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Transcript of Life-cycle Performance, Reliability, Risk, Resilience and ... · Lehigh University, Bethlehem, PA,...
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Dan M. Frangopol Department of Civil and Environmental Engineering,
ATLSS Engineering Research Center, Lehigh University, Bethlehem, PA, USA
Life-cycle Performance, Reliability, Risk, Resilience and Sustainability of Civil
Infrastructure November 1, 2013
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2 Introduction
• The United States has four million (4,067,076) miles of public roads (as of 2010)*.
• The road network carries 86% of passenger transportation and
60% of freight transportation. • The road network contains more than 600,000 bridges (604,460) *.
RC 41.5%
Steel 30.4%
PC 23.6%
→ % of bridge types by number → % of bridge types by deck area
RC 19.2%
Steel 43.6%
PC 35.7%
* FHWA, (2011). “National bridge inventory.” United States Department of Transportation, Federal Highway Administration.
Other 4.5% Other 1.5%
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3 Introduction
• Approximately 42% of the bridges in the United States are more than 50 years old*.
• 24.2% of bridge inventory are either structurally deficient or
functionally obsolete*.
TIME (years)
0
10.000
20.000
30.000
40.000
50.000
60.000
NU
MB
ER O
F B
RID
GES
, × 1
04 6
5
2
4
3
1
0 0,00E+00
1,00E+05
2,00E+05
3,00E+05
4,00E+05
5,00E+05
6,00E+05
7,00E+05FUNCTIONALLY OBSOLETE STRUCTURALLY DEFICIENT PROPERLY FUNCTIONAL
TIME (years)
6
5
2
7
4
3
1
0 NU
MB
ER O
F B
RID
GES
, × 1
05
FHWA, (2011). “National bridge inventory.” United States Department of Transportation, Federal Highway Administration.
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• The number of structurally deficient and functionally obsolete is in continuous decrease since 1990.
• Improving the bridge inventory condition requires an average
annual investment of $17 billion*.
• In 2004, a total of $10.4 billion was spent on bridge rehabilitation*.
Introduction
24
25
26
27
28
29
30
31
32
1996 1998 2000 2002 2004 2006 2008 2010
TIME (years)
PER
CEN
TAG
E O
F D
EFIC
IEN
T B
RID
GES
, %
* ASCE, (2009). “Report Card for America’s Infrastructure.” American Society of Civil Engineers.
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Introduction
• This deficiency in funding requires innovative structural management techniques to plan for future inspections and repair actions and cost effective maintenance strategies.
• Bridges are mandated to be inspected at least every two years; however, these visual inspections may not ensure that fatal problems will be detected.
CONCRETE SLAB CRACKS
FATIGUE CRACKS
www.wikipedia.com www.wikipedia.com
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Aggressive environmental
conditions: • Corrosion
Structures deteriorate
progressively in time
Extreme events: • Floods • Hurricanes • Earthquakes • Blasts • Fires
Collapse if cannot withstand
adequate amount of local damage
Reduced safety or
collapse if no maintenance
Sudden damage
Different ways of damage occurrence
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How safety, redundancy and durability affect the life-cycle design, assessment, maintenance and management of civil infrastructure systems?
Motivation
Sources: Meteorological Satellite Program, Associated Press, CCTV News, and Minnesota State Department of Transportation
Northeast Blackout 2003
Laval Overpass Collapse 2006
Hurricane Katrina 2005
I35W Minneapolis Bridge 2007
How robust and resilient engineered systems be?
What is the appropriate level of safety for design?
How do we best inspect, maintain, repair, and manage aging infrastructure?
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An example to provide an estimate of risk as applied to highway bridges.
Site Recovery Costs $400 million
Winning bid for new structure $234 millionState liability cap of $1 million on 13 deaths $13 millionEstimated $10,000 hospital bill on 100 injured $ 1 millionLawsuits, legislation, loss of productivity, and investigation (not estimated)
Total Estimated Consequence of Failure US$893 million
Estimated user costs: 140,000 vehicles/day, 10 mile detour, IRS allocated .48 cent/mile, and 365 day construction time of new bridge
Table 1. Estimated costs associated with the collapse of the I35W bridge in Minneapolis, Minnesota, USA, 2007 [11, 12]
$245 Million
Risk (consequence of failure)
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2013 Report Card for America’s Infrastructure
( Gives Nation a D+, Estimates Cost at $3.6 Trillion )
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Grades for Insfrastructure Categories According to 2013 Report Card for America’s
Infrastructure
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11 ESTIMATED 5-YEAR INVESTMENT NEEDS IN BILLIONS OF DOLLARS
(taken from Failure to Act Report, ASCE, 2013)
Cumulative Infrastructure Needs by System Based on Current Trends Extended to 2020 and 2040 (Dollars in $2010 billions)
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BACKGROUND
Performance indicators for civil infrastructure
r or s
0
Sf ( s )Rf ( r )
( ) ( )0
F R Sp F s f s ds∞
= ∫
( )0 0
s
F R ,Sp f r ,s dr ds∞ = ∫ ∫
( )0
F Mp f m dm−∞
= ∫
0
Area = Probability of failure
Mf ( m )M Mµ βσ=
Mµ m
Reliability
Probability of failure M R S= −Safety Margin
Probability of failure
( )tβ Time dependence
Ang and Tang (1984); Leemis (1995)
R and S are statistically independent
General case
M
M
µβσ
=Reliability Index
2 2
R S
R S
µ µβσ σ−
=+ ( ) ( )1 1 1S Fp pβ − −= Φ = Φ −
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BACKGROUND Performance indicators for civil infrastructure
Risk ( )R t Time dependence
Risk is quantified by combining the probability of occurrence and the consequences of events generated by hazards
Ang and De Leon (2005); CIB (2001); Ellingwood (2001); Decò and Frangopol (2011)
1 2 X 1 2 1 2( , , , ) ( , , , )m m mR x x x f x x x dx dx dxκ= ⋅ ⋅ ⋅∫ ∫ ∫ Instantaneous total risk R
,1
[ | ] [ ]n
m i i ii
R C P F H P H=
= ⋅ ⋅∑
Zhu et al. (2013)
Consequences of hazard(s)
Joint PDF describing occurrence probability
of hazards
Cm,i : monetary value associated with the consequences of failure P[Hi] : probability of occurrence of an event resulting from a hazard P[F | Hi] : conditional failure probability given the occurrence of a hazard n : total number of hazards considered within the analysis
R p χ= ⋅
Simplest formulation
Sustainability
• Societal • Environmental • Economic
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BACKGROUND Hazard Analysis Hazards are actions that pose potential harm to a structure or the persons occupying a structure
1) Man made hazards
• Explosions • Accidents • Terrorism
2) Natural hazards
• Earthquakes • Floods • Wind • Fires
Perf
orm
ance
TH
Time
Deterioration
Sudden hazard
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BACKGROUND Consequence evaluation Necessary step of risk assessment
•The consequences of component and system failure depend on the type, size, and importance of the structure
•Each consequence is quantified in terms of monetary values •The consequences are categorized as direct and indirect costs
( )Direct g g gC t c G L= ⋅ ⋅The direct cost of a bridge girder failure
( )Reb RebC t c W L= ⋅ ⋅The indirect cost of rebuilding a bridge
structure
Saydam et al. (2013b)
( ) (1 )tFV t PV r= ⋅ +
Replacement cost of a bridge girder Example: bridge
• Running cost of the detoured vehicles, • Time loss due to the unavailability of the
highway segment
Future value of an expenditure
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Flow chart for risk-based optimization
Generate initial population
Stopping criteria?
Decision making for preferred solution
Genetic algorithms
Generate new population
No
Yes
Current Pareto optimal solutions
Evaluate condition, performance, and cost
For each solution
Calculate fitness of objectives
START
END
16
BACKGROUND Integrated probabilistic life-cycle management framework Effects of maintenance
Optimization Pe
rfor
man
ce
Time
Performance threshold
EM PM
Preventative maintenance (PM) Essential maintenance (EM)
Genetic algorithms are used •Robust against convergence to local minima •Ease of implementation (MATLAB) •Multiple objectives and complex constraints
Liu and Frangopol (2005)
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BACKGROUND Life-cycle management, optimization, and decision making Life-cycle performance assessment and intervention scheduling •Predict a structure’s performance throughout its lifetime •Determine possible intervention strategies and associated costs •Perform optimization to determine optimal intervention planning scheduling (inspection, maintenance, monitoring, removal, and renewal actions)
Life-cycle cost
Perf
orm
ance
Design variables: • t1 , t2 ,…, tn (time
intervention actions are performed)
• IA1 , IA2 ,…, IAn (respective intervention actions)
Life-cycle cost
Perf
orm
ance
Pareto optimal set
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CONTENTS
INTRODUCTION SYSTEM PERFORMANCE ASSESSMENT AND PREDICTION
INTEGRATION OF SHM IN LCM ROLE OF OPTIMIZATION CONCLUSIONS
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LEVELS OF PERFORMANCE QUANTIFICATION
Com
plex
ity o
f the
Ana
lysi
s
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20 20 PERFORMANCE PROFILE WITH CORROSION AND SEISMIC ACTION
PERFORMANCE PROFILE
REPAIR COST
TIME
PE
RFO
RM
AN
CE
IND
EX
CO
ST
TIME
EARTHQUAKE
EARTHQUAKE EARTHQUAKE
RETROFIT REPAIR (2) REPAIR (1)
RETROFIT
REPAIR (1)
REPAIR (2)
PERFORMANCE THRESHOLD
CORROSION INITIATION
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INTRODUCTION
LIFE-CYCLE INTEGRATED MANAGEMENT FRAMEWORK
Structural Performance Assessment & Prediction
Information from Structural Health Monitoring & Uncertainty Analysis
Improved Structural Performance
Assessment & Prediction
Optimum Maintenance-Monitoring-Management
Strategies TOOLS
Optimal Decision
Existing and New Civil Infrastructure Systems :
Bridges, Buildings, Networks,…
APPLICATIONS
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CONTENTS
INTRODUCTION SYSTEM PERFORMANCE ASSESSMENT AND PREDICTION
INTEGRATION OF SHM IN LCM ROLE OF OPTIMIZATION CONCLUSIONS
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SYSTEM PERFORMANCE ASSESSMENT AND PREDICTION
Commonly employed methodology to design based on component analysis:
• Considerable waste of resources due to over-conservatism for redundant
systems • Overestimation of the actual load carrying capacity for weakest-link
systems
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System Reliability
24
Performance indicators System reliability
• Load and resistance modeling • Limit state equations for components • System analysis
( ) ( ) ( )i i ig t R t S t= −
Series system 3 2 1 ( ){ }( )1
0N
F ii
p p g=
= ≤ X
Parallel system
1
2
3
( ){ }( )1
0N
F ii
p p g=
= ≤ X
Series-parallel system
2
3 1 ( ){ }( )
1 10
M K
F i ,kk i
p p g= =
= ≤ X
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SYSTEM PERFORMANCE ASSESSMENT AND PREDICTION
System Redundancy and Robustness • System redundancy → the ability of a structural system to redistribute the applied load after reaching
the ultimate capacity of its main load-carrying members
• Robustness → the ability of a structural system to resist extreme actions without suffering
from damages disproportionate with respect to the causes that have generated them
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SYSTEM PERFORMANCE ASSESSMENT AND PREDICTION
System Redundancy and Robustness • Time-variant redundancy indices (Okasha and Frangopol, Structural Safety, 2009)
( ) ( )( )
( ) ( )1
( )
( ) y sys f sys
f sys
P t P tRI t
P t−
=
( ) ( ) ( ) ( )2 ( ) f sys y sysRI t t t= −β β
( ) ( )( )3 ( ) wc s
s
An t An tRI t
An t−
=
Py(sys)(t) = probability of first member failure occurrence at time t
Pf(sys)(t) = probability of system failure occurrence at time t
βy(sys)(t) = reliability index wirth respect to first member failure occurrence at time t
βf(sys)(t) = reliability index with respect to system failure at time t
Ans(t) = unavailability of the system at time t
Anwc(t) = unavailability of the weakest component at time t
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Structural Analysis
Interface Algorithms
Optimization
Reliability Analysis
Life-Cycle Performance Assessment, Prediction, Optimization, and Decision
Making
Design Variables
Objectives and Constraints
Limit State Equations
Structural Response
Structural Properties
Performance Indicator
Risk Analysis
Expected Losses
Probability of Failure
Hazard Identification
Consequence Evaluation
Risk Attitudes Computational framework for the life-cycle management of structures
Risk Analysis
Optimization
Interface Algorithms
Life-Cycle Performance Assessment, Prediction, Optimization, and Decision
Making
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χ⋅= fPRPf probability of failure
χ consequences caused by failure in terms of monetary loss
Structural Vulnerability Consequences
Quantitative Risk Analysis
Hazard Identification
Aleatory and Epistemic Uncertainties
Decò, A. and Frangopol, D. M. (2011). “Risk Assessment of Highway Bridges under Multiple Hazards,” Journal of Risk Research, Taylor & Francis, 14(9), 1057–1089.
Risk Definition (Ang and De Leon 2005)
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Performance indicators
Risk Hazard Analysis
• Natural hazards • Man-made
hazards Probability of
occurrence
Vulnerability Analysis
Reliability Analysis System probability
of failure given hazard occurrence
P(F | H)
Consequence Evaluation
• Commercial losses • Safety loss • Impact to society • Environmental impact
Monetary cost associated with
structural failure Cf
Risk Assessment
Risk = P(H) · P(F | H) · Cf
P(H)
Sustainability
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Natural
Man
Made
Earthquakes
Hurricanes
Floods
Corrosion
Overloading
Explosions
Fire
Accidents
Hazards Identification
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I-39 Northbound Bridge over the Wisconsin River
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Time-dependent Vulnerability
CDFs of the Time-to-Failure
Time-to-Failure (years)
(d)
0 20 40 60 80 100 120 140 160 180 200
Bridge lifetime (80 years)
Scour κ = 1.54 λ = 0.014
Live loads κ = 5.57 λ = 0.0097
Earthquakes κ = 2.15
λ = 4.53x10-6
of T
ime-
to-F
ailu
re
(a)
0 10 20 30 40 50 60 70 80
Time (years)
Prob
abili
ty o
f Fai
lure
TDPf,sys
Live loads
Pf,sys
(b)
0 10 20 30 40 50 60 70 80
Time (years)
Prob
abili
ty o
f Fai
lure
TDPf,SC
Pf,SC
Scour
Earthquake
(c)
0 10 20 30 40 50 60 70 80
Time (years)
Prob
abili
ty o
f Fai
lure
PCD TDPCD
10 -6
10 -5
10 -4
10 -3
10 -2
10 -1
10 0
10 -3
10 -2
10 -1
10 0
10 -10
10 -9
10 -8
10 -7
0.000
0.005
0.010
0.015
0.020
0.025
PDFs of the Time-to-Failure
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0 10 20 30 40 50 60 70 80
Time (years)
Tim
e-D
epen
dent
Tot
al
Ris
k (U
SD m
illio
ns) µ(R) + σ(R)
µ(R) - σ(R)
µ(R)
(a)
(b)
0 10 20 30 40 50 60 70 80
Time (years)
Nor
mal
ized
Indi
rect
Ris
k
0.0
0.2
0.4
0.6
0.8
1.0
1.2
µ(NRID) - σ(NRID)
µ(NRID) + σ(NRID) µ(NRID)
0
2
4
6
8
10
12
14
16
18 Profiles of the Time-
Dependent Total Risk
Standard deviation of the time-dependent total risk grows over time
Profiles of the Time-Dependent
Normalized Indirect Risk Index
( ) ( )( ) ( )tRtR
tRtNRIDD
IDID +
=
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34
CONTENTS
INTRODUCTION SYSTEM PERFORMANCE ASSESSMENT AND PREDICTION
INTEGRATION OF SHM IN LCM ROLE OF OPTIMIZATION CONCLUSIONS
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PERFORMANCE INDEX PROFILE WITH AND WITHOUT MONITROING
TIME
PE
RFO
RM
AN
CE
IND
EX
WITHOUT MONITORING
WIHTOUT MONITORING
PERFORMANCE THRESHOLD
SERVICE LIFE WITH MONITORING
SERVICE LIFE WITHOUT MONITORING
UPDATING BASED ON MONITORING
Inaccurate prediction → Tremendous consequences
due to failure occurrence (later reaching of the threshold is
predicted)
INTEGRATION OF SHM IN LCM
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36
PERFORMANCE INDEX PROFILE WITH AND WITHOUT MONITROING
TIME
PE
RFO
RM
AN
CE
IND
EX
PERFORMANCE THRESHOLD
SERVICE LIFE WITHOUT MONITORING
SERVICE LIFE WITH MONITORING
UPDATING BASED ON MONITORING
WIHTOUT MONITORING
Inaccurate prediction → Unnecessary
Maintenance Action (earlier reaching of the threshold is
predicted)
WITHOUT MONITORING
INTEGRATION OF SHM IN LCM
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37
Combining SHM & LCM
Structural Health Monitoring
Actual Structural Data
Predictive in nature? Actionable Information?
Life-Cycle Management
Predictive Management Tool
Accuracy of random variables? Limited use of structure-specific
structural data
Combined Approach
Predictive Tool
Actual Structural Data
Actionable Information for the bridge manager
Combining SHM and LCM has the benefit that each method’s advantages complement the other’s disadvantages
Frangopol and Messervey "Maintenance Principles for Civil Structures,“ Chapter 89 in Encyclopedia of Structural Health Monitoring, John Willey & Sons, 2009
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38
SHM design considerations: Bridge Importance
isys
netiRIF
,ββ
∂∂
=
A bridge manager will likely desire to focus effort on the most critical bridge, or bridges in a network. Such an analysis requires the consideration of connectivity, user satisfaction, and network reliability.
The reliability importance factor (RIF) is defined as the sensitivity of the bridge network reliability with respect to a change in an individual bridge’s reliability
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39 MONITORING WITHIN A LIFE-CYCLE CONTEXT
THE MOST WIDELY USED DESIGN CRITERION → MINIMUM EXPECTED LIFE-CYCLE COST
ET T PM INS REP FC C C C C C= + + + +
CET= expected total cost, CT= initial cost,
CPM= expected cost of maintenance, CINS= expected cost of inspection,
CREP= expected cost of repair, and CF= expected cost of failure
Inclusion of monitoring cost
0 0 0 0 0 0ET T PM INS REP F MONC C C C C C C= + + + + +
General form of the expected LCC
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40 MONITORING WITHIN A LIFE-CYCLE CONTEXT
COST OF MONITORING CMON
MON T OP INS REPC M M M M= + + +
MT= expected initial design/construction cost of the monitoring system,
MOP= expected operational cost of the monitoring system,
MINS= expected cost of inspection of the monitoring system,
MREP= expected cost of repair cost of the monitoring system
BENEFIT OF THE MONITORING SYSTEM, BMON
0MON ET ETB C C= −
Timely maintenance intervention,
Reduction of failure cost
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41
Optimum Solution based on LCC Minimization without Monitoring
TOTAL LIFE-CYCLE COST
OPTIMUM SOLUTION A
INITIAL COST
FAILURE COST
COSTA
PERFORMANCE INDEX
PR
ES
EN
T VA
LUE
OF
EX
PE
CTE
D C
OS
TS
MAINTENANCE COST
NEAR-OPTIMAL REGION
MONITORING WITHIN A LIFE-CYCLE CONTEXT
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42
OPTIMUM SOLUTION B
TOTAL LIFE-CYCLE COST
INITIAL COST
FAILURE COST
COSTB
PR
ES
EN
T VA
LUE
OF
EX
PE
CTE
D C
OS
TS
PERFORMANCE INDEX
NEAR-OPTIMAL REGION
MAINTENANCE COST & MONITORING COST
Optimum Solution based on LCC Minimization with Cost-Effective Monitoring
MONITORING WITHIN A LIFE-CYCLE CONTEXT
0 0MON ET ETB C C= − >
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43
OPTIMUM SOLUTION C
TOTAL LIFE-CYCLE COST
FAILURE COST
INITIAL COST
PR
ES
EN
T VA
LUE
OF
EX
PE
CTE
D C
OS
TS
COSTC
PERFORMANCE INDEX
NEAR-OPTIMAL REGION
MAINTENANCE COST & MONITORING COST
Optimum Solution based on LCC Minimization without Cost-Effective Monitoring 0 0MON ET ETB C C= − <
MONITORING WITHIN A LIFE-CYCLE CONTEXT
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44
CONTENTS
INTRODUCTION SYSTEM PERFORMANCE ASSESSMENT AND PREDICTION
INTEGRATION OF SHM IN LCM ROLE OF OPTIMIZATION CONCLUSIONS
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45
ROLE OF OPTIMIZATION
• Under uncertainty, decision related to the civil infrastructure management should be made by
maximizing the structural performance & minimizing the life-cycle cost
Design and Maintenance planning can be best formulated as a multi-objective optimization problem
PERFORMANCE INDEX
LIFE
-CYC
LE C
OS
T
GROUP OF OPTIMIZED TRADE-OFF SOLUTIONSWITHOUT MONITORING
TRADE-OFF SOLUTIONS BETWEEN TWO CONFLICTING OBJECTIVES
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46
ROLE OF OPTIMIZATION
PERFORMANCE INDEX
LIFE
-CYC
LE C
OS
T
GROUP OF OPTIMIZED TRADE-OFF SOLUTIONS WITHOUT MONITORING
GROUP OF OPTIMIZED TRADE-OFF SOLUTIONS WITH MONITORING
OPTIMAL PARETO FRONT
TRADE-OFF SOLUTIONS BETWEEN TWO CONFLICTING OBJECTIVES
A
B
C
A to B: Cost-Effective SHM B to C: Not Cost-Effective SHM
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47
Risk-based Optimum Maintenance
Reducing the failure probabilities of the structure under hazards
Reducing the consequences caused by structure failure
Risk mitigation strategies:
Two types:
Essential maintenance
Kong et al. (2000)
Preventive maintenance
Zhu, B. and Frangopol, D. M. (2011). “Risk-Based Approach for Optimum Maintenance of Bridges under Traffic and Earthquake Loads”, Journal of Structural Engineering, ASCE, 139(3), 422–434.
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48
Application: E-17-AH Highway Bridge
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49
Case Study: E-17-AH Bridge
Essentials maintenance:
Risk threshold: 5.0×105 Optimum: the lowest cost per year increase of service life
Estes (1997)
t=47 years t=88 years
Replacing deck
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50
Case Study: E-17-AH Bridge
Preventive maintenance:
Risk threshold: 5.0×105
Optimum: the lowest cost per year increase of service life
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51
Case Study: E-17-AH Bridge
Preventive maintenance:
Number of PM =5
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Resilience as Optimization Criterion for the Rehabilitation of Bridges Belonging to a
Transportation Network Subject to Earthquake
Advanced Technology for Large Structural Systems (ATLSS) Engineering Research Center Department of Civil and Environmental Engineering
Lehigh University
Dan M. Frangopol Dist.M.ASCE and Paolo Bocchini M.ASCE
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53
DESCRIPTIVE DEFINITIONS OF RESILIENCE
Economic
Social
Organizational
Technical
Resourcefullness
Redundancy
Rapidity
Robustness
Faster recovery
More reliability
Lower consequences
RESILIENCE
4 dimensions of resilience
4 properties of resilience
3 results of resilience
[Bruneau et al. 2003]
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PROPOSED APPROACH • Robustness
• Rapidity
• Redundancy
• ...
• ...
• Social impact
• Economic impact
• ...
• Reliability
• Risk
• ...
• ...
RESILIENCE
Multi-criteria Pareto
Efficiency
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55
MULTI-CRITERIA APPROACH
POSSIBLE OBJECTIVES • Maximize resilience index 𝑅𝑅4
• Minimize the total cost of interventions (associated with resourcefullness)
• Minimimize the total recovery time (rapidity)
• Minimize the time required to reach a target functionality level (advanced use of rapidity)
• Minimize the impact of an extreme event (robustness)
POSSIBLE CONSTRAINTS • Total cost has to be lower
than the available budget.
• Deliver minimum functionality levels at certain instants (minimum acceptable recovery path)
• Maximum number of simultaneous interventions (associated with resourcefullness)
• additional constraints on the rehabilitation parameters
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56
PARETO FRONT
Resilience index
Tota
l re
stor
atio
n c
ost
Maximum cost
Pareto front
Optimal and feasible
strategies
non-feasible strategies
Region of feasible, but non-optimal strategies
No strategies in this region
Region of non-feasible strategies
Optimal but
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57
APPLICATION TO BRIDGE NETWORKS
System: bridge network
Functionality 𝑄𝑄(𝑡𝑡): ability to effectively redistribute traffic flows
Data: damage level of all the bridges after an earthquake
Rehabilitation strategies: defined by the schedule of the interventions and the recovery speed (budget)
Objectives: maximize resilience index, minimize cost of interventions
Constraints: maximum budget, maximum simultaneous interventions, limited ranges for design variables
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58
RECOVERY PROCESS OF A BRIDGE
no
Damage level
Time, 𝑡𝑡
Intervention in progress
minor moderate
major collapse
Functionality carried traffic
Functionality crossed traffic
100%
0%
50%
100%
0%
50%
Intervention in progress
extreme event
2 lanes closed out of 4
2 lanes closed out of 4
Out of service
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59
ILLUSTRATIVE EXAMPLE
0%
25%
50%
75%
100%
Time,
Func
tiona
lity,
𝑄𝑄(𝑡𝑡
)
𝑡𝑡 𝑡𝑡0 𝑡𝑡0 + 𝑡𝑡ℎ 𝑡𝑡1𝑇𝑇 𝑡𝑡2𝑇𝑇
𝑄𝑄1𝑇𝑇
𝑄𝑄2𝑇𝑇 𝑄𝑄1
Strategy A
Strategy B
Strategy C
Minimum acceptable
path
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60
ILLUSTRATIVE EXAMPLE
0 50% 0
Resilience, 𝑅𝑅
Tota
l Reh
abilit
atio
n C
ost,
𝐶𝐶
𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚
Pareto Front
100%
Strategy A
Strategy B
Strategy C
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61
COMPUTATIONAL PROCEDURE
Network level
Functionality over time
Individual bridge level
Serviceability over time
Interface Traffic assignement
and distribution
MULTI-OBJECTIVE OPTIMIZATION
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62 DESIGN VARIABLES: (i) time between occurrence of an extreme event and the beginning of the rehabiliattion activities, and (ii) damage recovery rate
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63
CONSTRAINTS ON DESIGN VARIABLES
t0 t0+δb t0+δb+lb0/tan(θb) t0+th 0
1
2
3 lb0 4
Time t
Dam
age
leve
l l
b Idle time δ b Works in progress
Damage recovery rate θ b
COMPONENT b
θb cannot be higher than an upper limit (maximum recovery speed 80°). Moreover θb is never convenient below a lower limit (30°).
δb has to be included in [0, th] = [0, 2 years]
Maximum number of simultaneous interventions: 6
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64
ANALYTICAL FORMULATION
Given: (input)
network topology; traffic data; road capacities; secondary detour routes characteristics; bridge locations; approximate rehabilitation costs; discount rate of money; 𝑙𝑙𝑏𝑏0 (post-event damage level for bridge 𝑏𝑏) ∀ 𝑏𝑏 = 1,2, … ,𝑁𝑁𝐵𝐵 ;
find: (design variables)
𝛿𝛿𝑏𝑏 (idle time for bridge 𝑏𝑏) ∀ 𝑏𝑏 = 1, 2, … ,𝑁𝑁; 𝜃𝜃𝑏𝑏 (damage recovery rate for bridge 𝑏𝑏) ∀ 𝑏𝑏 = 1, 2, … ,𝑁𝑁𝐵𝐵;
so that: (objectives)
𝑅𝑅 = 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 ; 𝐶𝐶 = 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 ;
subject to: (constraints)
0 ≤ 𝛿𝛿𝑏𝑏 ≤ 𝑡𝑡ℎ , ∀ 𝑏𝑏 = 1, 2, … ,𝑁𝑁𝑏𝑏 ; 𝜃𝜃𝑚𝑚𝑚𝑚𝑚𝑚 ≤ 𝜃𝜃𝑏𝑏 ≤ 𝜃𝜃𝑚𝑚𝑚𝑚𝑚𝑚 , ∀ 𝑏𝑏 = 1, 2, … ,𝑁𝑁𝑏𝑏 ; 𝐶𝐶 ≤ 𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 ; 𝑁𝑁𝑆𝑆𝑆𝑆 𝑡𝑡 ≤ 𝑁𝑁𝑆𝑆𝑆𝑆𝑚𝑚𝑚𝑚𝑚𝑚 , ∀𝑡𝑡 ∈ [𝑡𝑡0, 𝑡𝑡0 + 𝑡𝑡ℎ] .
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65
NUMERICAL EXAMPLE (Bocchini and Frangopol, Prob. Eng. Mech. 2011)
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66
REPRESENTATIVE SOLUTION S2
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67
LATEST APPLICATION: SANTA BARBARA
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LATEST APPLICATION: SANTA BARBARA
7880
8284
8688
66.5
77.5
840
41
42
43
44
45
46
Time to 80% functionality
[months]
Total cost of interventions
[$ million]
Resilience index [%]
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San Francisco
Richmond San Rafael
San Jose
Santa Clara
Oakland
Hayward
Fremont
San Mateo
San Francisco
Bay
Berkeley
Redwood City
Pacific Ocean
Highway Network of Upper Bay
Area
Highway Network of Lower Bay
Area
Highway Segment Link between Networks
5 mi
10 km
FUTURE TARGET: SF BAY AREA
Credits: Duygu
Saydam
69
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San Francisco
Richmond San Rafael
San Jose
Santa Clara
Oakland
Hayward
Fremont San Mateo
San Francisco Bay
Berkeley
Redwood City
Pacific Ocean
Highway Segment
Link b etween Networks
5 mi
10 km
Highway Network of U pper Bay Area
Highway Network of Lower Bay Area
70
Applications
Bridge networks
Node (Intersection)
Highway Bridge
Highway Segment
N5 mi
10 km
N1
N2
N3
N4
N5
N6 N7
B1
B2B3 B4 B5
B6B7B8
B9
B10-11
B12B13
B14-15B16
Saydam et al. (2013a)
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Applications
Ships
Sea Fighter (FSF – 1)
High Speed Vessel (HSV-2 Swift)
Other engineering systems Movable bridges
Bridge – ship interaction
Gokce et al. (2013) Gokce et al. (2013)
Gokce et al. (2013)
Wikipedia (2008)
GenDisasters (2013)
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Sustainability of Bridge Networks under Earthquake and Flood-Induced Scour
72
Lehigh University Bethlehem, PA, USA
You Dong, Dan M. Frangopol, and Duygu Saydam
June 16-20, 2013
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Infrastructure systems are critical for the economy and society. The probabilistic time-variant risk assessment under multiple hazards is a relatively new research area.
The sustainability aims to improve the quality of life for present and future generations. There is the need for well established methods for quantifying the metrics of sustainability.
Social
Environmental
Economic
Adams, 2006
Sustainable
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• Flowchart for Hazard Risk Assessment
1. Hazard Analysis Seismic Scenarios
2. Structural Analysis Seismic Demand and Capacity
3. Damage Analysis Damage States
4. Loss Analysis Monetary Loss
Probabilistic Time-Dependent
Probabilistic and Time-Dependent SUSTAINABILITY
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Proposed Flowchart
Compute the total risk and use this information in
decision making
Identify seismic scenario events reflecting seismic
activity of the region
Compute economic metrics (e.g., repair cost)
Compute social metrics (e.g., downtime)
Compute environmental metrics (e.g., carbon dioxide emissions)
Seismic performance quantification of
network link
REP
EAT
FOR
EA
CH
LIN
K
Single bridge Seismic fragility
analysis
REP
EAT
FOR
EA
CH
BR
IDG
E
Compute economic loss (e.g., replacement
and repair cost)
Compute social loss (e.g.,
downtime)
Compute environmental loss (e.g., carbon dioxide
emissions)
Bridge Damage Index
Link
D
amag
e In
dex
Brid
ge
Dam
age
Stat
e
REP
EAT
FOR
EA
CH
TIM
E ST
EP
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Bridge highway segments
4 nodes and 16 bridges
N
Orange County, CA
2Mile
0
0 2Kilometer
33.7000 N
33.5400 N
33.6200 N
117.9000 W 117.6700 W117.7850 W
LegendRoad linksNodes connecting the links
Bridges
B1B2
B3B4
B5 B6B7
B8B9
B10 B11
B12
B13
B14
B15B16
: Single-Span Simply-Supported Concrete : Multiple-Span Continuous Concrete : Multiple-Span Discontinuous Concrete
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N
Orange County, CA
2Mile
0
0 2Kilometer
33.7000 N
33.5400 N
33.6200 N
117.9000 W 117.6700 W117.7850 W
LegendRoad linksNodes connecting the links
Bridges
B1B2
B3B4
B5 B6B7
B8B9
B10 B11
B12
B13
B14
B15B16
∑=
=n
jj tBDItLDI
1
2))(()(
The seismic performance of the link (LDI) depends on the damage states of the bridges in the links.
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HAZARD ANALYSIS
78
Hazard analysis
Example: seismic hazard
Probability of occurrence
Effect on structural vulnerability
Poisson process Fragility analysis
1
1
Probability of exceeding a damage state
Peak ground acceleration (g) 0
Age of the structure increases
t = 0 years
t = 30 years
t = 60 years
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The conditional probability of exceeding moderate damage state under PGA = 0.5g is about 0.64 at t = 25 year; this value reaches 0.87 at t = 75 years without scour. This value is 0.95 at t =75 years with flood-induced scour.
The findings highlight importance of considering effects of aging and flood-
induced scour on the seismic vulnerability of
bridges. 0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
25 Years
Exce
edan
cePr
obab
ility
Peak Ground Acceleration (g)
Moderate Damage
Without Flood-Induced ScourWith Flood-Induced Scour
25 Years
75 Years
75 Years
Type B Bridge: Fragility Curve
Time Effects+ Flood-Induced Scour )1()( 210 Scourii Ztmtm ⋅−⋅−⋅= γγ
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The expected economic loss increases with time and reaches the maximum value at the end of the time-interval under investigation. The difference between the cases with and without flood-induced scour increases with time.
0 25 50 750
4
8
12
16
Time (years)
Expe
cted
Los
s (U
SD M
illio
ns)
Time-Variant Expected Economic Loss
Without Flood-Induced Scour
With Flood-Induced Scour
Expected Annual Economic Loss Bridge Network
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CONCLUSIONS
1. Effective and practical methods for capturing system performance including redundancy and robustness in a time-dependent context will continue to present an important challenge.
2. Development of prediction models for the structural performance assessment and prediction with higher accuracy will improve the results of any optimization process. Incorporation of SHM in this process is a field in its infancy.
3. Improvements in probabilistic and physical models for evaluating and comparing the risks and benefits associated with various alternatives for maintaining or upgrading the reliability of existing structures are needed.
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FUTURE CHALLENGES
Acquire reliable data and develop advanced computational tools in order to :
• PROVIDE BETTER KNOWLEDGE ON DEGRADATION AND
PERFORMANCE OF CIVIL AND MARINE INFRASTRUCTURE SYSTEMS
• SUPPORT BETTER DESIGN METHODS AND
PERFORMANCE PREDICTIVE MODELS • SUPPORT ADVANCED MANAGEMENT DECISION-MAKING
TOOLS
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IABMAS Italian Group – Milan, Italy | October 14-15, 2013
84 IABMAS Conferences
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IABMAS 2014
IABMAS 2014 will be held in Shanghai, China on July 7-11 2014
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IABMAS 2016
IABMAS 2016 Iguazu Falls
Paraná, Brazil June 26 – 30, 2016
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National Groups of IABMAS
Portuguese Association for Bridge
Maintenance and Safety www.ascp.pt
China Group of IABMAS www.iabmas-cg.org
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IABMAS Italian Group – Milan, Italy | October 14-15, 2013
89 89
IABMAS Italian Group
Foundation Meeting Regina Palace Hotel, Azalea Room
Stresa, Lake Maggiore, Italy | July 9th, 2012
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THANK YOU