28.04.2011
[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
Source: Lehrstuhl für Holzbau und Baukonstruktion, TUM
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28.04.2011
Poorly managed risks lead to severe consequences
Quelle: wikispaces.com
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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.
From: Bautechnik (1966)
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Reliability is required
and in the 1940s quantified
Demand
Capacity
Probability of failure = Pr ( Demand > Capacity)
Pugsley (1942), Freudenthal (1947)
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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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28.04.2011
1970s: Reliability updating
f(x)
Measurement
Original model
x
• A large part of the uncertainty is due to limited information
 Include information by Bayesian updating
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1970s: Reliability updating
• Bayes’ rule: f  x E   Pr  E x  f  x 
• A large part of the uncertainty is due to limited information
 Include information by Bayesian updating
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28.04.2011
Probaability
1970s: From reliability to risk
Consequences
Straub (2010). Lecture notes in Engineering Risk Analysis
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Risk analysis is essential for optimal use of resources
Straub (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
Inspections are performed
f
d to reduce
d
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
corrosion, erosion
erosion,
SCC, etc…
– Concrete structures (tunnels, bridges) subject to
corrosion of the reinforcement
– Aircraft structures
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Zona de plataformas
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Plan and optimize inspections
• We model the entire service life through event trees:
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Probabilistic deterioration modelling
• Fracture mechanics based probabilistic models of crack growth:
Fatigue loads
Structural response
Crack growth
b
d
17
16
15
14
TP [s]
13
S
12
11
10
1/pF = 25yr
9
1/pF = 100yr
1/pF = 250yr
8
7
1/pF = 1000yr
4
6
8
10
H [m]
S
12
14
m fm
da
 CP ,a  K a  a, c  
dN
m fm
dc
 CP ,c  K c  a, c  
dN
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28.04.2011
Reliability analysis
•
Results
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Inspection modeling
Probability of Detection on tubulars, underwater
• Inspections are also
modeled qualitatively
1
ACFM
MPI
POD
0.8
0.6
0.4
0.2
0
0
2
4
6
8
10
Crack depth [mm]
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Probability of failure as a function of time
and the influence of inspection
Straub D., Faber M.H. (2006). Computer‐Aided Civil and Infrastructure Engineering, 21(3), pp. 179‐192.
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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
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Straub D., Faber M.H. (2004). J. of Offshore Mechanics and Arctic Engineering, 126(3), pp. 265‐271. Quantifying different inspection strategies
60000
Failure
Repair
p
50000
Inspection
Cost
40000
30000
20000
10000
0
RBI
4yr interval
Inspection strategy
20yr interval
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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
Dropped objects
Scour
Marine growth
Caída de Obj.
Obs. Inspección VGE
Impactos
Observado
s
Posición del elemento
Localizació
n
Exp. Caída de Obj.
Exp. Imp. de Embarcaci
ones
Tiempo de exposición
Crecimient
o Marino
Huracanes Observado
s
Relación (SH/SV)
Tiemp. Ult. Inspecció
n
Resultados Inspección
Edad del Rec.
Exposición a huracán
Fecha Med. Ant. Corrosión
Espesores Medidos
Tiempo Falla Rec.
Inspección VDE
Falla por sobrecarga
Inspección con PND
Eficiencia Rec.
Tasa de Corrosión
Inspección de Elem. Inundados
Abolladura
s
Daño pintura y recubrimie
nto
Pandeos
Daño por corrosión
Resistencia del elemento
Bayesian networks
Capacidad de la estructura
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28.04.2011
Monitoring, Inspection and Maintenance for Concrete Structures
Zone A
Zone B

t,1
...
Straub D., et al. (2009). Structure and Infrastructure Engineering, t,i
...
t,n
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Aspects of Sustainability
Nishijima 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 risk
assessment
• Where is it safe to build?
• Where should protection
measures be
implemented?
• When should roads be
closed / buildings be
evacuated?
Source: Kt. St. Gallen, Switzerland
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Avalanche risk analysis
Avalanche model:
Straub 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. friction
parameter 
Straub 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. friction
parameter 
Straub D., Grêt‐Regamey A. (2006). Cold Regions Science and Technology, 46(3) , pp. 192‐203.
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Avalanche risk analysis
• Observations
available
(here 50 years)
Straub D., Grêt‐Regamey A. (2006). Cold Regions Science and Technology, 46(3) , pp. 192‐203.
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28.04.2011
Avalanche risk analysis
• Observations
available
(here 50 years)
Straub D., Grêt‐Regamey A. (2006). Cold Regions Science and Technology, 46(3) , pp. 192‐203.
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Avalanche risk analysis – Information updating
Straub D., Grêt‐Regamey A. (2006). Cold Regions Science and Technology, 46(3) , pp. 192‐203.
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Avalanche risk analysis
Straub D., Grêt‐Regamey A. (2006). Cold Regions Science and Technology, 46(3) , pp. 192‐203.
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Bayesian networks for avalanche risk assessment
Grêt‐Regamey A., Straub D. (2006). Natural Hazards and Earth System Sciences, 6(6), pp. 911‐926.
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Implementation of the BN models
in software is straightforward
• Implementation in a
GIS environment
• Regional risk analysis
Grêt‐Regamey A., Straub D. (2006). Natural Hazards and Earth System Sciences, 6(6), pp. 911‐926.
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Earthquake risk management
• Calculate risk:
Total Risk [$]
0
0 – 200’000
200’000 – 400’000
400’000 – 600’000
600’000 – 800’000
Bayraktarli et al. (2006)
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Earthquake risk management requires an
understanding of system dependences
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Bayesian network is a powerful modeling tool
• Tsunami warning example:
Straub 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 graphs
• Models the joint probability
distribution of a set of variables
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Bayesian network in a nutshell
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28.04.2011
Bayesian network in a nutshell
• Efficient factoring of the joint
probability distribution into
conditional (local) distributions
given the parents
Here:
p ( x1 , x2 , x3 , x4 ) 
 p( x1 ) p( x2 | x1 ) p( x3 | x1 ) p( x4 | x3 )
General:
n
p (x)   p[ xi | pa ( xi )]
i 1
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Bayesian network in a nutshell
• Facilitates Bayesian updating when
additional information (evidence)
is available
E.g.:
p ( x3 | e2 ) 
p (e2 , x3 )
p(e2 )
 p ( x ) p (e
1

X1
2
| x1 ) p ( x3 | x1 )
 p ( x ) p (e
1
2
e
| x1 )
X2
Straub D., (2010). Lecture Notes in Engineering Risk Analysis. TU München
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28.04.2011
Modelling with BN:
System dependence through common factors
• Performance of an electrical
substation during an EQ
1
0.9
0.8
Fragil
gility
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
PGA [g]
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Can we observe the statistical dependence ?
20
1
Number of failures in 20 components
Failures are statistically independent
Fragility
0.8
Failures are statistically dependent
15
0.6
10
0.4
5
0.2
0
0
0
0.3
0.6
0.9
PGA [g]
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And finally…
• Accounting for statistical dependence among observations:
Transformer TR1
Circuit breaker CB9
1
1
a) Traditional model (posterior mean)
0.9
0.9
b) Improved model (posterior mean)
0.8
c) Improved model (predictive)
0.7
0.7
0.6
0.6
Fragility
Fragility
0.8
0.5
0.4
0.5
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
PGA [g]
0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
PGA [g]
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Straub D., Der Kiureghian A. (2008). Structural Safety, 30(4), pp. 320‐366.
System fragility
• Redundant system:
(parallel system with
5 components)
Parallel system TR 1
0
10
−1
System fragility
10
−2
10
−3
10
−4
10
−5
Including dependence
Neglecting dependence
10
−6
10
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
PGA [g]
Straub D., Der Kiureghian A. (2008). Structural Safety, 30(4), pp. 320‐366.
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28.04.2011
Reliability of an infrastructure system
• Determine the reliability (connectivity) under evolving
information on hazards, system performances, measurement
Straub D., Der Kiureghian A., (2010). Journal of Engineering Mechanics
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EQ: Modeling systems and portfolio of structures
UR
R1
R2
R3
V
M4
M5
R4a‘
R5a‘
R4
R5
R4b‘
R5b‘
Q
Q1
Q2
Q20
E(1)
E(2)
E(20)
H1(1)
H1(2)
H1(20)
H(1)
H(2)
H(20)
UH1
UH2
UH20
UH
Straub D., Der Kiureghian A., (2010). Journal of Engineering Mechanics
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Temporal model
Straub D., Der Kiureghian A., (2010). Journal of Engineering Mechanics
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Spatial
model
Straub D., Der Kiureghian A., (2010). Journal of Engineering Mechanics
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28.04.2011
Reliability of the infrastructure system is updated
in near-real-time as information becomes available
Small earthquake event (proof loading effect)
One year later
One year later
Detailed inspection
of structures
Prior model
First observations after EQ
after
Q
Immediately after
EQ event
Straub D., Der Kiureghian A., (2010). Journal of Engineering Mechanics
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Decisions in complex systems under conditions of uncertainty
Aging of the infrastructure
system:
‐ Monitoring & Inspection
‐ Maintenance
‐ Replacement
R l
t / redesign
/ d i
Natural hazards in the system
„built environment“
‐ Prevention
‐ Emergency response
‐ Rehabilitation
R h bilit ti
Safety in the system „society“
‐ Target reliability
‐ Prescriptive limits
‐ Service life duration
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Vision
• Decision support systems which:
–
–
–
–
–
Provide 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
Bensi M.T. (2010). PhD thesis, UC Berkeley.
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Questions?
Contact:
www era bv tum de
www.era.bv.tum.de
[email protected]
Next
e t week
ee Reliability
e ab ty se
seminar
a o
on :
Information updating in reliability and risk analysis
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