Why and how civil engineers must manage uncertainty and …€¦ · Why and how civil engineers...

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28.04.2011 1 [SEMM Seminar, UC Berkeley, March 28, 2011 ] Why and how civil engineers must manage uncertainty and risk Daniel Straub Engineering Risk Analysis Group TU München Uncertainty on the state of the structural system leads to collapses Bad Reichenhall 2 Source: Lehrstuhl für Holzbau und Baukonstruktion, TUM

Transcript of Why and how civil engineers must manage uncertainty and …€¦ · Why and how civil engineers...

Page 1: Why and how civil engineers must manage uncertainty and …€¦ · Why and how civil engineers must manage uncertainty and risk ... estructura Pandeos ... Decisions in complex systems

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[SEMM Seminar, UC Berkeley, March 28, 2011 ]

Why and how civil engineers must manage uncertainty and risk

Daniel StraubEngineering Risk Analysis GroupTU München

Uncertainty on the state of the structural systemleads to collapses

• Bad Reichenhall

2Source: Lehrstuhl für Holzbau und Baukonstruktion, TUM

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Poorly managed risks lead to severe consequences

3Quelle: wikispaces.com

The responsibility of the engineer:Codex Hammurabi (Babylon, 1728-1686 BC)

If an engineer builds a house for a man and does not sufficently strengthen the structure, causing its failure and the death of the owner: this engineer shall be killed.

4From: Bautechnik (1966)

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Reliability is requiredand in the 1940s quantified

Demand

Capacity

5Pugsley (1942), Freudenthal (1947)

Probability of failure = Pr ( Demand > Capacity)

1970s: Modern structural reliability methods

Transform into standard Normal space and linearize limit state surface at the location closest to the origin (design point)

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1970s: Reliability updating

f(x)

Original model

Measurement

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• A large part of the uncertainty is due to limited information Include information by Bayesian updating

x

• Bayes’ rule:

1970s: Reliability updating

Prf x E E x f x

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• A large part of the uncertainty is due to limited information Include information by Bayesian updating

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1970s: From reliability to riskability

9Straub (2010). Lecture notes in Engineering Risk Analysis

Proba

Consequences

Risk analysis is essential for optimal use of resources

10Straub (2010). Lecture notes in Engineering Risk Analysis

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Risk-based inspection, maintenance, repair planning

• Structures deteriorate with time• Deterioration is associated with large uncertainty

f d d• Inspections are performed to reduce uncertainty The effect of inspections (and monitoring) can only be

appraised probabilistically

• Applications:– Offshore structures subject to fatigue, corrosion,

scour, ship impact, …Process systems subject to corrosion erosion

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– Process systems subject to corrosion, erosion, SCC, etc…

– Concrete structures (tunnels, bridges) subject to corrosion of the reinforcement

– Aircraft structures

Zona de plataformas

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Plan and optimize inspections

• We model the entire service life through event trees:

13

• Fracture mechanics based probabilistic models of crack growth:

Probabilistic deterioration modelling

Fatigue loads Structural response Crack growth

d

b

17

14

,

,

,

,

fm

fm

m

P a a

m

P c c

daC K a c

dNdc

C K a cdN

S

4 6 8 10 12 147

8

9

10

11

12

13

14

15

16

HS [m]

TP [

s]

1/pF = 25yr

1/pF = 100yr

1/pF = 250yr

1/pF = 1000yr

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Reliability analysis

• Results

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Inspection modeling

• Inspections are also modeled qualitatively

Probability of Detection on tubulars, underwater

0.8

1ACFM

MPI

0

0.2

0.4

0.6

0 2 4 6 8 10

Crack depth [mm]

PO

D

16

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Probability of failure as a function of time and the influence of inspection

17Straub D., Faber M.H. (2006). Computer‐Aided Civil and Infrastructure Engineering, 21(3), pp. 179‐192.

Structural importance

• Member/joint importance is determined through pushover analyses

• Compare intact structure versus structure with element removed

• Determine conditional probability of collapse given element failure

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Optimization

19Straub D., Faber M.H. (2004). J. of Offshore Mechanics and Arctic Engineering, 126(3), pp. 265‐271. 

Quantifying different inspection strategies

50000

60000

Failure

Repair

20000

30000

40000

50000

Co

st

p

Inspection

20

0

10000

RBI 4yr interval 20yr interval

Inspection strategy

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IT implementation (iPlan)

• Calculating inspection plans using the generic approach:

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Extension to other deterioration mechanisms

• Corrosion• Ship impact

Resultados Inspección Edad del 

Rec.

Fecha Med. Ant. Corrosión

Tiemp. Ult. 

Inspección

Localización

Posición del 

elemento

Caída de Obj.Obs. 

Impactos

Observados

Huracanes Observado

s

Relación (SH/SV)

Tiempo de exposición

• Dropped objects• Scour• Marine growth

Espesores Medidos

Tiempo Falla Rec.

Eficiencia Rec.

Tasa de Corrosión

Exposición a huracánExp. Caída 

de Obj.Exp. Imp. 

de Embarcaci

ones

Inspección VGE

Inspección VDE

Inspección con PND

Inspección de Elem. 

Inundados

Falla por sobrecarga

Crecimiento Marino

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Daño pintura y recubrimie

nto

Daño por corrosión

Abolladuras

Resistencia del 

elemento

Capacidad de la 

estructura

Pandeos

Bayesian networks

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Monitoring, Inspection and Maintenance for Concrete Structures

Zone A

Zone B

23Straub D., et al. (2009). Structure and Infrastructure Engineering, 

t,1 t,i t,n. . . . . .

Aspects of Sustainability

24Nishijima K., Straub D., Faber M.H. (2007). Australian Journal of Civil Engineering, 4(1), pp. 59‐72.

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Natural hazards risk management:Support optimal decision making

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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

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Avalanche risk analysis

Avalanche model:

27Straub D., Grêt‐Regamey A. (2006). Cold Regions Science and Technology, 46(3) , pp. 192‐203.

Avalanche risk analysis

• Parameter uncertainty

• E.g. frictionparameter

28Straub D., Grêt‐Regamey A. (2006). Cold Regions Science and Technology, 46(3) , pp. 192‐203.

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Avalanche risk analysis

• Parameter uncertainty

• E.g. frictionparameter

29Straub D., Grêt‐Regamey A. (2006). Cold Regions Science and Technology, 46(3) , pp. 192‐203.

Avalanche risk analysis

• Observationsavailable(here 50 years)

30Straub D., Grêt‐Regamey A. (2006). Cold Regions Science and Technology, 46(3) , pp. 192‐203.

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Avalanche risk analysis

• Observationsavailable(here 50 years)

31Straub D., Grêt‐Regamey A. (2006). Cold Regions Science and Technology, 46(3) , pp. 192‐203.

Avalanche risk analysis – Information updating

32Straub D., Grêt‐Regamey A. (2006). Cold Regions Science and Technology, 46(3) , pp. 192‐203.

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Avalanche risk analysis

33Straub D., Grêt‐Regamey A. (2006). Cold Regions Science and Technology, 46(3) , pp. 192‐203.

Bayesian networks for avalanche risk assessment

34Grêt‐Regamey A., Straub D. (2006). Natural Hazards and Earth System Sciences, 6(6), pp. 911‐926.

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Implementation of the BN modelsin software is straightforward

• Implementation in a GIS environmentGIS environment

• Regional risk analysis

35Grêt‐Regamey A., Straub D. (2006). Natural Hazards and Earth System Sciences, 6(6), pp. 911‐926.

Earthquake risk management

• Calculate risk:

36

00 – 200’000

200’000 – 400’000400’000 – 600’000600’000 – 800’000

Total Risk [$]

Bayraktarli et al. (2006)

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Earthquake risk management requires an understanding of system dependences

37

• Tsunami warning example:

Bayesian network is a powerful modeling tool

38Straub D., (2010). Lecture Notes in Engineering Risk Analysis. TU München

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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

39

Bayesian network in a nutshell

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Bayesian network in a nutshell

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

)|()|()|()(

),,,(

3413121

4321

xxpxxpxxpxp

xxxxp

Here:

41

3413121

])(|[)(1

n

iii xpaxpp x

General:

Bayesian network in a nutshell

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

)(

),()|(

2

3223 ep

xepexp

E.g.:

42

2

1

)|()(

)|()|()(

121

13121

X

X

xepxp

xxpxepxp e

Straub D., (2010). Lecture Notes in Engineering Risk Analysis. TU München

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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

gilit

y

43

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

gil

Can we observe the statistical dependence ?

1 20 Number of failures in 20 components

Failures are statistically independent

0.4

0.6

0.8

Frag

ilit

y

5

10

15 Failures are statistically dependent

Failures are statistically independent

44

0 0.3 0.6 0.90

0.2

PGA [g]

0

5

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And finally…

• Accounting for statistical dependence among observations:

0.4

0.5

0.6

0.7

0.8

0.9

1

Fra

gilit

y

Transformer TR1

0.4

0.5

0.6

0.7

0.8

0.9

1

Fra

gilit

y

Circuit breaker CB9

a) Traditional model (posterior mean)

b) Improved model (posterior mean)

c) Improved model (predictive)

45

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

PGA [g]0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0

0.1

0.2

0.3

0.4

PGA [g]

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

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

46

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

10− 5

10

PGA [g]

Including dependenceNeglecting dependence

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

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Reliability of an infrastructure system

47

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

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

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)

48

H1(1) H

1(2) H

1(20)

UH1

UH2

UH20

UH

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

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

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Temporal model

49Straub D., Der Kiureghian A., (2010). Journal of Engineering Mechanics

Spatialmodel

50Straub D., Der Kiureghian A., (2010). Journal of Engineering Mechanics

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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

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

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

53Bensi M.T. (2010). PhD thesis, UC Berkeley.

Questions?

Contact:www era bv tum [email protected]

Next week Reliability seminar on :

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e t ee e ab ty se a o :Information updating in reliability and risk analysis