Engineering Structures 30 (2008) 3034–3044

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Engineering Structures

journal homepage: www.elsevier.com/locate/engstruct

Dynamic monitoring of a long span arch bridge

Filipe Magalhães ∗, Álvaro Cunha, Elsa CaetanoFaculty of Engineering of the University of Porto (FEUP), R. Dr. Roberto Frias, 4200-465 Porto, Portugal

a r t i c l e i n f o

Article history:Received 29 January 2008Received in revised form15 April 2008Accepted 16 April 2008Available online 22 May 2008

Keywords:Ambient vibration testDynamic monitoring systemAutomatic modal parameters identificationFrequency domain decomposition

a b s t r a c t

A new multi-channel dynamic monitoring system was recently installed in a long span concrete archbridge that crosses the Douro River in the city of Porto, Portugal: the “Infante D. Henrique” bridge. Thispaper describes the experimental and numerical studies developed shortly after construction of thebridge, characterizes the installed monitoring system and presents the results achieved with the softwaredeveloped to process the data that is continuously received through the Internet. Preliminary studiesincluded the development of an ambient vibration test and the construction of a numerical model of thebridge that was “tuned” to fit the bridge dynamic properties identified by the ambient vibration test. Theroutines implemented include the on-line automatic identification of the bridge’s natural frequencieswith the Frequency Domain Decomposition method, enabling the tracking of the bridge’s first 12 naturalfrequencies. This unique feature is only possible due to the combination of high-quality acquisitionequipment with state of the art processing algorithms.

© 2008 Elsevier Ltd. All rights reserved.

1. Introduction

An increasing interest in permanent observation of the dynamicbehaviour of bridges has been observed during the last years,not only owing to the ageing of a huge number of structures,but also because of the increasing complexity of new bridges. Inaddition, recent technological advances have contributed to makethe installation and operation of permanent dynamic monitoringsystems more practical and economical and to permit an almostimmediate analysis of the bridge’s condition. System remotecontrol and real-time data retrieving are allowed by nowadays-standard technology. According to Ko and Ni [1], all over the world,there are so far about 40 long-span bridges (with spans longer than100 m) instrumented with health monitoring systems.

In order to profit from the latest technological developmentsand to have a system that is really useful for evaluation ofthe structure’s condition, a continuous online processing of thecollected data is required. The outputs produced should thenserve as indicators of the structure’s health. Modal parametersand especially natural frequencies can be used for that purpose,as demonstrated in [2]. It is however of utmost importance thatsubsequent to the identification of natural frequencies, numericalmodels are applied in order to extract the effect on naturalfrequencies of environmental variables (e.g. air temperature andhumidity) and, if significant, the effect of the extra mass associated

∗ Corresponding author. Tel.: +351 225081854; fax: +351 225081835.E-mail address: filipema@fe.up.pt (F. Magalhães).URL: http://www.fe.up.pt/vibest (F. Magalhães).

0141-0296/$ – see front matter © 2008 Elsevier Ltd. All rights reserved.doi:10.1016/j.engstruct.2008.04.020

with the traffic over the bridge. After elimination of the influenceof these factors, frequency changes can only be due to stiffnessreductions associated with damage.

In this context, the development and validation of tools forautomatic identification of natural frequencies based on themeasurement of bridge responses during its normal operationis fundamental, as the success of subsequent damage detectionalgorithms depends on the accuracy of these natural frequencyestimates. Furthermore, it is essential that these routines aresufficiently robust to run on an online basis, in order to providein almost real-time parameters that characterize the structure’scondition. This feature is especially helpful for rapid assessmentof critical infrastructures after the occurrence of natural or man-made disasters.

At present, it is opportune to perform practical applications onfull-scale bridges with advanced commercially available dynamicmonitoring hardware combined with processing routines based onthe latest theoretical developments.

Under these circumstances, a multi-channel dynamic monitor-ing system was recently installed in a long span concrete archbridge to continuously evaluate the variation of its dynamic modalparameters. The final goal of the application is to show the feasibil-ity of the use of damage detection methodologies based on modalparameters shifts.

This paper describes experimental and numerical studiesdeveloped before equipment installation, characterizes the mon-itoring system used and presents the results achieved with Mat-lab routines developed to process the data received through theInternet.

Preliminary studies included the development of an ambientvibration test that provided important information for the design

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Fig. 1. Aerial view of Maria Pia, Infante D. Henrique and Luiz I bridges (from bottomto top).

of the monitoring system and the construction of a numericalmodel of the bridge that was “tuned” to fit the bridge dynamicproperties identified by the ambient vibration test. This numericalapproach was essential to improve the understanding of thestructure dynamic behaviour and to create a baseline model forfuture damage detection studies.

The routines implemented perform on-line automatic identifi-cation of the bridge’s natural frequencies based on the FrequencyDomain Decomposition method, enabling tracking of the bridge’sfirst 12 natural frequencies. This unique feature is possible becausehigh-quality acquisition equipment was combined with state ofthe art processing algorithms.

2. Description of the bridge

The Douro River is crossed by several outstanding bridgeslinking the cities of Porto and Gaia, located at the north of Portugal.The 19th Century metallic Maria Pia and Luiz I Bridges and the 20th

Century concrete Arrábida and S. João Bridges got, at the beginningof the 21st Century, the company of a new concrete arch bridge: the“Infante D. Henrique” bridge (Fig. 1).

The “Infante D. Henrique” Bridge is composed of two mutuallyinteracting fundamental elements: a very rigid prestressed rein-forced concrete box beam, 4.50 m deep, supported by an extremelyshallow and thin reinforced concrete arch, 1.50 m thick, as shownin the elevation and cross-sections represented in Fig. 2. The archspans 280 m between abutments and rises 25 m until the crown,thus exhibiting a shallowness ratio greater than 11/1. In the 70 mcentral segment, arch and deck meet to define a box-beam 6 mdeep. The arch has constant thickness and its width increases lin-early from 10 m in the central span up to 20 m at the springs [3].Owing to the high stiffness of the deck with respect to the slender-ness of the arch, the structure behaves as a beam bridge definedbetween abutments and with intermediate elastic supports 35 mapart.

The extreme shallowness and flexibility of the arch impliedsignificant complexity of construction and required very accuratecontrol of geometry, deformations and forces. This control wasperformed by three separate instrumentation systems: one forconcrete elements (comprising strain gages, clinometers andtemperature sensors); another for temporary stay cables; andanother one for granite rocky slopes. The Laboratory of Vibrationsand Structural Monitoring (ViBest, http://www.fe.up.pt/vibest) ofFEUP was contracted to measure on a regular basis the tensionforces installed in the provisional stay cables using vibrationchord theory [4]. Those three instrumentation systems provided anaccurate understanding of the structural behaviour, and supportedimportant decisions of the designer and the constructor at severalcritical moments of construction. Owing to the evident usefulnessof the monitoring activity during this phase, the owner decidedto keep the static monitoring system working after the bridgeopening to traffic, and agreed to install a new long term dynamicmonitoring system, suggested by ViBest with the support of thedesigner.

It is relevant to point out that the bridge is one of the mainentrances into the Porto city centre and so it is crossed by highvolumes of traffic. During rush hours, the deck is frequentlycongested with cars and buses.

Fig. 2. Elevation and cross-sections of the bridge.

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Fig. 3. Instrumented cross-sections (the ellipse indicates the reference cross-section) and image of one tri-axial strong motion recorder with the external GPS sensor.

3. Ambient vibration test and numerical modelling

3.1. Ambient vibration test procedure

The design of a dynamic monitoring system requires previousknowledge of the structure’s natural frequencies and mode shapeconfigurations. The most convenient way to estimate the modalparameters experimentally is with an ambient vibration test.Furthermore, the data collected during these tests is of the sametype of the data recorded by the dynamic monitoring systems, sothe same identification algorithms can be used.

The ambient vibration test of the “Infante D. Henrique” bridgewas developed without disturbing its normal use, taking profitfrom the vibrations induced by traffic and wind. To measurevery low amplitude accelerations, 4 tri-axial 18-bit strong motionrecorders were used (Fig. 3, http://www.geosig.com). Thesedevices are constituted by high sensitivity internal force balanceaccelerometers, 18 bit analog-to-digital converters, batteries thatenable autonomy for one day of tests, internal memories to storethe acquired data and external GPS sensors to ensure accurate time,so that synchronous measurements are recorded by the variousunits independently, avoiding the use of cables.

During the ambient vibration test, two recorders served asreference permanently located at the reference cross-section(section 8 in Fig. 3) of the deck, at both sides of the deck (upstreamand downstream). The other two recorders scanned the bridgedeck measuring the acceleration along three orthogonal directionsat both sides of the other 15 cross-sections represented in Fig. 3.

For each sensor layout, time series of 16 min were collected.The sampling frequency was 100 Hz, a value that is imposed byfilters of the acquisition equipment [5] and which is much higherthan that required for this bridge, as the most relevant naturalfrequencies of the bridge are below 10 Hz. Therefore, a decimation(reduction of the sampling rate after the application of a digitallow-pass Chebyshev filter with a cutting frequency equal to 0.4times the new sampling frequency) was applied before the useof the identification tools, reducing the sampling frequency from100 Hz to 20 Hz.

3.2. Identification of modal parameters

Identification of modal parameters from data collected duringthe ambient vibration test was achieved with two separate output-only identification methods with different theoretical bases: theFrequency Domain Decomposition (developed in the frequencydomain) and the Data-driven Stochastic Subspace Identification(developed in the time domain). A detailed description of theresults provided by both methods is presented in [6], where it isalso shown that estimates provided by the two approaches are veryconsistent. In this paper, only the results of the FDD method arepresented, as an adaptation of this method is going to be used inprocessing of data collected by the monitoring system.

Fig. 4. Average normalized singular values.

The first step of the FDD method is to construct a spectrummatrix of ambient responses for each test setup, with one rowfor each measurement degree of freedom and with one columnfor each degree of freedom elected as reference. Therefore,columns contain cross spectra relating the structural response atall measurement points with the corresponding response at eachreference point.

In the present application, four time series were considered foreach instrumented section: upstream and downstream vertical ac-celerations, mean values of the two measured lateral accelerationsand mean values of the two measured longitudinal accelerations.Hence, spectra matrices with 8 rows and 4 columns were organizedfor each setup. The elements of these matrices were estimated us-ing the Welch procedure [7] by dividing the available time seriesin segments of 102.4 s (2048 points), considering an overlap of 66%between segments and adopting a Hanning window to reduce theleakage. The selected parameters allowed the realization of aver-ages over 26 time segments and produced spectra with a frequencyresolution of 0.00977 Hz.

It can be shown [8] that, under some assumptions (white noiseexcitation, low damping and orthogonal mode shapes for closemodes), the singular values of the spectrum matrix in the vicinityof each natural frequency form auto-spectrum density functionsof single degree of freedom systems with the same frequency anddamping as the structure vibration modes.

Fig. 4 presents the average of normalized singular valuescovering all setups. This graphic is a synthesis of the frequencycontent present in each setup and allowed the identification ofthirteen resonant frequencies (marked with the dashed verticallines) in the frequency range of analysis (0–5 Hz).

Mode shapes are estimated from singular vectors of spectrummatrices evaluated at the identified natural frequencies andassociated with singular values that contain the peaks. In eachsetup, eight mode shape components are calculated (number oftime series processed in each setup). These are then groupedtogether using the components at reference sections (estimated inall setups) to correctly scale the segments identified in each setup.

Figs. 5–7 show some of the identified modes of vibration of thebridge deck plotted with Artemis software [9]. These are comparedwith the ones provided by the numerical model that is describedin the next sub-section.

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Fig. 5. Top view of the first, second and third lateral bending modes.

Fig. 6. Lateral view of the first 5 vertical bending modes.

3.3. Numerical modelling

Structural behaviour of the bridge was modelled with ANSYSsoftware using 3D bar finite elements. Cross section properties(area, moments of inertia, torsion moment of inertia and sheardeflection constants) were defined according to the geometry ofthe deck, arch and columns. The same elasticity modulus of 37 GPa(value provided by tests performed during the bridge construction)was adopted for the deck and arch concrete and an elasticitymodulus of 34 GPa (value defined by the Eurocodes for a C35/45concrete) was considered for the concrete of the columns.

Connections between deck and the highest columns (M1 andM6, Fig. 2) are monolithic, whereas connections with othercolumns and abutments are provided by two unidirectionalsliding pot bearings. These bearings allow movements along thelongitudinal direction of the bridge and rotation in all directions.

However, for low levels of excitation, as is the case during ambientvibration tests, the behaviour of these connections can be different.For low levels of vibration, friction forces can prevent displacementor rotation.

To analyse the influence of the behaviour of these connectionson the modal parameters, three alternative models were devel-oped:

- Model 1 (M1): longitudinal displacement and rotation free in allpot bearings;

- Model 2 (M2): longitudinal displacement and rotation fixed inall pot bearings;

- Model 3 (M3): longitudinal displacement and rotation fixed inthe pot bearings of the columns but free in the pot bearings ofthe abutments.

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Fig. 7. Lateral view of the first and second torsion modes.

Table 1Modal parameters obtained with the numerical models that were developed

Modea Exp. Model 1 Model 2 Model 3 Model 4Freq. (Hz) Freq. (Hz) Error (%) Freq. (Hz) Error (%) Freq. (Hz) Error (%) Freq. (Hz) Error (%) MAC

V1 0.810 0.541 −33.29 1.054 29.96 0.701 −13.56 0.810 −0.12 0.995V2 1.135 1.081 −4.76 1.164 2.56 1.144 0.79 1.149 1.23 0.994V3 1.405 1.244 −11.46 1.473 4.84 1.465 4.27 1.466 4.34 0.992V4 1.993 1.766 −11.35 2.088 4.82 2.086 4.72 2.086 4.72 0.994

L1 0.770 0.794 3.12 0.799 3.77 0.794 3.12 0.794 3.12 0.996L2 1.734 1.767 1.90 1.788 3.11 1.768 1.96 1.768 1.96 0.989L3 3.309 3.353 1.30 3.394 2.54 3.357 1.42 3.357 1.42 0.965

T1 2.212 2.169 −1.90 2.211 0.00 2.185 −1.18 2.185 −1.18 0.956T2 3.734 3.632 −2.73 3.724 −0.27 3.641 −2.49 3.641 −2.49 0.952

a Mode type, defined considering the most relevant components (L– lateral bending; V– vertical bending; T– torsion).

Fig. 8. Normalized auto-spectra of longitudinal accelerations measured simulta-neously at the deck and at the Gaia abutment.

Natural frequencies of the most relevant modes provided by thethree models are presented in Table 1. Models 1 and 2 establishthe lower and upper bounds of the numerical natural frequenciescalculated using the material properties previously defined. Asignificant variation of the natural frequencies of vertical modesis noted (especially the associated with the first mode).

Modes identified experimentally show that the deck undergoeslongitudinal movements. Therefore, the hypothesis of fixinglongitudinal movements in the abutments is not correct. Onthe other hand, model M3 shows that, even fixing the relativemovements and rotation in all columns, the numerical frequencyof the first mode is considerably lower than the experimental one.

In order to better understand the longitudinal behaviourof the bridge, two additional measurements were performed:longitudinal acceleration at the deck near the expansion joint inthe Gaia bank and longitudinal acceleration of the Gaia abutment.Spectra of the collected time series are represented in Fig. 8. Thesegraphics show the presence of some of the natural frequenciesof the bridge in the response of the abutments and, in particular,the presence of the natural frequency of the first vertical mode.This means that the abutment is mobilized in the movementsassociated with the first vertical bending mode, due to the

existence of friction forces. Therefore, the appropriate modellingof the behaviour of the bridge requires the inclusion in Model 3 ofhorizontal springs to simulate the additional stiffness provided bythe abutments.

This last conclusion led to the development of a “more correct”model of the bridge (Model 4). This model is similar to Model 3but includes a horizontal spring at each abutment with a stiffnessconstant that was adjusted in order to obtain good matchingbetween numerical and experimental frequencies. Table 1 showsthat the correlation between modal parameters of the finalnumerical model and the experimental ones is very good, withrelative errors of natural frequencies lower than 5% and MACvalues always greater than 0.95 [10] (ratio that measures thecorrelation between mode shapes:1– means that the mode shapesonly differ on a scale factor; 0– means that the modes shapes areorthogonal).

4. The monitoring system

Traditional monitoring systems are based on one centralacquisition system to which all the sensors are connected.However, it is more convenient to have the digitizers distributedalong the monitored structure, in order to reduce the length ofthe sensor cables, as these are sensitive to electrical interferencesthat can corrupt the sensor’s electrical signals. Additionally, afterdigitization, the information collected by several sensors canbe transmitted by a single Ethernet cable. Therefore, with thisalternative solution, the installation becomes simpler and thesignal noise is reduced. These advantages are enhanced whenlarge civil structures are involved. Whenever the distance betweendigitizers is longer than 90 m, it is necessary to replace the Ethernetcable by a fibre optical cable, that can span long distances withoutsignal interference, making this arrangement even more flexible.As high signal synchronization is essential for modal analysis,this type of architecture of the monitoring system requires goodsynchronization of the digitizers’ clocks. This can be achievedwith a synchronization cable connecting the distributed digitizersor with one GPS antenna and receiver for each digitizer to

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Fig. 9. Scheme of the monitoring system

synchronize their internal clocks using the information providedby the “in view” satellites.

The dynamic monitoring system of the “Infante D. Henrique”bridge is essentially composed by 12 force balance accelerometers,2 digitizers and recoding units and an internet router, which areinstalled inside the deck box girder and distributed along thebridge according to the scheme presented in Fig. 9.

Since the structure is almost symmetric and the previouslyperformed ambient vibration test has proven that the modeshapes are also approximately symmetric, it was decided toinstrument just one half of the bridge. Therefore, the 12 availableaccelerometers were distributed along four sections. Three sensorsequip each section: one to measure the lateral acceleration and twofor the vertical acceleration at the downstream and upstream sides(the ambient test showed the existence of torsion modes in theanalysed frequency range).

The force balance accelerometers used (FBA ES-U2 fromKinemetrics) have a dynamic range of 145 dB, are sensitive inthe frequency range DC to 200 Hz and their measuring rangecan go up to 4 g. In the present application a measuring rangebetween −0.25 and +0.25 g was fixed, in order to optimize thesensitivity of the sensors and so reduce the effect of noise, whilekeeping a conservative acceleration range (the maximum observedacceleration is lower than 10 mg).

Each digitizer (www.Q330.com) allows the connection of sixdynamic channels, is equipped with a 24-bit analog-to-digitalconverter and permits simultaneous telemetry of the acquired datato a central site and a link to a local recording unit. In the presentinstallation, the digitizers were placed at sections S2 and S4 (Fig. 9)together with local backup disks. These recording units guaranteethat there are no data losses in case of failure of the Internetconnection. Digitizers located at sections S2 and S4 are connectedto each other by an Ethernet cable. Another Ethernet cable linkssection S4 and the router that is the interface between the localnetwork and the Internet.

Synchronization between digitizers is achieved with two GPSantennas and receivers that allow continuous update of theinternal clocks of both units.

The data produced by the two digitizers is received at FEUP(Faculty of Engineering of the University of Porto), where dataintegrator software generates ASCII files with as many columnsas the number of sensors, corresponding to the acceleration timeseries sampled with a predefined rate and length. For monitoringthis bridge, a sampling frequency of 50 Hz and a length of 30 minwere selected. Consequently, each half an hour a new ASCII filewith 12 columns and 30 × 60 × 50 = 90 000 lines is created at aPC located at FEUP. These files are then processed by the softwaredescribed in the next section.

In the selection of the time series length, priority was givento the quality of modal parameters estimates in order to obtaina system that is able to detect small stiffness changes. If thepurpose was to have a rapid alarm at the occurrence of an anomaly,the length of the files could be reduced, but the accuracy of theestimates would decrease. A good compromise could be then topresent less accurate natural frequency estimates using shortertime periods, to rapidly detect important and sudden anomalies,and obtain more accurate estimates at the end of each 30 min.

Finally, it is important to state that the configuration of thesystem (e.g. sampling frequency and length of the time segments)and the analysis of parameters used to check the system condition(e.g. quality of the GPS signals, digitizer internal temperature andinput voltage) are performed remotely.

This dynamic monitoring system is complemented by anindependent static monitoring system (performing one or twoacquisitions per hour) that was installed in the bridge duringconstruction [11], and comprises strain gages, clinometers andtemperature sensors. Measurements of the temperature sensorsembedded in the concrete are essential for the developmentof numerical models that extract the effect of temperaturefrom identified natural frequencies. Furthermore, a weather

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Fig. 10. Dataflow inside the monitoring system.

station exists close to the bridge recording all the importantenvironmental variables (air temperature, humidity and windvelocity and direction) whose measures can also be used toinvestigate the possible effect of these variables on the identifiedmodal parameters.

5. Routines for data processing

In the context of a monitoring program, it is very important tohave good tools for continuous processing of data arriving, in orderto permanently extract parameters with physical meaning that canthen be used to evaluate the structure health.

Fig. 10 presents the dataflow inside the monitoring system,highlighting the Matlab routines that are being developed in orderto execute several tasks every 30 min (after the creation of a new30 min duration ASCII file). Routines already implemented includeonline execution of following tasks:

- creation of a database with the original data (sampled at50 Hz) that can be used later to test alternative processingmethodologies;

- pre-processing of the data to eliminate the offset and to reducesampling frequency from 50 to 12.5 Hz (the first 12 modes arebelow 5 Hz);

- processing of the data, with automatic identification of modalparameters;

- creation of a database with processing results;- display of plots with the most relevant results.

Analysis of modal parameter changes with environmentalconditions (e.g. temperature and humidity) has not yet been done,because that study requires several months of measurementsand the system has been working for just two months. Thedefinition of thresholds for damage detection is dependent on theprevious analysis. Routines already developed for the automaticidentification of modal parameters are described in Section 5.1.

Fig. 11 presents the plots created by the software that has beendeveloped for two groups of pre-processed time series associatedwith two distinct periods: during the night under little traffic andduring a rush hour.

5.1. Automatic identification of the modal parameters

Automatic identification of natural frequencies is one of themost important features of a continuous dynamic monitoringsystem, since the success of damage detection algorithms based onthese dynamic parameters is strongly dependent on the accuracyof the estimates. Consequently, much research is being developedon this subject following different approaches. Lau et al. [12]present a literature review on the last developments of themethods that fit a numerical model to data. Brincker et al. [13]present an alternative non-parametric method in the frequencydomain that is an automatic implementation of the FrequencyDomain Decomposition method (FDD– the method applied to thedata collected during the ambient vibration test).

As a first approach to interpret data collected by the monitoringsystem installed, the FDD method was used. Therefore, this methodwas implemented in Matlab to automatically process the timeseries that are created each half an hour. In this paper, the resultsof the first two months of the system operation (from 2007/10/17to 2007/12/17) are presented.

As already mentioned, the first step of the FDD method consistsof the calculation of a spectrum matrix for each data set. In thepresent application, all the sensors were elected as references andso, this is a 12 by 12 matrix (the number of acceleration channelsis equal to 12). The auto and cross spectra of the matrix werecalculated with a resolution of 0.0061 Hz, using segments from thetime series with a total length of 30 min and adopting a Hanningwindow and an overlap of 50%. Then, singular value decompositionof this matrix was performed, producing, for each frequency, 12singular values and vectors.

The graphic of the first singular values as a function of thefrequency allows visual identification of the natural frequencies,which are associated with the peaks. Fig. 12 presents a colourmap that consists of a top view (the colour is a function of the

Fig. 11. Time series after pre-processing, collected during the night and during a rush hour.

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Fig. 12. Colour map with the variation of the signals frequency content over time(from 2007/10/17 to 2007/12/17).

amplitude) of all the first singular values spectra associated toall 30 min intervals of the observation period (from 2007/10/17to 2007/12/17, a total of 48 × 61 = 2928 setups). Thirteenvertical alignments are evident in this figure. They characterizethe evolution of the bridge natural frequencies during the periodunder study. It is also shown that a single picture can be used toprovide an overview of the structure dynamic behaviour during along observation period.

The spectra of the first singular values are the starting pointfor the automatic identification of the natural frequencies. Themethodology adopted was based on the one described in [13] andconsists on the repeated application of the following steps:

- identification of the maximum of the spectra in the searchdomain; at the beginning this is equal to a user predefinedfrequency range;

- selection of the points around the identified peak that lead tosimilar mode shapes (identified from the first singular vectors),using the MAC coefficient [10] as similitude measure;

- if the number of selected of points is larger than a predefinedvalue and if there are points in both sides of the peak, theidentified peak is elected as a natural frequency and the selectedgroup of points is called the modal domain; otherwise, the peakis assumed to be related to data noise (this simple criterion forthe selection of peaks with physical meaning worked very wellin this application, but for the processing of lower quality data amore robust criterion may be required, implying analysis of the“bell” shape);

- redefinition of the frequency search domain by removal of thepreviously selected group of points;

- repetition of these steps in the reduced search domain, untila specified number of identified natural frequencies has beenachieved, the search set is empty or the maximum spectrumamplitude is lower than a eventually predefined noise level.

One of the advantages of this method is the relatively smallnumber of user-defined parameters. These include frequencyresolution, the frequency interval under analysis, the MAC valuelimit of the points in the same modal domain and the minimumnumber of points of the modal domains. The number of expectednatural frequencies and the noise level are optional parametersthat can be used to shorten the number of searches for maxima.In the present application, the analysis was performed over thefrequency range from 0.5 to 4.5 Hz, with a frequency resolutionof 0.0061 Hz (0.8% of the lowest natural frequency). A number of12 natural frequencies was specified for automatic identification, alimit value of 0.4 was selected for the MAC and only modal domainswith more than 7 points were considered.

The specification of frequency resolution is critical. If thevalue is too small (the segments used are longer, the numberof averages is lower), the amount of noise is higher, and soautomatic identification becomes more difficult. On the otherhand, higher values limit the accuracy on the identification ofnatural frequencies.

Experience gained in the analysis of data from this bridgeshowed that it is better to select low values for the MAC (0.4). Inthis way, the number of points in the search domain is reducedmore rapidly and the number of false identifications is minimized.However, it should be pointed out that this strategy is not adequateif the number of sensors is small (the ability of the MAC todistinguish mode shapes increases with the number of sensors)and similar modes shapes for adjacent natural frequencies areexpected. The minimum number of points in the modal domainis obviously related to the MAC limit.

To sum up, it is important to stress that the correct selectionof all the parameters for automatic identification of modalparameters should result from sensitivity tests performed duringan evaluation period.

Fig. 13 illustrates the output of the implemented automaticidentification algorithm applied to one of the time series setscollected during the observation period. The graphic shows thefirst two singular values and the modal domain associated to eachpeak. The colour of the modal domains is dependent on the orderof the natural frequencies identification and the correspondingordinates are the MAC values. It can be noticed that in the vicinitythe 2.2 Hz natural frequency, there are small peaks that wereincluded in the respective modal domain and not identified as

Fig. 13. Automatic identification of natural frequencies in the setup: 2007/11/18 12:00.

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Fig. 14. Identified natural frequencies of the first 12 modes during the period from 2007/10/17 to 2007/12/17.

Fig. 15. Two zooms of Fig. 14 to show the successful identification of closely spaced natural frequencies and variation of the 11th mode natural frequency with dailytemperature oscillations.

new natural frequencies, as it would have happened if a simplealgorithm of peaks selection were used.

Automatic identification of the natural frequencies of all the2928 collected setups allowed the construction of the graphicpresented in Fig. 14, which contains the estimates provided by theindependent analysis of all the datasets. This shows the variationof the first natural frequencies of the bridge during the observationperiod (some blank spaces exist due to maintenance tasks thatwere needed during the first months of the system’s operation).It is clear that the algorithm for automatic modal identificationprovided very good results, as the number of points associatedwith wrong estimates (the ones that are clearly apart from thehorizontal alignments) is quite small.

Moreover, it is possible to eliminate the wrong estimates,considering these points as outliers. In the present application, thepoints outside the interval defined by the average values +/−1.5times the standard deviation were classified as false estimates(outliers). Using this statistic classification, the percentage of falsenatural frequencies estimates is equal to 1.9%.

Fig. 15 presents two zooms of the graphic presented in Fig. 14after elimination of the outliers. It is relevant to observe that themethodology was able to identify the first two closely spacednatural frequencies and the very small changes of the naturalfrequencies of the 11th mode with the oscillation of ambienttemperature. During the monitoring period associated with thepresented zoom, the daily average temperature was about 16 ◦Cand the amplitude of daily temperature variation was around 10 ◦C.The 11th mode is one of the modes that exhibit higher frequencydependency with temperature and, in this case, daily variations ofabout 1% (aprox. 0.04 Hz) were observed.

Table 2 presents the mean values and standard deviationsof natural frequencies estimates provided by the monitoringsystem and compares these values with the ones previouslyobtained with the ambient vibration test. Mean values associatedwith the ambient vibration test are consistently lower. Thisdifference can be explained by the temperature effect, because the

Table 2Natural frequencies identified by the Ambient Vibration Test and by the MonitoringSystem

Modea Ambient Vibration Test Monitoring SystemFrequency (Hz) Std. F. (Hz) Frequency (Hz) Std. F. (Hz)

L1 0.770 0.0011 0.780 0.0027V1 0.810 0.0029 0.825 0.0057V2 1.135 0.0014 1.147 0.0020V3 1.405 0.0013 1.419 0.0033L2 1.734 0.0012 1.755 0.0039V4 1.993 0.0029 2.017 0.0051T1 2.212 0.0025 2.230 0.0046V5 3.013 0.0051 3.049 0.0074L3 3.309 0.0050 3.345 0.0069V6 3.490 0.0052 3.525 0.0069T2 3.734 0.0049 3.769 0.0074V7 4.339 0.0051 4.391 0.0108

a Mode type, defined considering the most relevant components (L– lateralbending; V– vertical bending; T– torsion).

ambient vibration test was performed during the summer (naturalfrequencies decrease with temperature increase), and also byhardening of the concrete during the last 2 years (last pouring–June2002; ambient vibration test – June 2005; monitoring - October–December 2007). On the other hand, the standard deviationsof the estimates provided by the monitoring system for thenatural frequencies are higher than the ones resulting from theambient vibration test, owing to the effect of temperature, whichis obviously more significant during a long observation period.

The mode shapes associated with natural frequencies identifiedby the monitoring system are estimated by the first singularvectors associated with the selected peaks. The average modalordinates of the first 12 modes estimated from all the setupscollected during 2007/12/17 are represented in the complexdomain at Fig. 16 (the vertical and lateral modal ordinates arerepresented in different colours in order to allow the distinctionbetween the different types of modes). All the modal ordinates areover the horizontal axis, meaning that all the mode shapes are real.

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Fig. 16. First 12 mode shapes identified with the continuous monitoring system using the time series collected during 2007/12/17, and means and minima of the MACratios between the plotted modes and all the modes identified in the period between 2007/10/17 and 2007/12/17. Lateral modal ordinates represented in red; verticalmodal ordinates represented in blue.(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 17. Comparison between the mode shapes identified with the ambient vibration test and with the continuous monitoring system using the time series collected during2007/12/17.

These results prove the quality of the identified modal parametersand show good synchronization of the digitizers provided by theGPS sensors (an imperfect synchronization would lead to phaseangles different from 0 or 180 between the degrees of freedommeasured by different digitizers).

The mode shapes plotted were compared with the mode shapesidentified from all the data sets collected during the monitoringperiod under analysis, using the MAC ratio. Fig. 16 also presents theaverage MAC values and the minima MAC values that resulted fromthis comparison. The mean values are always greater than 0.99 andthe minima values are always above 0.8, showing that the modeshapes estimated during the first two months of monitoring arevery consistent.

Direct comparison between the mode shapes provided by theambient vibration test (represented in Figs. 5–7) and the onesestimated by the monitoring system is not possible, becausethe measured degrees of freedom are not exactly the same.However, the overlay of both estimates shows that they are verysimilar. Fig. 17 presents such comparison for the first four modeshapes.

The main limitations of the described procedure for theautomatic identification of modal parameters are the accuracy ofthe natural frequencies estimates dependency on the frequencyresolution and the inadequacy to estimate modal damping ratios.It is possible to obtain estimates for these coefficients, fromauto-correlation function resulting from the inverse Fast FourierTransforms of the points of the selected modal domains, by thefitting of exponential decays to the envelopes of those functions.However, the quality of this fitting relies on the adequacy of theselected interval and this task is not easy to automate. Limitedfrequency resolution prevents the observation of temperatureeffects on lower frequencies, as very low variations are expected.

6. Conclusions

This paper presents the experimental and numerical workdeveloped before setting up a continuous dynamic monitoringsystem in a long span concrete arch bridge, characterises theinstalled monitoring equipment and shows the most relevantresults provided by the application of the routines implemented,to the data collected during the first 2 months of monitoring.

3044 F. Magalhães et al. / Engineering Structures 30 (2008) 3034–3044

A preliminary ambient vibration test was essential for thedesign of the monitoring system, especially for the selection ofmeasuring points, and for calibration of the developed numericalmodel. The latter is an important basis to simulate damagescenarios in order to test the feasibility of application of vibrationbased damage detection techniques. The numerical model was alsofundamental to understand the strong effect of the bridge supportson its dynamic properties.

The Matlab routines developed to perform on-line processing ofthe data continuously transmitted through the Internet proved tobe very efficient and robust. In fact, they allowed fully automaticidentification of the bridge’s first 12 resonant frequencies witha very small number of false identifications. This unique featurewas only possible because high-quality acquisition equipment wascombined with state of the art processing algorithms, after anevaluation period necessary to specify the parameters required bythe automatic identification procedure.

The automatic version of the Frequency Domain Decompositionmethod showed also ability to identify closely spaced modes (as itis the case of the bridge first two modes) and to detect very smallfrequency variations (aprox. 0.04 Hz) motivated by the oscillationof air temperature.

As a future system enhancement, implementation of an alterna-tive procedure for automatic identification of natural frequenciesbased on the SSI–COV method is now under development. Thesenew routines will certainly allow an even more accurate identifi-cation of the natural frequencies and also identification of modaldamping ratios.

The results presented are related with a relatively short periodof observation; the next months of operation will be surely veryuseful to confirm the efficiency of the routines developed andto create a database for the development of numerical modelsto extract the influence of environmental variables and of trafficintensity (if relevant) on the identified modal parameters.

Acknowledgments

The authors would like to acknowledge: (1) all the supportsprovided by the Portuguese Foundation for Science and Technology(FCT) to ViBest/FEUP for the development of research in thearea of Long-Term Dynamic Monitoring; (2) the Ph.D. Scholarship(SFRH/BD/24423/2005) provided by FCT to the first author; (3) thesupport provided by the bridge designer, Prof. Adão da Fonseca,and the bridge owner, Metro do Porto.

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