Design Knowledge Gain by Structural Health Monitoring

Chapter 4
Design Knowledge Gain by Structural
Health Monitoring
Stefania Arangio and Franco Bontempi
Department of Structural and Geotechnical Engineering, Sapienza University of Rome,
Rome, Italy
Abstract
The design of complex structures should be based on advanced approaches able to take
into account the behavior of the constructions during their entire life-cycle. Moreover,
an effective design method should consider that the modern constructions are usually
complex systems, characterized by strong interactions among the single components
and with the design environment. A modern approach, capable of adequately consider-ing
these issues, is the so-called performance-based design (PBD). In order to profitably
apply this design philosophy, an effective framework for the evaluation of the overall
quality of the structure is needed; for this purpose, the concept of dependability can
be effectively applied. In this context, structural health monitoring (SHM) assumes
the essential role to improve the knowledge on the structural system and to allow
reliable evaluations of the structural safety in operational conditions. SHM should be
planned at the design phase and should be performed during the entire life-cycle of the
structure. In order to deal with the large quantity of data coming from the continu-ous
monitoring various processing techniques exist. In this work different approaches
are discussed and in the last part two of them are applied on the same dataset. It is
interesting to notice that, in addition to this first level of knowledge, structural health
monitoring allows obtaining a further more general contribution to the design knowl-edge
of the whole sector of structural engineering. Consequently, SHM leads to two
levels of design knowledge gain: locally, on the specific structure, and globally, on the
general class of similar structures.
Keywords
ANCRiSST benchmark problem, complex structural systems, dependability, enhanced
frequency domain decomposition, neural networks, performance-based design, soft
computing, structural health monitoring, structural identification, system engineering,
Tianjin Yonghe bridge.
4.1 Introduction
In recent years more and more demanding structures and infrastructures, like tall build-ings
or long span bridges, are designed, built and operated to satisfy the increasing
DOI: 10.1201/b17073-5
http://dx.doi.org/10.1201/b17073-5

96 Maintenance and Safety of Aging Infrastructure
needs of society. These constructions require high performance levels and should be
designed taking into account their durability and their behavior in accidental con-ditions
(Koh et al., 2010; Petrini & Bontempi, 2011; Crosti et al., 2011; 2012;
Petrini & Palmeri, 2012). Their design should be able to consider their intrinsic
complexity that can be related to several aspects, such as for example the strong non-linear
behavior in case of accidental actions and the fact that, while safety checks
are carried out considering each structural element per sé, structures are usually sys-tems
composed by deeply interacting components. Moreover the structural response
shall be evaluated taking into account the influence of several sources of uncertainty,
both stochastic and epistemic, that characterize either the actions or the structural
properties, as well as the efficiency and consistency of the adopted structural model
(Frangopol & Tsompanakis, 2009; Elnashai & Tsompanakis, 2012, Biondini et al.,
2008; Bontempi & Giuliani, 2010). Only if these aspects are properly considered, the
structural response can be reliably evaluated, and the performance of the constructions
ensured.
Furthermore, the recent improvement in data measurement and in elaboration
technologies has created the proper conditions to improve the decisional tools based
on the performance on site, leading to a system design philosophy based on the per-formance,
known as performance-based design (PBD). In order to apply the PBD
approach, an effective framework for the evaluation of the overall quality of a struc-ture
is needed. For this purpose, a specific concept has been proposed: the so-called
structural dependability. This is a global concept that was originally developed in the
field of computer science but that can be extended to civil engineering systems (Arangio
et al., 2010).
In this context, structural health monitoring assumes an essential role to improve
the knowledge on the structural system and to allow reliable evaluations. It should be
planned since the design phase and carried out during the entire life-cycle because it rep-resents
an effective way to control the structural system in a proactive way (Frangopol,
2011): the circumstances that may eventually lead to deterioration, damage and unsafe
operations can be diagnosed and mitigated in a timely manner, and costly replacements
can be avoided or delayed.
Different approaches exist for assessing the structural performance starting from the
monitoring data: they are based on deterministic indexes or on sophisticated proba-bilistic
evaluations and they can be developed at different levels of accuracy, according
to the considered situation. In the last part of the work, a case study is analyzed by
using two different approaches, the structural identification in the frequency domain
and a neural network-based damage detection strategy, and the results are compared.
The concepts discussed above are schematized in the flow chart in Figure 4.1 and
detailed in the following paragraphs.
4.2 Knowledge and Design
It is well known, and perhaps it is an abused slogan, that we are in the Era of Knowl-edge.
This is of course true in the field of structural design. Generally speaking, the
knowledge of the people involved in structural design can be schematically represented
by the large rectangle shown in Figure 4.2. But this actual knowledge usually does not
cover all the design necessities and there are areas of knowledge that are not expected
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Design Knowledge Gain by Structural Health Monitoring 97
Figure 4.1 Logical process for an innovative design by exploiting the knowledge gained by
structural health monitoring.
Figure 4.2 Knowledge gain process.

at the beginning of the project. According to the required additional knowledge, design
can be classified as:
I. evolutive design (small rectangle at the bottom) that does not require a large
amount of new knowledge because well-known concepts, theories, schemes, tools
and technologies are employed;
II. innovative design (small rectangle at the top) that does need new expertise because
something new is developed and introduced.
At the end of each project the design team gains further areas of knowledge
and this is an important point in engineering: one acquires expertise making things
directly. Also, the order of the knowledge, meaning having the right thing at the
right place, is an a-posteriori issue: sense-making is often organized after, looking at
the past.
A rational question can be raised looking at Figure 4.2: generally speaking, is the
necessity for the designers of an innovative structure so well-founded, to have already a
strong experience in this kind of structures? This question seems, but only superficially,
very provocative. In fact, if one is framed by its self-experience and culture, it is
reasonable to expect him to be caged in ideas and schemes securely useful in evolutive
situations, where only small changes are expected, whereas a largely innovative context
needs new frameworks that cannot be extrapolated from the past.
This concept is presented also in Figure 4.3 where the trend of the structural quality
vs. the design variables is shown for both types of design. In the case of evolutive
designs, the variables are few and it is possible to obtain the optimal structural con-figuration
with a local optimization. On the other hand, innovative design allows
reaching higher values of structural quality but needing a global optimization that
involves numerous variables.
Figure 4.3 Structural quality or performance vs. design variables for evolutive and innovative
design.

4.3 System Engineering Approach & Performance-based
Design
In order to define an appropriate procedure for dealing with complex structures, it
is interesting to define first the aspects that make a construction complex. They can
be understood looking at the plot in Figure 4.4 (adapted from Perrow (1984)) that
shows in an ideal but general way a three dimensional Cartesian space where the axes
indicate:
1 the nonlinearities of the system. In the structural field the nonlinearities affect the
behavior at different levels: at a detailed micro-level, for example, they affect
the mechanical properties of the materials; at a macro-level they influence the
behavior of single elements or even the entire structure as in the case of instability
phenomena;
2 the interactions and connections between the various parts;
3 the intrinsic uncertainties; they could have both stochastic and epistemic nature.
In this reference system the overall complexity of the system increases as the values
along each of the axes increase.
In order to adequately face all these aspects, complex structures require high per-formance
levels and should be designed taking into account their durability during
the entire life cycle and their behavior in accidental situations. All these requirements
are often in contrast with the simplified formulations that are still widely applied in
structural design.
It is possible to handle these aspects only evolving from the simplistic idealization of
the structure as a device for channeling loads to the more complete idea of the struc-tural
system, intended as a set of interrelated components working together toward a
common purpose (NASA – SE Handbook, 2007), and acting according System Engi-neering,
which is a robust approach to the creation, design, realization and operation
of an engineered system. It has been said that the notion of structural systems is a
‘marriage of Structural Engineering and Systems Science’ (Skelton, 2002).
Figure 4.4 Aspects that increase the complexity of a system (adapted by Perrow, 1984).

Figure 4.5 Functional/hierarchical breakdown of a system/problem.
In the System Engineering framework, an operational tool that can be useful for deal-ing
with complex systems is the breakdown. The hierarchical/functional breakdown
of a system (or a problem) can be represented graphically (as shown in Figure 4.5) by a
pyramid, set up with various objects positioned in a hierarchical manner. The peak of
the pyramid represents the goal (the whole system), the lower levels represent a descrip-tion
of fractional objects (the sub-systems/problems in which it can be divided), and the
base corresponds to basic details. By applying a top-down approach, a problem can be
decomposed by increasing the level of details one level at a time. On the other hand, in
those situations where the details are the starting point, a bottom-up approach is used
for the integration of low-level objectives into more complex, higher-level objectives.
In common practice, however, actual problems are unclear and lack straightforward
solutions. In this case, the strategy becomes a mixed recipe of top-down and bottom-up
procedures that may be used alternately with reverse-engineering approaches and
back analysis techniques.
The whole structural design process can be reviewed within this system view,
considering also that the recent improvement in measurement and elaboration data
technologies have created the proper conditions to integrate the information on the
performance on site in the design process, leading to the so-called performance-based
design (PBD) (Smith, 2001; Petrini & Ciampoli, 2012). The flow chart in Figure 4.6
summarizes the concepts at the base of the PBD. The first five steps in the figure
are those considered in the traditional design approach and lead to the “as built’’
construction; they are:
1 formulation of the problem;
2 synthesis of the solution;
3 analysis of the proposed solution;
4 evaluation of the solution performances;
5 construction.

Figure 4.6 Steps of the Performance Based Design (PBD) approach (adapted from Smith,
2001).
Difficulties associated with this kind of approach are evident: the as built structure
could be very different from the as designed one for various reasons, as fabrication mis-takes
or unexpected conditions during the construction phase, or also non-appropriate
design assumptions. In order to evaluate the accomplishment of the expected perfor-mance,
a monitoring system can be used. Under this perspective, three further steps
will be added to the aforementioned traditional ones:
6 monitoring of the real construction;
7 comparison of monitored and expected results;
8 increase of the accuracy of the expectation.
These three additional steps are the starting point of the PBD and lead to other
following steps devoted to the possible modification of the project in order to fulfill
the expected performance:
9 reformulation: development of advanced probabilistic methods for a more
accurate description of the required performance;
10 weak evaluation, that assumes that the analysis is exact and all the actions are
known, from the probabilistic point of view;
11 improvement of the model;
12 strong evaluation that is carried out when the improvement (see point 11) aims
at assigning more accurate values to the assigned parameters.

Looking at the flow chart in Figure 4.6, it is possible to make two observations:
I. the structural monitoring plays a key role in the PBD approach because it is the
tool that allows the first comparison between the ‘as designed’ structure with the
‘as built’ one. If it is managed in the right way, it can lead to a significant gain of
design knowledge that can assure the long term exploitation of the structure;
II. in order to evaluate the quality of the structure it is necessary to take into account
numerous aspects and to consider at the same time how the system works as a
whole, and how the elements behave singularly. For a comprehensive evaluation
of the overall performance a new concepts should be used, as for example that of
structural dependability discussed in the next section.
Finally, step 10, weak evaluation, can lead to a local specific increase of knowledge,
while step 12, strong evaluation, can lead to a global – general increase of knowledge
referring to a whole class of structures or even to a whole sector of the structural
engineering. If these knowledge step increases are recognized and organized by the
design team, the overall scheme reported in Figure 4.1 is developed.
4.4 Structural Dependability
As anticipated, for the purpose of evaluation of the overall quality of structural systems
a new concept has been recently proposed: the structural dependability. It can be intro-duced
looking at the scheme in Figure 4.7, where the various aspects discussed in the
previous section are ordered and related to this concept (Arangio, 2012). It has been
said that a modern approach to structural design requires evolving from the simplistic
idea of ‘structure’ to the idea of ‘structural system’, and acting according to the System
Engineering approach; in this way it is possible to take into account the interactions
between the different structural parts and between the whole structure and the design
environment. The grade of non-linearity and uncertainty in these interactions deter-mines
the grade of complexity of the structural system. In case of complex systems,
it is important to evaluate how the system works as a whole, and how the elements
behave singularly.
In this context, dependability is a global concept that describes the aspects assumed
as relevant to describe the quality of a system and their influencing factors (Bentley,
1993). This concept has been originally developed in the field of computer science
but it can be reinterpreted in the civil engineering field (Arangio et al., 2010). The
dependability reflects the user’s degree of trust in the system, i.e., the user’s confidence
that the system will operate as expected and will not ‘fail’ in normal use: the system
shall give the expected performance during the whole lifetime.
The assessment of dependability requires the definition of three elements
(Figure 4.8):
• the attributes, i.e. the properties that quantify the dependability;
• the threats, i.e. the elements that affect the dependability;
• the means, i.e. the tools that can be used to obtain a dependable system.

Figure 4.7 Roadmap for the analysis and design of complex structural systems (Arangio, 2012).
In structural engineering, relevant attributes are reliability, safety, security, main-tainability,
availability, and integrity. Note that not all the attributes are required for
all the systems and they can vary over the life-cycle.
The various attributes are essential to guarantee:
• the ‘safety’ of the system under the relevant hazard scenarios, that in current
practice is evaluated by checking a set of ultimate limit states (ULS);
• the survivability of the system under accidental scenarios, considering also the
security issues; in recent guidelines, this property is evaluated by checking a set of
‘integrity’ limit states (ILS);
• the functionality of the system under operative conditions (availability), that in
current practice is evaluated by checking a set of serviceability limit states (SLS);
• the durability of the system.
The threats to system dependability can be subdivided into faults, errors and fail-ures.
According to the definitions 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; failure is
a permanent interruption of the system ability to perform a required function under
specified operating conditions. Error may or may not cause failure or activate a fault.

Figure 4.8 Dependability: attributes, threats and means (from Arangio et al., 2010).
In case of civil engineering constructions, possible faults are incorrect design, construc-tion
defects, improper use and maintenance, and damages due to accidental actions or
deterioration.
With reference to Figure 4.5, the problem of conceiving and building a dependable
structural system can be considered at least by four different points of view:
1 how to design a dependable system, that is a fault-tolerant system;
2 how to detect faults, i.e., anomalies in the system behavior (fault detection);
3 how to localize and quantify the effects of faults and errors (fault diagnosis);
4 how to manage faults and errors and avoid failures (fault management).
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.
A system is taken as dependable if it satisfies all requirements with regards to various
dependability performance and indices, so the various attributes, such as reliability,
safety or availability, which are quantitative terms, form a basis for evaluating the
dependability of a system. Dependability evaluation is a complex task because this is
a term used for a general description of the quality of a system and it cannot be easily

expressed by a single measure. The approaches for its evaluation can be qualitative
or quantitative and usually are related to the phase of the life cycle that it is consid-ered
(design or assessment). In the early design phase a qualitative evaluation is more
appropriate than a detailed one, as some of the subsystems and components are not
completely conceived or defined.
Qualitative evaluations can be performed, for example, by means of failure mode
analyses approaches, as the Failure Mode Effects and Criticality Analysis (FMECA)
or the failure tree analysis (FTA), or by using reliability block diagrams. On the other
hand, in the assessment phase, numerous aspects should be taken into account and
all of them are affected by uncertainties and interdependencies, so quantitative evalu-ations,
based on probabilistic methods, are more suitable. It is important to evaluate
whether the failure of a component may affect other components, or whether a recon-figuration
is involved upon a component failure. These stochastic dependencies can be
captured for example by Markov chains models, which can incorporate interactions
among components and failure dependence. Other methods are based on Petri Nets
and stochastic simulation. At the moment, most of the applications are on electrical
systems (e.g., Nahman, 2002) but the principles can be applied in the civil engineering
field. When numerous different factors have to be taken into account and dependabil-ity
cannot be described by using analytical functions, linguistic attributes by means of
the fuzzy logic reasoning could be helpful (Ivezi´c et al., 2008).
4.5 Structural Health Monitoring
As aforementioned, structural monitoring has a fundamental role in the PBD because it
is the tool that allows the comparison between the expected behavior and the observed
one in order to verify the accomplishment of the expected performance and guarantee
a dependable system. Moreover, the recent technological progresses, the reduction
of the price of hardware, the development of accurate and reliable software, not to
mention the decrease in size of the equipment have laid the foundations for a widely
use of monitoring data in the management of civil engineering systems (Spencer et al.,
2004).
However, it is also important to note that the choice of the assessment method
and level of accuracy is strictly related to the specific phase of the life-cycle and to
the complexity and importance of the structure (Bontempi, 2006; Casas, 2010). The
use of advanced methods is not justified for all structures; the restriction in terms of
time and cost is important: for each structural system a specific assessment process,
which would be congruent with the available resources and the complexity of the
system, should be developed. In Bontempi et al. (2008) for example, the structures
are classified for monitoring purposes in the following categories: ordinary, selected,
special, strategic, active and smart structures. The information needed for an efficient
monitoring, shown in Figure 4.9 by means of different size circles, increases with the
complexity of the structure.
For those structural systems subjected to long term monitoring, data processing is
a crucial step because, as said earlier, they represent the measurable symptoms of the
possible damage (fault). However, the identification of the fault from the measurement
data is a complex task, as explained in Figure 4.10. The relationship between fault and
symptoms can be represented graphically by a pyramid: the vertex represents the fault,

Figure 4.9 Relationship between classification of structures and characteristics of the monitoring
process.
Figure 4.10 Knowledge-based analysis for structural health monitoring.
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. 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: the underlying physical
laws are often not known in analytical form, or too complicated for numerical cal-culation.
Moreover, intermediate events between faults and symptoms are not always
recognizable (as indicated in Figure 4.3).
The solution strategy requires integrating different procedures, either forward or
inverse; this 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 4.10 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, acceleration, natural
frequencies, etc.) is known but the parameters of the structure have to be determined.
For this purpose different methods can be used; a great deal of research in the past
30 years has been aimed at establishing effective local and global assessment meth-ods
(Doebling et al., 1996; Sohn et al., 2004). The traditional global approaches are
based on the analysis of the modal parameters obtained by means of structural iden-tification.
On the other hand, in recent years, also other approaches based on soft
computing techniques have been widely applied. These methods, as for example the
neural networks applied in this work, have proved to be useful in such case where con-ventional
methods may encounter difficulties. They are robust and fault tolerant and
can effectively deal with qualitative, uncertain and incomplete information, making
them highly promising for smart monitoring of civil structures. In the sequence both
approaches are briefly presented and, in the last part of the work, they are applied on
the same dataset and the results are compared.
4.5.1 Structural Identification
Structural identification of a civil structure includes the evaluation of its modal param-eters,
which are able to describe its dynamic behavior. The basic idea behind this
approach is that modal parameters (natural frequencies, mode shapes, and modal
damping) are functions of the physical properties of the structure such as mass, damp-ing
and stiffness. Therefore, changes in the physical properties, as for example the
reductions of stiffness due to damage, will cause detectable changes in the modal
properties. During the last three decades extensive research has been conducted in
vibration-based damage identification and significant progress has been achieved (see
for example: Doebling, 1996; Sohn et al. 2004; Gul & Catbas 2008; Frangopol et al.,
2012; Li et al., 2006; Ko et al., 2009).
The methods for structural identification belong to two main categories: Experimen-tal
Modal Analysis (EMA) and Operational Modal Analysis (OMA or output-only
analysis). The first class of methods requires knowledge of both input and output,
which are related by a transfer function that describes the system. This means that
the structure has to be artificially excited in such a way that the input load can be

measured. In case of large structures, to obtain satisfactory results, it is necessary to
generate a certain level of stress to overcome the ambient noise, but this is difficult
and expensive and moreover could create undesired nonlinear behavior. Operational
modal analysis, on the other hand, requires only measurement of the output response,
since the excitation system consists of ambient vibrations, such as wind and traffic.
For these reasons, in recent years, output-only modal identification techniques have
being largely used. This can lead to a considerable saving of resources, since it is not
necessary any type of equipment to excite the structure. In addition, it is not necessary
to interrupt the operation of the structure, which is very important in case of strategic
infrastructures that, in case of closure, will strongly affect the traffic. Another key
aspect is that the measurements are made under real operating conditions. In this work,
the used approach belongs to this latter category: the identification was carried out
by using an output only approach in the frequency domain, the Enhanced Frequency
Domain Decomposition (EFDD) technique (Brincker et al., 2001).
4.5.2 Neural Network-based Data Processing
Whenever a large quantity of noisy data need to be processed in short time there
are other methods, based on soft computing techniques, that have proven to be very
efficient (see for example: Adeli, 2001; Arangio & Bontempi, 2010; Ceravolo et al.,
1995; Choo et al., 2009; Dordoni et al., 2010; Freitag et al., 2011; Ni et al., 2002; Kim
et al., 2000; Ko et al., 2002; Sgambi et al., 2012; Tsompanakis et al., 2008) and have
attracted the attention of the research community. In particular, in this work a neural
network-based approach is applied for the assessment of the structural condition of a
cable-stayed bridge.
The neural network concept has its origins in attempts to find mathematical repre-sentations
of information processing in biological systems, but a neural network can
also be viewed as a way of constructing a powerful statistical model for nonlinear
regression. It can be described by a series of functional transformations working in
different correlated layers (Bishop, 2006):
yk(x,w)=h
⎛
⎝
M
j=1
w(2)
kj g
⎛
⎝
D
j=1
w(1)
ji xi + b(1)
j0
⎞
⎠ + b(2)
k0
⎞
⎠ (4.1)
where yk is the k-th neural network output; x is the vector of the D variables in
the input layer; w consists of the adaptive weight parameters, w(1)
ji and w(2)
kj , and the
biases, b(1)
j0 and b(2)
k0 ; H is the number of units in the hidden layer; and the quantities in
the brackets are known as activations: each of them is transformed using a nonlinear
activation function (h and g).
Input–output data pairs from a system are used to train the network by ‘learning’ or
‘estimating’ the weight parameters and biases. Usually, the values of the components
of w are estimated from the training data by minimizing a proper error function. The
estimation of these parameters, i.e. the so called model fitting, can be also derived as
a particular approximation of the Bayesian framework (MacKay, 1992; Lampinen
Vethari, 2001). More details are given in (Arangio Beck, 2012).

A key aspect in the use of neural network models is the definition of the optimal
internal architecture that is the number of weight parameters needed to adequately
approximate the required function. In fact, 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 parameters 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 performance is
achieved by the model whose complexity is neither too small nor too large.
The issue of model complexity can be solved in the framework of Bayesian proba-bility.
In fact, the most plausible model class among a set M of NM candidate ones can
be obtained by applying Bayes’ Theorem as follows:
p(Mj|D,M) ∝p

D|Mj

p

Mj|M

(4.2)
The factor p(D/Mj) is known as the evidence for the model class Mj provided by the
data D. Equation (4.2) illustrates 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
non informative prior, i.e. p(Mj)=1/NM, can be assigned; then different models with
different architectures can be objectively compared just by evaluating their evidence
(MacKay, 1992; Lam et al., 2006).
4.6 Knowledge Gain by Structural Health Monitoring:
A Case Study
4.6.1 Description of the Considered Bridge and Its Monitoring System
In the following it is presented a case study that shows the key role of structural
monitoring for increasing our knowledge on the operational behavior of the structures,
allowing the detection of anomalies in a timely manner. The considered structure is a
real bridge, the Tianjin Yonghe Bridge, proposed as benchmark problem by the Asian-
Pacific Network of Centers for Research in Smart Structure Technology (ANCRiSST
SHM benchmark problem, 2011) (see Figure 4.11). In October 2011 they shared some
data of the long term monitoring of the bridge with the Structural Health Monitoring
community. The benchmark data included also an ANSYS finite element model of the
structure that was at the base of the numerical analyses carried out in this work.
The Tianjin Yonghe Bridge is one of the earliest cable-stayed bridges constructed in
mainland China. It has a main span of 260m and two side spans of 25.15+99.85m
each. The full width of the deck is about 13.6 m, including a 9m roadway and
sidewalks. The bridge was opened to traffic since December 1987 and significant
maintenance works were carried out 19 years later. In that occasion, for ensuring the
future safety of the bridge, a sophisticated SHM system has been designed and imple-mented
by the Research Center of Structural Health Monitoring and Control of the
Harbin Institute of Technology (Li et al., 2013).

Figure 4.11 Skyline of the Tianjin Yonghe bridge with the main dimensions (top); cross section
(bottom). The distribution of the sensors is indicated.
The continuous monitoring system designed for the bridge includes 14 uniaxial
accelerometers permanently installed on the bridge deck and 1 biaxial accelerometer
that was fixed on the top of one tower to monitor its horizontal oscillation. An
anemometer was attached on the top of the tower to measure the wind speed in three
directions and a temperature sensor were installed at the mid-span of the girder to
measure the ambient temperature. The accelerometers of the deck were placed half
downstream and half upstream. The skyline of the bridge with the main dimensions
of the structure and the scheme of the distribution of the sensor is shown in Fig-ure
4.11. While it was monitored, the bridge experienced some damages, thus, the
data that were made available for the researchers regard both health and damaged
conditions.
Data in the health condition include time histories of the accelerations recorded
by the 14 deck sensors and environmental information (wind and temperature). They
consist in registrations of 1 hour that have been repeated for 24 hours on January 17th,
2008. The sampling frequency is 100 Hz. The second part of available data includes
other measurements recorded at the same locations after some months, on July 31st,
2008. The damage observed in the meantime regarded cracking at the closure segment
of both side spans and damage at the piers (partial loss of the vertical supports due
to overloading). The dataset includes again registrations of 1 hour repeated for the 24
hours at the same sampling frequency (100 Hz). The available data have been processed
by using both a structural identification approach and a neural network-based strategy.
In the following the results are presented and compared.
4.6.2 Application of the Enhanced Frequency Domain
Decomposition
In this work the structural identification has been carried out by using the Enhanced
Frequency Domain Decomposition (EFDD) technique that is based on the analysis of
the frequency content of the response by using the auto-cross power spectral density

Figure 4.12 Averaged Singular Values Decompositions (health condition – left; damaged
condition – right).
(PSD) functions of the measured time series of the responses. The PSD matrix is then
decomposed by using the Singular Value Decomposition (SVD) tool. The singular
values contain information from all spectral density functions and their peaks indicate
the existence of different structural modes, so they can be interpreted as the auto
spectral densities of the modal coordinates, and the singular vectors as mode shapes
(Brincker et al., 2001).
It should be noted that this approach is exact when the considered structure is lightly
damped and excited by a white noise, and when the mode shapes of closed modes
are geometrically orthogonal (Ewins, 2000). If these assumptions are not completely
satisfied, the SVD is an approximation, but the obtained modal information is still
enough accurate (Brincker et al., 2003). The first step of the FDD is to construct a PSD
matrix of the ambient responses G(f ):
G(f )=E[A(f )AH(f )] (4.3)
where the vector A(f ) collects the acceleration responses in the frequency domain, the
superscript H denotes the Hermitian transpose operation and E denotes the expected
value. In the considered case, the spectral matrix G(f ) was computed by using the
Welch’s averaged modified periodogram method (Welch, 1967). In addition, an over-lapping
of 50% between the various segments was considered and a periodic Hamming
windowing was applied to reduce the leakage.
After the evaluation of the spectral matrix, the FDD technique involves the Singular
Value Decomposition (SVD) of G(f ) at each frequency and the inspection of the curves
representing the singular values (SV). The SVD have been carried out for the 24 hour
registrations carried out on January 17th, 2008. The consistency of the spectral peaks
and the time invariance of resonant frequencies has been investigated by analyzing the
auto-spectra of the vertical accelerations acquired at different time of the day and by
evaluating the corresponding average auto-spectral estimates.
The averaged SVD plot in health conditions is shown in the left side of Figure 4.12.
The attention was focused on the frequencies below 2 Hz. The selection of this range
has been done for two reasons: first, because the most important modes for the dynamic

Figure 4.13 FEM model of the bridge (left); Comparison of the frequencies of the first six
modes obtained from the Finite Element Model (FEM) and from the vibration-based
identification in undamaged and damaged conditions (right).
description of large structural systems generally are below 2 Hz; in addition, the avail-able
data included the measurements of 14 stations (7 downstream and 7 upstream)
that made difficult to identify clearly higher frequency. Looking at the plot, is possible
to note that the fourth mode is not characterized by a single well-defined peak on the
SV line, but by different close peaks around the frequency 1 Hz, suggesting a nonlinear
behavior of the bridge.
The same procedure has been applied for processing the time series of the response
in damaged conditions. In the plot on the right of Figure 4.12 the related averaged
SVD is shown. It is possible to note three singular values coming up around 1.1 and
1.3 Hz that indicate the presence of three modes in this range. The other modes are
reasonable separated.
The results of the vibration-based identification have been compared with the output
of the modal analysis carried out with the finite element model of the structure. For this
comparison it has to be considered that the FE model represents the “as built’’ bridge
where the mechanical properties and the cross sections were assigned as reported in
the original project, while the monitored data represent the behavior of the bridge
after years of operation. The comparison of the first six frequencies is summarized in
the table on the right side of Figure 4.13 and the first three mode shapes are shown
in Figure 4.14. More details are given in (Arangio et al., 2013; Arangio Bontempi,
2014).
Looking at the plots in Figure 4.14, it is possible to note that the mode shapes iden-tified
using the time series recorded in undamaged condition are in good agreement
with those given by the finite element model. The mode shapes remains similar also
after damage because probably it affects the higher modes. The deterioration of the
structure during time and the occurrence of damage are suggested by the decrement of
the frequencies: those of the FEM model, which represent the “as built’’ structure are
higher of those obtained from the signal recorded in January 2008, showing that the

Figure 4.14 Comparison of the first three mode shapes obtained from the Finite Element
Model (FEM) and from the vibration-based identification in undamaged and damaged
conditions.
years of operation have reduced the overall stiffness of the structure. This phenomenon
is even more evident looking at the decrement of the frequencies in the damaged
condition.
4.6.3 Application of a Neural Networks-based Approach
The results obtained with the structural identification have been cross validated with
those obtained by applying a neural network-based strategy. The proposed method
consists in building different neural network models, one for each measurement point
and for each hour of measurements (that is, the number of network models is equal
to 14 (sensor locations)×24 (hours)=336). The neural network models are built and
trained using the time-histories of the accelerations recorded in the selected points in
the undamaged situation. The purpose of these models is to approximate the behavior
of the undamaged bridge taking into account the variation of the traffic during the
different hours of the day.
The procedure for network training is shown in Figure 4.15. The time-history of
the response f is sampled at regular intervals, generating series of discrete values ft .
In order to obtain signals that could be adequately reproduced, the time series needed

Figure 4.15 Scheme of the proposed damage detection strategy.
to be pre-processed by applying appropriate scaling and smoothing techniques. After
that, a set d of values of the processed time series, ft−d+1, . . . , ft , is used as input of
the network model, while the next value ft+1 is used as 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 architecture of the model is chosen by applying the Bayesian approach discussed
in section 4.2 and the models with the highest evidence have been selected. They
have four inputs and three internal units. The performance of the models is tested by
proposing to the trained networks input patterns of values recorded some minutes after
those used for training ft+n−d . . . ft+n, and by predicting the value of ft+n+1. The models
are considered well trained when they show to be able to reproduce the expected values
with a small error. Subsequently, these trained neural networks models are tested with
data recorded in the following days. The testing patterns include time series recorded
in both undamaged and damaged conditions.
For each pattern of four inputs, the next value is predicted and compared with the
target output. If the error in the prediction is negligible the models show to be able to
reproduce the monitoring data and the bridge is considered undamaged; if the error
in one or more points is large, the presence of an anomaly (that may represent or
may not represent damage) is detected. The results of the training and test phases are
elaborated as shown in Figure 4.16. 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 testing, in undamaged (left) and damaged (right) conditions. It is possible to note

Figure 4.16 Error in the approximation for training and test in health and damaged conditions.
that the mean values of err (indicated by the straight lines) obtained in training and test
are comparable (

e∼=
0) if the structure remains undamaged. In contrast, in case of
anomalies that may correspond to damage, there is a significant difference

e between
the values of the error in testing and training.
To distinguish the actual cause of the anomaly, the intensity of

e is checked at
different measurement points: if

e is large in several points, it can be concluded that
the external actions (wind, traffic) are probably changed. In this case, the trained neural
network models are unable to represent the time-histories of the response parameters,
and they have to be updated and re-trained according to the modified characteristics
of the action. If

e is large only in one or few points it can be concluded that the bridge
experienced some damage.
In the following the results of the strategy are shown. As previously mentioned, 14
groups of neural networks have been made, one group for each measurement point,
which have been trained with the time histories of the accelerations in health conditions
(data recorded on January 17th, 2008). In order to take into account the change in the
vibrations of the structures caused by the different use during the day, one network
model for each hour of monitoring has been created (24 network models for each
point). For the training phase of each model, 4 steps of the considered time history
are given as input and the following step as output. The training set of each network
model includes 5000 examples chosen randomly in the entire set.
The trained networks have been tested by using the time histories of the accelerations
recorded at the same points and at the same time some month after, on July 31st 2008.
The difference between the root mean squares of the error, ERMS, calculated in the
two dates for each point is shown in Figures 4.17 and 4.18. Each plot represents one
hour of the day (H1, H3, etc.) and has on the x-axis the measurement points and on
the y-axis the value of the difference of the errors ERMS; the results every two hours
are shown. The measurement points are represented on two rows: the first one (deep
grey) represents the results of the downward sensors (#1, 3, 5, 7, 9, 11, 13) while the
second one (light grey) represents the results of the upward sensors (#2, 4, 6, 8, 9, 10,
12, 14) (see also Figure 4.11 for the location of the sensors).
Looking at the plots, it is possible to notice that, apart from some hours of the day
that look difficult to reproduce, the neural networks models are able to approximate
the time history of the acceleration with a small error in almost all the measurement
points, except that around sensor #10. Considering that in the undamaged situation

Figure 4.17 Root mean square of the error in the 14 locations of the sensors (from H1 to H11).
Figure 4.18 Root mean square of the error in the 14 locations of the sensors (from H13 to H23).
the error was small in all the points, this difference is interpreted as the presence of an
anomaly (damage) in the structure. Between 6 a.m. and 9 a.m. and around 9 p.m. the
error is larger in various sensors but it is possible that this depends on the additional
vibrations given by the traffic in the busiest hours of operation of the bridge.
Note that there is another factor which was not examined in this study, but which
could have partially influenced the results: the dependence on the temperature, as
stated by (Li et al., 2010). Actually, the two signals have been recorded in two different
periods of the year that are characterized by significant climatic differences. However,
the results obtained with the two methods suggest that the detected anomalies do
not depend only on the temperature, but they could be related to the presence of
deterioration or damage.

Design Knowledge Gain by Structural Health Monitoring

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