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Near-Real-Time Decision Support forInfrastructure Subject to Earthquake Hazard

Daniel Straub

Engineering Risk Analysis Group, TU Munich

[ Performance-Based EQ Engineering Workshop Capri July 2009]

2

Vision

• Decision support system which:– Provides an accurate assessment of system state at all times

– Includes state-of-the-art models

– Accounts for past observations

– Uses near-real-time observation

– Suggests optimal decisions

3

Challenges that I am working on

• Spatial system modelling– Infrastructure performance models

– Model statistical dependence in systems

• Practical application of Bayesian methodology– Information updating

– Decision analysis and optimization

4

A tool I am using:Bayesian Networks (BN)

• Probabilistic models based on directed acyclic graphs

• Models the joint probability distribution of a set of variables

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

X1

X2 X3

)|()|()(),,( 13121321 xxpxxpxpxxxp

Here:

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n

i

ii xpaxpp x

General:

5

A tool I am using:Bayesian Networks (BN)

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

X1

X2 X3

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)|()(

)|()|()(

)(

),,()|,(

121

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X

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xxpxepxp

ep

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E.g.:

e

8

PBEE in a nutshell

DM EDP IM

DMEDPIMIMfIMEDPfEDPDMfDMLossLoss ddd)()|()|()(]E[

9

The relevance of system dependences:A case study

A simple system:

10


A simple system:

11


A simple system:

12

Can we observe the statistical dependence ?

0 0.3 0.6 0.90

0.2

0.4

0.6

0.8

1

PGA [g]

Frag

ilit

y

0

5

10

15

20 Number of failures in 20 components

Failures are statistically dependent

Failures are statistically independent

13

Yes we can

Observations

Regression analysis

14

Fragility model

• Limit state function for a single component i in substation jduring earthquake k:

• log of capacity of component i in substation j (assumed normal)

• log of estimated intensity at substation j during earthquake k

• measurement error in estimation of (assumed normal)

• uncertain factor common to all observations in substation j during

earthquake k (accounts for common ground motion, similar age,

similar functional conditions, etc.; assumed normal with zero-mean)

ˆijk ij jk jk jkg r s y

ijr

ˆjks

jk

jky

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

15

Posterior statisticestimated from the data using MCMC

Table 1. Posterior statistics of model parameters.

Equipment θ θM̂ θS θθR̂

TR1

r

0.03

1.39

0.35

0.63

0.68

0.17

1 0.86 0.16

0.86 1 0.23

0.16 0.23 1

CB9

r

1.71

5.06

0.71

0.88

4.24

0.12

1 0.12 0.09

0.12 1 0.16

0.09 0.16 1


16

And finally

• Accounting for statistical dependence among observations:


17

Statistical dependence reduces effective data size

• With data and confidence bounds


18

System fragility

• Redundant system:(parallel system with5 components)


19

If we can model the system, can we compute it?

20

If we can model the system, can we compute it?

• Utilize Structural Reliability Methods (SRM)

Enhanced Bayesian network (eBN)

Straub D., Der Kiureghian A., in submission

21

Eliminate Nodes in the eBN throughStructural Reliability Methods

: Domain defining the kith state of discrete RV Yi given the state kpa of the discrete parents of Yi

( )

( )

( )

,

i

i C

i

pa

i C

k

i i P

Y

k

i k

Y

p y pa Y f d

Y x x

Y

x y x

x x

( )

,i

pa

k

i k x


22

This theory seems complicated. Do we really needthis?

• Modeling is relatively simple and graphical

• It facilitates consistent representation of dependences

• The model enables Bayesian updating in near-real-time

• The model can be extended to decision graphs

23

Life-cycle model withtime-varying load

24

Time dependent reliability conditional on various evidence


25

Decision analysis:Terminal analysis and value of information

4( ) 1802VOI M

5( ) 1168VOI M

4 5( , ) 2763VOI M M

26

Modeling systems and portfolios

27

Modeling systems and portfolio of structures

28

Temporal model

29

Spatialmodel

30

– Distribution of PGA conditional on observations:

Conditional distribution of PGA

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

Observation: PGA at site 4 equal to 0.75g

31

Conditional infrastructure reliability


32

Do we now have the Deus Ex Machina?

• Limitations of the analysis:– Number of SRM computations required

– Complexity of resulting rBN

• In particular, spatial correlation can be handled onlyapproximately

• Certain dependence must be simplified (Markovassumption)

33

The vision again

recordings ofground motion,shock wave, etc.

Bayesian network& decision graph

structural reliabilitymodule

network connectivity& flow module

health monitoringmodule

sensors

inspections,expert knowledge,etc.

hazard module

monitoring of gas, power,water, transportationnetwork services

34

• Develop / utilize simple probabilistic models(not oversimplifying)

• Use all observations to update the models(reduce uncertainty)

Standardization of information gathering

A more realistic goal

35

and all of that is not limited to EQ engineering

,

,

,

,

fm

fm

m

P a a

m

P c c

daC K a c

dN

dcC K a c

dN

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