining exact BN inference algorithms with structural reliability methods

• Eliminate continuous RV (nodes):

Y2

Y1

Y3

X1

Y5

Y4

Y6

Y2

Y1

Y3

X1

Y5

Y4

Y6

reverse (X1,Y5)

Y2

Y1

Y3

X1

Y5

Y4

Y6

reverse (X1,Y6)

Y2

Y1

Y3

Y5

Y4

Y6

remove X1

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• Compute new conditional PMF using FORM

Y7

Y5 Y6

Y7

Y5 Y6

Y7

Y5 Y6

Y7

Y5 Y6


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Enhanced BN:

• Eliminate continuous RV (nodes):

Structural model:

R1

R2 R3 R4

R5

H

V

5m

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• Compute new conditional PMF using FORM


Reliability of an infrastructure system

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• Determine the reliability (connectivity) under evolvinginformation on hazards, system performances, measurement


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Temporal model


Spatialmodel


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EQ: Modeling systems and portfolio of structures

M4

M5

Q1

R5

R1

UR

R3

R2

R4

V

R4a‘

R4b‘

R5a‘

R5b‘

Q

Q2

Q20

E(1) E(2) E(20)

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H1(1) H

1(2) H

1(20)

UH1

UH2

UH20

UH

H(1) H(2) H(20)


Reliability of the infrastructure system is updatedin near-real-time as information becomes available

Small earthquake event (proof loading effect)

One year later

Prior model

Detailed inspectionof structures

First observations after EQ

One year later

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Immediately afterEQ event

after Q


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Do we now have the Deus Ex Machina?

• Limitations of the analysis:– Complexity of the BNComplexity of the BN– Number of SRM computations required

• In particular, spatial correlation can be handled onlyapproximately

• Certain dependence must be simplified (Markovassumption)

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Spatial modelling of the EQ hazard

51Straub D., Bensi M., Der Kiureghian A. (2008). Proc. EM’08

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Approximate spatial models

52Bensi M. et al. (2010). Submitted to Structural Safety

– Distribution of PGA conditional on observations:

Conditional distribution of PGA

Observation: PGA at site 4 equal to 0.75g

53Straub D., Bensi M., Der Kiureghian A. (2008). Proc. EM’08

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System performance models are also not straightforward

• But a formalism forestablishing them hasestablishing them hasbeen developed:

54Bensi M., (2010). PhD thesis, UC Berkeley

Discussion

• Bayesian network models enable the probabilistic modelingof complex systemsof complex systems

• Particularily efficient when he problem can becompartialized (conditional statistical independences)

• They are ideal for problems with evolving information (asthey allow model updating ad learning)

• Computational limitations exist, which make a carefulmodeling necessary

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modeling necessary• BNs are a modelling tool: The models must still be

developed and data must be collected

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Outlook

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Documents

Bayesian Networks for Modeling and Managing Risks of ... · 09.09.2010 3 Bayesian network in a nutshell • Probabilistic models based on directed acyclic graphsdirected acyclic graphs