Bayesian

In: Science

Submitted By liangxuav
Words 861
Pages 4
01.06.2012

[APSSRA 2012, May 25, 2012 ]

Bayesian Updating in Structural Reliability
Daniel Straub
Engineering Risk Analysis Group TU München

Ever increasing amounts of information are available

Sensor data

Satelite data

Spatial measurements on structures

Advanced simulation

Sources: Frey et al. (in print); Gehlen et al. (2010); Michalski et al (2011); Schuhmacher et al. (2011)

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1

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1973:

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Probabilistic Updating of Flaw Information Tang (1973)
• Imperfect information through inspection modeled by probability-ofdetection:

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2

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Probabilistic Updating of Flaw Information Tang (1973)

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Updating models and reliability computations with (indirect) information
• Bayes‘ rule: ∝

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How to compute the reliability of a geotechnical site conditional on deformation monitoring outcomes? -> Integrate Bayesian updating in structural reliability methods

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Prior model in structural reliability

• Failure domain: Ω 0

• Probability of failure: Pr
∈Ω

d

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Information in structural reliability

• Inequality information:
Ω 0

• Conditional probability of failure:
Pr | Pr ∩ Pr
∈ Ω ∩Ω ∈Ω

d d
9

Information in structural reliability

• Equality information:
Ω 0

• Conditional probability of failure:

Pr

|

Pr ∩ Pr

0 0

?
10

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In statistics, information is expressed as likelihood function
• Likelihood function for information event Z:

∝ Pr |

• Example: – Measurement of system characteristic s(X) – Additive measurement error  • Equality information: • Likelihood function:
,

,
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By expressing equality information as a likelihood function, it can be represented by an inequality domain
• Let
– P be a standard uniform random variable – c be a constant, such that 0 1 for any x…...

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