IMPLEMENTATION OF A DYNAMIC MONITORING SYSTEM AT COIMBRA FOOTBRIDGE 1
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Carlos Moutinho , Wei-Hua Hu ,Elsa Caetano & Álvaro Cunha 2 3 4 1 Assistant, Student, Associate Professor, Full Professor Faculty of Engineering of University of Porto (FEUP), Rua Dr. Roberto Frias, 4200 Porto, Portugal E-mail:
[email protected]; Website: www.fe.up.pt/vibest.
1.
ABSTRACT
Coimbra footbridge is a new structure that connects both banks of Mondego River. Preliminary studies conducted during design stage indicated some vulnerability to vibrations induced by pedestrians, both for lateral and vertical directions. As result, it was decided to install Tuned Mass Dampers in 5 different sections of the deck, as well as a dynamic monitoring system to evaluate the vibration levels observed in the footbridge during a period of one year after construction. This paper describes the architecture of the monitoring system, the type of results permanently displayed in a web site specially developed for this application, and some additional software created with the purpose of analysing and reporting the information collected along periods of several months.
2. INTRODUCTION The new footbridge Pedro and Inês over Mondego River, at Coimbra, is located in the centre of the City Park recently developed along the two banks of the river. This new infrastructure, conceived to become a landmark for the city and to contribute to the quality of a new leisure area, was designed by Adão da Fonseca [1], leading a team from AFAssociados, in collaboration with Cecil Balmond, leading the architectural team from Ove Arup. The bridge has a total length of 275m and is formed by a parabolic central arch with a span of 110m and two half lateral arches, in steel, supporting with total continuity a composite steel-concrete deck (Figure 1). The anti-symmetry of both arch and deck cross-sections along the longitudinal axis of the bridge is a unique feature of this bridge, leading to the creation of a central square with 8mx8m at mid-span.
Figure 1: Lateral view of the new Coimbra footbridge.
Preliminary dynamic studies developed by the bridge designers indicated that the bridge would be prone to vibrations induced by pedestrians, requiring control devices. A detailed numerical study was then developed by the Laboratory of Vibration and Monitoring (ViBest – www.fe.up.pt/vibest) from the Faculty of Engineering of the
University of Porto (FEUP) to better characterize the dynamic behavior of the bridge under pedestrian loads and evaluate the required control measures [2]. This study showed not only that the first lateral mode is critical, owing to the proximity between its estimated natural frequency and the frequency of lateral excitation induced by walking pedestrians, but also that significant levels of vibration may occur when some vertical vibration modes are excited. Therefore, the addition of several tuned mass dampers (TMDs) was proposed. It is well known that the optimal characteristics of TMDs depend very much on the real modal parameters of the bridge. So, the development of dynamic tests at the end of the bridge construction was essential to provide accurate estimates of the modal parameters of the real constructed bridge, enabling the updating of the finite element modeling and the final design of the TMDs. After installation of the TMDs, additional dynamic tests were also performed by ViBest/FEUP in order to accurately identify the dynamic properties of the controlled structure and the efficiency of the control devices employed. In particular, forced vibrations tests were developed so as to identify the dynamic characteristics of each unit of the TMD used to control the critical lateral mode. At last, a dynamic monitoring system was installed by ViBest/FEUP aiming the permanent characterization of vibration levels in the footbridge during one year after construction, and allowing the remote access to collected data through the Internet. This paper describes the architecture of the monitoring system implemented, the type of results permanently displayed in a web site for this application, and some additional software created with the purpose of analysing and reporting the information collected along periods of several months.
Figure 2: View of Pedro and Inês footbridge
3. DESCRIPTION OF THE BRIDGE The bridge is a slender structure with a length of 275m and a width of 4m, except in the central square with dimensions of 8mx8m (Figure 3). The metallic arch spans 110m and rises 9m and has a rectangular box crosssection with 1.35m x 1.80m. The deck has a L-shaped box cross-section with its top flange formed by a composite steel-concrete slab 0.11m thick (Figure 4). In the central part of the bridge, each L-shaped box cross-section and corresponding arch “meet” to form a rectangular box cross-section 8m x 0.90m. In the lateral spans, arch and deck generate a rectangular box cross-section 4m x 0.90m. The significant slenderness of the bridge and the geometric characteristics lead to a complex structural behaviour. Beyond that, the arch foundations are formed by vertical piles 35m deep, which cross soil layers of poor quality, providing an elastic support condition. Therefore the bridge has an intermediate structural behaviour between an arch and a girder.
Figure 3: Plan and lateral views of Pedro and Inês Bridge
Figure 4. Cross section at the central square and at an intermediate position of the arch
The preliminary design of the control devices suggested the adoption of a maximum number of 8 TMDs, placed at the positions defined in Figure 5. The lateral TMD, located at mid span, is crucial to control the first lateral mode, while the others are positioned at the anti-nodes of vertical modes that can also be excited by pedestrians. This preliminary design was very important to prepare the bridge to accommodate the TMD masses since the beginning of the construction.
Figure 5: Location of the TMDs suggested in the preliminary design (7 vertical and 1 lateral at mid-span).
4. EXPERIMENTAL CHARACTERIZATION OF THE BRIDGE The experimental characterization of the bridge was done based on ambient and free vibration tests [3], whose main results are summarized in reference [4]. The ambient vibration test allowed the identification of a high number of natural frequencies and modes of vibration, whereas the free vibration tests permitted to obtain high accuracy estimates of damping ratios associated to the most important modes of vibration. The ambient vibration test was developed in April 2006, based on the use of four high sensitivity seismographs, including a triaxial force-balance accelerometer and a 18-bit A/D converter, duly synchronized through external GPS sensors. The 20 sections indicated in Figure 6 were instrumented, performing measurements upstream and downstream at sections 9, 10 and 11, and measurements along the central line of the deck at the remaining sections.
Knowing that several vertical modes of vibration were of local nature, and aiming to identify as many modes as possible, three of the measurement units were used as references, permanently located at sections 1, 6 and 8, while the fourth one was successively placed at the remaining measurement points. Acceleration time series with 16-minute duration were recorded at 100Hz sampling rate for each setup. The natural frequencies and modes of vibration were evaluated using the Frequency Domain Decomposition (FDD) method.
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Figure 6: Instrumented sections at the ambient vibration test
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Mode 1: fexp=0.91Hz; fnum=0.93Hz
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Figure 7: Examples of identified and calculated modes of vibration
Table 1 summarizes the values of identified natural frequencies associated with twelve out of the fourteen lower modes of vibration, in the interval 0-4.3Hz. The characteristics of the modes of vibration are indicated in correspondence, as well as the values of the frequencies obtained after updating the finite element model. Note that these frequencies do not correspond to the final stage of construction, but to a situation prior to installation of the timber pavement and of the glass panels of the handrails, and were appropriately considered in the numerical modelling, for the purpose of comparison with measured values, by changing of mass. Figure 7 shows the transversal (t) and vertical (v) components of the first identified modes of vibration, which are also compared with
the corresponding calculated components. It is observed that this excellent correlation could be only achieved based on the development of an entirely new numerical model, using a very refined mesh of shell finite elements reproducing the bridge geometry. In this model all the openings in the deck were modelled and the transversal stiffening elements were included by equivalent beam elements, the stiffening constants of the springs at the foundations of the arches having been iteratively adjusted [5].
Table 1: Calculated and identified modal parameters (timber pavement and glass panels not installed yet) Mode number
Calculated frequency (Hz)
Measured frequency (Hz)
Damping ratio (%)
Modal shape
1 2 3 4 5 6 7 8 9 10 11 12 13 14
0.93 1.55 1.97 1.99 2.15 2.48 2.93 2.98 3.07 3.34 3.62 4.21 4.26 4.29
0.91 1.54 1.95 1.88 2.05 2.54 2.88
0.58 0.53 1.04
transversal vertical/ transv. vertical vertical transversal vertical transversal vertical vertical vertical vertical vertical vertical/ torsion vertical/ torsion
1.90 0.90 0.28 0.38 0.86
3.36 3.57 3.83 4.44 4.28
The free vibration tests consisted of the sudden release of masses suspended from different points of deck, whose location was chosen so as to stimulate the most relevant modes of vibration. The sudden release of the masses causes impulsive forces that induce free decays from which estimates of modal damping ratios can be obtained. The structural response was measured at points 1,6, 8 and 10 indicated in Figure 6, based on the seismographs previously used at the ambient vibration test. Figure 8 shows the apparatus used to release a mass of 3t inducing a lateral impulsive load, as well as an acceleration time series recorded in that direction, at mid-span, which allowed to obtain an estimate of 0.55% for the modal ratio of the lateral mode shape with a frequency of 0.9Hz. Table 1 summarizes the mean values of the modal damping ratios identified on the basis of the free vibration tests, which are particularly low, of about 0.5% 0.6% for the first two modes of vibration with lateral components.
Acceleration (m/s2)
18/4/2006: Release of mass for lateral excitation (máx: 0.075m/s2; x=0.55%)
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Figure 8: Sudden lateral mass release at mid-span
With the purpose of analysing experimentally the lateral behaviour of the bridge, a test was developed during which the bridge response was measured to the action of a continuous stream of pedestrians with a gradually
increasing number to a maximum of 145 persons. The test was possible due to the gentle participation of students from the Universities of Porto and Coimbra. These students walked freely along the bridge between points 5 and 15 indicated in Figure 6. Figures 9 and 10 show the envelopes of the measured lateral accelerations at mid-span along the time and the variation of the maximum lateral acceleration with the number of pedestrians on the bridge, 2 respectively. At that section, extreme values of acceleration of ±1.2 m/s , and of displacement of ±4 cm, were recorded when 145 pedestrians were walking on the bridge. Figure 10 shows that the increase of acceleration with the number of pedestrians on the bridge is not linear, but instead exhibits a “jump” precisely for values of the number of pedestrians close to 70, which is coherent with the estimate provided by the Dallard formula (73 pedestrians) developed in the context of the studies on the Millennium Bridge, in London, [6], which enables to estimate the critical number of pedestrians above which significant lateral oscillations may occur in a bridge deck with a lateral frequency of about 1Hz.
Aceleração (g)
Envolvente da aceleração lateral na secção 10
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Figure 9: Envelope of lateral acceleration at section 10
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Figure 10: Variation of the amplitude of lateral accelerations at mid-span with the number of pedestrians
5.
SYSTEM FOR CONTROL OF VIBRATIONS
The design of the TMDs needed to control the critical modes, susceptible to be excited in resonance by pedestrians, leading to levels of vertical or lateral acceleration above some acceptable limit, was based on the studies of Bachmann and Weber [7], and involved the definition of the mass of the mechanical system, mT, usually in the range 1-10 % of the corresponding modal mass, followed by the evaluation of the stiffness and damping constants, kT and cT, of the spring and the linear viscous damper that form the TMD, respectively. These constants should have an optimum value, defined so as to equalize the amplitudes of the peaks of the frequency response function, expressed in terms of displacements, of the 2-DOF system in which it is transformed the SDOF system idealized on the basis of the characteristics of the mode of vibration to be tuned: mass MH, stiffness KH and damping constant CH. Thus, the choice of the mass of the TMD determines the damping achieved by the new 2-DOF system formed by addition of the TMD to the structural system idealized as a 1-DOF based on the vibration mode to be controlled.
This aspect is particularly relevant in terms of the control of the first lateral mode, which could be responsible by a lock-in phenomenon during the passage of a continuous flow of pedestrians. In this case, assuming the validity of formula developed by Dallard et al. [6], it is possible to fix the number of pedestrians for which lock-in should not occur, which leads to an estimate of damping that the control solution based on TMDs should introduce. Table 2 2 shows the results obtained, assuming human densities of 1.0, 1.3 and 1.5 pedestrians/ m , and considering or not 2 the influence of the mass of pedestrians on the modal mass. In the first situation (1.0 pedestrians/ m ), which would require 560 pedestrians on the bridge, the concentration of people leads already to some constrain on the 2 movement. In the last case (1.5 pedestrians/ m ), that will only occur on very exceptional occasions, the pedestrian movement becomes extremely difficult, and so the occurrence of lock-in is also very much constrained. Taking into account the dimensions of the bridge, it is considered that the first situation has already exceptional nature. However, the value of 6% was adopted as the value of damping ratio to achieve after installation of a TMD tuned for this lateral mode of vibration. Considering the necessity to accommodate the TMD inside the midspan section (antinode of this critical mode), corresponding to a box girder of 8mx0.90m, divided internally by transversal beams, it was necessary to subdivide the TMD in several units with equal characteristics, each of them having a mass of 2465kg (Figure 11).
Table 2: Required damping to avoid lock-in
Pedestrian density 2 (people/m )
Number of pedestrians
Required damping ξ(%)
1.0 1.3 1.5
560 730 845
3.7 – 4.0 4.8 – 5.2 5.6 – 6.1
Figure 11: Horizontal TMD installed at the midspan section
The option to install 6 units, with a total mass of 14970kg, corresponding to a mass ratio μ = m T M H x100 = 7.3% , was dictated by the Designer and provides a minimum theoretical damping of 7.8%.
This option stems essentially from the knowledge of the sensitivity of the TMDs with regard to the achieved frequency tuning. In effect, a slight deviation of the frequency of the TMD with regard to the optimum value determined by the frequency of the mode to be controlled leads to a significant loss of efficiency of the TMD. This deviation can be induced either by the change of material properties, or simply by effect of the pedestrian loading, as in light footbridges the mass of pedestrians can represent a relatively important parcel of the total mass [8]. It’s worth noting that the control of horizontal vibrations based on a TMD is substantially more complex than the control of vertical vibrations, as the horizontal oscillation of the mass of the TMD requires the sliding along two rods, which must be conceived so as to mobilize the minimum friction force and installed with accurate levelling. As total elimination of friction forces is not feasible, it is understandable that the activation of the TMD for horizontal vibrations is not instantaneous, but it just takes place for certain levels of structural vibration. On the
contrary, in vertical TMDs, the friction forces in the rods are rapidly overcome with a slight oscillation of the mass of the TMD and the corresponding activation is almost instantaneous. Therefore, in the specific case of horizontal vibrations, it is important to guarantee that the activation of the TMDs 2 is achieved for accelerations below the comfort limit, of about 0.1m/s . With regard to the structure, in a real situation, an intermittent activation of the TMD occurs and so the bridge exhibits a variation of dynamic properties. This effect can be observed in the record captured at bridge midspan 2 when crossed by a group of 140 people (Figure 12), in which a maximum acceleration of 0.067m/s and a maximum lateral displacement of 2.8mm were observed. Although the pedestrians were not uniformly distributed, this record shows that, close to the instant 100s, there is a clear attenuation of the response, meaning the activation of the TMD and a change of frequency, which leads to a beating phenomenon and a reduction of the response. Subsequently, the TMD is again de-activated by the instant 170s, originating a new amplification of the response and progressive attenuation, as consequence of gradual unloading.
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30/9/2006: Crossing by 140 persons 0.004 0.003 0.002 0.001 0 -0.001 -0.002 -0.003 -0.004 0
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Figure 12: Intermittent activation of the lateral TMD units under the passage of a group of pedestrians
6.
LONG-TERM DYNAMIC MONITORING SYSTEM
With the purpose of permanently monitoring the dynamic response of the footbridge during 12 months after construction and detect eventual episodes of excessive vibration, the bridge was instrumented with 6 uniaxial piezoelectric accelerometers installed in correspondence with the location of the TMDs, which were implemented at the antinodes of the critical vibration modes. Five of these accelerometers measure vertical accelerations, whereas another one measures lateral vibrations at mid-span (Figure 13). These sensors are installed inside the metallic deck and are wired to an acquisition system located inside one of the concrete abutments of the structure. Figure 14 shows a photo of that place, where some boxes containing the equipments related with the dynamic and static monitoring of the footbridge can be observed, as well as the equipments for data communication. By this means, the equipments are protected against some undesirable external environment like humidity and dust, and at same time the level of security against vandalism is increased.
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Figure 13: Location of the accelerometers (left); Accelerometer used to measure lateral accelerations at midspan (right)
The acquisition system used for the dynamic monitoring of the footbridge is composed by a signal conditioner, a digital computer incorporating an analogue-digital conversion board and a UPS system (Figure 13). The signal conditioner amplifies the signal from the accelerometers integrated in a ICP circuit and performs some basic signal processing like analogue filtering. The data acquisition is carried out by an A/D card fitted in a digital computer based on software developed with LabVIEW from National Instruments. The UPS improves the
performance of the monitoring system by stabilizing the electrical power and covering some eventual gaps in power supply. The equipments are prepared to face prolonged loss of electrical power by the switching of some automatic shutdown mechanisms complemented by the automatic restart in the case of normalization of the situation. Beyond that, there is also a communication system responsible to transmit data to FEUP using an ADSL line. This communication system sends permanently to computer located at FEUP the most recent data to be processed, which makes possible the virtually on-line monitoring of the structure.
Figure 14: General view of the monitoring system (left); Signal conditioner, digital computer and UPS (right) The basic architecture of the whole monitoring system is schematically illustrated in Figure 15, which divides this system in three distinct modules corresponding to the different stages of the monitoring process. The first module involves the signal acquisition and conditioning at the Coimbra footbridge and the respective storage in a local database. It is important to combine these components because, in case of a communication failure, the data acquisition system keeps collecting signals to the local database. After the reestablishment of the communications, the data corresponding to that period is transmitted to FEUP in such way that there is no data loss during this anomaly. The second module of the monitoring system includes all the operations related with signal processing carried out at FEUP. After transmission from the footbridge site, the signals are organized in a main database which can be accessed at any time by some post-processing tools. In order to satisfy the main objective of this monitoring system, a web site was developed which allows the visualization of the time signals of the six accelerometers and subsequently the monitoring of the vibration levels of the structure (Figure 16). In addition, some spectral analysis routines are available, which involve the calculation of the Average Normalized Power Spectrum Densities (ANPSD), in order to evaluate the frequency content of the signals. The corresponding graphics also allow to clearly identify the most relevant natural frequencies of the structure.
Figure 15: Schematic representation of the architecture of the monitoring system
Figure 16: Web site to access the measured acceleration time series and corresponding Fourier spectra
7.
AUTOMATIC ANALYSIS AND VISUALIZATION OF MEASURED DATA DURING LONG PERIODS
In order to enable an automatic and users friendly procedure to observe and interpret the very significant amount of data collected along several months, two other toolkits were developed in LabView. The first one is the Automatic Analysis Toolkit, which allows the systematic processing of all the date captured in each month along successive periods of 20 minutes. By analysing and processing each file corresponding to such measurement period, this toolkit enables: •
The elimination of spurious spikes in the signal, based on a wavelet analysis technique [9];
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The detection and evaluation of peak acceleration values related with the lateral and vertical vibration of the footbridge;
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The evaluation of mean maximum values of acceleration in successive short periods of duration (e.g. 5 seconds);
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The representation of all time series in the frequency domain, by application of FFTs;
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The statistical characterization of all data captured during each day or each month;
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The automatic identification of the first natural frequencies, mode shapes and modal damping ratios, based on the Peak-Picking (PP), Enhanced Frequency Domain Decomposition (EFDD) or Covariancedriven Stochastic Subspace Identification (SSI-COV) methods;
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To plot waterfall diagrams to detect eventual variations of natural frequencies during one day or one month;
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To save all the analysis results, including data and plots, both in time and frequency domains, in a complex database in a server computer.
Figure 17: Maximum vertical (left) and lateral (right) accelerations measured during the month of June 2007 (mean peak values in periods of 5 seconds)
Figure 18: Record corresponding to the maximum vertical acceleration measured in June 2007 (left, 1 June); Mean maximum values evaluated in successive periods of 5 seconds (right)
Figure 19: Record corresponding to the maximum lateral acceleration measured in June 2007 (left, 15 June); Mean maximum values evaluated in successive periods of 5 seconds (right)
Figure 20: Maximum vertical accelerations measured in each channel on 22 July 2007
The second toolkit is the Result Viewer Toolkit, which enables the easy visualization of all results and plots by simply pressing buttons. This result viewer system can also be published in the web, allowing the access through the Internet. Figures 17-20 show some of the plots obtained with these toolkits in order to get an overview of the whole data acquired during the months of June and July 2007. Inspection of these results shows that the limit level of lateral 2 acceleration to avoid lock-in, assumed as 0.1m/s , was never reached, and that the situation is more comfortable with regard to vertical accelerations.
8.
CONCLUSIONS
This paper presents a short description of Pedro and Inês footbridge, of the dynamic tests performed to evaluate its dynamic characteristics after construction, of the passive control system designed and installed to attenuate lateral and vertical vibrations, and describes in particular the architecture of the monitoring system implemented and the type of results permanently displayed in a web site for this application, and some additional software created in LabView with the purpose of analysing and reporting the information collected along periods of several months. This monitoring system is now in a stabilized stage of development, enabling a virtually real time inspection of the dynamic behaviour of the bridge through the Internet. A systematic analysis of all data acquired during 2 months (June and July 2007) shows that the maximum lateral 2 accelerations don’t exceed the limit of 0.1m/s associated to the lock-in phenomenon. With regard to vertical vibrations, the situation is more comfortable.
9.
REFERENCES
[1] A. Adão da Fonseca and Cecil Balmond - Conceptual design of a footbridge over river Mondego, Coimbra, Footbridge 2005, Venice, Italy, 2005 [2] E. Caetano, A. Cunha, A. Adão da Fonseca, R. Bastos and A. Adão da Fonseca Jr - Assessment and Control of Human Induced Vibrations in the New Coimbra Footbridge, Footbridge 2005, Venice, Italy, 2005 [3] Magalhães, F., Caetano, E. & Cunha, A. - Ensaios dinâmicos da ponte pedonal e de ciclovia sobre o rio Mondego, VIBEST Report (in Portuguese), FEUP (Confidential), 2006 [4] Magalhães, F., Cunha, A. & Caetano, E. - Dynamic testing of the new Coimbra footbridge before implementation of control devices, XXV IMAC, International Modal Analysis Conference, Orlando, Florida, SEM, 2007 [5] Caetano, E., Cunha, A. - Estudos dinâmicos para avaliação das características dos TMDs da ponte pedonal e de ciclovia sobre o rio Mondego, VIBEST Report (in Portuguese), FEUP (Confidential), 2006 [6] Dallard, P. et al – the London Millennium Footbridge, The Structural Engineer, Vol 79, No 22, 2001 [7] Bachmann, H. et al. - Vibration Problems in Structures: Practical Guidelines, Birkhäuser Verlag, Basel, 234pp., 1995 [8] Caetano, E., Cunha, A. and Moutinho, C. - Implementation of passive devices for vibration control at Coimbra footbridge, Int. Conf. on Experimental Vibration Analysis for Civil Engineering Structures, EVACES'07, Porto, Portugal, 2007 [9] Goring, D.G. and Nikora, V.I. – Despiking acoustic Doppler velocimeter data, Journal of Hydraulic Engineering, Vol.128(1), 117-126, 2002
