To those who may have an interest in how Bayes has inspired and influenced my research and industrial activities. What you will see is indeed only selected parts of the works of my student and colleagues in academia and industry - over more than 30 years. There is much more - and much more to come.
FAIRSpectra - Enabling the FAIRification of Analytical Science
Bayes Inspired Research and Applications.pdf
1. Selected Bayesian Research
Topics and Applications
Awesome Bayesian Podcast – January 26, 2022
Michael Havbro Faber
Department of the Built Environment, AAU, DK
Risk, Resilience and
Sustainability in the Built Environment
2. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Time Line
PhD (Prof. T.-Christensen, Aalborg, DK,1989)
Post-doc. (Prof. Rackwitz, Munich)
Independent consultant - RCP
COWI, DK
Visiting prof. (Uni. Newcastle, AU)
Consultant (DNV, Norway)
ETH-Zürich, CH, 2000
DTU, 2011
AAU
2017
Sabbatical, Tsinghua
AU, China
3. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
My Mentor
Rüdiger Rackwitz, Prof. Dr.-Ing. habil.
Professor in structural safety and reliability at Technical University of
Munich from 1968 to 2008.
4. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Some of the Early and Strong Movers in Structural Reliability
Influencers - Selected
Professor O. Ditlevsen Professor F. Borges
Professor A. M. Freudenthal Professor Carl A. Cornell Professor N. C. Lind
Professor R. Rackwitz
5. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
• Daniel Straub
• Jochen Köhler
• Oliver Kübler
• Matthias Schubert
• Kazuyoshi Nishijima
• Vasiliki Malioka
• Yahya Bayraktarli
• Sebastian Thöns
• Gerhard Fink
• Jianjun Qin
• Joan Hee Roldsgaard
• Mathias Graf
• Shuoyun Zhang
• Marcus Deublein
• Rocco Custer
My PhD students
• Katharina Fischer
• Harikrishna Narasimhan
• Gianluca de Sanctis
• Guang Zou
• Sebastian Glavind
• Domenic Di Francesco
• Juan Sepulveda
• Kashif Ali
• Yue Guang
• Akinyemi Olugbenga Akinsanya
• Min Liu
• Weiheng Zhang
• Mónica Patricia Santamaría Ariza
• Zehra Irem Turksezer
• Thomas Bull
6. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
• Decision contexts
• How to represent the decision context – systems modelling
• Digital Twins – fusing knowledge and data
• How to decide - Bayesian decision analysis
• Which is the best system representation - Occam’s razor
• Best practices in industry
• Challenges for research
Topics Addressed
7. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Integrity management
Decision Contexts
Structures are
subject to
deterioration
processes such as
fatigue and
corrosion
and
also to damages
caused by extreme
load events
8. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Integrity management
Inspection and monitoring of the structures and/or
load environment facilitate that we may take
action to:
- intervene operations to reduce consequences
- repair damages
- renew structural parts
cost-optimally, and before the condition of the
structures, exposes individuals and/or the qualities
of the environment to unaccepable risks
Decision Contexts
9. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Generic Risk Based Inspection (RBI) Planning
Select joint type
- SN curve
- SIF
- Critical crack depth
Determine acceptance criteria
Calculate probability of failure and
probability of repairs for different
FDF1, FDF2, FDFi,..
)
(RSR
P j
AC
0,00E+00
2,00E-03
4,00E-03
6,00E-03
8,00E-03
1,00E-02
1,20E-02
1,40E-02
1,60E-02
1,80E-02
2,00E-02
1,0E-04 1,0E-03 1,0E-02
Acceptance criteria
Expected
total
costs
Determine inspection plans for
different FDF1, FDF2, FDFi,.. and
different target levels
Determine costs for inspection plans
for different FDF 1, FDF2, FDFi,..
Choose cost optimal inspection plan
fulfilling the acceptance criteria
T
f
P
FDFi
1,00E-05
1,00E-04
1,00E-03
1,00E-02
0 5 10 15 20 25
Time in service
Probability
of
failure
1,00E-06
1,00E-05
1,00E-04
1,00E-03
1,00E-02
1,00E-01
1,00E+00
0 5 10 15 20 25
Year in service
Probability
of
failure
Hot Spot
Decision Contexts
10. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Large Scale Earthquake Risk Modeling and Management
Before
Optimal allocation of available
resources for risk reduction
- retrofitting
- rebuilding
in regard to possible earthquakes
After
Rehabilitation of infrastructure
functionality
Condition assessment and
updating
Optimal allocation of resources
for retrofitting and rebuilding
Damage monitoring/control
Emergency help and rescue
Aftershock hazard assessment
Identification of the seismic event
During
(adapted from Yilmaz Aslantürk)
Risk Management
Risk Management
On-site observations
On-site observations
Official/insurance data
Official/insurance data
Airplane observations
Airplane observations
Satellite Observations
Satellite Observations
Real World
Exposure
Exposure
Vulnerability
Vulnerability
Robustness
Robustness
Indicators
Indicators
Exposure
Exposure
Vulnerability
Vulnerability
Robustness
Robustness
Indicators
Indicators
Models of real world
Risk
reduction
measures
Risk
reduction
measures
Risk
reduction
measures
Risk
reduction
measures
Actions
GIS Interface Platform
GIS Interface Platform
0
0 – 200’000
200’000 – 400’000
400’000 – 600’000
600’000 – 800’000
Total Risk [$]
Exposure
Vulnerability
Robustness
Ductility
capacity
Irregularity
Damage
No of
fatalities
Prob. of
escape
EQ
Time
Business
interruption
No. of
injuries
Age of
People
Period
No of
stories
Soil
subclass
Density
Damping
Structural
system
SPT
CPT
Ductility
demand
Soil
response
Liquefact.
triggering
Liquefact.
suscept.
Planimetry
measure
Planimetry
measure
Planimetry
measure
Seismic
demand
EQ
duration
PGA
Soil
Type
Fault
type
Aerial
photos
Flight
height
Rupture
length
Average
slip
Hangingwall Resolution
Terrestrial
photos
EQ
distance
EQ
magnitude
Directivity
Design code
Max.
displ.
Lab test
HCA
GW
level
Base shear
capacity Costruction
quality
Structure
class
Residual
displ.
No of people
at risk
Occupancy
class
Costs Actions
Altimetry
measure
Decision Contexts
11. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Typhoon Risk Modeling and Management
Knowledge
modeling
updating
conditioning
Transition model
Occurrence model
Wind field model
Surface friction model
Vulnerability model
Typhoon
model
Data
Information
Translation
speed
Latitude Longitude Translation
direction
Cental
pressure
Current time step
DTranslation
speed
DTranslation
direction
DCental
pressure
D: incremental change
in 6 hours
Transition model
Cental
pressure
Distance
from center
Wind speed
Wind field model
Decision Contexts
12. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Rock-fall Risk Modeling and Management
Decision Contexts
13. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Spatial Modeling of Deterioration
Zone B
Zone A
Zone B
Correlation radius
Density
function
c. Model assessment
r
r
d. Idealization
r
a. Component sector b. Basic inspection
t,1 t,i t,n
. . . . . .
0
200
400
600
800
1000
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
Year
Expected
costs
Major repair
Minor repair
Inspections
0
200
400
600
800
1000
1200
1400
1600
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
Year
Expected
costs
Major repair
Minor repair
Inspections
Without inspections
Major inspection in year 30
Decision Contexts
14. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Large Scale Concrete Structures under Degradation
Decision Contexts
15. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
:
Flood
Ship impact
Explosion/
Fire
Earthquake
Vehicle impact
W ind loads
Traffic loads
Deicing salt
W ater
Carbon dioxide
Yielding
Rupture
Cracking
Fatigue
W ear
Spalling
Erosion
Corrosion
Loss of functionality
partial collapse
full collapse
Use/
functionality
Location
Environment
Design life
Societal importance
Design codes
Design target reliability
Age
Materials
Quality of workmanship
Condition
Protective measures
Ductility
Joint characteristics
Redundancy
Segmentation
Condition
control/
monitoring
Emergency preparedness
Direct consequences
Repair costs
Temporary loss or reduced
functionality
Small number of injuries/
fatalities
Minor socio-economic losses
Minor damages to environment
Indirect consequences
Repair costs
Temporary loss or reduced
functionality
Mid to large number of
injuries/
fatalities
Moderate to major socio-
economic losses
Moderate to major damages to
environment
Exposure
Vulnerability
Robustness
Exposure
Vulnerability
Robustness
Exposure
Vulnerability
Robustness
Exposure
Vulnerability
Robustness
Physical
characteristics
Scenario representation Indicators Potential
consequences
Hazards/threaths Constituent damage states Systemdamage states
Phase1
Disturbanceeffects
Phase2
Redistributioneffects
Damages andfailure caused
directly by disturbances
Damages andfailures during
internal redistribution
Direct consequences are associated with
damages andfailures of the constituents
inphase 1 - marginally
Indirect consequences are associated with
loss of functionality of the systemcausedby
damages andfailures inphase 1 and phase 2
Exposure
Decision Contexts
Probabilistic Modelling of Systems Robustness
16. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Life Safety and Risk Acceptance
Optimization factors
Investmentsinto health and life saving
Typeand duration of
education/training
Taxesand publicservices
Typeand placeof occupation
Place and type of habitation
Consumption
Typeof transportation
Ageof retirement
Work
time
Free time
Economicaloutput
Lifeexpectation
Work to free time ratio
Societal
performance
Productivity
Efficiency
Best practices
- technical
- organisational
Best practices
- working conditions
- safety/health
Work leisure
optimization
( ) ( )
y x PE
g
dC p C N kdm p
q
−
Decision Contexts
17. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Decision Contexts
Tunnel/Roadway Accident Risk Modeling
18. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
a
X
( , , )
b e a x
e
Ẑ
a
X
( , )
b a x
Decision Event Benefit
Decision Event
Decision
0
1
Time
DataBase
Jointobservations of
atmospheric characteristics
and icing events
- Temperature
- Wind
- Humidity
- …
Probabilistic model
Icing events
o
C V H o
C V H
Forecast weather
Temperature
Time
Vind velocity
Humidity
Forecast of future icing events
- Probability of icing event
Pastobservations Real time observations
Decision Contexts
Stay Cable Ice Accretion Risk Management
19. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
19
Indicators Virtual Lab
F E D R E M A I N I N G
T R A I N I N G T I M E
T R A I N I N G
S T A G E S 4 4
T I M E
Decision Contexts
Tunnel Fire Risk Management
20. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Decision Contexts
Knowledge Domain Modeling; Risk, Resilience and Sustainability
Nielsen, L., & Havbro Faber, M. (2021).
Toward an information theoretic ontology
of risk, resilience and sustainability and
a blueprint for education-part II.
Sustainable and Resilient
Infrastructure, 1-23.
21. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Decision Contexts
Development of Knowledge over Time
Nielsen, L., Tølbøll Glavind, S., & Faber, M. H. (2021.
On Course for Calamity? – on Knowledge and Memory
in Capacity Building for Risk Governance., submitted to
Civil Engineering and Environmental Systems, 36(1),
32-54.
22. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Demand for sustainability
Decision Contexts
We must:
• Be more efficient
• Use less ressources
• Impose less greenhouse gasses on the
environment
And yet ensure safe and reliable structural
performances
The only available basis we have for
decision making is information – so how to
proceed?
Population growth, Wikepedia, UN
Planetary boundaries, Steffen et al.
2015[1]
23. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Decision Contexts
Decision Differentiated
consequences
Categorized
consequences
Probabilistic model
of ELSS capacities
and loads
LCA
Probabilistic
sustainability
assessment
Demand for sustainability
24. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
The Joint Committee on Structural Safety
Pre-Normative Activities
25. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
The Joint Committee on Structural Safety
Pre-Normative Activities
26. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
All we know about systems may be expressed in terms of
information
We apply probability theory to represent information in our models
(aleatory and epistemic uncertainties)
Systems Modelling
27. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Systems Modelling
Event
Observation
Data
Indicator
Relation
Interpretation
Knowledge Decision making Action
Experience
From
measurement
to indicator
From
indicator to
performance
(likelihood)
Information to decision making – the value chain
28. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Information - knowledge – decision making
Systems Modelling
Time
DataBase
Jointobservations of
atmospheric characteristics
and icing events
- Temperature
- Wind
- Humidity
- …
Probabilistic model
Icing events
o
C V H o
C V H
Forecast weather
Temperature
Time
Vind velocity
Humidity
Forecast of future icing events
- Probability of icing event
Pastobservations Real time observations
29. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Information state perspective
Classification of information states:
• The information is relevant and precise.
• The information is relevant but imprecise and/or incorrect (biased)
• The information is irrelevant.
• The information is disrupted/delayed.
Hot Spot
The case of inspections for control of fatigue damage
d(t)
dCRIT
t
D(t)
PoFcrit
PoF(t)
Systems Modelling
30. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Approach – systems and information
Appreciate that the systems we are dealing with are not known.
There may be and in general are competing possible systems.
All relevant possible systems must be accounted for in search for
optimal decisions
Information flow and effects of information must be explicitly
accounted for as a cause of adverse consequences – but also as
means for management
Systems Modelling
31. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Systems modeling framework
Systems Modelling
Decisions
Models of real world Real world
Exposures/loads
Vulnerability / direct con.
Robustness / indirect con.
Observations/measurements
Site investigations
Load control
Environment control
….
Materials
Component design
….
System concept
Maintenance/monitoring
Evacuation strategy
…
Safety, risk and life-cycle costs
JCSS (2008) Risk assessment in engineering
Principles, System Representation & Risk Criteria
ISBN 978-3-909386-78-9. June 2008.
32. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Direct and indirect consequences
Hazards/threaths Constituent damage states Systemdamage states
Phase1
Disturbanceeffects
Phase2
Redistributioneffects
Damages andfailure caused
directly by disturbances
Damages andfailures during
internal redistribution
Direct consequences are associated with
damages andfailures of the constituents
inphase 1 - marginally
Indirect consequences are associated with
loss of functionality of the systemcausedby
damages andfailures inphase 1 and phase 2
Systems Modelling
33. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Robustness modeling
Exposure events
Direct consequences
Follow-upconsequences
Constituent damage states
Systemdamage states
Exposure
Condition
Functionality
Hazards
Vulnerability
Robustness
, ,
( , ( ), ( ), ( ), ( )))
D I D P ID
i p i c i c i c i
=
S
It is assumed that all relevant
scenarios have been identified
1,2,.., s
i n
=
( )
( )
( )
D
R
T
c i
I i
c i
=
,
, ,
( )
( )
( ) ( )
D I
R
D I D P
c i
I i
c i c i
=
+
, ,
, ,
( ) ( )
( )
( ) ( ) ( )
D I D P
R
D I D P ID
c i c i
I i
c i c i c i
+
=
+ +
Systems Modelling
34. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
System model
Graph model
Constituents model
Probabilistic model
Decision alternatives
Systems Modelling
𝐌 𝐚 = (Σ 𝐚 , C 𝐚 , 𝐗(𝐚))T
Σ 𝐚
C 𝐚
𝐗(𝐚)
𝐚
Probabilistic system representation
35. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
System representation
Systems Modelling
𝐌 𝐚 = (Σ 𝐚 , C 𝐚 , 𝐗(𝐚))T
• System models may be
established using “bottom-up”
approaches as in structural
engineering or by “top-down”
approaches as in data-mining
• Potentially a combination of
the two approaches would be
adequate
• Bayesian Networks lend
themselves for system
modelling in either case
36. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Systems Modelling
Systems representation
Top-down models – or data driven modelling approaches are
usually assumed to be better that bottom-up models – ”data
cannot lie”.
It is overseen that data-driven models depend entirely on the
data-bases, ”experiment” plans and algorithms they take basis in
– all of which are choices – and thus subjective – in the same
manner as bottom-up models
37. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
AI
On the representation of systems
Decisions Models of real world Real world
Likelihoods
Site investigations
Load control
Environment control
….
Materials
Component design
….
System concept
Maintenance/monitoring
Emergency management
…
1 1
( ) ( ) ( )
CSTA
EXP n
n
D l k D l k
k l
R p EX c p EX
= =
= C C
1 1 1
( , ( ))
( , ) ( ) ( )
CSTA SSTA
EXP n n
n
ID ID m D l
k l m
m l k l k k
R c S c
p S EX p EX p EX
= = =
=
C
C C
( )
p EX
JCSS, Probabilistic Model Code
( ) ( ( ), ( , ), ( ))T
=
S Σ c
m a m a m a X X a
Monte Carlo Simulation
Data base with scenarios
Decisions Models of real world Real world
Likelihoods
Site investigations
Load control
Environment control
….
Materials
Component design
….
System concept
Maintenance/monitoring
Emergency management
…
1 1
( ) ( ) ( )
CSTA
EXP n
n
D l k D l k
k l
R p EX c p EX
= =
= C C
1 1 1
( , ( ))
( , ) ( ) ( )
CSTA SSTA
EXP n n
n
ID ID m D l
k l m
m l k l k k
R c S c
p S EX p EX p EX
= = =
=
C
C C
( )
p EX
JCSS, Probabilistic Model Code
Data base with monitoring
information
Data mining
Discrepancy modelling
Model(s) adaptation
Probabilistic Digital Twins
Fusing (prior) Knowledge and Observations
Glavind, S. T., Sepulveda, J. G., & Faber, M. H. (2022).
On a simple scheme for systems modeling and identification
using big data techniques. Reliability Engineering & System
Safety, 220, 108219.
38. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Prior decision analysis
Decision Event Benefit
a
X
*
0 max ( , ) max ( , ) ( , )
X
a a
B E b a X b a x f x a dx
= =
( , )
b a x
Optimal decision maximizes the expected value of utility (benefit)
(Axioms of utility theory, von Neumann and Morgenstern, 1947)
Information is
bought by choice of
prior density
Bayesian Decision Analysis
Bayesian decision analysis as
framework for managing
information (Raiffa and
Schlaifer, 1961).
39. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Posterior decision analysis
By sampling information from the sample space using an experiment
we may update the probabilistic description of
ẑ
X
X
ˆ
( ) ( , )
ˆ
( , )
ˆ
( ) ( , )
X
X
X
L x f x a
f x a
L x f x a
=
z
z
z
ˆ ˆ
( ) ( , )
L x L x e
=
z z
Of course the likelihood of the sample depends on the experiment why
we write
ẑ e
e
Bayesian Decision Analysis
40. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Posterior decision analysis
Decision Event Benefit
a
X
ˆ
max ( , ) max ( , ) ( , )
X
a a
E b a X b a x f x a dx
= z
( , )
b a x
Bayesian Decision Analysis
41. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Pre-posterior decision analysis (extensive form)
Decision Event Benefit
a
X
( , , )
b e a x
e
Z
Decision Event
*
1 max max ( , , ) ( , )
X
e a
B E b e a x f x a dx
=
Z Z
The optimal experiment may be found from
e
Bayesian Decision Analysis
42. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Value of Information
max max ( , , ) ( , ) max ( , ) ( , )
X X
e a a
VoI E b e a x f x a dx b a x f x a dx
= −
Z Z
The value of information VoI is determined from:
a
X
( , , )
b e a x
e
Ẑ
a
X
( , )
b a x
Decision Event Benefit
Decision Event
Decision
0
1
Z
Shows the coupling between buying prior and
pre-posterior information (design/insp. and monitoring)
Bayesian Decision Analysis
43. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Decision optimization – multiple possible systems
Bayesian decision analysis as framework
for managing information.
S
n
S
2
S
1
S
1
2
s
n
When new information is available prior probability assignments may be updated
and the importance of the different possible systems will change – as well as the
probability assignments within the different possible systems
( )
( , ) max ( )max ( , ) ( , )
s
a s
s a
s a P s E U a E E U a
= = +
X X
X X
Faber and Maes, ICOSSAR 2005
Robustness =
E𝐗|s
′
(U(a∗
,X))
EΣs
′
EX|{Σs}
′
U a∗, X
Bayesian Decision Analysis
Faber, M. H. and Maes, M. A., 2005,
Epistemic Uncertainties in Decision
Making, OMAE2005-67241.
44. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Decision optimization – multiple possible systems
Pre-posterior decision analyses to identify how additional
information most efficiently contributes to the management of
the system(s)
S
n
S
2
S
1
S
1
2
s
n
( )
( , , ) max max ( )max ( , ) ( , )
s
a s
e s a
e s a E P s E U a E E U a
= = +
Z X X
z X X
Bayesian Decision Analysis
Nielsen, L., Tølbøll Glavind, S., Qin, J., & Faber, M. H. (2019).
Faith and fakes–dealing with critical information in decision
analysis. Civil Engineering and Environmental Systems,
36(1), 32-54.
45. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Which is the ”best” system representation
Occam’s Razor
System model
𝐌 𝐚 = (Σ 𝐚 , C 𝐚 , 𝐗(𝐚))T
AI
On the representation of systems
Decisions Models of real world Real world
Likelihoods
Site investigations
Load control
Environment control
….
Materials
Component design
….
System concept
Maintenance/monitoring
Emergency management
…
1 1
( ) ( ) ( )
CSTA
EXP n
n
D l k D l k
k l
R p EX c p EX
= =
= C C
1 1 1
( , ( ))
( , ) ( ) ( )
CSTA SSTA
EXP n n
n
ID ID m D l
k l m
m l k l k k
R c S c
p S EX p EX p EX
= = =
=
C
C C
( )
p EX
JCSS, Probabilistic Model Code
( ) ( ( ), ( , ), ( ))T
=
S Σ c
m a m a m a X X a
Monte Carlo Simulation
Data base with scenarios
Decisions Models of real world Real world
Likelihoods
Site investigations
Load control
Environment control
….
Materials
Component design
….
System concept
Maintenance/monitoring
Emergency management
…
1 1
( ) ( ) ( )
CSTA
EXP n
n
D l k D l k
k l
R p EX c p EX
= =
= C C
1 1 1
( , ( ))
( , ) ( ) ( )
CSTA SSTA
EXP n n
n
ID ID m D l
k l m
m l k l k k
R c S c
p S EX p EX p EX
= = =
=
C
C C
( )
p EX
JCSS, Probabilistic Model Code
Data base with monitoring
information
Data mining
Discrepancy modelling
Model(s) adaptation
46. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Which is the ”best” system representation
Occam’s Razor
William of Ockham, (1287–1347)
“This philosophical razor advocates that when
presented with competing hypotheses about the
same prediction, one should select the solution
with the fewest assumptions, and that this
is not meant to be a way of choosing between
hypotheses that make different predictions.”
Wikipedia, 2021
But how may we identify the right balance
between detail in the modeling and the
knowledge/evidence supporting the model?
47. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Which is the ”best” system representation
Traditionally we estimate models through statistical concepts such
as the Maximum Likelihood Method (MLM) or Maximum a-
Posterior Probability Expectation (MAP)
However such model estimation schemes do not account for the
decision context for which the modelling is meant to serve
Thus – in the search for the most relevant model to choose as a
representation of the considered system in a given decision
context we should integrate the model estimation into the
integrity management decision optimization problem
Occam’s Razor
48. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Which is the ”best” system representation
For the simple case of one possible system representation we
may formulate the decision context driven model estimation
problem as:
Occam’s Razor
,
, ( ( ) [ ( , )])
argmax D F
A
A C A E C A
= +
49. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Which is the ”best” system representation
Comparing traditional statistical modelling with decision context
driven modelling for the case where we have a cost optimization
of the design of a short concrete column under compression due
to an uncertain load
Occam’s Razor
Glavind, S. T., Brüske, H.,
Christensen, E. D., & Faber, M. H. (2021).
Bayesian probabilistic representation of
complex systems: With application to
wave load modeling. Computer‐Aided
Civil and Infrastructure Engineering.
50. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Examples of Industrial Applications
Risk Based Inspection Planning
- 100+ jacket structures in the Gulf of
Mexico
- 40 Mærsk Oil and Gas jackets in the
Danish North Sea
- 15 jackets in the Gulf of Thailand
- 4 FSO/FPSO (Norway/Nigeria/Brazil)
- As basis for the design of FPSOs in the
Mexican part of the Gulf of Mexico
- As basis for the design of semi-subs in the
Mexican part of the Gulf of Mexico
- Repair/maintenance prioritization of 70
Cantarell field jacket structures in the Gulf of Mex.
- Platform safety case revisions
51. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Examples of Industrial Applications
TRANSIT – Tunnel Risk Management
Methodology is:
- law in Switzerland
- requirement in Norway
52. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Examples of Industrial Applications
Gudenå pæledæk
QP
Q3
Q4
Q1
QP
Q2
Q3
Q4
53. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Examples of Industrial Applications
Zarate Brazo Largo Bridges - Argentina
1.0E-11
1.0E-10
1.0E-09
1.0E-08
1.0E-07
1.0E-06
1.0E-05
1.0E-04
1.0E-03
0 5 10 15 20 25
Zeit- Jahren
Jährliche Wahrscheinlichkeit
( )
( ) ( ) ( )
( ) ( )
( )
=
=
=
=
n
j
O
j
N
d
P
O
j
N
d
i
N
d
P
O
i
N
d
P
0
1
1 ,
54. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Examples of Industrial Applications
Frigg - decommissioning
LAT
LAT LAT
LAT
AirSystemFailu
CellIntegrity
MissionFailure
Control_Monito
TriCellCrack
ShipImpact
ColumnDamag
GroutFallsOffB
MaxAscent
Retraction
GroutFallsOff ApparentWeig
AcceptableCol ColumnBallast
RemRetraction
ESDVFailure
PenetrationFail ColumnBal
HydrJack_2nd
HydrJack_1stT
Tilt
DynamicAmplif
TricellRupture
TCP2 B Step6
DelayCosts DirectCosts
MF B2 MF B1
Step 7
Step 1 Inspection and testing
Step 2 Engineering
Step 3 Remove, repair and install / test equipment
Step 5 Deballasting
Step 6 Retraction, break loose and ascent
Step 7 Tow the platform to offshore disposal site
Step 8 Disposal of platform
Step 4 Remove topside modules and MSF
Step 1 Inspection and testing
Step 2 Engineering
Step 3 Remove, repair and install / test equipment
Step 5 Deballasting
Step 6 Retraction, break loose and ascent
Step 7 Tow the platform to offshore disposal site
Step 8 Disposal of platform
Step 4 Remove topside modules and MSF
1 3 4 5 6 7
Wahrscheinlichkeit
für
Missionsversagen
Erwartete
Kosten
1 3 4 5 6 7
Zeit [steps]
Wahrscheinlichkeit
für
Missionsversagen
Erwartete
Kosten
55. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Where are risk informed approaches applied
Offshore oil and gas industry Significantly
Aeronautical industry Significantly
Bridge infrastructure systems Rarely
Building structures Hardly
Wind turbine industry Just now beginning
Best Practices in the Industry
56. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Which are the bottle necks for application
• Lack of understanding of what risk is – i.e. that a consistently
assessed:
• ”Risks associated with future operation” are equivalent to ”out
of pocket” losses in the present moment
• Insufficient training of personnel
• Lack of adequate tools for risk based operation and
maintenance planning
• Construction industry driven by a highly competitive market,
with dominating focus on price/costs/time and simplicity,
rather than on always doing better
Best Practices in the Industry
57. Awesome Bayesian Podcast, M. H. Faber – January 26, 2022
Where to go for research
• Adequate address of the monitoring and inspection activities in
the representation of the systems utilized as basis of
optimization of risk based operation and maintenance.
Including modeling of dependencies;
- in inspection outcomes
- data collected through monitoring
• Consistent integration of risk based maintenance planning with
monitoring of structural responses
• Approaches facilitating address of portfolios of structures
• Further developments of tools – with focus on the
potentials associated with Machine Learning and AI
Challenges for Research