Damage Identification on the Tilff Bridge by Vibration Monitoring Using Optical Fiber Strain Sensors

Vibration testing is a well-known practice for damage identification of civil engineering structures. The real modal parameters of a structure can be determined from the data obtained by tests using system identification methods. By comparing these measured modal parameters with the modal parameters of a numerical model of the same structure in undamaged condition, damage detection, localization, and quantification is possible. This paper presents a real-life application of this technique to assess the structural health of the 50-year old bridge of Tilff, a prestressed three-cell box-girder concrete bridge with variable height. A complete ambient vibration survey comprising both vertical accelerations and axial strains has been carried out. The in situ use of optical fiber strain sensors for the direct measurement of modal strains is an original contribution of this work. It is a big step forward in the exploration of modal curvatures for damage identification because the accuracy in calculating the modal curvatures is substantially improved by directly measuring modal strains rather than deriving the modal curvatures from acceleration measurements. From the ambient vibrations, natural frequencies, damping factors, modal displacements and modal curvatures are extracted by the stochastic subspace identification method. These modal parameters are used for damage identification which is performed by the updating of a finite element model of the intact structure. The obtained results are then compared to the inspections performed on the bridge.     

Finite-Element Analysis and Vibration Testing of a Two-Span Masonry Arch Bridge

This paper presents the analytical modeling, modal testing, and finite-element model updating for a two-span masonry arch bridge. An Ottoman masonry arch bridge built in the 19th century and located at Camlihemsin, Rize, Turkey is selected as an example. Analytical modal analysis is performed on the developed 3D finite-element model of the bridge to obtain dynamic characteristics. The ambient vibration tests are conducted under natural excitation such as human walking. The operational modal analysis is carried out using peak picking method in the frequency domain and stochastic subspace identification method in the time domain, and dynamic characteristics (natural frequencies, mode shapes, and damping ratios) are determined experimentally. Finite-element model of the bridge is updated to minimize the differences between analytically and experimentally estimated dynamic characteristics by changing boundary conditions. At the end of the study, maximum differences in the natural frequencies are reduced on average from 18 to 7% and a good agreement is found between analytical and experimental dynamic characteristics after finite-element model updating.     

Modal Testing, Finite-Element Model Updating, and Dynamic Analysis of an Arch Type Steel Footbridge

This paper describes an arch type steel footbridge, its analytical modeling, modal testing, finite-element model updating, and dynamic analysis. A modern steel footbridge which has an arch type structural system and is located on the Karadeniz coast road in Trabzon, Turkey is selected as an application. An analytical modal analysis is performed on the developed three-dimensional finite-element model of footbridge to provide analytical frequencies and mode shapes. Field ambient vibration tests on the footbridge deck under natural excitation such as human walking and traffic loads are conducted. The output-only modal parameter identification is carried out by using peak picking of the average normalized power spectral densities in the frequency domain and stochastic subspace identification in the time domain, and dynamic characteristics such as natural frequencies, mode shapes, and damping ratios are determined. The finite-element model of the footbridge is updated to minimize the differences between analytically and experimentally estimated modal properties by changing some uncertain modeling parameters such as material properties. Dynamic analyses of the footbridge before and after finite-element model updating are performed using the 1992 Erzincan earthquake record. At the end of the study, maximum differences in the natural frequencies are reduced from 22 to only 5% and good agreement is found between analytical and experimental dynamic characteristics such as natural frequencies and mode shapes by model updating. Also, maximum displacements and principal stresses before and after model updating are compared with each other.     

Geometrically Nonlinear Buffeting Response of a Cable-Stayed Bridge

A geometrically nonlinear buffeting analysis of a cable-stayed bridge in the time domain is described. The bridge structure is modeled with three-dimensional thin-walled beam elements and three-dimensional elastic catenary cable elements. Spatially correlated wind velocity fluctuations are modeled and simulated using an algorithm for generating sample functions of a stationary, multivariate stochastic process according to its prescribed cross-spectral density matrix. Aerodynamic damping and aerodynamic stiffness are formulated based on experimentally determined flutter derivatives. The focus of this paper is on the effect of fluctuating components of the spatially correlated wind velocity on the geometrically nonlinear buffeting response for an 870 m cable-stayed bridge.     

Identification of Natural Frequencies and Dampings of In Situ Tall Buildings Using Ambient Wind Vibration Data

An accurate prediction for the response of tall buildings subject to strong wind gusts or earthquakes requires the information of in situ dynamic properties of the building, including natural frequencies and damping ratios. This paper presents a method of identifying natural frequencies and damping ratios of in situ tall buildings using ambient wind vibration data. Our approach is based on the empirical mode decomposition (EMD) method, the random decrement technique (RDT), and the Hilbert–Huang transform. Our method requires only one acceleration sensor. The noisy measurement of the building acceleration is first processed through the EMD method to determine the response of each mode. Then, RDT is used to obtain the free vibration modal response. Finally, the Hilbert transform is applied to each free vibration modal response to identify natural frequencies and damping ratios of in situ tall buildings. The application of the proposed methodology is demonstrated in detail using simulated response data of a 76-story benchmark building polluted by noise. Both the along-wind and across-wind vibration measurements have been illustrated. Simulation results demonstrate that the accuracy of the proposed method in identifying natural frequencies and damping ratios is remarkable. The methodology proposed herein provides a new and effective tool for the parametric identification of in situ tall buildings.     

Dynamic Field Test, System Identification, and Modal Validation of an RC Minaret: Preprocessing and Postprocessing the Wind-Induced Ambient Vibration Data

The investigation of dynamic response for civil engineering structures largely depends on a detailed understanding of their dynamic characteristics, such as the natural frequencies, mode shapes, and modal damping ratios. Dynamic characteristics of structures may be obtained numerically and experimentally. The finite-element method is widely used to model structural systems numerically. However, there are some uncertainties in numerical models. Material properties and boundary conditions may not be modeled correctly. There may be some microcracks in the structures, and these cracks may directly affect the modeling parameters. Modal testing gives correct uncertain modeling parameters that lead to better predictions of the dynamic behavior of a target structure. Therefore, dynamic behavior of special structures, such as minarets, should be determined with ambient vibration tests. The vibration test results may be used to update numerical models and to detect microcracks distributed along the structure. The operational modal analysis procedure consists of several phases. First, vibration tests are carried out, spectral functions are produced from raw measured acceleration records, dynamic characteristics are determined by analyzing processed spectral functions, and finally analytical models are calibrated or updated depending on experimental analysis results. In this study, an ambient vibration test is conducted on the minaret under natural excitations, such as wind effects and human movement. The dynamic response of the minaret is measured through an array of four trixial force-balanced accelerometers deployed along the whole length of the minaret. The raw measured data obtained from ambient vibration testing are analyzed with the SignalCAD program, which was developed in MATLAB. The employed system identification procedures are based on output-only measurements because the forcing functions are not available during ambient vibration tests. The ModalCAD program developed in MATLAB is used for dynamic characteristic identification. A three-dimensional model of the minaret is constructed, and its modal analysis is performed to obtain analytical frequencies and mode shapes by using the ANSYS finite-element program. The obtained system identification results have very good agreement, thus providing a reliable set of identified modal properties (natural frequencies, damping ratios, and mode shapes) of the structure, which can be used to calibrate finite-element models and as a baseline in health monitoring studies.     

Control of Wind-Induced Self-Excited Oscillations by Transfer of Internal Energy to Higher Modes of Vibration. I: Analysis in Two Degrees of Freedom

This paper and its companion paper present a new remedy to control wind-induced self-excited oscillation of long and flexible structures with low-internal damping, such as stay cables in cable-stayed bridges. A simple magnetic or mechanical device is used to disturb the cable motion in the lower modes of vibration and thus to transfer a portion of the internal energy of the system from the lower modes to higher modes. Because higher modes generally have high-positive aerodynamic damping when lower modes are excited by wind, the transferred energy is dissipated during the decay of high-frequency vibration. The present paper aims at capturing the fundamentals of energy transfer and dissipation through a detailed theoretical analysis based on a simplified model: A two-degree-of-freedom system with galloping-type self-exciting wind forces. The efficiency to reduce the amplitude of oscillation with a passive device and two types of semiactive devices is demonstrated using energy considerations. Results of numerical simulations are also presented.     

Vibration Control of Stay Cables of the Shandong Binzhou Yellow River Highway Bridge Using Magnetorheological Fluid Dampers

The Shandong Binzhou Yellow River Highway Bridge is a three-tower, cable-stayed bridge in Shandong Province, China. Because the stay cables are prone to vibration, 40 magnetorheological (MR) fluid dampers were attached to the 20 longest cables of this bridge to suppress possible vibration. An innovative control algorithm for active and semiactive control of mass-distributed dynamic systems, e.g., stay cables, was proposed. The frequencies and modal damping ratios of the unimpeded tested cable were identified through an ambient vibration test and free vibration tests, respectively. Subsequently, a series of field tests were carried out to investigate the control efficacy of the free cable vibrations achieved by semiactive MR dampers, “Passive-off” MR dampers and “Passive-on” MR dampers. The first three modal damping ratios of the cable incorporated with the MR dampers were also identified from the in situ experiments. The field experiment results indicated that the semiactive MR dampers can provide significantly greater supplemental damping for the cable than either the Passive-off or the Passive-on MR dampers because of the pseudonegative stiffness generated by the semiactive MR dampers.     

Ambient Vibration of Long-Span Cable-Stayed Bridge

The investigation of dynamic response for long-span cable-stayed bridges largely depends on a detailed understanding of their dynamic characteristics, such as the natural frequencies, mode shapes, and modal damping ratios. In this paper, the dynamic characteristics of a fairly long cable-stayed bridge in Hong Kong are studied using finite-element analysis and ambient vibration measurements. A three-dimensional finite-element model is first established for the bridge based on design drawings. The dynamic characteristics are then analyzed from the statically deformed configuration. Ambient vibration measurements are also conducted to obtain the dynamic characteristics of the bridge. Comparison between these two results shows that, for the most part, a total of 31 modes can be correlated with a reasonable agreement. However, the frequency differences of the higher modes can range between 15 and 30%. This implies that, if the measurement is more reliable, a finite-element model updating is necessary in order to achieve better correlation between these two results.     

Modal Identification through Ambient Vibration: Comparative Study

An analytical comparison between three techniques for the identification of modal properties of structures when subjected to ambient vibrations is performed. The algorithms examined include the eigensystem realization algorithm with data correlations, the prediction error method through least squares, and the stochastic subspace identification (SSI) technique. Both analytical and experimental data from a four-storey building scaled at 1:3 are used to perform these evaluations. The level of noise added to the simulated data is varied to study the robustness of the techniques. All techniques are fully automated, allowing for assessments to be conducted through Monte Carlo simulations. The results indicate that the SSI technique provides the most accurate identification of natural frequencies and mode shapes even with high noise levels, all while requiring the least amount of experience for implementation.     

Combined Experimental-Operational Modal Testing of Footbridges

In combined vibration testing, an artificial, measured force is used in operational conditions. This requires the identification of a system model that takes both the measured and the operational excitation into account. Advantages with respect to the classical operational modal analysis approach are the possibility of obtaining mass-normalized mode shapes and the increase of the excitation level and its frequency content. An advantage with respect to the classical experimental modal analysis approach, where the ambient excitation is not modeled, but considered as disturbing noise, is the possibility of using excitation levels that are of the same amplitude, or even smaller, than the ambient excitation levels. In this paper, combined modal testing of footbridges is explored using two case studies: a steel arch footbridge with spans of 75.2 m and 30.3 m and a concrete stress-ribbon footbridge with spans of 30 m and 28 m. The comparison of the modal parameters (eigenfrequencies, damping ratios, mode shapes, and modal scaling factors) obtained from a combined vibration test with the ones obtained from other modal tests and from a finite-element model, demonstrates the feasibility of using small and practical excitation devices for the modal testing of footbridges.     

Modified Cross-Correlation Method for the Blind Identification of Structures

Recently, blind source separation (BSS) methods have gained significant attention in the area of signal processing. Independent component analysis (ICA) and second-order blind identification (SOBI) are two popular BSS methods that have been applied to modal identification of mechanical and structural systems. Published results by several researchers have shown that ICA performs satisfactorily for systems with very low levels of structural damping, for example, for damping ratios of the order of 1% critical. For practical structural applications with higher levels of damping, methods based on SOBI have shown significant improvement over ICA methods. However, traditional SOBI methods suffer when nonstationary sources are present, such as those that occur during earthquakes and other transient excitations. In this paper, a new technique based on SOBI, called the modified cross-correlation method, is proposed to address these shortcomings. The conditions in which the problem of structural system identification can be posed as a BSS problem is also discussed. The results of simulation described in terms of identified natural frequencies, mode shapes, and damping ratios are presented for the cases of synthetic wind and recorded earthquake excitations. The results of identification show that the proposed method achieves better performance over traditional ICA and SOBI methods. Both experimental and large-scale structural simulation results are included to demonstrate the applicability of the newly proposed method to structural identification problems.     

Vibration Testing at Meazza Stadium: Reliability of Operational Modal Analysis to Health Monitoring Purposes

In the last years an increasing interest has been devoted to all the topics related to the security and safety of people. Particular attention has been paid to health monitoring of large civil structures hosting many people, such as high-rise buildings and stadiums. Some extraordinary events, such as the Millennium Bridge oscillations in London, excited by pedestrians, or the Bruce Springsteen concert at the Ullevi Stadium in which coordinated jumps from the crowd caused serious damage to the structure, and drew attention toward a deeper and more careful study of all those problems related to the dynamic behavior of civil structures and their interaction with crowds. Research on these topics is also aimed, among others, at developing techniques allowing for a continuous monitoring of the structure, starting from a set of measurements that can be performed continuously, 24?h a day, without the need to stop the structure's functionality. The vast scientific literature confirms the possibility of relating structural health to the evolution of modal parameters, often reaching the aim of localizing any eventual damage, a task otherwise impossible with different techniques. This paper shows part of a long lasting project involving Politecnico di Milano in the setting up of a permanent health monitoring system at the G. Meazza Stadium in Milan. The aim of this project was the evaluation of the actual health state of the structures constituting the stands of the stadium and the deployment of a permanent monitoring system to record the vibration levels reached in all substructures during each event. Evaluation of the actual structure condition was performed by the use of ambient vibration, which was also checked against traditional experimental modal analysis, performed by using an inertial force given by a hydraulic actuator and a detailed measurement mesh. This offered the chance to exploit all possible information concerning natural frequencies, modal shapes, and damping factors. This task is extremely time consuming and expensive, therefore, it cannot be repeated very often. The possibility of using the data coming from the permanent monitoring system, which is about to be installed, is then an attractive perspective to improve structural diagnosis. It is expected that using operational modal analysis techniques will mean knowledge of the excitation applied to the structure will not be required. The parameter estimation obtained by this technique is usually affected by a spread, given both by the uncertainty of the adopted identification techniques and the influence of external parameters, such as crowd loading or temperature. As damage identification is related to changes of the modal parameters, the evaluation of their normal spread is fundamental to fix a threshold in order to identify possible worrysome situations. This paper deals with the identification of the spread in the modal parameter estimation of one of the grandstands of the so-called 3° ring of the G. Meazza Stadium in Milan, performed analyzing data collected over more than one year. Vibration data have been recorded during different events, such as soccer matches and concerts. The considered data came from a set of sensors similar to that which is to be installed for the permanent monitoring system, to check about the possibility to use the monitoring system as a diagnostic tool for the structure. A study was also carried out to identify critical aspects in the sensors’ choice and their placement, in order to provide useful information about the design of the permanent monitoring system. The presented results can be used to determine confidence intervals out of which changes in the modal properties can be considered anomalous, and so, worthy of being deeply investigated to assess structural integrity.     

Damping of Vibration by Actively Controlled Initial Distortions

A concept for the artificial damping of free vibration by means of actively controlled initial distortions imposed on the structure is presented. Two formulations for active control are presented: The first simulates the natural damping properties of structures, while the second uses a more sophisticated modal strategy of control (but with a faster damping process). The general idea of damping by actively forced distortions is explained and followed by a simple example for a one‐degree‐of‐freedom system. Then, the simulation of natural damping (which is a particular case of active control) and the possibility of accelerating the damping process by the modal optimal strategy are discussed and demonstrated with some examples for a two‐degree‐of‐freedom system. Finally, the vibration control of a four‐degree‐of‐freedom system is presented to demonstrate the efficiency of the proposed method. The method of active damping is described for truss structures, but it can be easily generalized to include frame structures as well.     

Active Vibration Damping of Composite Beam using Smart Sensors and Actuators

This paper discusses active vibration control of an E-glass/epoxy-laminated composite beam using smart sensors and actuators. The smart sensors and actuators used in this study are piezoelectric ceramic patches. The composite beam is in a cantilevered configuration. Both theoretical and numerical (finite-element analysis) studies of the laminated composite beam are conducted to reveal the beam’s fundamental modal frequencies and modal shapes. The results based on the theoretical predication and numerical simulation are then compared with those from experimental modal testing, and a good correlation is obtained. Utilizing results from the model analysis and experimental modal testing, two control algorithms, namely, positive position feedback control and strain rate feedback control, are designed. Both single-mode vibration suppression and multimode vibration suppression are studied. An experimental apparatus has been developed to implement the control algorithms. The apparatus consists of a voltage amplifier and a data acquisition and real-time control system, in addition to the composite beam with bonded piezoelectric ceramic sensors and actuators. Experiments show that the proposed controllers can achieve active vibration damping of the composite beam.     

Experimental Verification of Smart Cable Damping

Stay cables, such as are used in cable-stayed bridges, are prone to vibration due to their low inherent damping characteristics. Transversely attached passive viscous dampers have been implemented in many bridges to dampen such vibration. However, only minimal damping can be added if the attachment point is close to the bridge deck. For longer bridge cables, the relative attachment point becomes increasingly smaller, and passive damping may become insufficient. A recent analytical study by the authors demonstrated that “smart” semiactive damping can provide increased supplemental damping. This paper experimentally verifies a smart damping control strategy employing H2/linear quadratic Gaussian (LQG) clipped optimal control using only force and displacement measurements at the damper for an inclined flat-sag cable. A shear mode magnetorheological fluid damper is attached to a 12.65?m inclined flat-sag steel cable to reduce cable vibration. Cable response is seen to be substantially reduced by the smart damper.     

Analytical Study on Bending Effects in a Stay Cable with a Damper

The effects of bending on the modal properties of a stay cable with a transverse damper are analytically studied. Considering that the value of the flexural rigidity in the stay cable is small in practice, an explicit asymptotic formula for the modal damping of a cable with a general type of damper is derived. For a viscous damper, the asymptotic formula obtained is compact, accurate, and thus is very suitable for practical design. Furthermore, for the first few vibration modes of interest, the asymptotic solution is independent of the modal index. It is shown that flexure in the cable reduces the maximum attainable modal damping, possibly up to 20%, while it significantly increases the optimal damping coefficient of the damper.     

Double Modal Transformation and Wind Engineering Applications

Modal transformation techniques are usually adopted in structural dynamics with the aim of decoupling the equations of motion. They are based on the search for an abstract space in which the solution of the problem results simplified. Analogous transformation techniques have recently been developed with the aim of defining a space where a multivariate stochastic process is expressed by a linear combination of one-variate uncorrelated processes. This paper proposes a method, called double modal transformation, by which the dynamic analysis of a linear structure is carried out through the simultaneous transformation of the equations of motion and the loading process. By adopting this technique, the structural response is obtained through a double series expansion in which structural and loading modal contributions are superimposed. Its effectiveness and application are discussed with reference to two classic wind engineering problems—the alongwind response and the vortex-induced crosswind response of slender structures—which provide a wide panorama of the most relevant properties of this procedure.     

Effects of False Floors on Vibration Serviceability of Building Floors. I: Modal Properties

This is the first of two papers that present the results of a comprehensive and systematic study into the effects of false flooring on the vibration serviceability of long-span concrete floors. In this paper, advanced modal testing technology was utilized to determine modal properties of long-span concrete floors (natural frequencies, modal damping ratios, and mode shapes) before and after the installation of false flooring. It was found that false flooring had the capacity to change modal properties significantly, particularly modal damping ratios, which had increases of up to 89%. Parametric studies using updated finite element models were also performed, which showed that the false flooring contributed also to floor stiffness. However, changes in modal properties were not consistent across all modes of vibration and it was not possible to predict easily which modes would be affected beneficially by the installation of false flooring.     

Neural Networks for Decentralized Control of Cable-Stayed Bridge

The system identification and vibration control of a cable-stayed bridge are considered difficult to achieve due to the bridge’s structural complexity and system uncertainties. In this paper, based on the concept of decentralized information structures, a decentralized, nonparametric identification and control algorithm with neural networks is proposed for the purpose of suppressing the vibration of a documented six-cable-stayed bridge model induced by earthquake excitations. The control strategy proposed here uses the stay cables as active tendons to provide control forces through appropriate actuators. Each individual actuator is controlled by a decentralized neurocontroller that only uses local information. The feature of decentralized control simplifies the implementation of the control algorithms and makes decentralized control easy to practice and cost effective. The effectiveness of the decentralized identification and control algorithm based on neural networks is evaluated through numerical simulations. And the adaptability of the decentralized neurocontrollers for different kinds of earthquake excitations and for a damaged cable-stayed bridge model is demonstrated via numerical simulations.