IABMAS 2010
A framework for evaluating the
impact of structural health monitoring
on bridge management
Matteo Pozzi & Daniele Zonta
University of Trento
Wenjian Wang
Weidlinger Associates Inc., Cambridge, MA
Genda Chen
Missouri University of Science and Technology
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
motivation
permanent monitoring of bridges is commonly presented
as a powerful tool supporting transportation agencies’
decisions
 in real-life bridge operators are very skeptical
 take decisions based on their experience or on
common sense
 often disregard the action suggested by instrumental
damage detection.
 we propose a rational framework to quantitatively
estimate the monitoring systems, taking into account
their impact on decision making.
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
benefit of monitoring?
 a reinforcement intervention
improves capacity
 monitoring does NOT change
capacity nor load
 monitoring is expensive
 why should I spend my money
on monitoring?
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
layout of the presentation
 Theoretical basis of the approach of the Value of
Information:
- overview of the logic underlying
- general formulation
 Application on a on a cable-stayed bridge taken as
case study:
- description of the bridge and its monitoring system;
- application of the Value of Information approach.
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
value of information (VoI)
 money saved every time the manager interrogates the
monitoring system
 maximum price the rational agent is willing to pay for the
information from the monitoring system
 implies the manager can undertake actions in reaction to
monitoring response
VoI = C - C*
C=
operational cost w/o monitoring
C* = operational cost with monitoring
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
cost per state and action
Damaged
Undamaged
Do Nothing
Inspection
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
cost per state and action
Do Nothing
Inspection
Damaged
Undamaged
Long
downtime
(CL)
0
0
Short
downtime
(CS)
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
2 states, 2 outcomes
possible states
possible responses
“Damage”
D
“no Damage”
U
“Alarm”
A
“no Alarm”
¬A
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
ideal monitoring system
states
responses
D
A
U
¬A
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
ideal monitoring system
states
responses
D
A
U
¬A
modus tollens: [(p→q),¬q] →¬p
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
value of information
 ideal monitoring allows the manager to always follow the
optimal path
VoI = C - C*
C=
operational cost w/o monitoring
C* = operational cost with monitoring=0
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
decision tree w/o monitoring
action
state
cost
D
U
DN
LEGEND
action:
state:
DN
Do Nothing
D
Damaged
I
Inspection
U
Undamaged
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
decision tree w/o monitoring
action
state
cost
D
CL
U
DN
LEGEND
action:
0
c/s-a matrix
D
U
DN CL
0
I
0
CS
state:
DN
Do Nothing
D
Damaged
I
Inspection
U
Undamaged
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
decision tree w/o monitoring
action
state
cost
D
CL
U
DN
LEGEND
action:
0
probability
c/s-a matrix
D
U
DN CL
0
P(D)
P(U)
I
0
CS
state:
DN
Do Nothing
D
Damaged
I
Inspection
U
Undamaged
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
decision tree w/o monitoring
action
state
cost
D
CL
P(D)
U
0
P(U)
DN
probability
CDN = P(D) · CL
LEGEND
action:
expected cost
state:
DN
Do Nothing
D
Damaged
I
Inspection
U
Undamaged
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
decision tree w/o monitoring
action
state
cost
D
CL
P(D)
U
0
P(U)
DN
probability
CDN = P(D) · CL
I
expected cost
D
U
LEGEND
action:
state:
DN
Do Nothing
D
Damaged
I
Inspection
U
Undamaged
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
decision tree w/o monitoring
action
state
cost
D
CL
P(D)
U
0
P(U)
DN
probability
CDN = P(D) · CL
I
LEGEND
action:
D
0
P(D)
U
CS
P(U)
CI = P(U) · CS
state:
DN
Do Nothing
D
Damaged
I
Inspection
U
Undamaged
expected cost
expected cost
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
decision tree w/o monitoring
action
state
cost
D
CL
probability
decision criterion
P(D)
n
DN
U
DN
0
y
CI < CDN ?
I
P(U)
CDN = P(D) · CL
I
LEGEND
action:
D
0
P(D)
U
CS
P(U)
CI = P(U) · CS
state:
DN
Do Nothing
D
Damaged
I
Inspection
U
Undamaged
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
decision tree w/o monitoring
action
state
cost
D
CL
probability
decision criterion
P(D)
n
DN
U
DN
0
y
CI < CDN ?
I
P(U)
CDN = P(D) · CL
Optimal cost
I
D
U
LEGEND
action:
0
P(D)
C = min { CDN , CI }
= min { P(D)·CL , P(U)·CS }
CS
P(U)
CI = P(U) · CS
state:
DN
Do Nothing
D
Damaged
I
Inspection
U
Undamaged
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
value of information (VoI)
 ideal monitoring allows the manager to always follow the
optimal path
VoI = C - C*
C = min { P(D)·CL , P(U)·CS }
C* = 0
depends on:
 prior probability of scenarios
 consequence of action
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
non-ideal monitoring system
likelihood
P(D)
P(A|D)
A
U
¬A
a priori
D
P(U)
P(¬A|U)
states
responses
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
decision tree with monitoring
outcome
D
DN
I
A
U
D
U
D
¬A
DN
I
U
D
U
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
decision tree with monitoring
test outcome
action
state
cost
D
CL
probability
P(D|A)
CDN | A = P(D|A) · CL
ALARM!
DN
U
0
P(U|A)
D
0
P(D|A)
A
I
CI | A = P(U|A) · CS
U
CS
P(U|A)
C|A = min { CDN | A , CI | A }
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
decision tree with monitoring
test outcome
action
state
cost
D
CL
probability
P(D|A)
CDN | A = P(A|D) · P(D) · CL
ALARM!
DN
U
0
P(U|A)
D
0
P(D|A)
P(A)
A
I
CI | A = P(A|U) · P(U) · CS
U
CS
P(U|A)
P(A)
C|A = min { CDN | A , CI | A }
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
decision tree with monitoring
cost given
outcome
outcome
probability
of outcome
D
DN
U
C|A
I
A
P(A)
min { P(D)·P(A|D)·CL ,
P(U)·P(A|U)·CS }
D
U
D
¬A
DN
U
C|¬A
I
D
P(¬A)
min { P(D)·P(¬A|D)·CL ,
P(U)·P(¬A|U)·CS }
U
C* = min { P(D)·P(A|D)·CL , P(U)·P(A|U)·CS } + min { P(D)·P(¬A|D)·CL , P(U)·P(¬A|U)·CS }
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
value of information (VoI)
 maximum price the rational agent is willing to pay for the
information from the monitoring system
VoI = C - C*
C=min { P(D)·CL , P(U)·CS }
C* = min { P(D)·P(A|D)·CL , P(U)·P(A|U)·CS }
+ min { P(D)·P(¬A|D)·CL , P(U)·P(¬A|U)·CS }
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
general case
M available actions: from a1 to aM
cost per state and action
matrix
N possible scenario: from s1 to sN
scenario
s1
sk
sN
actions
a1
ai
ci,k
aM
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
decision tree w/o monitoring
action
a1
...
ai
...
state
s1
...
c1,1
probability expected
cost
P(s1)
sk
...
c1,k
P(sk)
c1,N
P(sN)
s1
...
ci,1
P(s1)
sk
...
ci,k
P(sk)
ci,N
P(sN)
s1
...
cM,1
P(s1)
sk
...
cM,k
P(sk)
cM,N
P(sN)
sN
sN
cost
decision criterion
∑k P(sk)·c1,k
∑k P(sk)·ci,k
C = min { ∑k P(sk)·ci,k }
i
aM
sN
∑k P(sk)·cM,k
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
decision tree with monitoring
outcome
action
a1
...
X
ai
...
state
s1
...
c1,1
probability expected
cost
P(s1|x)
sk
...
c1,k
P(sk|x)
c1,N
P(sN|x)
s1
...
ci,1
P(s1|x)
sk
...
ci,k
P(sk|x)
ci,N
P(sN|x)
s1
...
cM,1
P(s1|x)
sk
...
cM,k
P(sk|x)
cM,N
P(sN|x)
sN
sN
cost
decision criterion
∑k P(sk|x) ·c1,k
∑k P(sk|x)·ci,k
C|x = min { ∑k P(sk|x)·ci,k }
i
aM
sN
∑k P(sk|x)·cM,k
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
value of information (VoI)
 maximum price the rational agent is willing to pay for the
information from the monitoring system
VoI = C - C*
C = min { ∑k P(sk)·ci,k }
C* = ∫Dx min { ∑k P(sk)· PDF(x|sk)· ci,k }dx
depends on:
 prior probability of scenarios
 consequence of action
 reliability of monitoring system
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
the Bill Emerson Memorial Bridge
It carries Missouri State Highway 34, Missouri State Highway 74 and Illinois
Route 146 across the Mississippi River between Cape Girardeau, Missouri, and
East Cape Girardeau, Illinois.
Opened to traffic on December, 2003.
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
the Bill Emerson Memorial Bridge
Carrying two-way traffic, 4 lanes, 3.66 m (12 ft) wide vehicular plus two
narrower shoulders.
Total length: 1206 m (3956 ft)
Main span: 350.6 m (1150 ft)
12 side piers with span: 51.8 m (170 ft) each.
Total deck width: 29.3 m (96 ft).
Two towers, 128 cables, and 12 additional piers in the approach span on the
Illinois side
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
the Bill Emerson Memorial Bridge
Bridge
Located approximately 50 miles (80 km) from the New Madrid Seismic Zone.
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
the Bill Emerson Memorial Bridge
Bridge
Located approximately 50 miles (80 km) from the New Madrid Seismic Zone.
Instrumented with 84 EpiSensor accelerometers, installed throughout the
bridge structure and adjacent free field sites.
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
damage assessment scheme
k
BRIDGE
RESPONSE
ENN
EMULATOR
NEURAL NETWORK
k+1
-
PENN
PARAMETER EVALUATOR
NEURAL NETWORK
RMS
DAMAGE
INDICES
X
k+1
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
training of the networks
 networks calibrated using a 3-D FEM
of the bridge
 four pairs of damage locations A, B,
C and D were considered and each
damage location includes two
plastic hinges
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
damage assessment scheme
k
BRIDGE
RESPONSE
ENN
EMULATOR
NEURAL NETWORK
k+1
-
PENN
PARAMETER EVALUATOR
NEURAL NETWORK
RMS
DAMAGE
INDICES
X
k+1
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
estimation of the VoI
Two scenarios:
(U) undamaged;
(D) 12% stiffness reduction at hinges A.
Undamaged
Damaged
Response:
x: rotational stiffness amplification factor;
x=1 : hinges are intact,
x<1 : the reduced stiffness is x times the original one.
Missouri
side
A
Missouri
side
A
A
A
In an ideal world,
U → yield x=1, D → x=0.88 .
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
estimation of the VoI
Two scenarios:
(U) undamaged;
(D) 12% stiffness reduction at hinges A.
Undamaged
Damaged
Response:
x: rotational stiffness amplification factor;
x=1 : hinges are intact,
x<1 : the reduced stiffness is x times the original one.
Missouri
side
A
Missouri
side
A
A
A
In an ideal world,
U → yield x=1, D → x=0.88 .
From a Monte Carlo analysis on the FEM:
PDF(x|U) = logN(x,-0.0278,0.1389)
PDF(x|D) = logN(x,-0.1447,0.1328)
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
estimation of the VoI
Two scenarios:
(U) undamaged;
(D) 12% stiffness reduction at hinges A.
Undamaged
Damaged
Response:
x: rotational stiffness amplification factor;
Missouri
side
x=1 : hinges are intact,
x<1 : the reduced stiffness is x times the original one.
A
Missouri
side
A
A
A
In an ideal world,
U → yield x=1, D → x=0.88 .
4
PDF(x|U) = logN(x,-0.0278,0.1389)
PDF(x|D) = logN(x,-0.1447,0.1328)
PDF
From a Monte Carlo analysis on the FEM:
PDF(xIU)
PDF(xID)
3
2
1
probability
0
1
0.4
0.6
0.8
1
x
1.2
1.4
1.6
1.8
pozzi, zonta, wang &0.5chen • evaluating the impact of SHM on BMS
0
Application of the VoI
Two decision options:
- Do-Nothing
- Inspection.
Assumptions:
- prior probability of damage prob(D);
- inspection cost CI and undershooting cost CUS.
Damaged
Undamaged
Do Nothing
Undershooting
Cost (CUS)
0
Inspection
Inspection
Cost (CI)
Inspection
Cost (CI)
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
Application of the VoI
Two decision options:
- Do-Nothing
- Inspection.
Assumptions:
- prior probability of damage prob(D);
- inspection cost CI and undershooting cost CUS.
Damaged
P(D)=30%
Undamaged
P(U)=70%
Do Nothing
$ 2M
0
Inspection
$ 700k
$ 700k
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
decision tree w/o monitoring
action
state
cost
D
CUS
P(D)
U
0
P(U)
DN
probability
CDN = P(D) · CL
I
LEGEND
action:
D
CI
P(D)
U
CI
P(U)
CI
state:
DN
Do Nothing
D
Damaged
I
Inspection
U
Undamaged
expected cost
expected cost
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
decision tree w/o monitoring
action
state
cost
D
2M
30%
U
0
70%
DN
probability
CUS= $ 600k
I
LEGEND
action:
D
700k
30%
U
700k
70%
CI= $ 700k
state:
DN
Do Nothing
D
Damaged
I
Inspection
U
Undamaged
expected cost
expected cost
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
value of information (VoI)
VoI = C - C*
C = min { ∑k P(sk)·ci,k }= $ 600 k
C* = ∫Dx min { ∑k P(sk)· PDF(x|sk)· ci,k }dx
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
1.5
PDF(x)
1
Application of the VoI
0.5
0
C* = $ 600 K, Cneat* = $ 500 K, VoI = $ 100 K
probability
2.5
0
2
2
1.5
cost [M$]
3.5
0.5
3
PDF
1
4
Likelihoods and
prob(UIx)
evidence
prob(DIx)
PDF(xIU)
PDF(xID)
C Ix
PDF(x)
CNx
1
1
Cneat*(x)
0.5
0
0
0.4
0.6
0.8
1
1
probability
1.2
1.4
1.6
1.8
x
prob(UIx)
prob(DIx)
0.5
0
cost [M$]
2
C Ix
CNx
1
Cneat*(x)
0
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
x
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
4
3.5
Application of the VoI
3
probability
PDF
PDF
2.5
PDF(xIU)
PDF(xID)
PDF(x)
C* = $ 600 K, Cneat* = $ 500 K, VoI = $ 100 K
2
4
1.5
3.5
1
3
0.5
2.5
0
2
1
1.5
Likelihoods and
evidence
PDF(xIU)
PDF(xID)
PDF(x)
1
0.5
prob(UIx)
prob(DIx)
0.5
0
Updated probabilities
12
probability
cost [M$]
C Ix
CNx
prob(UIx)
prob(DIx)
C
*(x)
0.51
neat
0
0.4
0.6
0.8
1
2
cost [M$]
1.2
1.4
1.6
1.8
x
C Ix
CNx
1
Cneat*(x)
0
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
x
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
Application of the VoI
C* = $ 600 K, Cneat* = $ 500 K, VoI = $ 100 K
Likelihoods and
evidence
4
3.5
3
PDF
2.5
PDF(xIU)
PDF(xID)
PDF(x)
2
1.5
1
0.5
0
Updated probabilities
probability
1
prob(UIx)
prob(DIx)
0.5
0
Updated costs
cost [M$]
2
C Ix
CNx
1
Cneat*(x)
0
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
x
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
value of information (VoI)
VoI = C - C*
C = min { ∑k P(sk)·ci,k }= $ 600 k
C* = ∫Dx min { ∑k P(sk)· PDF(x|sk)· ci,k }dx= $500k
VoI = C - C*= $600k-$500k=$100k
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
conclusions
 an economic evaluation of the impact of SHM on BM
has been performed
 utility of monitoring can be quantified using VoI
 VoI is the maximum price the owner is willing to pay for
the information from the monitoring system
 implies the manager can undertake actions in reaction
to monitoring response
 depends on: prior probability of scenarios;
consequence of actions; reliability of monitoring
system
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
Thanks. Questions?
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS