Structural integrity monitoring for dependability

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Structure and Infrastructure Engineering:
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Structural integrity monitoring for dependability
S. Arangio
a
, F. Bontempi
a
& M. Ciampoli
a
a
Department of Structural and Geotechnical Engineering, Sapienza Università di Roma, Via
Eudossiana 18, 00184, Roma, Italy
Published online: 06 Apr 2010.
To cite this article: S. Arangio , F. Bontempi & M. Ciampoli (2011) Structural integrity monitoring for dependability,
Structure and Infrastructure Engineering: Maintenance, Management, Life-Cycle Design and Performance, 7:1-2, 75-86, DOI:
10.1080/15732471003588387
To link to this article: http://dx.doi.org/10.1080/15732471003588387
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Structural integrity monitoring for dependability
S. Arangio*, F. Bontempi and M. Ciampoli
Department of Structural and Geotechnical Engineering, Sapienza Universita` di Roma, Via Eudossiana 18, 00184, Roma, Italy
(Received 21 October 2008; final version received 16 December 2009; published online 6 April 2010)
Dependability of a structural system is a comprehensive concept that – by definition – describes the quality of the
system as its ability to perform as expected in a way that can justifiably be trusted. One of the attributes of
dependability is integrity, which can be interpreted as the absence of improper alterations of the structural
configuration. The assessment of the integrity during the whole life-cycle can be carried out efficiently by
implementing a monitoring system able to detect and diagnose any fault at its onset. The essential feature of the
monitoring system dealt with in the paper is the elaboration of data gathered on site by a combination of simulation
and heuristics. In detail, the first part of the paper deals with the extension of the concept of dependability, as
formulated in computer science, to structural engineering. The second part illustrates a two-step hierarchical strategy
for the assessment of the integrity of a structure through monitoring of its response under ambient vibrations;
Bayesian neural network models are used for fault detection and diagnosis from observable symptoms. In the first
step, the occurrence of any fault is detected and the relevant portion of the structure identified; in the second step the
specific element affected by the fault is recognised and the intensity of the alteration of the structural performance
evaluated. The strategy is applied to assess the integrity of a long-span suspension bridge subjected to wind action
and traffic loading. As the bridge is under design, measured data are simulated by analysing the response of a
detailed FE model of the whole structural system. The final objective of the study is the optimal design of the
integrity monitoring system for the bridge.
Keywords: structural systems; dependability; integrity monitoring; fault detection; fault diagnosis; Bayesian neural
network models
1. Introduction
The design of a valuable and safety-critical construc-
tion requires advanced approaches to take into
account the intrinsic ‘complexity’ of the structural
system. A relevant aspect of the complexity is the fact
that structures are usually systems composed of
strongly interacting components. Structural design
cannot rely on a simplistic idealisation of the structure
as a ‘device for channelling loads’, that allows safety
checks carried out considering each structural element
per se; it must be based on the analysis of the structural
system as a whole, being interpreted as ‘a set of
interrelated components working together toward a
common purpose’ (NASA-SEH 1995).
Another aspect that is worth mentioning is the fact
that when subjected to accidental or exceptional
actions, such as earthquakes and windstorms, or to
deterioration mechanisms, structural systems may
exhibit a non-linear behaviour, and a realistic evalua-
tion of the structural performance during the whole
life-cycle can be extremely cumbersome. Moreover,
any structural response shall be evaluated by taking
into account the influence of the several sources of
uncertainty that characterise both the actions and the
structural properties, as well as the efficiency and
consistency of the model of structural response.
In principle, the design process shall include
requirements concerning the construction phase and
the operation and maintenance during the whole life-
cycle. To this aim, data collected on site (e.g. through a
continuous monitoring) are essential both for checking
the accomplishment of the expected performance
during the service life, and for validating the original
design. Only if the aforementioned features are
properly considered, the structural response can be
reliably evaluated, and the performance of the building
construction ensured during the intended lifetime:
System Engineering represents the robust approach
that takes properly into account the different aspects
related to conceptual and structural design, construc-
tion and maintenance (Bontempi et al. 2008).
The overall approach requires the definition of the
quality of a complex structural system by a compre-
hensive concept, like dependability. The concept of
dependability has been originally developed in the field
of computer science, where it is defined as ‘the ability
*Corresponding author. Email: stefania.arangio@uniroma1.it
Structure and Infrastructure Engineering
Vol. 7, Nos. 1–2, January–February 2011, 75–86
ISSN 1573-2479 print/ISSN 1744-8980 online
Ó 2011 Taylor & Francis
DOI: 10.1080/15732471003588387
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to deliver services that can justifiably be trusted’
(Avizˇ ienis et al. 2004): the dependability of a system
reflects (i.e. represents, measures, . . .) the user’s degree
of trust in that system, i.e. the user’s confidence that
the system will operate as the user expects and will not
fail in normal use during the whole lifetime (Sommer-
ville 2000). The definition can be extended to
Structural Engineering: the design process shall be
aimed at justification of trust through the fulfilment of
some ‘attributes’ of dependability, mainly reliability,
safety, maintainability, and integrity.
According to the original definitions given in
Avizˇ ienis et al. (2004), reliability can be interpreted
as the continuity of correct service for the whole service
life; safety corresponds to the absence of catastrophic
consequences of system operation on the users and the
environment; maintainability is the ability to undergo
modifications and repairs; integrity corresponds to the
absence of improper system alterations and is some-
times related to the completeness and consistency of
the structural configuration (Bontempi and Giuliani
2008).
Other attributes of dependability are the availabil-
ity, originally defined as the readiness for correct
service at a given point of time, and the security, that is
a property that reflects the ability of the system to
protect itself from accidental or deliberate external
attack and is an essential pre-requisite for availability,
reliability and safety.
All attributes can be subdivided in high level or
active performances (reliability, availability, maintain-
ability) and low level or passive performances
(safety, security and integrity); the latter are exclusive
requirements, in the sense that they exclude undesir-
able situations rather than specifying required
performances.
It is evident that the dependability specification of a
structural system must include the requirements for the
dependability attributes in terms of admissible fre-
quency and severity of failures in a given environment;
obviously, one or more attributes may not be required
at all for a given system. The attributes can vary over
the life-cycle; in particular, the integrity and conse-
quently the overall dependability can be lowered by
deterioration due to effects of wear during ordinary
service, improper use and maintenance, as well as
environmental and accidental events.
Structural monitoring represents the tool for the
assessment of the evolution in time of the integrity,
thus of the dependability of an existing structural
system. It integrates, in a unified framework, advanced
engineering analyses and experimental data processing.
Therefore it is a very complex task, and includes issues
such as the definition and analysis of the structural
performances, from regular exercise to out-of-service
and collapse, the assessment of the environmental
conditions, the choice of the sensor systems and their
optimal placement, the use of data transmission
systems and signal processing techniques, and the
methods for damage identification, location and
quantification and for structural model updating
(Berthold and Hand 1999).
Soft computing methods can be very useful to
process data gathered by monitoring. In this paper, the
Bayesian neural network models are used to formulate
a two-step hierarchical strategy for structural integrity
monitoring. In the first step the occurrence of
abnormal alterations of the structural response is
checked and eventually the damaged section of the
structure identified; in the second step, the specific
damaged element in the considered section is recog-
nised and the intensity of damage evaluated.
In the following, the dependability assessment is
explained in detail with reference to structural systems
and the two-step strategy for structural integrity
monitoring illustrated. The strategy is applied to assess
the integrity of a long-span suspension bridge sub-
jected to wind action and traffic loading. As the bridge
is under design, measured data are simulated by
analysing the response of a detailed finite element
model of the whole structural system. The final
objective of the study is the optimal design of the
integrity monitoring system for the bridge.
2. Dependability assessment and structural integrity
monitoring
As specified above, the dependability of a structural
system is a comprehensive concept that includes and
describes the relevant aspects with reference to the
system quality and its influencing factors. The assess-
ment of dependability requires the definition of three
elements (Figure 1): the attributes, i.e. the properties
that quantify the dependability; the threats, i.e. the
elements that affect dependability; the means, i.e. the
tools that can be used to increase dependability.
In structural engineering, the relevant attributes are
reliability, safety, maintainability and integrity. These
properties are essential to guarantee, with reference to
the whole life-cycle, the survivability of the system
under the relevant accidental or exceptional hazard
scenarios, considering also the security issue, and the
system robustness, serviceability in operating condi-
tions and durability.
The threats to system dependability can be
subdivided into faults, errors and failures. According
to the definitions given in Avizˇ ienis et al. (2004), an
active or dormant fault is a defect or an anomaly in the
system behaviour that represents a potential cause of
error; an error is the cause for the system being in an
76 S. Arangio et al.

incorrect state; failure is a permanent interruption of
the system ability to perform a required function
under specified operating conditions. For building
constructions, possible faults are incorrect design,
construction defects, improper use and maintenance,
and damages due to accidental actions or deteriora-
tion; errors may or may not cause failure, and may
also activate a fault.
Following the approach proposed in Isermann
(2006), the design of a dependable structural system
is basically the problem of the design of a fault-tolerant
system: however, it includes also features like fault
detection, that is detection of alterations of the system
behaviour, fault diagnosis, that is, localisation and
quantification of the effects of faults and errors, and,
finally, the management of faults and errors aimed at
avoiding failure.
This paper is focused mainly on fault detection and
diagnosis. These elements are strictly related to the
monitoring of the integrity of the structural system: in
fact an efficient monitoring programme is expected to
be able to preserve the structural dependability,
diagnosing alterations, that is deterioration and
damage, at their onset (Li and Ou 2006).
In analogy with biological systems, and even if
there is no general consensus on its definition, an
integrity monitoring system should (Aktan et al. 1998,
Isermann 2006): sense the loading environment as well
as the structural response; reason by assessing the
structural condition and health; communicate through
a proper interface with other components and systems,
including controllers of the system behaviour; learn
from experience as well as by interfacing with human
for heuristic knowledge; be precise, so that even small
faults should be detected and diagnosed; decide and
take action for alerting controllers in case of accidental
situations, or activate fault tolerant configurations in
case of a reconfigurable system.
An ‘optimal’ integrity monitoring system allows the
control of the structural system in a proactive way: the
circumstances that may eventually lead to deteriora-
tion, damage and unsafe operations can be diagnosed
and mitigated in a timely manner, and costly replace-
ments can be avoided or delayed. Analysing the
problem in terms of cost–benefit analysis, it comes
out that, in case of complex structures, the integrity
monitoring should be planned since the design phase
and carried out during the entire life-cycle in order
to assess the structural health and performance under
in-service and accidental conditions (Aktan et al. 2002).
Over the past 30 years a huge research effort has
been devoted to developing effective methods for
integrity monitoring of civil structures. An extensive
survey of global methods (so-called because they are
based on the analysis of the whole structure) has been
presented in Doebling et al. (1996), and updated by
Sohn et al. (2004), where it is observed that, usually,
non-destructive global methods can be used for fault
Figure 1. Dependability: attributes, threats and means (adapted from Avizˇ ienis et al. 2004).
Structure and Infrastructure Engineering 77

detection, whereas local inspections and pattern
recognition approaches for fault diagnosis.
Regarding the temporal extent of the measure-
ments, continuous measurements are usually needed to
capture environmental effects such as those due to
wind and temperature; periodic inspections and
measurements are needed to evaluate the response
under operating conditions. Extensive use of long term
continuous monitoring is quite new, enabled by recent
advances in data acquisition, processing and manage-
ment. Long term monitoring of the structural response
was pioneered in China and Japan (Abe and Amano
1998, Wong et al. 2000, Ko and Ni 2005): nowadays,
several bridges are instrumented in Europe (Casciati
2003), United States (Pines and Aktan 2002), Canada
(Mufti 2001), Korea and other countries. Recent
developments consist in formulating a general frame-
work of asset management in a life-cycle perspective
(Messervey and Frangopol 2008).
3. Neural network models for fault detection and
diagnosis
In general, a fault causes events that, as intermediate
steps, influence or determine measurable or observable
symptoms. In order to detect, locate and quantify a
system fault, it is necessary to process data obtained
from monitoring and to interpret the symptoms.
However, this is a very complex task, as explained in
Figures 2 and 3. The relationship between fault and
symptoms can be represented graphically by a pyramid
(Figure 2); the vertex represents the fault, the lower
levels the possible events generated by the fault and the
base corresponds to the symptoms. The propagation of
the fault to the symptoms follows a cause–effect
relationship, and is a top-down forward process. The
fault diagnosis proceeds in the reverse way; it is a
bottom-up inverse process that relates the symptoms to
the fault. To solve the problem implies the inversion of
the causality principle. But one cannot expect to
rebuild the fault–symptom chain only by measured
data because the causality is not reversible or the
reversibility is ambiguous (Fu¨ ssel 2002): the underlying
physical laws are often not known in analytical form,
or too complicated for numerical calculation. More-
over, intermediate events between faults and symptoms
are not always recognisable (as indicated in Figure 3).
The solving strategy requires integrating different
procedures, either forward or inverse; the mixed
approach has been denoted as the total approach by
Liu and Han (2004), and different computational
methods have been developed for this task, that is, to
interpret and integrate information coming from on
site inspection, database and experience. In Figure 3 an
example of knowledge-based analysis is shown. The
results obtained by instrumented monitoring (the
detection and diagnosis system on the right side) are
processed and combined with the results coming from
the analytical or numerical model of the structural
response (the physical system on the left side).
Information technology provides the tool for such
integration. The processing of experimental data is the
bottom-up inverse process, where the output of the
system (the measured symptoms: displacements, accel-
eration, natural frequencies, etc) is known but the
parameters of the structure have to be determined.
Different computational methods can be used to this
aim. In several applications, soft computing techni-
ques, like the neural network models used in this study,
have shown their effectiveness in processing informa-
tion coming from monitoring. For a review on the
subject, it is possible to refer to Adeli (2001), who
illustrated the applications of neural networks to civil
engineering during a decade, and to Waszczyszyn
(1999), who collected in a book various papers on the
use of neural networks for the analysis and design of
structures. As concerns more specifically the problem
of damage identification and structural health mon-
itoring, Ni et al. (2002) presented a two-stage neural
network-based damage detection method, where
damage location is identified in a first stage and
damage severity is estimated in a second stage; Ko
Figure 2. Fault–symptoms relationship.

et al. (2002) used neural networks in a multi-stage
identification scheme for detecting damage in a cable-
stayed bridge in Hong Kong; Xu and Humar
(2006) presented a two-step algorithm that uses a
modal energy-based damage index to locate the
damage and a neural network technique to determine
its magnitude.
The neural network concept has its origins in
attempts to find mathematical representation of
information processing in biological systems. Actually
there is a definite probability model behind it; in fact a
neural network is an efficient statistical model for
nonlinear regression. It can be described by a series of
functional transformations working in different corre-
lated layers (Bishop 2006), that, in case of two layers,
takes the form:
yk x;wð Þ ¼ h
XM
j¼1
w
ð2Þ
kj g
XD
j¼1
w
ð1Þ
ji xi þb
ð1Þ
j0
!
þb
ð2Þ
k0
!
ð1Þ
where yk is the k th output variable in the output
layer, x is the vector of the D input variables in the
input layer, w is the matrix including the adaptive
weight parameters w
1ð Þ
ji and w
2ð Þ
kj and the biases b
1ð Þ
j0 and
b
2ð Þ
k0 that are set during the training phase (the
superscript refers to the considered layer), M is
the total number of units in the hidden layer, the
quantities within the brackets are the so called
activations, that are transformed using the activation
functions h and g.
The values of the components of w are obtained
during the training phase by minimising a proper error
function: in the considered case, the sum of squared
errors with weight decay regularisation (Bishop 1995)
given by:
E ¼
1
2
XN
n ¼ 1
XNo
k¼1
yk xn
; wð Þ À tn
k
È É2
þ
a
2
XW
i ¼ 1
wij j2
ð2Þ
where yk is the k th neural network output correspond-
ing to the n th realisation 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
parameters in w.
Neural network learning can be interpreted in the
framework of Bayesian inference (MacKay 1995),
where probability is treated as a multi-valued logic
that may be used to perform plausible inference
(Jaynes 2003). Within this framework it is possible to
solve a crucial problem of neural network application:
the choice of the optimal model complexity, which is
given by the number of units included in the hidden
layers. This number has to be fixed before training, and
affects significantly the generalisation performance of
the network model.
In general the number of hidden units is selected by
experience or rule of thumb, and depends heavily on
the subjective judgment of the designer: in this paper
the optimal architecture of the network model for a
given set of training data is selected by a Bayesian
Figure 3. Knowledge-based analysis for structural integrity monitoring.

model class selection approach (Beck and Yuen 2004).
As a result, the selection of the neural network model
class is mathematically rigorous and systematic; the
Bayesian approach allows an objective comparison
among alternative solutions and eliminates reliance on
the judgment of the neural network designer (MacKay
1995). The mathematical approach for neural network
model class selection is illustrated in detail in Arangio
and Beck (2010), where the most plausible model class
among a set of candidate ones is obtained by applying
Bayes’ Theorem and maximising the posterior prob-
ability of the model class given a set of training data. In
this respect, let us remember that it is not correct to
choose simply the model that better fits data: more
complex models will always fit the data in a better way,
but they may be over-parameterised and give poor
prediction for new cases.
4. A two-level strategy for bridge integrity assessment
Bayesian neural network models have been used to
formulate the two-step hierarchical strategy for the
integrity assessment of the bridge that is schematically
represented in Figure 4. It is a long span suspension
bridge that was recently reconsidered in Italy: a
preliminary design scheme elaborated in 2005 has
been considered for numerical calculations. The main
span is 3300 m long, while, including the two side
spans, the total length is 3666 m. The towers are 383 m
high and the bridge suspension system relies on two
pairs of steel cables, each with a diameter of 1.24 m
and a total length, between the anchor blocks, of
approximately 5000 m; the secondary suspension
system consists of 121 pairs of rope hangers. The cross
section of the deck is composed of three box elements
supported every 30 m by transversal beams; the deck
carries six road lanes in the external portions of the
deck and two railway tracks in the central one. More
detailed information on the bridge design can be
found, for example, in Bontempi (2006).
The two-step strategy considers the tasks of
damage detection, location, and quantification. As
shown in Figure 5, in the first step the occurrence of
anomalies in the bridge response is detected: if the
anomalies correspond to possible alterations of the
bridge response due to any damage, the damaged
portion of the whole structural system is identified. If
some damage has been detected, the second step is
initiated: by using a pattern recognition approach,
the specific damaged member within the whole
section is identified and the intensity of damage
evaluated. The two steps are illustrated in detail in
the following.
4.1. Step 1: Damage detection
As shown in Figure 5, it is assumed that the response
of the structure, represented by the time-histories of
the displacements, is monitored by sensors at various
measurement points. In the example case, they are
located in groups of three (A–B–C) every 30 m along
the bridge deck; each group individuates a test section.
Different Bayesian neural network models are
trained; in this step, one for each intermediate point
(B). The models are built and trained using the time-
histories of the displacements of the structure subjected
to wind action and traffic loads (that correspond, in the
examined case, to the passage of one train) in the
undamaged situation. The procedure for network
training is shown in Figure 6: the time-history of the
response parameter f is sampled at regular intervals,
generating a series of discrete values ft. A set of d such
values: ft-dþ1, . . ., ft, is used as input of the network
model, while the next value ftþ1 is used as the target
output. By stepping along the time axis, a training data
set consisting of many sets of input vectors with the
corresponding output values is built, and the network
models are trained. The trained models are then tested
with a set of observed values ftþn-d, . . . , ftþn, to predict
the value of ftþnþ1, according to the procedure of one-
step ahead forecast (Bishop 1995). After the initial
training phase, new input sets, corresponding to both
undamaged and damaged situations, are tested on the
trained models. For each set, the one-step ahead value
of the parameter is forecast and compared with the
target.
Figure 4. Scheme of the considered bridge.

The results of the training and test phases are
elaborated as shown in Figure 7. The two plots show
the difference err between the network output value y
and the target value t at several time steps for both
training and test in undamaged and damaged condi-
tions. It is possible to note that the mean values of err
(indicated by a straight line) obtained both in training
and test are comparable if the structure remains
undamaged. On the contrary, in case of anomalies
that may correspond to damages, there is a difference
De between the mean values of err corresponding to the
damaged and undamaged conditions in the test phase.
It has to be noted that the detected anomaly may
correspond to a damage state or simply to a change of
the characteristics of the excitation. To individuate the
actual cause of the anomaly, the intensity of De is
checked in different test sections, according to the
procedure that is schematically represented in the flow
chart shown in Figure 8. In the left side of Figure 8, the
start-up of the procedure is shown: given a data set, the
optimal neural network model is selected according to
the Bayesian approach, that is, the model with the
highest posterior probability is chosen and trained
(Arangio and Beck 2010). Then, as shown in the right
side of Figure 8, the model is tested with new input
data sets. If the difference De of the errors between
training and test is different from zero in several test
sections, it can be concluded that the characteristics of
the excitation are probably different from those
hypothesised. The adopted neural network models
are thus unable to represent the actual time-histories of
the response parameters, and have to be updated and
trained according to the modified characteristics of the
excitation. If De is different from zero only in one or
few test sections and generally decreases with the
distance from the selected section, it can be concluded
that the considered section of the structure is damaged
and the second step of the procedure is actuated.
Figure 5. Sketch of the two-step strategy for the assessment of the structural integrity.
Figure 6. Procedure for network training.

In real applications, not all cases in which De is
different from zero should be considered as relevant;
also, because it is essential to take properly into
account the noise corrupting the signals and the
accuracy of the measuring instruments, the choice of
the threshold value for initiating the second step must
be left to the experience of the operator. In the
numerical applications illustrated below, all cases in
which De is different from zero have been considered.
In the considered example, data are simulated by
analysing the dynamic response of a FE model of the
suspension bridge. Damage is modeled as a reduction
Figure 7. Difference err between output y and target t values as a function of time for training and test in undamaged and
damaged conditions in a case example (considered damage: 5% reduction of stiffness in one cable).
Figure 8. Flow-chart of the first step of the procedure.

of stiffness of a structural element in a test section and
the following damage scenarios are considered:
. Hangers: reduction of stiffness from 5% to 80%.
. Cables: reduction of stiffness from 1% to 10%.
. Transverse beam: reduction of stiffness from 5%
to 30%.
Data adopted for training every network model
consist of 1000 samples of the time-histories of the
response parameters that were found to be the more
sensitive to a stiffness reduction (Arangio and Petrini
2007): the deck twist in case of wind actions, and the
vertical displacement of the centroid of the deck cross
section in case of traffic loads. The number of samples
has been chosen after some trials, where it has been
noticed that no significant improvements in the
generalisation capacity of the network are obtained
for a higher number.
4.2. Step 2: Identification of damage location and
intensity
Having recognised that a test section is damaged, the
second step of the procedure is start up. It is aimed at
identifying the specific damaged element (Figure 5: one
of the two cables – the transverse beam – one of the
two hangers), and at evaluating the intensity of
damage. A pattern recognition approach is used: in
order to improve the quality of the procedure, the
mean values of the errors err in the prediction of the
response time-histories for all three measurement
points (A, B and C) in the considered test section are
taken as input of the selected neural network model.
As shown in Figure 5, each damage scenario is
described by a vector of five components: each
component indicates the state (represented by a
number denoting the presence – if different from zero
– and the intensity) of damage of a structural element
in the test section.
Simulated damage scenarios have been assumed as
output of the neural network model in numerical
calculations. The data set for the second step has been
gathered by simulating 400 damage scenarios (corre-
sponding to different positions and intensities of
damage): 370 out of them have been used for network
training, the remaining 30 for testing the network
generalisation performance.
5. The case example: Results of the procedure for the
integrity assessment
5.1. Results of step 1: Damage detection
The optimal model for the prediction of the time-
histories of the response parameters has been selected
by considering the structural response in the unda-
maged condition, and exploiting the procedure for
Bayesian model selection that is fully explained in
Arangio and Beck (2010); it consists of 2, 2 and 1 units
in, respectively, the input, hidden and output layers.
The model optimised in this way is also the most
efficient in terms of sensitivity to changes in structural
behavior: it corresponds to the lowest error in
the training phase and to the highest error in the
approximation of the signal when anomalies are
detected (Arangio 2008).
In Figure 9 (a), (b), (c), the differences between the
mean values of the errors De in the damaged and
undamaged conditions are shown for different inten-
sities of damage (that is, of stiffness reduction)
respectively to the cables, the transverse beam, and
the hangers.
Looking at the plots in Figure 9, it is evident that
the adopted strategy is more effective when responses
to high speed excitations (like traffic loads) are
considered instead of responses to slow speed excita-
tions (like wind actions). Thus, in the following step,
only the structural response due to the transit of train
is considered. The possibility of detecting the damages
is different for the various elements, as expected: in
fact, a small damage to the cables determines a much
higher value of De than strong damages to the
transverse beam and the hangers. Nonetheless, the
strategy allows detecting even small damages, and is
characterised by a high level of precision.
5.2. Results of step 2: Identification of damage
location and severity
Once a damaged section is detected, the specific
damaged element and the intensity of damage are
identified by using the pattern recognition approach.
The optimal network model, that is the most efficient
in terms of localisation and quantification of damage
(Arangio and Beck 2010), is selected by the Bayesian
approach on the base of the 370 patterns considered
for training. It consists of three input variables, that is,
the errors err evaluated at A, B, and C, five output
variables, that is, the possible locations (coincident
with a structural element) and intensities of damage,
and two hidden layers with 11 units (obtained by the
Bayesian selection process). After the training phase,
the network is tested with the remaining 30 patterns.
To evaluate the efficiency of the assessment, two
quantities are defined and evaluated for each test
pattern: the position, which gives a measure of the
prediction error made in any damaged location, and
the intensity, which gives a measure of the error made
in estimating the damage intensity. These quantities
are obtained by comparing the vectors of the output

variables corresponding to the evaluated y and the
target t damage scenarios, and are expressed by:
pos ¼
t Â y
tj j Á yj j
ð3Þ
int ¼
tj j
yj j
ð4Þ
where 6 denotes the inner product and jÁj is the norm
of the vector. If pos and int are (approximately) equal
to 1, it can be assumed that the damage is well localised
and its intensity correctly estimated.
The results of the numerical application are shown
in Figure 10: the damaged element is correctly located
in almost 90% of the considered cases, and the
intensity is correctly estimated in approximately 66%
of the considered cases. Therefore, it appears that the
proposed strategy is more efficient in locating the
damage than in quantifying it.
6. Final remarks
In the first part of the paper, the concept of
dependability, originally developed in the field of
computer science, has been extended to structural
engineering, in order to define and measure the quality
of a complex structural system. The whole design
process is then understood as aimed at ‘justification of
trust’ through the fulfilment of some ‘attributes’ of
dependability, mainly reliability, safety, maintainabil-
ity and integrity.
As a further development of the concept of
dependability, it seems useful to add the attribute of
sustainability: a structure should be acceptable for its
environment and ‘meet present needs without com-
promising the ability of future generations to meet
their needs’, as indicated in a 1987 UN Conference.
This aspect will be dealt with in future studies.
In the second part of the paper, a two-step strategy
for structural integrity monitoring has been discussed.
Figure 9. Differences between the mean errors De in training and test for different intensities of damage in (a) one of the two
cables, (b) the transverse beam, and (c) one of the two hangers.
Figure 10. Accuracy of the estimation of the position and intensity of damage in a bridge section (30 tests).

It represents an essential tool for the assessment of
existing structural systems as it allows controlling the
structural system in a proactive way: the circumstances
that may eventually lead to deterioration, damage and
unsafe operations can be diagnosed and mitigated in a
timely manner, and costly replacements avoided or
delayed.
Fundamental tasks of integrity monitoring are
fault detection and diagnosis. It has been observed
that the diagnosis from experimental data is an inverse
problem and the backwards assessment of the fault-
symptom chains cannot be done solely from measured
data, since the causality is not reversible or the
reversibility is ambiguous. The problem has been
solved by developing and applying a knowledge-based
procedure that integrates forward and inverse solving
methods with the heuristic knowledge coming from
experience or qualitative information. More specifi-
cally, the Bayesian neural network model has been
proposed to formulate the two-step hierarchical
strategy for integrity assessment. The strategy has
been applied to the case of a long-span suspension
bridge subjected to wind actions and traffic loadings,
and the capability of detecting the location and
intensity of damages to the main structural elements
of the superstructure has been examined.
Acknowledgements
This paper is dedicated to Professor Giuliano Augusti who
always gave, and still gives, impetus to the research of the
authors with stimulating suggestions. Thanks are due to
Professors Pier Giorgio Malerba, Dan Frangopol and Fabio
Biondini for fruitful discussions and comments on the
manuscript, and to James L. Beck, who introduced the first
author to the exciting subject of Bayesian neural networks. A
partial support from the Italian National Ministry for
University and Research (in the framework of PRIN 2007
– Research Project Wi-POD) is gratefully acknowledged.
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