Bayesian Approaches to Ei Akli Rii Engineering Risk ...€¦ · Australian Journal of Civil...
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University of Illinois at Urbana-Champaign Last Coating Inspection Observed Ship Impacts Observed Vertical-to- Horizontal Loading (SH/SV) Exposure February 4, 2008 Coating Lifetime Time of Past Corr. measurements Past Corrosion measurements Coating Failure Time Last Coating Inspection Time Corrosion Hurricane Exposure Dropped Objects Exposure Ship Impacts Exposure Location Orientation Observed Dropped Objects Hurricanes Marine Growth Time Coating Efficiency Corrosion Rate Corrosion Damage Dents Member Resistance Member Failure from Overloading Bends Bayesian Approaches to E i i Ri k A l i System Capacity Engineering Risk Analysis in Research and Practice Daniel Straub UC Berkeley UC Berkeley, Civil and Environmental Engineering
Transcript of Bayesian Approaches to Ei Akli Rii Engineering Risk ...€¦ · Australian Journal of Civil...
University of Illinois at Urbana-Champaign Last Coating
InspectionObserved Ship Impacts
Observed
Vertical-to-Horizontal Loading (SH/SV)
Exposure
February 4, 2008Coating Lifetime Time of Past Corr.
measurements
Past Corrosion measurements
Coating Failure Time
Last Coating Inspection Time
Corrosion
Hurricane ExposureDropped Objects
ExposureShip Impacts
Exposure
Location OrientationObserved Dropped Objects
Hurricanes
Marine Growth
pTime
Coating Efficiency
Corrosion Rate
Corrosion DamageDents
Member Resistance
Member Failure from Overloading
Bends
Bayesian Approaches to E i i Ri k A l i
System Capacity
Engineering Risk Analysisin Research and Practice
Daniel Straub
UC Berkeley UC Berkeley, Civil and Environmental Engineering
Outline
– Basic concepts (Reliability analysis, reliability updating, risk optimization)
– Risk-based planning of inspection and maintenance planning:– Fatigue in offshore structures
– General deterioration mechanismsGeneral deterioration mechanisms
– Life-cycle analysis and sustainability
– Natural hazards risk assessment– Avalanche risk assessment
– Seismic fragility modeling for infrastructure systems
– Discussion
1940s: The structural reliability problem
– Probability of failure: ( ) ( )Pr PrF R S= ≤
f(r), f(s)
Capacity RDemand S
r, s
1940s: The structural reliability problem
Deterministic
– Probability of failure: ( ) ( )Pr PrF R S= ≤
f(r), f(s)f(r), f(s)
Deterministicsafety margin
Capacity RDemand S Capacity RDemand S
r, sr, sμ μμS μR
1940s: The structural reliability problem
Deterministic
– Probability of failure: ( ) ( )Pr PrF R S= ≤
f(r), f(s)f(r), f(s)
Deterministicsafety margin
Capacity RDemand S Capacity RDemand S
r, sr, sμ μμS μR
– Applications:– Probabilistic design
Safety factor calibration– Safety factor calibration– Deterioration modelling
1970/80s: Reliability updating
– Bayes’ rule: ( ) ( ) ( )Prf x E E x f x∝
f(x) Measurement
Original model
x
– A large part of the uncertainty is due to limited informationInclude information by Bayesian updating
1970s: Reliability updating
– Bayes’ rule: ( ) ( ) ( )Prf x E E x f x∝
– A large part of the uncertainty is due to limited informationInclude information by Bayesian updating
1970s: Optimization of risk
Risk
Total expected cost
d co
stRisk
Design/Mitigation costEx
pect
ed
Decision alternatives
– Optimize decisions by minimizing total expected cost (decisions on e.g., safety factors, inspection intervals, material quality)
n
– Risk = [ ] ( )1
E Prn
i ii
C E C=
=∑
1970s: Optimization of risk
Risk
Total expected cost
d co
stRisk
Design/Mitigation costEx
pect
ed
Decision alternativesOptimum
– Optimize decisions by minimizing total expected cost (decisions on e.g., safety factors, inspection intervals, material quality)
n
– Risk = [ ] ( )1
E Prn
i ii
C E C=
=∑
1990s: Getting realistic
– Structural reliability models now allow for a realistic representation of uncertainty
– Challenges:– Determining realistic probability models
– Determining consequencesDetermining consequences
– System modeling
– Societal acceptance
– Efforts to standardize probability models (probabilistic codes)– More and more applications
Risk-based inspection, maintenance, repair planning
– Structures deteriorate with time– Deterioration is associated with large g
uncertainty– Inspections are performed to reduce
uncertaintyThe effect of inspections (and monitoring) can only be appraised probabilistically
– Applications:– Offshore structures subject to fatigue,
corrosion scour ship impactcorrosion, scour, ship impact, …
– Process systems subject to corrosion, erosion, SCC, etc…
Concrete structures (tunnels bridges) subject– Concrete structures (tunnels, bridges) subject to corrosion of the reinforcement
Zona de plataformas
Plan and optimize inspections
– We model the entire service life through event trees:
Probabilistic deterioration modelling
– Fracture mechanics based probabilistic models of crack growth:
Fatigue loads Structural response Crack growth
b
d
b
15
16
17
( )( ), , fmmP a a
da C K a cdN
= Δ
S
10
11
12
13
14
T P [s
]
1/pF = 25yr( )
( )( ), , fmmP c c
dNdc C K a cdN
= Δ4 6 8 10 12 14
7
8
9
HS [m]
1/pF 25yr1/pF = 100yr1/pF = 250yr1/pF = 1000yr
Reliability analysis
– Results
Inspection modeling
– Inspections are also modeled qualitatively
Probability of Detection on tubulars, underwater
0 8
1 ACFMMPI
0.4
0.6
0.8
POD
0
0.2
0 2 4 6 8 100 2 4 6 8 10
Crack depth [mm]
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.
Structural importance
– Member/joint importance is determined through pushover
lanalyses:– Compare: intact structure
versus structure with element removedremoved
– Determine conditional probability of collapse given element failureelement failure
Optimization
Straub D., Faber M.H. (2004). J. of Offshore Mechanics and Arctic Engineering, 126(3), pp. 265-271.
Quantifying different inspection strategies
60000
Failure
40000
50000
FailureRepair Inspection
30000
40000
Cos
t
20000
0
10000
RBI 4yr interval 20yr interval
Inspection strategy
IT implementation (iPlan)
– Calculating inspection plans using the generic approach:
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
Observados
Relación (SH/SV)
Tiempo de
exposición
p p– Dropped objects– Scour
M i th EspesoreExposici
ón aExp Exp ImpCrecimie
– Marine growth Espesores
MedidosTiempo
Falla Rec.
Eficiencia Rec.
Tasa de Corrosión
ón a huracán
Exp. Caída de
Obj.
Exp. Imp. de
Embarcaciones
Inspección VGE
Inspección VDE
Inspección con PND
Falla por sobrecarg
a
nto Marino
Daño pintura y recubrimi
Daño por corrosión
Abolladu
Inspección de Elem.
Inundados
PandeosentoAbolladu
ras
Resistencia del
elemento
Capacidad de la
estructura
Bayesian networks
Monitoring, Inspection and Maintenance for Concrete Structures
Zone A
Zone B
Α
Θ Θ Θ
Straub D., et al. (2008). Structure and Infrastructure Engineering, published online.
Θt,1 Θt,i Θt,n. . . . . .
Aspects of Sustainability
Nishijima K., Straub D., Faber M.H. (2007). Australian Journal of Civil Engineering, 4(1), pp. 59-72.
Planning of inspection, monitoring, maintenance: Research needs
– Improved spatial modeling of deterioration– Improved modeling of system behavior of a deteriorated structurep g y– System effects: Inspection provide indirect information through
correlation in the system
3
FDF*tInsp
0.55 yr
Info
rmat
ion
2.5·10-3
3.0·10-3
0.510 yr
110 yr
ueof
Sam
ple 2.0·10-3
1.5·10-3
Expe
cted
Valu * of the inspected
hot spots1.0·10-3
0.5·10-3
00 5 10 15 20 25
Number of hot spots inspected
E
Natural hazards risk assessment
– Alpine natural hazards– Decision problems:p
– Land-use planning
– Road closures
E ti– Evacuation
– Emergency response
Avalanche risk assessment model
Part 1: Hazard modelinga) Semi-empirical-physical models are availableb) Site specific observations are available from the past 50 years– a & b are combined using Bayesian updating of the model with the
observations
Φ ΘR
Model parameters
Θμ R
Pmodel
P ε
Prediction
i i
Observation i Observation error
Avalanche risk assessment model
– Resulting hazard model (annual rate of exceedance)
Straub D., Grêt-Regamey A. (2006). Cold Regions Science and Technology, 46(3) , pp. 192-203.
Bayesian Network for avalanche risk modeling
Grêt-Regamey A., Straub D. (2006). Natural Hazards and Earth System Sciences, 6(6), pp. 911-926.
Avalanche risk assessment model - Implementation
Avalanche risk assessment model
– Results are used to assess the existing risk
– Model shall be used for land-use planning and regulation
– Model should be extended to serve as a real-time decision support tool
2000s: Challenges and opportunities
– Modelling complex systems (dependence)– Realistic system models require representation of y q p
inter- and intra- system dependences
– Tools are now developed
– Near real time decision support systems– Integrate large amount of data into the model in near
real timereal time.
– Applications as:• Warning systems
St t l h lth it i• Structural health monitoring• Emergency response• Asset management / insurance
Stochastic dependence in systems: Example seismic fragility of electrical substation equipment and systems
– Common uncertain factors introduce statistical dependence among component performances, e.g:– Local site conditions
Observations
Grouping 1
Grouping 2Local site conditions
– Characteristics of ground motion beyond PGA
– Age & condition of system components
Grouping 2
– Identical capacity in subsequent events
Stochastic dependence in systems: Example seismic fragility of electrical substation equipment and systems
Including dependence in the fragility model
Systems: Components:
100Parallel system TR 1
1Circuit breaker CB9
10− 2
10− 1
gilit
y
0.6
0.8
ty10− 4
10− 3
Syst
em fr
ag
0.4
0.6
Frag
ili
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.910− 6
10− 5 Including dependenceNeglecting dependence
0
0.2Improved modelTraditional model
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
PGA [g] PGA [g]
Straub D., Der Kiureghian A. (2008). Structural Safety, published online.
Dependence in infrastructure risk analysis
– Infrastructure risk analysis should account for spatial dependences – Approach based on Bayesian networkspp y
SP 6S 6
SP 4
SP 5
SP 2
SP 3
SP 1
Straub D., Bensi M., Der Kiureghian A. (2008). Proc. EM’08, to be subm.
Dependence in infrastructure risk analysis
– Updating of seismic intensity measures at site 9 after an observation at site 1 (PGA = 0.5g):
Site 90.9
0.6
0.7
0.8No Evidence
Evidence PGA @ 1 = State 2
Evidence PGA @ 1 = State 6
0.3
0.4
0.5
f(PG
A)
Evidence PGA @ 1 = State 9
0
0.1
0.2
0
0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 1.69PGA
Dependence in infrastructure risk analysis
– Updating of seismic intensity measures at site 2 after an observation at site 1 (PGA = 0.5g)
– Comparing a model with the spatial error included or excluded
Site 2
0.120.140.16
No Correlation Model
Correlation Model
0.040.060.080.1
f(PG
A)
00.020.04
0277
1275
2272
3269
4266
5263
6261
7258
8255
9252
0.02
0.12
0.22
0.32
0.42
0.52
0.62
0.72
0.82
0.92
PGA
Summary
– There are more and more exciting opportunities for research and g ppapplication in engineering risk analysis!
References
– Straub D., Schubert M. (2008). Modelling and managing uncertainty in rock-fall hazards. Georisk, 2(1), pp. 1-15.
– Straub D., Der Kiureghian A. (2007). Improved Seismic Fragility Modeling from Empirical , g ( ) p g y g pData. Structural Safety, in print.
– Straub D., Grêt-Regamey A. (2006). A Bayesian probabilistic framework for avalanche modelling based on observations. Cold Regions Science and Technology, 46(3) , pp. 192-203.
– Grêt-Regamey A., Straub D. (2006). Spatially explicit avalanche risk assessment linking G S S S ( )Bayesian networks to a GIS. Natural Hazards and Earth System Sciences, 6(6), pp. 911-926.
– Straub D., Faber M.H. (2006). Computational Aspects of Risk Based Inspection Planning.Computer-Aided Civil and Infrastructure Engineering, 21(3), pp. 179-192.
– Straub D., Faber M.H. (2005). Risk Based Inspection Planning for Structural Systems.Structural Safety 27(4) pp 335 355Structural Safety, 27(4), pp 335-355.
– Montes-Iturrizaga R., Heredia-Zavoni E., Vargas F., Faber M.H., Straub D., De la O J. (2007).Risk Based Structural Integrity Management Using Bayesian Probabilistic Networks.Accepted for publication in ASME Journal of Offshore Mechanics and Arctic Engineering.
– Straub D Malioka V Faber M H (2007) A framework for the asset integrity management of– Straub D., Malioka V., Faber M.H. (2007). A framework for the asset integrity management oflarge deteriorating concrete structures. Structure and Infrastructure Engineering, in print.
System 2:„ FPSO"Exposure:
System 1:„ Oil field"Exposure:
- Wave-loads- Wind-loads- Ship impacts...System 3:„ Frame" E
VulnerabiliVs obus
tnes
s
- Oil & gas demand- Hurricanes- Earthquakes...
Syste 3 „ a e Exposure:
- Extremeenviron. loads
- Corrosion- FatiguelitV Vss sRo
Fatigue
Every model is limited
