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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
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Here:
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General:
5
A tool I am using:Bayesian Networks (BN)
• Facilitates Bayesian updating when additional information (evidence) is available
X1
X2 X3
2
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121
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X
xepxp
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ep
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E.g.:
e
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
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
Straub D., Der Kiureghian A. (2008). Structural Safety, 30(4), pp. 320-366.
16
And finally
• Accounting for statistical dependence among observations:
Straub D., Der Kiureghian A. (2008). Structural Safety, 30(4), pp. 320-366.
17
Statistical dependence reduces effective data size
• With data and confidence bounds
Straub D., Der Kiureghian A. (2008). Structural Safety, 30(4), pp. 320-366.
18
System fragility
• Redundant system:(parallel system with5 components)
Straub D., Der Kiureghian A. (2008). Structural Safety, 30(4), pp. 320-366.
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
Straub D., Der Kiureghian A., in submission
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
24
Time dependent reliability conditional on various evidence
Straub D., Der Kiureghian A., in submission
25
Decision analysis:Terminal analysis and value of information
4( ) 1802VOI M
5( ) 1168VOI M
4 5( , ) 2763VOI M M
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
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
,
,
,
,
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m
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