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![Page 1: Pozzi, zonta, wang & chen evaluating the impact of SHM on BMS A framework for evaluating the impact of structural health monitoring on bridge management.](https://reader038.fdocuments.net/reader038/viewer/2022103004/56649c875503460f9493f887/html5/thumbnails/1.jpg)
pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
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
IABMAS 2010
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pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
motivationpermanent 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.
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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?
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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.
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pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
value of information (VoI)
VoI = C - C*
operational cost w/o monitoringC =
operational cost with monitoringC* =
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
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pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
cost per state and action
Do Nothing
Inspection
Damaged Undamaged
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pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
cost per state and action
Longdowntime
(CL)0Do Nothing
Inspection
Damaged Undamaged
Shortdowntime
(CS)0
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pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
2 states, 2 outcomes
possible states possible responses
D
“Damage”
“no Damage”
“Alarm”
“no Alarm”
U
A
¬A
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pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
ideal monitoring system
D
U
A
¬A
states responses
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pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
ideal monitoring system
D
U
A
¬A
states responses
modus tollens: [(p→q),¬q] →¬p
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pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
value of information
VoI = C - C*
operational cost w/o monitoringC =
operational cost with monitoring=0C* =
ideal monitoring allows the manager to always follow the optimal path
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pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
decision tree w/o monitoring
DN
D
U
action state cost
Do Nothing
Inspection
Damaged
Undamaged
DN D
U
action: state:
LEGEND
I
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pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
decision tree w/o monitoring
DN
D
U
action state cost
Do Nothing
Inspection
Damaged
Undamaged
DN D
U
action: state:
LEGEND
CL 0
0 CS
DN
I
D U
c/s-a matrix
CL
0
I
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pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
decision tree w/o monitoring
DN
D
U
action state cost
0
CL
probability
P(D)
P(U)
Do Nothing
Inspection
Damaged
Undamaged
DN D
U
action: state:
LEGEND
CL 0
0 CS
DN
I
D U
c/s-a matrix
I
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pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
decision tree w/o monitoring
DN
D
U
action state cost
0
CL
probability
P(D)
P(U)
CDN = P(D) · CL
Do Nothing
Inspection
Damaged
Undamaged
DN D
U
action: state:
LEGEND
expected cost
I
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pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
decision tree w/o monitoring
DN
D
U
action state cost
0
CL
probability
P(D)
P(U)
ID
U
CDN = P(D) · CL
Do Nothing
Inspection
Damaged
Undamaged
DN
I
D
U
action: state:
LEGEND
expected cost
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pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
decision tree w/o monitoring
DN
D
U
action state cost
0
CL
probability
P(D)
P(U)
D
U CS
0 P(D)
P(U)
CDN = P(D) · CL
CI = P(U) · CS
Do Nothing
Inspection
Damaged
Undamaged
DN D
U
action: state:
LEGEND
expected cost
expected cost
I
I
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pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
decision tree w/o monitoring
DN
D
U
action state cost
0
CL
probability
P(D)
P(U)
D
U CS
0 P(D)
P(U)
CDN = P(D) · CL
CI = P(U) · CS
Do Nothing
Inspection
Damaged
Undamaged
DN D
U
action: state:
LEGEND
decision criterion
CI < CDN ?yn
IDN
I
I
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pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
decision tree w/o monitoring
DN
D
U
action state cost
0
CL
probability
P(D)
P(U)
D
U CS
0 P(D)
P(U)
CDN = P(D) · CL
CI = P(U) · CS
C = min { CDN , CI }
= min { P(D)·CL , P(U)·CS }
Optimal cost
Do Nothing
Inspection
Damaged
Undamaged
DN D
U
action: state:
LEGEND
decision criterion
CI < CDN ?yn
IDN
I
I
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pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
value of information (VoI)
VoI = C - C*
C =
C* = 0
ideal monitoring allows the manager to always follow the optimal path
min { P(D)·CL , P(U)·CS }
depends on: prior probability of scenariosprior probability of scenarios consequence of action
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pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
non-ideal monitoring system
D
U
A
¬A
P(A|D)
P(¬A|U)
P(A
|U)
P(¬A|D
)
likelihood
states responses
a p
rio
ri
P(D)
P(U)
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pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
decision tree with monitoring
A
outcome
DN
D
U
D
U
I
DN
D
U
D
U
I
¬ A
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pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
decision tree with monitoring
DN
D
U
action state cost
0
CL
probability
A
ALARM!
test outcome
P(D|A)
P(U|A)
D
U CS
0
C|A = min { CDN | A , CI | A }
IP(D|A)
P(U|A)
CI | A = P(U|A) · CS
CDN | A = P(D|A) · CL
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pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
decision tree with monitoring
DN
D
U
action state cost
0
CL
probability
A
ALARM!
test outcome
P(D|A)
P(U|A)
D
U CS
0
C|A = min { CDN | A , CI | A }
IP(D|A)
P(U|A)
CI | A = P(A|U) · P(U) · CS
CDN | A = P(A|D) · P(D) · CL
P(A)
P(A)
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pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
decision tree with monitoring
A
outcome
DN
D
U
D
U
I
DN
D
U
D
U
I
¬ A
cost given outcome
C|A
C|¬A
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 }
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 }
probability of outcome
P(A)
P(¬A)
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pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
value of information (VoI)
VoI = C - C*
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 }
maximum price the rational agent is willing to pay for the information from the monitoring system
C=min { P(D)·CL , P(U)·CS }
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pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
general case
ci,kai
sk
scenarioac
tions
a1
aM
s1 sN
M available actions: from a1 to aM
N possible scenario: from s1 to sN
cost per state and action matrix
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pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
decision tree w/o monitoring
a1
action state cost
c1,1
probability
P(s1)
c1,k
s1
sN
sk
ai
aM
c1,N
...
ci,1
ci,k
s1
sN
sk
ci,N
...
cM,1
cM,k
s1
sN
sk
cM,N
...
P(sk)
P(sN)
P(s1)
P(sk)
P(sN)
P(s1)
P(sk)
P(sN)
C = min { ∑k P(sk)·ci,k }
...
i
decision criterion
∑k P(sk)·c1,k
∑k P(sk)·ci,k
∑k P(sk)·cM,k
expected cost
...
...
...
...
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pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
decision tree with monitoring
a1
state cost
c1,1
probability
P(s1|x)
c1,k
s1
sN
sk
ai
aM
...
c1,N
...
ci,1
ci,k
s1
sN
sk
ci,N
...
cM,1
cM,k
s1
sN
sk
cM,N
...
... C|x = min { ∑k P(sk|x)·ci,k }
...
i
decision criterion
∑k P(sk|x) ·c1,k
∑k P(sk|x)·ci,k
∑k P(sk|x)·cM,k
expected cost
outcome
X
P(sk|x)
P(sN|x)
P(s1|x)
P(sk|x)
P(sN|x)
P(s1|x)
P(sk|x)
P(sN|x)
action
...
...
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pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
value of information (VoI)
VoI = C - C*
maximum price the rational agent is willing to pay for the information from the monitoring system
C = min { ∑k P(sk)·ci,k }
C* = ∫Dx min { ∑k P(sk)· PDF(x|sk)· ci,k }dxdepends on:
prior probability of scenariosprior probability of scenarios consequence of action reliability of monitoring system
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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.
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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
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pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
the Bill Emerson Memorial Bridge
Located approximately 50 miles (80 km) from the New Madrid Seismic Zone.
Bridge
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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.
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pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
PENNPENNPARAMETER EVALUATORPARAMETER EVALUATOR
NEURAL NETWORKNEURAL NETWORK
damage assessment scheme
ENNENNEMULATOREMULATOR
NEURAL NETWORKNEURAL NETWORK
-- RMSRMS
k k+1
k+1
DAMAGE DAMAGE INDICESINDICES
XX
BRIDGE BRIDGE RESPONSERESPONSE
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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
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pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
PENNPENNPARAMETER EVALUATORPARAMETER EVALUATOR
NEURAL NETWORKNEURAL NETWORK
damage assessment scheme
ENNENNEMULATOREMULATOR
NEURAL NETWORKNEURAL NETWORK
-- RMSRMS
k k+1
k+1
DAMAGE DAMAGE INDICESINDICES
XX
BRIDGE BRIDGE RESPONSERESPONSE
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pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
estimation of the VoITwo scenarios:(U) undamaged;(D) 12% stiffness reduction at hinges A.
Response:x: rotational stiffness amplification factor;
x=1 : hinges are intact, x<1 : the reduced stiffness is x times the original one.
In an ideal world,U → yield x=1, D → x=0.88 .
A A
Missouri side
A
Missouri side
A
DamagedUndamaged
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pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
estimation of the VoITwo scenarios:(U) undamaged;(D) 12% stiffness reduction at hinges A.
Response:x: rotational stiffness amplification factor;
x=1 : hinges are intact, x<1 : the reduced stiffness is x times the original one.
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)
A A
Missouri side
A
Missouri side
A
DamagedUndamaged
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pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
estimation of the VoITwo scenarios:(U) undamaged;(D) 12% stiffness reduction at hinges A.
Response:x: rotational stiffness amplification factor;
x=1 : hinges are intact, x<1 : the reduced stiffness is x times the original one.
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)
A A
Missouri side
A
Missouri side
A
DamagedUndamaged
0.4 0.6 0.8 1 1.2 1.4 1.6 1.80
1
2
3
4
PD
F
0
0.5
1
prob
abili
ty
0.4 0.6 0.8 1 1.2 1.4 1.6 1.80
1
2
cost
[M
$]
x
PDF(xIU)
PDF(xID)
prob(UIx)
prob(DIx)
C I x
C N x
Cneat
*(x)
x
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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.
InspectionCost (CI)
0Do Nothing
Inspection
Damaged Undamaged
UndershootingCost (CUS)
InspectionCost (CI)
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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.
$ 700k
0Do Nothing
Inspection
DamagedP(D)=30%
UndamagedP(U)=70%
$ 2M
$ 700k
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pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
decision tree w/o monitoring
DN
D
U
action state cost
0
CUS
probability
P(D)
P(U)
D
U CI
P(D)
P(U)
CDN = P(D) · CL
CI
Do Nothing
Inspection
Damaged
Undamaged
DN D
U
action: state:
LEGEND
expected cost
expected cost
I
ICI
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pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
decision tree w/o monitoring
DN
D
U
action state cost
0
2M
probability
30%
70%
D
U
30%
70%
CUS= $ 600k
CI= $ 700k
Do Nothing
Inspection
Damaged
Undamaged
DN D
U
action: state:
LEGEND
expected cost
expected cost
I
I700k
700k
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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
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pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
Application of the VoI
0
0.5
1
1.5
2
2.5
3
3.5
4
PD
F
C* = $ 600 K, Cneat
* = $ 500 K, VoI = $ 100 K
0
0.5
1
prob
abili
ty
0.4 0.6 0.8 1 1.2 1.4 1.6 1.80
1
2
cost
[M
$]
x
PDF(xIU)
PDF(xID)
PDF(x)
prob(UIx)
prob(DIx)
C I x
C N x
Cneat
*(x)
0
0.5
1
1.5
2
2.5
3
3.5
4
PD
F
C* = $ 600 K, Cneat
* = $ 500 K, VoI = $ 100 K
0
0.5
1
prob
abili
ty
0.4 0.6 0.8 1 1.2 1.4 1.6 1.80
1
2
cost
[M
$]
x
PDF(xIU)
PDF(xID)
PDF(x)
prob(UIx)
prob(DIx)
C I x
C N x
Cneat
*(x)
Likelihoods and evidence
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pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
Application of the VoI
0
0.5
1
1.5
2
2.5
3
3.5
4
PD
F
C* = $ 600 K, Cneat
* = $ 500 K, VoI = $ 100 K
0
0.5
1
prob
abili
ty
0.4 0.6 0.8 1 1.2 1.4 1.6 1.80
1
2
cost
[M
$]
x
PDF(xIU)
PDF(xID)
PDF(x)
prob(UIx)
prob(DIx)
C I x
C N x
Cneat
*(x)
0
0.5
1
1.5
2
2.5
3
3.5
4
PD
F
C* = $ 600 K, Cneat
* = $ 500 K, VoI = $ 100 K
0
0.5
1
prob
abili
ty
0.4 0.6 0.8 1 1.2 1.4 1.6 1.80
1
2
cost
[M
$]
x
PDF(xIU)
PDF(xID)
PDF(x)
prob(UIx)
prob(DIx)
C I x
C N x
Cneat
*(x)
Likelihoods and evidence
Updated probabilities
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pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
Application of the VoI
0
0.5
1
1.5
2
2.5
3
3.5
4
PD
F
C* = $ 600 K, Cneat
* = $ 500 K, VoI = $ 100 K
0
0.5
1
prob
abili
ty
0.4 0.6 0.8 1 1.2 1.4 1.6 1.80
1
2
cost
[M
$]
x
PDF(xIU)
PDF(xID)
PDF(x)
prob(UIx)
prob(DIx)
C I x
C N x
Cneat
*(x)
Likelihoods and evidence
Updated probabilities
Updated costs
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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
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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 VoIVoI
VoI is the maximum priceprice the owner is willing to paywilling to pay for the informationfor the information from the monitoring system
implies the manager can undertake actions in reaction to monitoring response
depends on: prior probabilityprior probability of scenarios; consequenceconsequence of actions; reliability of monitoringreliability of monitoring system
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pozzi, zonta, wang & chen • evaluating the impact of SHM on BMS
Thanks. Questions?