Soft computing based multilevel strategy for bridge integrity monitoring

Computer-Aided Civil and Infrastructure Engineering 25 (2010) 348–362
Soft Computing Based Multilevel Strategy for Bridge
Integrity Monitoring
S. Arangio & F. Bontempi∗
Department of Structural and Geotechnical Engineering, University of Rome “La Sapienza,”
Via Eudossiana 18, Rome, Italy
Abstract: In recent years, structural integrity monitor-
ing has become increasingly important in structural en-
gineering and construction management. It represents an
important tool for the assessment of the dependability of
existing complex structural systems as it integrates, in a
unified perspective, advanced engineering analyses and
experimental data processing. In the first part of this work
the concepts of dependability and structural integrity are
discussed and it is shown that an effective integrity assess-
ment needs advanced computational methods. For this
purpose, soft computing methods have shown to be very
useful. In particular, in this work the neural networks
model is chosen and successfully improved by apply-
ing the Bayesian inference at four hierarchical levels: for
training, optimization of the regularization terms, data-
based model selection, and evaluation of the relative im-
portance of different inputs. In the second part of the ar-
ticle, Bayesian neural networks are used to formulate a
multilevel strategy for the monitoring of the integrity of
long span bridges subjected to environmental actions: in
a first level the occurrence of damage is detected; in a fol-
lowing level the specific damaged element is recognized
and the intensity of damage is quantified.
1 INTRODUCTION
The realization of high-cost and safety-critical construc-
tions requires advanced approaches to take into ac-
count their intrinsic complexity (Ciampoli, 2005). The
complexity of this kind of structures can be related to
several aspects, as for example, nonlinear dynamic be-
havior (Adeli et al., 1978), various sources of uncertain-
ties, both objective and cognitive, and strong interaction
between components.
∗To whom correspondence should be addressed. E-mail: franco.
bontempi@uniroma1.it.
Only by considering these aspects can a consistent
evaluation of the structural performance be obtained.
Therefore, it is necessary to evolve from the simplis-
tic idealization of the structure as “device for channel-
ing loads” to the analysis of the structural system as a
whole, intended as “a set of interrelated components
working together toward a common purpose” (NASA
System Engineering Handbook, 2007). The correlation
between different aspects can be taken into account by
applying the principles and techniques of System Engi-
neering, which is a robust approach to the creation, de-
sign, realization, and operation of an engineered system
(Bontempi et al., 2008).
If the entire design process needs to be reviewed in
the System Engineering framework, one includes re-
quirements concerning the construction phase and the
operation and maintenance during the whole life-cycle
(Sarma and Adeli, 2002). To this aim, data collected on
site are important both for checking the accomplish-
ment of the expected performance during the service
life and for validating the original design (Smith, 2001).
This approach requires the definition of the quality of
a complex structural system in a comprehensive way by
an integrated concept, like dependability. The concept
of dependability has been originally developed in the
field of Computer Science and it is extended to struc-
tural engineering as “the ability to deliver service that
can justifiably be trusted” (Avižienis et al., 2004). This
definition stresses the need for justification of trust. The
alternate definition considers dependable “a system that
has the capability to avoid service failures which are
more frequent and more severe than acceptable.”
All these factors are connected to the integrity of
the structural systems, considered as the completeness
and consistency of the structural configuration. Specif-
ically, structural integrity refers “to the safe opera-
tion of engineering components, structures and mate-
rials, and addresses the science and technology which is
C
2010 Computer-Aided Civil and Infrastructure Engineering.
DOI: 10.1111/j.1467-8667.2009.00644.x

Multilevel strategy for bridge integrity monitoring 349
used to assess the margin between safe operation and
failure.”
During the service life the integrity, and conse-
quently the overall dependability, can be lowered by
deterioration and damage. The structural monitoring
represents an essential tool to assess the evolution in
time of the dependability of existing structural systems
(Soyoz and Fukuda, 2009; Li et al., 2006). It includes
issues like definition and analysis of the structural per-
formance, from regular exercise to out-of-service and
collapse, assessment of the environmental conditions,
choice of the sensor systems and their optimal place-
ment, use of data transmission systems and signal pro-
cessing techniques, and methods for damage identifica-
tion and model updating (Jiang and Adeli, 2005; Adeli
and Jiang, 2006; Psimoulis and Stiros, 2008).
In case of complex structural systems it can be diffi-
cult to deal with the huge quantity of data coming from
the monitoring process and various soft computing tech-
niques have shown to be effective tools for data pro-
cessing (Adeli and Jiang, 2006; Carden and Brownjohn,
2008; He et al., 2008; Jiang and Adeli, 2008a).
In this article, a soft computing model, the Bayesian
neural networks (Castillo et al., 2008; Adeli and
Panakkat, 2009), is used to formulate a multilevel strat-
egy for the assessment of the integrity of a long span
suspension bridge subjected to wind actions and traffic
loads. In the first step of the proposed strategy the oc-
currence of damage is detected and the damaged por-
tion of the bridge is identified; in the second step the
specific damaged element is recognized and the inten-
sity of damage evaluated.
In the following, the concept of integrity monitoring
for dependability is explained with reference to struc-
tural systems and the multilevel strategy is illustrated.
2 STRUCTURAL INTEGRITY MONITORING
FOR DEPENDABILITY
For complex structural systems, where there are signif-
icant dependencies among elements or subsystems, it is
important to have a solid knowledge of both how the
system works as a whole, and how the elements behave
individually. In this contest, dependability is an inte-
grated property that includes and describes the relevant
aspects with reference to the system quality and its in-
fluencing factors (Bentley, 1993). System dependability
can then be thought of as being composed of three ele-
ments (Figure 1):
1. the attributes, that is, the properties that
quantify the dependability;
2. the threats, that is, the elements that can affect de-
pendability;
ATTRIBUTES
THREATS
MEANS
MAINTAINABILITY
RELIABILITY
SAFETY
AVAILABILITY
FAILURE
ERROR
FAULT
FAULT TOLERANT
DESIGN
FAULT DETECTION
FAULT DIAGNOSIS
FAULT MANAGING
DEPENDABILITY
Fig. 1. Dependability: attributes, threats, and means.
3. the means, that is, the tools that can be used to in-
crease dependability.
In structural engineering, relevant attributes are re-
liability, safety, availability, and maintainability. These
properties are essential to guarantee the safety of the
system under relevant hazard scenarios, the survivabil-
ity under accidental or exceptional scenarios, and the
functionality under operative conditions.
The threats for system dependability can be subdi-
vided into faults, errors, and failures. According to the
definition given in Avižienis et al. (2004), an active or
dormant fault is a defect or an anomaly in the system
behavior that represents a potential cause of error; an
error is the cause for the system being in an incorrect
state and it may or may not cause failure; failure is a per-
manent interruption of the system ability to perform a
required function under specified operating conditions.
The problem of conceiving and building a dependable
structural system can be considered at least by four dif-
ferent points of view:
1. how to design a dependable system, that is a fault
tolerant system;
2. how to detect faults, that is, anomalies in the sys-
tem behavior;
3. how to localize and quantify (that is, diagnose) the
effects of faults and errors;
4. how to manage faults and errors to avoid failures.
This article is focused on points 2 and 3: fault de-
tection and fault diagnosis. These aspects are strictly
related to the integrity monitoring of the structural sys-
tem: an efficient integrity monitoring system is expected

350 Arangio Bontempi
to be able to preserve the structural dependability, diag-
nosing deterioration and damage at their onset (Ou and
Li, 2006).
Even if there is no general consensus on its defini-
tion, in analogy with biological systems, an intelligent
monitoring system is expected to (Aktan et al., 1998;
Isermann, 2006):
1. sense the loading environment as well as the struc-
tural response;
2. reason by assessing the structural condition and
health; even small faults should be detected and
diagnosed;
3. communicate through proper interface with other
components and systems;
4. learn from experience as well as by interfacing with
humans for heuristic knowledge;
5. decide and take action for alerting controllers in
case of accidental situations, or activate fault tol-
erant configurations in case of reconfigurable sys-
tems.
Structural monitoring has a key role in the mainte-
nance scheduling of the bridge structures and a great re-
search effort has been devoted in the past 30 years to es-
tablishing effective local and global methods for health
monitoring in civil structures (Doebling et al., 1996; De
Roeck 2003; Sohn et al., 2004, 2008; Jiang and Adeli,
2007; Li and Wu, 2008; Moaveni et al., 2008).
Analyzing the problem in terms of the expected pay-
off, it comes out that, in cases of complex structures, like
long span bridges, for example, the monitoring process
should be planned during the design phase and should
be carried out during the entire life cycle to assess the
structural health and performance under in-service and
accidental conditions (Bontempi et al., 2008).
This long-term monitoring of bridges, where long-
term designates a period of time from 1 year to decades
and desirably the entire life cycle, is a quite recent
concept, enabled by recent advances in sensing, data
acquisition, computing, communication, data, and infor-
mation management (Ou and Li, 2006). Exploring long-
term monitoring of structural responses was pioneered
in China and in Japan (Abe and Amano, 1998; Lau
et al., 1999; Wong et al., 2000). Nowadays several
bridges are instrumented in Europe (Casciati, 2003), the
United States (Aktan et al., 2002), Korea, and other
countries, and the administration of the major coun-
tries have developed guidelines to explain the advan-
tages of long-term monitoring and to help the engineers
in building effective monitoring systems (Aktan et al.,
2002; Mufti, 2001; ISO, 2002; Task Group 5.3, 2002).
In accord with the concepts reported in these guide-
lines, long-term monitoring is based on the integration
of different kinds of technologies (Figure 2): experimen-
tal, analytical, and information technologies.
Mathematical modeling Finite Element modeling
ANALYTICAL TECHNOLOGIES
INFORMATION TECHNOLOGIES
EXPERIMENTAL TECHNOLOGIES
Non-destructive evaluation Continuous monitoring
Data acquisition Data processing
Communication Interpretation
Fig. 2. Issues in long-term monitoring implementation.
Fig. 3. Steps of the information technology.
Experimental technologies include nondestructive vi-
sual inspection and continuous monitoring. Analytical
technologies include mathematical and finite-element
modeling. The last one, the information technology,
assumes a key role: it covers the entire spectrum of
efforts related to the acquisition, communication, pro-
cessing, and interpretation of the data (Figure 3). The
entire monitoring process needs a team of experts in
civil, mechanical, and electrical engineering and com-
puter scientists working together to take full advantage
of the data. In fact, the desired outcome of structural
monitoring is not data collection, but it is the generation
of information and the creation of a base of knowledge
about potential and existent system symptoms that will
enhance decision making for fault management.
3 FAULTS-SYMPTOMS RELATIONSHIP
As mentioned in the previous section, to detect and di-
agnose a system fault, it is necessary to process the data

Fig. 4. Fault–symptoms relationship.
coming from the monitoring process, that is, the sys-
tem symptoms. However this is a complex task. The
relationship between fault and symptoms can be repre-
sented graphically by a pyramid (Figure 4). The vertex
represents the fault, and the lower levels the possible
events generated by the fault; the base corresponds to
the symptoms. The propagation of the fault to the ob-
servable symptoms follows a cause–effect relationship,
and is a top–down forward process: a fault determines
events that, as intermediate steps, influence the measur-
able or observable symptoms (Isermann, 2006). On the
other hand, the fault diagnosis proceeds in the reverse
way (Figure 4); it is a bottom–up inverse process that
relates the observed symptoms to the faults. This im-
plies the inversion of the causality principle. However,
one cannot expect to rebuild the chain only by measured
data because usually the causality is not reversible or the
reversibility is ambiguous (Füssel, 2002): the underlying
physical laws are often not known in analytical form,
or are too complicated for explicit numerical calcula-
tion. Moreover, intermediate events between faults and
symptoms are not always recognizable (Figure 4, right-
hand side).
The solving strategy requires integrating different
procedures, either forward or inverse: this mixed solv-
ing approach has been called total approach by Liu
and Han (2004) and different computational techniques
have been developed for this task (Adeli and Samant,
2000; Ghosh-Dastidar and Adeli, 2003).
4 KNOWLEDGE-BASED FAULT DETECTION
AND DIAGNOSIS
As shown in the previous section, fault diagnosis
needs the integration of forward and inverse proce-
dures with the heuristic knowledge coming from ex-
perience or qualitative information. For this task, a
knowledge-based analysis can be applied (Adeli and
Fig. 5. Knowledge-based analysis for structural integrity
monitoring.
Balasubramanyam, 1988; Paek and Adeli, 1990; Adeli
and Hawkins, 1991; Shwe and Adeli, 1993; Waheed and
Adeli, 2000; Aktan et al., 1998) (Figure 5). The results
obtained by visual inspection or instrumented monitor-
ing (the inverse diagnosis system of Figure 4) are pro-
cessed and combined with the results coming from the
analytical model (the forward physical system of Fig-
ure 4). Information technology provides the tool for
such integration. The output of the information technol-
ogy is then filtered by the available heuristic knowledge
for decision making.
An attractive aspect of the knowledge-based analysis
is that it can cope with incomplete or uncertain data in-
tegrating qualitative and quantitative information, com-
ing from modeling and heuristics. To carry out the var-
ious phases, different computational methods can be
used. In several applications, inference models and soft
computing techniques, like the Bayesian neural net-
works used in this work, have shown their effectiveness
(Adeli and Park, 1995; Pandey and Barai, 1995; Masri
et al., 1996; Faravelli and Pisano, 1997; Hajela, 1999;
Topping et al., 1999; Kim et al., 2000; Adeli, 2001; Ni
et al., 2002; Kao and Hung, 2003; Waszczyszyn and
Ziemianski, 2005; Ko and Ni, 2005; Xu and Humar,
2006; Lam et al. 2006; Jiang and Adeli, 2008a,b).

5 BAYESIAN NEURAL NETWORK FOR FAULT
DETECTION AND DIAGNOSIS
5.1 The neural network model and the probability
logic framework
The neural network concept has its origins in attempts
to find mathematical representations of information
processing in biological systems. Actually, there is a def-
inite probability model behind it: a neural network is
an efficient statistical model for nonlinear regression
(Cheng and Titterington, 1994). It can be described by a
series of functional transformation working in different
correlated layers (Bishop, 2006). For example, for two
layers
yk(x, w) = h
⎛
⎝
M

j=1
w
(2)
kj g
D

i=1
w
(1)
ji xi + b
(1)
j0

+ b
(2)
k0
⎞
⎠
(1)
where yk is the kth output variable in the output layer;
x is the vector of the D input variables in the 1input
layer; w is the matrix including the adaptive weight pa-
rameters w
(1)
ji and w
(2)
kj and the biases b
(1)
j0 and b
(2)
k0 (the
superscript refer to the considered layer); M is the to-
tal number of units in the hidden layer. The quantities
within the brackets are the so-called activations; each of
them is transformed using a nonlinear activation func-
tion (h and g). The nonlinear activation functions are
generally chosen to be sigmoidal or tanh functions be-
cause of the so-called universality property (Cybenko,
1989).
In the traditional learning approach, the values of the
parameters w are obtained during the training phase by
minimizing an error function (Adeli and Hung, 1994),
for example, the sum of squared errors with weight de-
cay (Bishop, 1995)
E =
1
2
N

n=1
No

k=1

yk (xn
; w) − tn
k

2
+
α
2
W

i=1
|wi |2
(2)
where yk is the kth neural network output correspond-
ing to the n-th realization of x, tn
k is the relevant target
value, N is the size of the considered data set, N0 is the
number of output variables, W is the number of param-
eters in w, and α is a regularization parameter. The sec-
ond term in the right-hand side is a decay regularization
that penalizes large weights.
Neural network learning can be framed as Bayesian
inference, where probability is treated as a multival-
ued logic that may be used to perform plausible infer-
ence (Jaynes, 2003). The roots of this probability logic
approach are in the work by Bayes published in 1763
(Bayes, 1763). He presented a method for updating
probability distributions based on available data that
would come to be known as Bayes’ theorem, and that
forms the foundation of a framework for probabilis-
tic inference. The power of this theorem was shown
by Laplace (1812) and Jeffreys (1939) who applied it
to the analysis of real data set. Although this frame-
work had its origin in the 18th century, the practical
application of Bayesian methods was for a long time
severely limited by the difficulties in carrying through
the full Bayesian procedure. The developments of ap-
proximation theories and stochastic sampling methods,
along with dramatic improvements in the power of com-
puters, have recently opened the door to the practi-
cal use of Bayesian techniques in an impressive range
of applications across all disciplines. In recent years in
civil engineering, for example, the probability logic ap-
proach has been successfully applied to system identifi-
cation problems and structural health monitoring (Beck
and Katafygiotis, 1998; Beck and Yuen, 2004; Muto and
Beck, 2008).
Starting from the early works of MacKay (1992) and
Buntine and Weigend (1991), there has been a growing
interest for the application of this framework in the field
of neural networks methods (MacKay, 1994; Neal, 1996;
Lampinen and Vethari, 2001; Barber, 2002; Lee, 2004;
Nabney, 2004).
To pose the neural network model within the
Bayesian framework, the learning process needs to be
interpreted probabilistically: the network output can be
considered as the conditional average of the target data
(Bishop, 1995). Because the model does not reproduce
the data set exactly, the error ε = t – y(x; w) between
the target value t and the network output y needs to
be interpreted probabilistically using a prediction-error
probability model: a Gaussian distribution with mean
zero and constant inverse variance β = 1/σD
2
is a model
supported by the principle of maximum differential en-
tropy (Jaynes, 2003). Thus, modeling the predictions as
independent and identically distributed (i.i.d.), the like-
lihood function for a data set D = xn
, ,tn
is given by
p(D | w, β, M)
=

β
2π

N·N0
exp

−
β
2
N

n=1
No

k=1

yk (xn
; w) − tn
k

2

(3)
where M denotes the Bayesian model class that specifies
the forms of the likelihood function and the prior prob-
ability distribution discussed next. Although the like-
lihood function does take into account the uncertain
prediction error, it does not quantify the uncertainty in
the values of the parameters w. In the Bayesian frame-
work, this can be represented by a prior PDF p(w | M)
over the parameters w, which expresses the relative

Fig. 6. Learning as inference.
plausibility of each value. Because generally there is a
little idea of what the values should be, it is usual to se-
lect the prior as a rather broad distribution. Using once
again the principle of maximum differential entropy,
this requirement suggests a Gaussian prior distribution
with zero mean of the form
p(w | α, M) =
α
2π
W/2
exp

−
α
2
|w|2

(4)
where α = 1/σ2
W represents the inverse variance of the
distribution. Using available data, Bayes’ theorem up-
dates the prior probability distribution over the parame-
ters p(w | α, M) to give the posterior PDF p(w | D, α, β,
M):
p(w | D, α, β, M) =
p(D | w, β, M) p(w | α, M)
p(D | α, β, M)
.
(5)
This posterior distribution is always more compact
than the prior distribution if the data informs the model,
as indicated schematically in Figure 6, expressing the
fact that something has been learned. Therefore, by
maximizing the posterior, the most plausible values of
the parameters wMAP can be found.
Instead of finding a maximum of the posterior prob-
ability in Equation (5), it is usually more convenient
to seek instead a minimum of its negative logarithm.
As shown in Figure 6, for the chosen prior distribution
and likelihood function, the negative log probability is
just the usual sum of squares function in Equation (2).
Therefore, the conventional learning approach can be
derived as a particular approximation of the Bayesian
framework where only the MAP (maximum a posteri-
ori) parameter values are utilized.
5.2 Bayesian enhancements for neural networks
The optimization of the parameters w, that is, the so-
called model fitting, is only one level of inference where
Bayesian approach can be applied to neural networks.
The potential enhancements that can be obtained by ap-
plying this framework at further levels in a hierarchical
fashion are often not appreciated. The various levels can
be summarized as follows (Arangio, 2008):
1. Level 1: Model fitting: task of inferring appropriate
values for the model parameters, given the model
and the data.
2. Level 2: Optimization of the regularization terms
α and β that make level 1 a better conditioned in-
verse problem.
3. Level 3: Model class selection: the Bayesian ap-
proach allows an objective comparison between
models using alternative network architectures.
4. Level 4: Automatic relevance determination
(ARD): the relative importance of different inputs
can be determined using separate regularization
coefficients.

Regarding the first two levels, the traditional and
the Bayesian framework usually give equivalent results
(MacKay, 1992). The addition of the third level, the
model class selection, has shown to be very effective.
In fact, the number of adaptive parameters of the net-
work model, that is, the model class, has to be fixed in
advance, and this choice has a fundamental importance.
It is not correct to choose simply the model that fits
the data better: more complex models will always fit the
data better but they may be over-parameterized and so
they make poor predictions for new cases.
The problem of finding the optimal number of param-
eters provides an example of Ockham’s razor, which is
the principle that one should prefer simpler models to
more complex models, and that this preference should
be traded off against the extent to which the models fit
the data (Sivia, 1996). The best generalization perfor-
mance is achieved by the model whose complexity is
neither too small nor too large.
The third level of inference mentioned above deals
with this task: the Bayesian framework provides an
objective and structured framework for dealing with
the issue of model complexity, and allows an objec-
tive comparison between models with alternative net-
work architectures (Beck and Yuen, 2004). The most
plausible model class among a set M of NM candi-
date ones is obtained by applying Bayes’ Theorem as
follows:
p(Mj | D, M) ∝ p(D | Mj ) p(Mj | M) . (6)
The factor p(D | Mj) is known as the evidence for the
model class Mj provided by the data D. Equation (6)
shows that the most plausible model class is the one that
maximizes p(D | Mj)p(Mj) with respect to j. If there is
no particular reason a priori to prefer one model over
another, they can be treated as equally plausible a priori
and a noninformative prior, that is, p(Mj) = 1/NM, can
be assigned; then different models can be compared just
by evaluating their evidence (MacKay, 1992).
Once the optimal architecture has been determined,
the last issue that should be considered is the relative
importance of each input variable. If the available data
comes from real systems it could be difficult to separate
the relevant variables from the redundant ones. In the
Bayesian framework, this problem can be addressed by
the ARD method, proposed by Mackay (1994) and Neal
(1996). To use this technique, a separate hyperparame-
ter αi is associated with each input variable: this value
represents the inverse variance of the prior distribution
of the parameters related to that input. In this way, ev-
ery hyperparameter explicitly represents the relevance
of one input: a small value means that large parameters
are allowed and the corresponding input is important;
on the contrary, a large value means that the parameters
are constrained near zero, and hence the corresponding
input is less important.
The ARD allows a fourth level of inference to be ap-
plied to the neural networks model. Once the architec-
ture of the model is defined, the importance of every in-
put is evaluated: if some hyperparameter is very large,
the related input will be dropped from the model and
the optimal architecture for the new model will be re-
estimated.
The four levels of inference are summarized in the
flowchart in Figure 7. Starting from the simple process
of model fitting, further steps have been added to in-
clude the other three levels of inference: evaluation of
the hyperparameters, model class selection, and ARD.
More details can be found in Arangio (2008).
The improvements that can be obtained by applying
the first three levels are well documented in the exist-
ing literature (MacKay, 1992, 1994). On the contrary,
the fourth level is usually applied independently and
in this way the benefits of an integrated approach are
not fully exploited. In this work the evaluation of the
relative importance of each input is included in the it-
erative process. In this way, once the optimal architec-
ture of the model is defined, it is possible to recognize
eventual redundant parameters and drop them from the
model.
6 MULTILEVEL STRATEGY FOR BRIDGE
INTEGRITY ASSESSMENT
The Bayesian neural networks discussed in the previous
section is applied in a multi-step strategy for the assess-
ment of the integrity of the long suspension bridge in
Figure 8 (Arangio, 2008). The considered bridge has a
main span of 3,300 m and it carries six road lanes in the
external box girders and two railway tracks in the cen-
tral one; detailed information on the bridge project and
its history can be found in Bontempi (2006).
A multi-step approach has been followed because it
has been shown that is more effective to consider inde-
pendently the tasks of damage detection, location, and
quantification (Ceravolo et al., 1995; Ko et al., 2002). In
the first step of the strategy the occurrence of damage
or anomalies in the bridge is detected, and the damaged
portion of the structure is identified. If some damage is
detected, the second step of the procedure is initiated:
using a pattern recognition approach, the specific dam-
aged member within the whole area is identified, and
the extent of damage is evaluated. The entire procedure
has been carried out working on a finite-element model
of the bridge but it could be applied in the same way to
an existent structure.

Fig. 7. Hierarchical Bayesian framework for neural networks.
Fig. 8. Steps of the damage identification strategy.
6.1 Step 1: Damage detection
In the first step of the proposed strategy, the response
of the structure is monitored at various measurement
points, located at groups of three (A, B, and C) every
30 m along the bridge deck. One neural network for
each intermediate point (B) is built and trained using
the time-histories of the response of the structure sub-
jected to wind actions and traffic loads (due to the pas-
sage of a train) in the undamaged situation. The time-
histories of selected structural response parameters are
sampled at regular intervals, thus generating series of
discrete values. A set of such values from the instant t –
k to t is used as input for the network models, and the
value at the instant t + 1 is used as the target output
(left-hand side of Figure 9).
Then, the trained models are tested on new input pat-
terns, corresponding to different time intervals and to

Fig. 9. Flowchart of the chart of the Step 1 procedure for damage detection.
both undamaged and damaged situations. For each pat-
tern, the set of values from ft+n−k to ft+n−1 is used as
input, and the value ft+n is predicted and compared with
the target one.
If the error in the prediction is negligible, the struc-
ture is considered as undamaged; if the error is higher
than a threshold value (eventually defined according to
expert opinion), the presence of an anomaly is detected
(Figure 10).
The anomaly may correspond to a damage state or
simply to a change of the characteristics of the exci-
tation. To distinguish the changes in the structural re-
sponse due to variations in the excitation from those due
to damage, the prediction errors are checked in all mea-
surement points, according to the procedure schemati-
cally represented in the flowchart of Figure 9.
If the prediction is wrong in several locations, that is
the difference e between the mean value of the errors
in training and testing is different from zero in different
measurement points, it can be concluded that the char-
acteristics of the excitation are probably different from
those assumed, and the trained neural network models
are unable to represent the actual time-history of the re-
sponse parameters. In this case, the models need to be
updated according to the new excitation. On the other
hand, if the difference e is large only at one or a few
points and generally decreases with the distance from
those points, it can be concluded that the considered
portion is damaged.
To illustrate the proposed approach, data is simu-
lated using a dynamic model of the suspension bridge
where damage is implemented as a reduction of stiff-
ness of a structural element. The following scenarios are
considered:
1. Hangers: reduction of stiffness from 5% to 80%;
2. Cables: reduction of stiffness from 1% to 10%;
3. Transverse beam: reduction of stiffness from 5%
to 30%.
The training data set for every network model in-
cludes 1,000 samples of the time-history of the response
parameters that were found to be the most sensitive to
a stiffness reduction (Arangio and Petrini, 2007), that is
the rotation of the deck around the longitudinal axis in
case of wind actions, and the vertical displacements of
the deck in case of traffic loads.
6.2 Step 2: Identification of damage location and
severity
Having recognized that a portion of the structure is
damaged, the second step of the procedure is initiated;
it is aimed at identifying the specific damaged element

Fig. 10. Location of the measurement points on the bridge deck and identification of the damaged portion by considering the
errors in the approximation; also shown the potentially damaged elements of each portion.
Fig. 11. Neural network for the identification of damage location and intensity.
(a hanger, the cable, or a transverse beam), and at eval-
uating the damage intensity. A pattern recognition ap-
proach is used.
To create the training data set, the errors in Step 1
obtained by the neural network approximation of the
response time-histories at three different points of the
damaged portion (A, B, and C in Figure 11) are col-
lected, by considering different damage scenarios.
For each damage scenario, the training data set has as
input the mean values of the errors in A, B, and C, and,
as output, a vector including the five possible locations
of damage and its intensity (Figure 11).
7 RESULTS OF THE INTEGRITY ASSESSMENT
PROCEDURE
7.1 Results of step 1: Damage detection
The different network models were trained using the
time-histories of the response of the bridge in undam-
aged conditions. The network architecture has been de-
termined by the Bayesian approach discussed in Sec-
tion 5: the optimal network models consist of 2, 2 and
1 nodes in the input, hidden and output layers, respec-
tively.
An example of the evolution in time of the differences
between the predicted and the target values in the sets
of training and test data is reported in Figures 12 and
13; both undamaged and damaged conditions are con-
sidered. It is possible to notice that when time-histories
related to various damage scenarios are proposed to the
trained networks the errors in the approximation in-
crease. There is a difference e between the mean val-
ues of the error in undamaged and damaged conditions.
In Figures 14 to 16 the increments e of the mean
values of the error with respect to the undamaged situ-
ation are shown for different levels of damage in the ca-
bles, the hangers, and the transverse beam. Both wind
actions and traffic loads are considered and the results
are compared.

0.0
0.3
0.6
0.9
0 20 40 60 80
Training error Test error (undamaged)
err
t [s]
Fig. 12. Differences between the network values and the
correct value in case of undamaged structure.
0.0
0.3
0.6
0.9
0 20 40 60 80
Training error Test error (damaged)
err
t [s]
Δe
mean -damaged
mean -undamaged
Fig. 13. Differences between the network values y and the
correct value t in damaged conditions in a case example
(considered damage: 5% reduction of stiffness in one cable).
(a) Damage intensity (%) – cable (pos 1/5)
0.0
0.3
0.6
0.9
1.0% 3.0% 5.0% 10%
train
wind
Δe
Fig. 14. Increment of the error in the approximation of the
response time-history of the cable under wind actions and
traffic load.
0.00
0.03
0.06
0.09
20% 40% 50% 80%
train
wind
(c) Damage intensity (%) – hanger (pos 2/4)
Δe
Fig. 15. Increment of error in the approximation of the
response time-history of the hanger under wind actions and
traffic load.
0.00
0.03
0.06
0.09
5% 10% 30% 50%
train
wind
(b) Damage intensity (%) – transverse beam (pos 3)
Δe
Fig. 16. Increment of error in the approximation of the
response time-history of the transverse beam under wind
actions and traffic load.
Looking at the results shown in Figures 14 to 16, it is
possible to note that the proposed method is more ef-
fective when responses from high speed excitation (like
traffic) are considered instead of responses due to slow
speed excitation (like wind). Thus, in the following step,
only the structural response due to the passage of one
train is considered.
7.2 Results of step 2: Identification of damage location
and intensity
Once the damaged portion of the whole structure is rec-
ognized, the specific damaged element and the intensity
of damage are identified using a pattern recognition ap-
proach. Various damage scenarios, corresponding to the
reduction of the stiffness in the hangers, the cables, and
the transverse beam in the identified damaged portion
is simulated, and a training set consisting of 370 exam-
ples is created. The network architecture is always de-
termined by the Bayesian approach discussed in Section
5. The optimal network model has 11 units in the hidden
layers.
After the training phase the network is tested with 30
new input vectors that are not included in the training
set, and the related damage scenarios are obtained and
compared with the target ones. To give a global and in-
tuitive representation of the results, two quantities are
defined:
1. The position, which gives a measure of the error in
the location:
pos(i) =
t × y
|t| · |y|
(7)
2. The intensity, which gives a measure of the error
in the quantification:
int(i) =
|t|
t|y|
. (8)
If these quantities are equal to one, the damage is well
localized and its intensity is correctly estimated. These

0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 10 20 30
Test number
pos
Fig. 17. Identification of the damage position in the test
examples.
0.0
0.3
0.5
0.8
1.0
1.3
1.5
0 10 20 30
Test number
int
Fig. 18. Identification of the intensity in the test examples.
quantities are evaluated for each of the 30 test samples
and the results are shown in Figures 17 and 18. The lo-
cation can be detected in almost 90% of the considered
cases and the intensity is correctly estimated in 66% of
the cases.
8 CONCLUSIONS
In this work the concept of dependability has been dis-
cussed and its original meaning has been extended to
the structural engineering field. It has been shown that
this term describes the overall quality performance of a
complex structural system and its influencing factors in
an integrated way.
The different aspects related to dependability are
strictly connected with the concept of structural in-
tegrity. During the service life the integrity, and conse-
quently the dependability, can be lowered by damages.
The structural monitoring represents an essential tool
to assess the evolution in time of the dependability of
existing structural systems.
Fundamental tasks of integrity monitoring are fault
detection and diagnosis. Fault diagnosis from experi-
mental data is an inverse problem and the reconstruc-
tion of the fault-symptom chain can be very difficult.
A solution can be achieved by applying a knowledge-
based procedure that integrates the solving procedures
with the heuristic knowledge coming from experience
or qualitative information. For this task, different soft
computing methods can be suitable. In particular, in
this work, the Bayesian neural network model has been
used to formulate a hierarchical integrity assessment
strategy.
The proposed approach has been applied for the anal-
ysis of the time-history of the response of a long span
suspension bridge subjected to ambient excitations. The
strategy could be useful for damage identification of
large structural systems instrumented with on-line mon-
itoring systems. The presented example case has been
developed on a numerical model of the structure but
the strategy can be applied on real structural systems as
well: various neural networks models could be selected
and trained in a continuous way using the time-histories
of the structural response; in this way the occurrence of
anomalies can be detected almost in real time. When
an anomaly is recognized, numerical simulations can be
carried out to create the data set to develop the second
step of the strategy. In this way experimental data are
used for damage detection and the results of the numer-
ical analyses can help to identify the damaged element
and to quantify the intensity of damage.
ACKNOWLEDGMENTS
The authors wish to thank Professors H. Li (Harbin In-
stitute of Technology), J.L. Beck (California Institute
of Technology), F. Casciati, and L. Faravelli (Univer-
sity of Pavia) for discussions related to this study. The
reviewers of the article are acknowledged for the care-
ful reading and the very useful suggestions. The sup-
port of Prof. H. Adeli is also recognized. The financial
support of University of Rome “La Sapienza” is also
acknowledged. The opinions and the results presented
here are however the responsibility only of the authors
and cannot be assumed to reflect the ones of University
of Rome “La Sapienza.”
REFERENCES
Abe, K. Amano, K. (1998), Monitoring system of the
Akashi Kaikyo Bridge, Honshi Technical Report, 22(86),
29–34.
Adeli, H. (2001), Neural networks in civil engineering: 1989–
2000, Computer-Aided Civil and Infrastructure Engineering,
16(2), 126–42.
Adeli, H. Balasubramanyam, K. V. (1988), A novel ap-
proach to expert systems for design of large structures, AI
Magazine, pp. 54–63.
Adeli, H., Gere, J. Weaver, W., Jr. (1978), Algorithms for
nonlinear structural dynamics, Journal of Structural Divi-
sion, ASCE, 104(ST2), 263–80.

Adeli, H. Hawkins, D. (1991), A hierarchical expert sys-
tem for design of floors in highrise buildings, Computers
and Structures, 41(4), 773–88.
Adeli, H. Hung, S. L. (1994), An adaptive conjugate gradi-
ent learning algorithm for effective training of multilayer
neural networks, Applied Mathematics and Computation,
62(1), 81–102.
Adeli, H. Jiang, X. (2006), Dynamic fuzzy wavelet neural
network model for structural system identification, Journal
of Structural Engineering, ASCE, 132(1), 102–11.
Adeli, H. Panakkat, A. (2009), A probabilistic neural net-
work for earthquake magnitude prediction, Neural Net-
works, 22, 1018–24.
Adeli, H. Park, H.S. (1995), Optimization of space struc-
tures by neural dynamics, Neural Networks, 8(5), 769–
81.
Adeli, H. Samant, A. (2000), An adaptive conjugate gradi-
ent neural network—wavelet model for traffic incident de-
tection, Computer-Aided Civil and Infrastructure Engineer-
ing, 15(4), 251–60.
Aktan, A. E., Catbas, F. N., Grimmelsman, K. A.
Pervizpour, M. (2002), Development of a Model Health
Monitoring Guide for Major Bridges, Report DTFH61-
01-P-00347, Federal Highway Administration Research
and Development, Drexel Intelligent Infrastructure and
Transportation Safety Institute, Federal Highway Admin-
istration, US Department of Transportation, available at:
http://www.ishmii.org/Download%20Folder/FHWA%20
Guide%209-8%20-%20SHM%20Guidelines.pdf, accessed
January 26, 2010.
Aktan, A. E., Helmicki, A. J. Hunt, V. J. (1998), Issues in
health monitoring for intelligent infrastructure, Smart Ma-
terials and Structures, 7, 674–92.
Arangio, S. (2008), Inference model for structural systems
integrity monitoring: Neural networks and Bayesian en-
hancements. Ph.D. thesis on Structural Engineering, Uni-
versity of Rome “La Sapienza.”
Arangio, S. Petrini, F. (2007), Application of neural net-
works for predicting the structural response of a long sus-
pension bridge subjected to wind actions, in Proceedings of
the Third International Conference on Structural Engineer-
ing, Mechanics and Computation, SEMC 2007, Cape Town,
South Africa.
Avižienis, I., Laprie, J. C. Randell, B. (2004), Dependabil-
ity and its threats: A taxonomy, 18th IFIP World Com-
puter Congress, Toulouse (France), Building the Infor-
mation Society, Kluwer Academic Publishers, 2004, ISBN
1-4020-8156-1, 12, 91-120.
Barber, D. (2002), Bayesian methods for supervised neural
networks, in Handbook of Brain Theory and Neural Net-
works, MIT Press, Cambridge, MA.
Bayes, T. (1763), An essay towards solving a problem in
the doctrine of chances, Philosophical Transactions of the
Royal Society of London, 53, 370–418.
Beck, J. L. Katafygiotis, L. S. (1998), Updating models and
their uncertainties-Bayesian statistical framework, Journal
of Engineering Mechanics, 124, 455–61.
Beck, J. L. Yuen, K.-V. (2004), Model selection using
response measurements: Bayesian probabilistic approach,
Journal of Engineering Mechanics, 130, 192–203.
Bentley, J. P. (1993), An Introduction to Reliability and Qual-
ity Engineering, Longman, Essex, U.K.
Bishop, C. M. (1995), Neural Networks for Pattern Recogni-
tion, Oxford University Press, London, U.K.
Bishop, C. M. (2006), Pattern Recognition and Machine
Learning, Springer, New York.
Bontempi, F. (2006), Basis of design and expected per-
formances for the Messina Strait Bridge, Proceedings of
BRIDGE 2006, Hong Kong [CD-ROM].
Bontempi, F., Gkoumas K. Arangio S. (2008), Systemic
approach for the maintenance of complex structural sys-
tems, Structure and Infrastructure Engineering, 4, 77–94,
doi: 10.1080/15732470601155235.
Buntine, W. Weigend, A. (1991), Bayesian back-
propagation, Complex Systems, 5, 603–43.
Carden, E. P. Brownjohn, J. M. W. (2008), Fuzzy clustering
of stability diagrams for vibration-based structural health
monitoring, Computer-Aided Civil and Infrastructure Engi-
neering, 23(5), 360–72.
Casciati, F. (2003), An overview of structural health monitor-
ing expertise within the European Union, in Z. S. Wu and
M. Abe (eds.), Structural Health Monitoring and Intelligent
Infrastructure, Lisse, Balkema., pp. 31–7.
Castillo, E., Menéndez, J. M. Sánchez-Cambronero,
S. (2008), Traffic estimation and optimal counting lo-
cation without path enumeration using Bayesian net-
works, Computer-Aided Civil and Infrastructure Engineer-
ing, 23(3), 189–207.
Ceravolo, R., de Stefano, A. Sabia, D. (1995), Hierarchical
use of neural techniques in structural damage recognition,
Smart Material and Structures, 4, 270–80.
Cheng, B. Titterington, D. M. (1994), Neural networks:
A review from a statistical perspective, Statistical Science,
9(1), 2–54.
Ciampoli, M. (2005), Reliability assessment of complex struc-
tural systems, Proceedings of AIMETA 2005, Firenze Uni-
versity Press, Florence, Italy, ISBN 88-8453-248-5.
Cybenko, G. (1989), Approximation by superpositions of a
sigmoidal function, Mathematics of Control, Signals, and
Systems, 2, 303–14.
De Roeck, G. (2003), The state-of-the-art of damage detection
by vibration monitoring: The SIMCES experience, Journal
of Structural Control, 10, 127–43.
Doebling, S. W., Farrar, C. R., Prime, M. B. Shevitz,
D. W. (1996), Damage identification and health monitoring
of structural and mechanical systems from changes in their
vibration characteristics: A literature review, Los Alamos
National Laboratory Report LA-13070-MS, available at:
http://www.lanl.gov/projects/ei/shm/pubs/lit review.pdf, ac-
cessed January 26, 2010.
Faravelli, L. Pisano, A. A. (1997), A neural network ap-
proach to structure damage assessment, Proceedings of In-
telligent Information Systems (IIS), Grand Bahama Island,
Bahamas, December 1997.
Füssel, D. (2002), Fault diagnosis with tree-structured neuro-
fuzzy systems, Fortschr-Ber, VDI Reihe 8, 957, VDI Verlag,
Düsseldorf.
Ghosh-Dastidar, S. Adeli, H. (2003), Wavelet-clustering-
neural network model for freeway incident detection,
Computer-Aided Civil and Infrastructure Engineering,
18(5), 325–38.
Hajela, P. (1999), Application of neural networks in modelling
and design of structural systems, in Z. Waszczyszyn (ed.),
Neural Networks in the Analysis and Design of Structures,
Springer-Verlag, New York.
He, X., Moaveni, B., Conte, J. P. Elgamal, A. (2008),
Modal identification study of Vincent Thomas Bridge
using simulated wind-induced ambient vibration data,

Computer-Aided Civil and Infrastructure Engineering,
23(5), 373–88.
Isermann, R. (2006), Fault-Diagnosis Systems. An Introduc-
tion from Fault Detection to Fault Tolerance, Springer, New
York.
ISO (2002), Mechanical vibrations—Evaluation of measure-
ment results from dynamic tests and investigations on
bridges, ISO /TC 108/SC 2, DIS 18649:2002(E).
Jaynes, E. T. (2003), Probability Theory: The Logic of Science,
Cambridge University Press, Cambridge, UK.
Jeffreys, H. (1939), Theory of Probability, Clarendon Press,
Oxford, UK.
Jiang, X. Adeli, H. (2005), Dynamic wavelet neural network
for nonlinear identification of highrise buildings, Computer-
Aided Civil and Infrastructure Engineering, 20(5), 316–30.
Jiang, X. Adeli, H. (2007), Pseudospectra, MUSIC, and
dynamic wavelet neural network for damage detection
of highrise buildings, International Journal for Numerical
Methods in Engineering, 71(5), 606–29.
Jiang, X. Adeli, H. (2008a), Dynamic fuzzy wavelet neu-
roemulator for nonlinear control of irregular highrise build-
ing structures, International Journal for Numerical Methods
in Engineering, 74(7), 1045–66.
Jiang, X. Adeli, H. (2008b), Neuro-genetic algorithm for
nonlinear active control of structures, International Journal
for Numerical Methods in Engineering, 75(7), 770–86.
Kao, C. Y. Hung, S. L. (2003), Detection of structural dam-
age via free vibration responses generated by approximat-
ing artificial neural networks, Computers and Structures, 81,
2631–44.
Kim, S. H., Yoon, C. Kim, B. J. (2000), Structural monitor-
ing system based on sensitivity analysis and a neural net-
work, Computer-Aided Civil and Infrastructure Engineer-
ing, 15(4), 309–18.
Ko J. M. Ni, Y. Q (2005), Technology developments in
structural health monitoring of large-scale bridges, Engi-
neering Structures, 27, 1715–25.
Ko, J. M., Sun, Z. G. Ni, Y. Q. (2002), Multi-stage iden-
tification scheme for detecting damage in cable-stayed
Kap Shui Mun Bridge, Engineering Structures, 24, 857–
68.
Lam, H. F., Yuen, K. V. Beck, J. L. 2006, Structural health
monitoring via measured Ritz vectors utilizing artificial
neural networks, Computer-Aided Civil and Infrastructure
Engineering, 21, 232–41.
Lampinen, J. Vethari, A. (2001), Bayesian approach for
neural networks-review and case studies, Neural Networks,
14(3), 7–24.
Laplace, P. S. (1812), Théorie Analytique des Probabilités,
Courcier.
Lau, C. K., Mark, W. P. N., Wong, K. Y., Chan, W. Y. K.
Man, K. L. D. (1999), Structural health monitoring of three
cable-supported bridges in Hong Kong, in F. K. Chang
(ed.), Structural Health Monitoring 2000, Lancaster, Tech-
nomic, pp. 450–60.
Lee, H. K. H. (2004), Bayesian Nonparametrics via Neural
Networks, ASA-SIAM Series on Statistics and Applied
Probability.
Li, H., Ou, J., Zhao, X., Zhou, W., Li, H. Zhou, Z. (2006),
Structural Health Monitoring System for the Sahndong
Binzhou Yellow River Highway Bridge, Computer-Aided
Civil and Infrastructure Engineering, 21(4).
Li, S. Wu, Z. (2008), A non-baseline method for damage
locating and quantifying in beam-like structure based on
dynamic distributed strain measurements, Computer-Aided
Civil and Infrastructure Engineering, 23(5), 404–13.
Liu, G. R. Han, X. (2004), Computational Inverse Tech-
niques in Nondestructive Evaluation, CRC Press, Boca Ra-
ton, FL.
MacKay, D. J. C. (1992), A practical Bayesian framework
for back-propagation networks, Neural Computation, 4(3),
448–72.
MacKay, D. J. C. (1994), Bayesian methods for backpropa-
gation networks, Model of Neural Networks III, chapter 6,
Springer, New York, pp. 211–54.
Masri, S. F., Nakamura, M., Chassiakos A. G. Caughey,
T. K. (1996), Neural network approach to detection of
changes in structural parameters, ASCE Journal of Engi-
neering Mechanics, 122, 350–60.
Moaveni, B. He, X. Conte, J. P. (2008), Damage identi-
fication of a composite beam based on changes of modal
parameters, Computer-Aided Civil and Infrastructure Engi-
neering, 23(5), 339–59.
Mufti, A. (2001), ISIS Canada Corporation 2002, Guidelines
for Structural Health Monitoring, Design Manual no. 2,
available online on 02.2008 at http://www.isiscanada.com/
manuals.html/, accessed January 26, 2010.
Muto, M. Beck, J. L. (2008), Bayesian updating of hysteretic
structural models using stochastic simulation, Journal of Vi-
bration and Control, 14(1–2), 7–34.
Nabney, I. T. (2004), NETLAB—Algorithms for Pattern
Recognition, Springer, New York.
National Aeronautics and Space Administration (NASA).
(2007), Systems Engineering Handbook, Available on-
line at http://education.ksc.nasa.gov/esmdspacegrant/
Documents/NASA%20SP-2007-6105%20Rev%201%20
Final%2031Dec2007.pdf, accessed January 26, 2010.
Neal, R. M. (1996), Bayesian Learning for Neural Networks,
Springer, Lecture Notes in Statistics 118, Springer, New
York.
Ni, Y. Q., Wong, B. S. Ko, J. M. (2002), Constructing input
vectors to neural networks for structural damage identifica-
tion, Smart Materials and Structures, 11, 825–33.
Ou, J. Li, H.,(2006), The state of the art and the state of the
practice of structural control and monitoring in the Main-
land of China, Proceedings of the 4th Conference on Struc-
tural Control and Monitoring, San Diego, USA, July 13–15,
(Regional Panel Report).
Paek, Y. Adeli, H. (1990), Structural design language for
coupled knowledge-based systems, Advances in Engineer-
ing Software and Workstations, 12(4), 154–66.
Pandey, P. C. Barai, S. V. (1995), Multilayer perceptron in
damage detection of bridge structures, Computer and Struc-
tures, 54(4), 597–608.
Psimoulis, P. A. Stiros, S. C. (2008), Experimental as-
sessment of the accuracy of GPS and RTS for the de-
termination of the parameters of oscillation of major
structures, Computer-Aided Civil and Infrastructure Engi-
neering, 23(5), 389–403.
Sarma, K. C. Adeli, H. (2002), Life-cycle cost optimiza-
tion of steel structures, International Journal for Numerical
Methods in Engineering, 55(12), 1451–62.
Shwe, T. T. Adeli, H. (1993), AI and CAD for earthquake
damage evaluation, Engineering Structures, 15(5), 315–19.
Sivia, D. S. (1996), Data Analysis: A Bayesian Tutorial, Oxford
Science, Oxford University Press, New York.
Smith, I. (2001), Increasing knowledge of structural perfor-
mance, Structural Engineering International, 12(3), 191–5.

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