Finite element modelling for fatigue stress analysis of large suspension bridges

Fatigue is an important failure mode for large suspension bridges under traffic loadings. However, large suspension bridges have so many attributes that it is difficult to analyze their fatigue damage using experimental measurement methods. Numerical simulation is a feasible method of studying such fatigue damage. In British standards, the finite element method is recommended as a rigorous method for steel bridge fatigue analysis. This paper aims at developing a finite element (FE) model of a large suspension steel bridge for fatigue stress analysis. As a case study, a FE model of the Tsing Ma Bridge is presented. The verification of the model is carried out with the help of the measured bridge modal characteristics and the online data measured by the structural health monitoring system installed on the bridge. The results show that the constructed FE model is efficient for bridge dynamic analysis. Global structural analyses using the developed FE model are presented to determine the components of the nominal stress generated by railway loadings and some typical highway loadings. The critical locations in the bridge main span are also identified with the numerical results of the global FE stress analysis. Local stress analysis of a typical weld connection is carried out to obtain the hot-spot stresses in the region. These results provide a basis for evaluating fatigue damage and predicting the remaining life of the bridge.     

Stochastic damage detection method for building structures with parametric uncertainties

Uncertainties, such as modeling errors and measurement errors, are inevitably involved in damage detection of a building structure. Most deterministic damage detection methods, however, do not consider uncertainties, thus limiting their practical application. A new stochastic damage detection method is therefore proposed in this paper for damage detection of building structures with parametric uncertainties. The proposed method contains two basic steps. The first step is to determine the probability density functions (PDFs) of the structural stiffness parameters before and after damage occurrence by integrating the statistical moment-based damage detection method with the probability density evolution method. In the second step, based on a special probability function calculated using the obtained PDFs, new damage indices are proposed and both damage locations and damage severities are identified. The feasibility and effectiveness of the proposed method are numerically demonstrated through a shear building structure with three damage scenarios. The first modal damping ratio of the building structure is regarded as a random parameter with a lognormal distribution. Numerical results show that both damage locations and damage severities can be identified satisfactorily. One of the advantages of the proposed method lies in that it can deal with uncertainty parameters of non-normal distributions.     

Modal flexibility-based damage detection of cantilever beam-type structures using baseline modification

This paper presents a new damage detection approach for cantilever beam-type structures using the damage-induced inter-storey deflection (DIID) estimated by modal flexibility matrix. This approach can be utilized for damage detection of cantilever beam-type structures such as super high-rise buildings, high-rise apartment buildings, etc. Analytical studies on the DIID of cantilever beam-type structures have shown that the DIID abruptly occurs from damage location. Baseline modification concept was newly introduced to detect multiple damages in cantilever beam-type structures by changing the baseline to the prior damage location. This approach has a clear theoretical base and directly identifies damage location(s) without the use of a finite element (FE) model. For validating the applicability of the proposed approach to cantilever beam-type structures, a series of numerical and experimental studies on a 10-storey building model were carried out. From the tests, it was found that the damage locations can be successfully identified by the proposed approach for multiple damages as well as a single damage. In order to confirm the superiority of the proposed approach, a comparative study was carried out on two well-known damage metrics such as modal strain-based damage index approach and uniform load surface curvature approach.     

IMPROVED DAMAGE IDENTIFICATION METHOD BASED ON MODAL INFORMATION

In this paper, a newly derived algorithm to predict locations and severities of damage in structures using changes in modal characteristics is presented. First, two existing algorithms of damage detection are reviewed and the new algorithm is formulated in order to improve the accuracy of damage localization and severity estimation by eliminating erratic assumptions and limits in the existing algorithms. Next, the damage prediction accuracy is numerically assessed for each algorithm when applied to a two-span continuous beam for which pre- and post-damage modal parameters are available for only a few modes of vibration. Compared to the existing damage detection algorithms, the new algorithm improved the accuracy of damage localization and severity estimation results in the test beam.     

Structural damage identification of the highway bridge Z24 by FE model updating

The development of a methodology for accurate and reliable condition assessment of civil structures has become very important. The finite element (FE) model updating method provides an efficient, non-destructive, global damage identification technique, which is based on the fact that the modal parameters (eigenfrequencies and mode shapes) of the structure are affected by structural damage. In the FE model the damage is represented by a reduction of the stiffness properties of the elements and can be identified by tuning the FE model to the measured modal parameters. This paper describes an iterative sensitivity based FE model updating method in which the discrepancies in both the eigenfrequencies and unscaled mode shape data obtained from ambient tests are minimized. Furthermore, the paper proposes the use of damage functions to approximate the stiffness distribution, as an efficient approach to reduce the number of unknowns. Additionally the optimization process is made more robust by using the trust region strategy in the implementation of the Gauss-Newton method, which is another original contribution of this work. The combination of the damage function approach with the trust region strategy is a practical alternative to the pure mathematical regularization techniques such as Tikhonov approach. Afterwards the updating procedure is validated with a real application to a prestressed concrete bridge. The damage in the highway bridge is identified by updating the Young's and the shear modulus, whose distribution over the FE model are approximated by piecewise linear functions.     

On the tuning of variable piezoelectric transducer circuitry network for structural damage identification

The concept of using piezoelectric transducer circuitry with tunable inductance has been recently proposed to enhance the performance of frequency-shift-based damage identification method. While this approach has shown promising potential, a piezoelectric circuitry tuning methodology that can yield the optimal damage identification performance has not been synthesized. This research aims at advancing the state-of-the-art by exploring the characteristics of inductance tuning such that the enrichment of frequency measurements can be effectively realized to highlight the damage occurrence. Analysis shows that when the inductance is tuned to accomplish eigenvalue curve veering, the change of system eigenvalues induced by structural damage will vary significantly with respect to the change of inductance. Therefore, by tuning the inductance near the curve-veering range, one may obtain a family of frequency response functions that could effectively reflect the damage occurrence. When multiple tunable piezoelectric transducer circuitries are integrated to the mechanical structure, multiple eigenvalue curve veering can be simultaneously accomplished, and a series of inductance tunings can be formed by accomplishing curve veering between different pairs of system eigenvalues. It will then be shown that, to best characterize the damage occurrence, the favorable inductance tuning sequence should be selected as that leads to a “comprehensive” set of eigenvalue curve veering, i.e., all measurable natural frequencies undergo curve veering at least once. An iterative second-order perturbation-based algorithm is used to identify the locations and severities of the structural damages based on the frequency measurements before and after the damage occurrence. Numerical analyses on benchmark beam and plate structures have been carried out to examine the system performance. The effects of measurement noise on the effectiveness of the proposed damage identification method are also evaluated. It is demonstrated that the damage identification results can be significantly improved by using the variable piezoelectric transducer circuitry network with the favorable inductance-tuning scheme proposed in this research.     

Response characteristics of local vibrations in stay cables on an existing cable-stayed bridge

This paper examines local parametric vibrations in the stay cables of a cable-stayed bridge. The natural frequencies of the global modes are obtained by using a three-dimensional FE model. The global motions generated by (1) sinusoidal excitations using exciter, (2) a traffic loading, and (3) an earthquake are analyzed by using the modal analysis method or the direct integration method. The local vibration of stay cable is calculated by using a model in which inclined cable is subjected to time-varying displacement at one support during global motions. This paper describes the properties of the local vibrations in stay cables under these dynamic loadings by using an existing cable-stayed bridge.     

Damage identification in beam type structures based on statistical moment using a two step method

This paper defines a novel damage index-strain statistical moment, and formulates the fourth strain statistical moment (FSSM) of beam-type structures under white noise excitation. Based on this newly defined strain statistical moment index and the least square optimization algorithm, a two-step damage identification method is proposed. This two-step method is operated like this: first use the difference curves of FSSMs before and after damage to locate damage elements; then for those identified damage elements, employ the model updating method based on the least square algorithm to assess their damage severity. Numerical studies on a simply supported beam and a two-span continuous beam are performed and the study results show that the newly defined index is effective to locate damages, even when the noise intensity is as high as 15 percent. Integrating with the least square-based model updating technique, the damage severities of beam-type structures can also be determined quantitatively. In this way, the proposed two-step method is verified and found to be capable of identifying damage positions and severities of beam-type structures and insensitive to measurement noise.     

A time-domain approach for damage detection in beam structures using vibration data with a moving oscillator as an excitation source

The problem of detecting local/distributed change of stiffness in bridge structures using ambient vibration data is considered. The vibration induced by a vehicle moving on the bridge is taken to be the excitation source. A validated finite element model for the bridge structure in its undamaged state is assumed to be available. Alterations to be made to this initial model, to reflect the changes in bridge behaviour due to occurrence of damage, are determined using a time-domain approach. The study takes into account complicating features arising out of dynamic interactions between vehicle and the bridge, bridge deck unevenness, spatial incompleteness of measured data and presence of measurement noise. The inclusion of vehicle inertia, stiffness and damping characteristics into the analysis makes the system time variant, which, in turn, necessitates treatment of the damage detection problem in time domain. The efficacy of the procedures developed is demonstrated by considering detection of localized/distributed damages in a beam-moving oscillator model using synthetically generated vibration data.     

A sensitivity-based structural damage identification method with unknown input excitation using transmissibility concept

Unknown input excitation and local damages universally coexist in a practical situation. Therefore, in this paper a structural damage identification method based on the transmissibility concept in state space domain is proposed without the need for input measurements. On the basis of the transformation matrix which is computed using the system Markov parameters in state space, the relationship between two different sets of acceleration response measurements can be formulated under the same input excitation. A sensitivity-based model updating approach is applied to identify the local damages by minimizing the difference between the measured response and the reconstructed response. The sensitivity of the dynamic acceleration response with respect to the elemental stiffness factors is derived analytically in the state space domain, which accelerates the process of damage identification. A numerical cantilever beam is employed to validate that the variation of structural parameters induced by the local damages can be accurately and effectively identified without the input excitation information by the proposed method even with measurement noise considered. A laboratory test is further carried out to verify the proposed structural damage identification method based on the response reconstruction technique.     

Damage localization in linear-form structures based on sensitivity investigation for principal component analysis

This paper addresses the problem of damage detection and localization in linear-form structures. Principal component analysis (PCA) is a popular technique for dynamic system investigation. The aim of the paper is to present a damage diagnosis method based on sensitivities of PCA results in the frequency domain. Starting from frequency response functions (FRFs) measured at different locations on the structure; PCA is performed to determine the main features of the signals. Sensitivities of principal directions obtained from PCA to structural parameters are then computed and inspected according to the location of sensors; their variation from the healthy state to the damaged state indicates damage locations. It is worth noting that damage localization is performed without the need of modal identification. Influences of some features as noise, choice of parameter and number of sensors are discussed. The efficiency and limitations of the proposed method are illustrated using numerical and real-world examples.     

Condition assessment of reinforced concrete beams using dynamic data measured with distributed long-gage macro-strain sensors

A new condition assessment strategy of reinforced concrete (RC) beams is proposed in this paper. This strategy is based on frequency analysis of the dynamic data measured with distributed long-gage macro-stain sensors. After extracting modal macro-strain, the reference-based damage index is theoretically deducted in which the variations of modal flexural rigidity and modal neutral axis height are considered. The reference-free damage index is also presented for comparison. Both finite element simulation and experiment investigations were carried out to verify the proposed method. The manufacturing procedure of long-gage fiber Bragg grating (FBG) sensor chosen in the experiment is firstly presented, followed by an experimental study on the essential sensing properties of the long-gage macro-strain sensors and the results verify the excellent sensing properties, in particular the measurement accuracy and dynamic measuring capacity. Modal analysis results of a concrete beam show that the damage appearing in the beam can be well identified by the damage index while the vibration testing results of a RC beam show that the proposed method can not only capture small crack initiation but its propagation. It can be concluded that distributed long-gage dynamic macro-strain sensing technique has great potential for the condition assessment of RC structures subjected to dynamic loading.     

Model updating using uncorrelated modes

FE model updating techniques are used to update dynamic FE models of structures in the light of modal test data. Iterative methods of model updating that update a set of chosen parameters of the model, so as to reduce the difference between the natural frequencies and the mode shapes of the FE model and the corresponding quantities obtained through a modal test on the structure, are probably the most widely used methods. Once experimental modal data has been identified, a necessary prior step, before updating can be carried out, is that of establishing the correspondence between the FE model modes and the experimentally identified modes.     

Structural damage evolution assessment using the regularised time step integration method

This paper presents an approach to identify both the location and severity evolution of damage in engineering structures directly from measured dynamic response data. A relationship between the change in structural parameters such as stiffness caused by structural damage development and the measured dynamic response data such as accelerations is proposed, on the basis of the governing equations of motion for the original and damaged structural systems. Structural damage parameters associated with time are properly chosen to reflect both the location and severity development over time of damage in a structure. Basic equations are provided to solve the chosen time-dependent damage parameters, which are constructed by using the Newmark time step integration method without requiring a modal analysis procedure. The Tikhonov regularisation method incorporating the L-curve criterion for determining the regularisation parameter is then employed to reduce the influence of measurement errors in dynamic response data and then to produce stable solutions for structural damage parameters. Results for two numerical examples with various simulated damage scenarios show that the proposed method can accurately identify the locations of structural damage and correctly assess the evolution of damage severity from information on vibration measurements with uncertainties.     

A local flexibility method for vibration-based damage localization and quantification

A method for vibration-based damage localization and quantification, based on quasi-static flexibility, is presented. The experimentally determined flexibility matrix is combined with a virtual load that causes nonzero stresses in a small part of the structure, where a possible local stiffness change is investigated. It is shown that, if the strain–stress relationship for the load is proportional, the ratio of some combination of deformations before and after a stiffness change has occurred, equals the inverse local stiffness ratio. The method is therefore called local flexibility (LF) method. Since the quasi-static flexibility matrix can be composed directly from modal parameters, the LF method allows to determine local stiffness variations directly from measured modal parameters, even if they are determined from output-only data. Although the LF method is in principle generally applicable, the emphasis in this paper is on beam structures. The method is validated with simulation examples of damaged isostatic and hyperstatic beams, and experiments involving a reinforced concrete free–free beam and a three-span prestressed concrete bridge, that are both subjected to a progressive damage test.     

STRUCTURAL DAMAGE DETECTION BASED ON A MICRO-GENETIC ALGORITHM USING INCOMPLETE AND NOISY MODAL TEST DATA

This paper describes a procedure for detecting structural damage based on a micro-genetic algorithm using incomplete and noisy modal test data. As the number of sensors used to measure modal data is normally small when compared with the degrees of freedom of the finite element model of the structure, the incomplete mode shape data are first expanded to match with all degrees of freedom of the finite element model under consideration. The elemental energy quotient difference is then employed to locate the damage domain approximately. Finally, a micro-genetic algorithm is used to quantify the damage extent by minimizing the errors between the measured data and numerical results. The process may be either of single-level or implemented through two-level search strategies. The study has covered the use of frequencies only and the combined use of both frequencies and mode shapes. The proposed method is applied to a single-span simply supported beam and a three-span continuous beam with multiple damage locations. In the study, the modal test data are simulated numerically using the finite element method. The measurement errors of modal data are simulated by superimposing random noise with appropriate magnitudes. The effectiveness of using frequencies and both frequencies and mode shapes as the data for quantification of damage extent are examined. The effects of incomplete and noisy modal test data on the accuracy of damage detection are also discussed.     

Statistical damage identification of structures with frequency changes

Model updating methods based on structural vibration data have being rapidly developed and applied to detect structural damage in civil engineering. But uncertainties existing in the structural model and measured vibration data might lead to unreliable damage detection. In this paper a statistical damage identification algorithm based on frequency changes is developed to account for the effects of random noise in both the vibration data and finite element model. The structural stiffness parameters in the intact state and damaged state are, respectively, derived with a two-stage model updating process. The statistics of the parameters are estimated by the perturbation method and verified by Monte Carlo technique. The probability of damage existence is then estimated based on the probability density functions of the parameters in the two states. A higher probability statistically implies a more likelihood of damage occurrence. The presented technique is applied to detect damages in a numerical cantilever beam and a laboratory tested steel cantilever plate. The effects of using different number of modal frequencies, noise level and damage level on damage identification results are also discussed.     

Distinguishing between the interior pressures induced from two independent sources within a room using the probabilistic approach

In this paper, a probabilistic approach is introduced and used to distinguish between the interior pressures that are induced from two independent sound sources within a rectangular room. One source is a vibrating wall of the room and the other is an interior point source. The model is set up using the modal analysis method. In the probabilistic method, the probability densities of the uncertain acoustic model parameters are computed. The values of highest probability density are identified and assigned to the uncertain parameters in the acoustic model. The contributions of the sound sources to the total pressure are then obtained from the acoustic model input with the identified parameters. The effects of the modal truncations, the modeling errors, and the measurement locations on the accuracies of the identification process are studied.     

Dynamic behavior monitoring and damage evaluation for arch bridge suspender using GFRP optical fiber Bragg grating sensors

Suspenders, as the main bearing components in an arch bridge, can only manage to serve for about tens of years, or even a few years due to the influences of corrosion and fatigue load. This paper proposes a method of testing the suspender dynamic behavior with optical fiber Bragg grating sensors embedded in the glass fiber reinforced polymer (GFRP–OFBGS). Firstly, layout method of FRP–OFBGS among the suspender and protection technology are studied, and the self-monitoring smart suspender is developed. Secondly, stretching experiments were carried out on the smart suspender. The test experimental results demonstrated that the whole procedure of the stretching test can be perfectly monitored. Finally, the self-monitoring smart suspender successfully was applied in Ebian Bridge to monitor the strain history of suspenders under traffic load, and traffic effect to suspenders with various lengths and to different steel strands of a single suspender. Based on the monitoring data, the arch bridge suspenders fatigue damage dynamic evaluation methods and calculation results were given. The field monitoring results demonstrated that, the self-monitoring smart suspender mentioned in this paper is capable of monitoring suspender dynamic response and possible fatigue damages.     

Numerical and experimental analysis of uncertainty on modal parameters estimated with the stochastic subspace method

Modal parameters of structures are often used as inputs for finite element model updating, vibration control, structural design or structural health monitoring (SHM). In order to test the robustness of these methods, it is a common practice to introduce uncertainty on the eigenfrequencies and modal damping coefficients under the form of a Gaussian perturbation, while the uncertainty on the mode shapes is modeled in the form of independent Gaussian noise at each measured location. A more rigorous approach consists however in adding uncorrelated noise on the time domain responses at each sensor before proceeding to an operational modal analysis. In this paper, we study in detail the resulting uncertainty when modal analysis is performed using the stochastic subspace identification method. A Monte-Carlo simulation is performed on a simply supported beam, and the uncertainty on a set of 5000 modal parameters identified with the stochastic subspace identification method is discussed. Next, 4000 experimental modal identifications of a small clamped–free steel plate equipped with 8 piezoelectric patches are performed in order to confirm the conclusions drawn in the numerical case study. In particular, the results point out that the uncertainty on eigenfrequencies and modal damping coefficients may exhibit a non-normal distribution, and that there is a non-negligible spatial correlation between the uncertainty on mode shapes at sensors of different locations.