why and how civil engineers must manage uncertainty and risk · 28.04.2011 1 [semm seminar, uc...
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28.04.2011
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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)
6
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1970s: Reliability updating
f(x)
Original model
Measurement
7
• 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
8
• 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
11
– Process systems subject to corrosion, erosion, SCC, etc…
– Concrete structures (tunnels, bridges) subject to corrosion of the reinforcement
– Aircraft structures
Zona de plataformas
12
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Plan and optimize inspections
• We model the entire service life through event trees:
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• 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
15
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?
26
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
40
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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)
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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
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• 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
51
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
52
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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 dewww.era.bv.tum.destraub@tum.de
Next week Reliability seminar on :
54
e t ee e ab ty se a o :Information updating in reliability and risk analysis
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