Overview on the Asset Integrity Management of Large …archiv.ibk.ethz.ch/emeritus/fa/people/straubd/...1 Overview on the Asset Integrity Management of Large Structures Daniel Straub,

1

Overview on the Asset Integrity Management of Large Structures

Daniel Straub, Vasiliki Malioka & Michael Havbro Faber

Swiss Federal Institute of Technology, ETH Zürich

3rd Probabilistic WorkshopBOKU Wien24 November 2005

Outline

• Decision problems in large deteriorating structures

• Quantitative modelling of deterioration

– in time

– in space

• The effect of inspections

– in time

– in space

• Computational strategies (paper)

• Calculating of the expected cost of inspection and repair strategies

• Conclusions

Example results are included throughout the presentation (Concrete structure subject to chloride-induced corrosion of the reinforcement)

2

Life-cycle of a structure

Unsicherheiten

Decision problems in large deteriorating structures

• Decisions must be made under uncertainty

• For individual structural elements, such decisions can be optimized using Bayesian decision analysis

Minimal inspection (codes, authorities ...)

Failure

Total

Inspection & repair

Optimal strategy

Inspection effort (Paccept)

Exp

ect

ed

co

st

3



4


• Decisions must be made under uncertainty

• For individual structural elements, such decisions can be optimized

• For large systems, many dependencies among individual elements/components must be considered:

– Dependencies in the deterioration performance

– Dependencies of the failure consequences

– Dependencies of the inspection/repair costs

– Inference from inspection of other parts of the system

• These dependencies must be taken into account when determining:

– What to inspect for

– Where to inspect

– When to inspect

– How to inspect

Outline



– in time

– in space


– in time

– in space



• Conclusions

5

Quantitative temporal modelling of deterioration

• The state of the structure is expressed in terms of condition states, e.g., corrosion initiation and visible corrosion.

• Condition states must be defined quantitatively in terms of the applied corrosion models.

Limit state functions must be defined for the different condition states.

Quantitative temporal modelling of deterioration: Example

6


tTXtgM II −== )(11

221 1

4CR

IS

d CT erfD C

−−⎛ ⎞⎛ ⎞= −⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠


tTTXtgM PII −+== )(22

221 1

4CR

IS

d CT erfD C

−−⎛ ⎞⎛ ⎞= −⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

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• Tidal vs. splash exposure:

• The differences are observed for the same structure in different exposure classes

Quantitative spatial modelling of deterioration

• Deterioration varies over the structure

• Combined spatial and temporal modelling:

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• Spatial model is required

• Discretize into zones and elements

• Zones: Areas with the same parameters


• Proposed spatial model:

• Discretize into zones and elements

• Zones: Areas with the same parameters

• Using hyper-parameters to represent the dependency among elements in one zone.

Α

Θt,1 Θt,i Θt,n. . . . . .

Hyper-parameters

Condition states at then individual elements atdifferent points in time t

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Determine spatial variability through experiments

Determine spatial variability through experiments

• Determine element size (elements are independent given the hyper-parameters)

0.000

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0 100 200 300 400 500 600 700 800

correlation radius: r = 80 cm

Horizontal distance (cm)

Cov

aria

nce

f unc

t ion

(

)

XX

C

0.76

0.78

0.8

0.82

0.84

0.86

0.88

0.9

0.92

0.94

0 200 400 600 800 1000

Horizontal distance (cm)

XXμ

Chl

orid

ec o

nduc

tivity

(mS/

c m)

1/2/2 11f ( ) (2 ) exp ( ) ( )2

m Tπ μ μ−− −⎡ ⎤= − − −⎢ ⎥⎣ ⎦X XX XX XX XXx C x C x

10

Outline



– in time

– in space


– in time

– in space



• Conclusions

The effect of inspections in time

• Probabilistic deterioration models can be updated using Bayes’ rule

11

The effect of inspections in time

• Probabilistic deterioration models can be updated using Bayes’ rule

The effect of inspections in space

• Inspections provide information on the state of the element, but also of the entire system

• The effect on the system is a function of the dependencies in the model:

– Full dependency: Inspection of 1 element is sufficient

– No dependency: All elements must be inspected

• The value of an inspection of an element with regard to the other elements can be assessed

(Straub & Faber, Structural Safety 2005)

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The effect of inspections in space

• The value of inspecting an element with regard to another element (or the system):

(Straub & Faber, Structural Safety 2005)

Outline



– in time

– in space


– in time

– in space



• Conclusions

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Computational framework (paper)

• The computational framework facilitates the efficient updating with inspection results, accounting for both the spatial and temporal variability.

• The framework is based on the pre-calculation of the updated probabilities for given hyper-parameters Α

• Using SRA/MCS, establish a database with:

• The probabilities for any structure are then calculated by an expectation operation over Α

• With the algorithms provided in the paper, all type of information (in time and space) can be used to update both the temporal and spatial distribution in a highly efficient manner

Α

Θt,1 Θt,i Θt,n. . . . . .

( ),

pt i iθΘ α

( ),

p ,t i i izθΘ α

( )pΑ α


• Example:

Resulting in no-indication

Time of HCPM Resulting in indication Probability of visible corrosion at t = 50yr

0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35

25 25 25 0.35 0.48 0.27 0.27 0.35 0.35 0.35 0.35 0.35 0.35

25 25 25 0.35 0.48 0.48 0.27 0.35 0.35 0.35 0.35 0.35 0.35

25 25 25 0.35 0.27 0.27 0.27 0.35 0.35 0.35 0.35 0.35 0.35

0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35

0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35

35 35 35 0.35 0.35 0.35 0.35 0.35 0.35 0.57 0.17 0.17 0.35

35 35 35 0.35 0.35 0.35 0.35 0.35 0.35 0.17 0.17 0.57 0.35

35 35 35 0.35 0.35 0.35 0.35 0.35 0.35 0.17 0.17 0.17 0.35

0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35

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Resulting in no-indication

Time of visual insp. Resulting in indication Probability of visible corrosion at t = 50yr

40 40 40 40 40 40 40 40 40 40 0.13 0.13 0.13 0.13 0.13 0.13 1 0.13 0.13 0.13

40 40 40 40 40 40 40 40 40 40 0.13 1 0.13 1 0.13 0.13 0.13 0.13 0.13 0.13

40 40 40 40 40 40 40 40 40 40 0.13 0.12 1 0.13 0.13 0.13 0.13 0.13 0.13 0.13

40 40 40 40 40 40 40 40 40 40 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13

40 40 40 40 40 40 40 40 40 40 0.13 1 1 0.13 0.13 0.13 0.13 0.13 0.13 0.13

0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27

0.27 0.27 0.27 0.27 0.27 0.27 0.48 0.13 0.13 0.27

0.27 0.27 0.27 0.27 0.27 0.27 0.13 0.13 0.48 0.27

0.27 0.27 0.27 0.27 0.27 0.27 0.13 0.13 0.13 0.27

0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27


• Example:


• Example (HCPM at year 25)

0

0.01

0.02

0.03

0.04

0 10 20 30 40 50 60 70 80 90 100

Number of elements with initiated corrosion

Prob

abili

ty

No-indication at 10elements

Indication at 10elements

No inspection

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Outline



– in time

– in space


– in time

– in space



• Conclusions

Define inspection strategies

• What percentage of the structure should be inspected when and with which method?

• Define inspection/repair strategies:

• When should repair actions be carried out? Repair criteria should be given as a function of the inspection outcomes

NDE Inspections

Visual Inspections

1VT

1NDET

NDETΔ

VTΔ

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Calculating the inspected costs

• Decision tree (with much additional complexity compared to the case for the single element)

Inspection e(1)

Outcom

e z(1)

Repair criteria

z(1) = 0%

z (1)= 100%

z(1)= x%

Failure F(2)

Timet

z (1)= y%

No repair

a(1) = Repair

a(1) = No rep.

No failure

Failure

No failure

Failure

z(2) = 0%

z (2)= 100%

z(2)= x%

z (2)= y%

No repair

a(2) = Repair

a(2) = No rep.

continued untilend of service life

Repair a

(1)

Failure F(1)

Inspection e(2)

Outcom

e z(2)

Repair a

(2)

e(1) e(2)

Optimizing inspection strategies

• Example (Zone with 100 elements) – Expected cost without inspections:

0

200

400

600

800

1000

5 10 15 20 25 30 35 40

Year

Expe

cted

cos

ts

Major repairMinor repairInspections

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• Example – Expected cost with 50% HCPM inspection at year 30:

0

200

400

600

800

1000

5 10 15 20 25 30 35 40

Year

Expe

cted

cos

ts


0

200

400

600

800

1000

1200

1400

1600

5 10 15 20 25 30 35 40

Year

Expe

cted

cos

ts



• Optimize repair criterion for HCPM outcome:

0

500

1000

1500

2000

2500

3000

3500

25 30 35 40 45 50 55

Repair criterion [%]

Expe

cted

cos

t

Total

Major repair(failure)

Minor repair

Inspection

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• Optimize inspection coverage for HCPM outcome:

0

500

1000

1500

2000

2500

3000

3500

25 30 35 40 45 50 55

Repair criterion [%]

Expe

cted

cos

t

Total


Minor repair

Inspection

0

500

1000

1500

2000

2500

3000

3500

4000

0 20 40 60 80 100

HCPM inspection coverage [%]

Expe

cted

cos

t

Total


Minor repair

Inspection

Conclusions

• Asset integrity management for large deteriorating structures requires that both the temporal & spatial variability is explicitly addressed by the model

• The presented framework allows for explicit consideration of inspection results at different times and locations

An updated probabilistic model is available at all points in time for the planning of future actions

• Due to the computational efficiency, the model allows for an optimization of inspection efforts and repair strategies

• Thank you for your attention

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Overview on the Asset Integrity Management of Large …archiv.ibk.ethz.ch/emeritus/fa/people/straubd/...1 Overview on the Asset Integrity Management of Large Structures Daniel Straub,