Modal Updating Research Articles

Model Updating of different Bridge types using ambient vibration and OMA identification.

Structural Health Monitoring (SHM) to date is an increasingly crucial issue in civil engineering. Many structures like bridges and viaducts nowadays are often older than their design life and show signs of structural deterioration that can potentially affect structural safety. One of the most popular monitoring techniques is dynamic monitoring under environmental vibrations using Operational Modal Analysis (OMA) techniques.OMA needs f.e.m. models that can simulate structural behavior under the real conditions and that can be used for interpretation of monitoring data and for possible damage detection.The study proposes a model updating for two different bridges: a girder and box deck one. After an OMA identification using ambient vibration, through the modal parameter identified, modal updating is performed on f.e.m. models, changing only few essential parameters. All the f.e.m. models are made with beam elements.The study highlights that even a simple f.e.m. model of the structure can describe accurately the dynamic and in general the structural behavior of a complex structure such as bridges and viaducts. The authors also show the differences between a f.e.m. model developed for the design and or verification and a f.e.m. model intended SHM. Model updating is performed through the management of a few parameters of the structure like the stiffness of bearing devices between superstructure and substructure, the deformability of foundation soil, the mechanical properties of concrete and reinforcement and the modal masses. The variation in each of these parameters can have a different role on the behavior of the structure.A good reliability of the f.e.m. model can be achieved through the management of a few structural parameters obtaining results that are sufficient for models that have the purpose of interpreting SHM data and are used to perform damage research.

Enhanced semi-automated Bayesian modal identification approach for Ultra-high voltage transmission towers

The accuracy and efficiency of the modal identification for Ultra-high voltage (UHV) transmission towers under harsh operational environments is seriously affected by environmental noises. In general, the initial natural frequency drowned in the noises is evaluated by the experience of engineers before performing a Bayesian modal identification approach. It will lead to potential errors and limitations to the application of the Bayesian modal identification approach. In this study, a coherent clustering enhanced semi-automated Bayesian modal identification method is proposed and then implemented in the operational modal analysis of an instrumented UHV transmission tower under ambient excitation. The coherent clustering is adopted to obtain the quantitative value of the initial natural frequency, in place of the empirical evaluation. Then, the Fast Bayesian Fast Fourier Transform (FBFFT) method could accurately identify the most probable values (MPV) and the corresponding posterior uncertainty of modal parameters. Moreover, the first ten modes of the UHV transmission tower are identified, and the results of modal parameters are compared to the stochastic subspace identification (SSI) method. The results show that the coherent clustering enhanced semi-automated Bayesian method could accurately identify modal parameters with posterior uncertainty, even for modes weakly excited. The proposed method could provide a reliable basis for the modal updating, damage detection, and dynamic reliability assessment of UHV transmission towers.

Estimation of the static bending modulus of elasticity in glulam elements by ultrasound and modal-updating NDT techniques

Glulam timber is gaining popularity as a structural element due to its cost-effectiveness, strength, and environmental benefits. However, being an organic material, it is susceptible to degradation. Therefore, nondestructive testing (NDT) methods are essential for assessing its structural health. In this study, two NDT approaches, ultrasound-based and modal updating, were used to predict the static bending modulus of elasticity (MOE) in Pinus Sylvestris and Spruce species. The results demonstrated that the modal updating and linear regression models outperformed the ultrasound technique in accurately determining the static MOE. Additionally, considering the influence of knots improved the accuracy of ultrasound predictions.

Appraising the Seismic Response of a Retrofitted Adobe Historic Structure, the Role of Modal Updating and Advanced Computations

The concepts of structural assessment and retrofit of historical constructions are of particular complexity and require advanced knowledge in material science, conservation techniques and structural analysis. In particular, adobe constructions, given their low mechanical properties and brittle failure modes, are in immense need of comprehensive assessment and retrofitting plans. The current work focuses on the adobe Church of Kuñotambo in Peru, having experienced long periods of deterioration and earthquake-related damage. Under the ongoing Seismic Retrofitting Project (SRP) of the Getty Conservation Institute (GCI), the structural assessment of the church initiated in 2015 confirmed the low lateral capacity of the building and the poor connectivity between the structural parts. Based on the existing cracks and damage, a strengthening scheme was optimized and validated. After the implementation of the retrofitting plan, the quality of its execution and efficiency were assessed in 2019 with a new in situ campaign, which included ambient vibration testing (AVT) and sonic testing. From the acquired field data, the FE model of the retrofitted church was optimized, by updating the stiffness properties of masonry and discontinuities. Moreover, nonlinear static analyses were performed on the updated model in all in-plan directions. Finally, a displacement-based performance assessment was undertaken, under different earthquake limit states, demonstrating the adequacy of the retrofitting.

Modeling stiffness of connections and non-structural elements for dynamic response of taller glulam timber frame buildings

Currently, there is limited knowledge of the dynamic response of taller glue laminated (glulam) timber buildings due to ambient vibrations. Based on previous studies, glulam frame connections, as well as non-structural elements (external timber walls and internal plasterboard partitions) can have a significant impact on the global stiffness properties, and there is a lack of knowledge in modeling and investigation of their impact on the serviceability level building dynamics. In this paper, a numerical modeling approach with the use of “connection-zones” suitable for analyzing the taller glulam timber frame buildings serviceability level response is presented. The “connection-zones” are generalized beam and shell elements, whose geometry and properties depend on the structural elements that are being connected. By introducing “connection-zones”, the stiffness in the connections can be estimated as modified stiffness with respect to the connected structural elements. This approach allows for the assessment of the impact of both glulam connection stiffness and non-structural element stiffness on the dynamic building response due to service loading. The results of ambient vibration measurements of an 18-storey glulam timber frame building, currently the tallest timber building in the world, are reported and used for validation of the developed numerical model with “connection-zones”. Based on model updating, the stiffness values for glulam connections are presented and the impact of non-structural elements is assessed. The updating procedure showed that the axial stiffness of diagonal connections is the governing parameter, while the rotational stiffness of the beam connections does not have a considerable impact on the dynamic response of the glulam frame type of building. Based on modal updating, connections exhibit a semi-rigid behavior. The impact of non-structural elements on the mode shapes of the building is observed. The obtained values can serve as a practical reference for engineers in their prediction models of taller glulam timber frame buildings serviceability level response.

Using Updated and Expanded Data to Estimate the Unmeasured Rotational Data of a Bolted Structure

For frequency-based substructuring (FBS) to be accurate, translational and rotational data must be available at the connection points between substructures. However, obtaining rotational FRFs from experimental modal analyses is very difficult in practice. In this paper, an alternative method for estimating rotational FRFs is proposed using an approximated simplified finite element model (ASFE), modal updating, and mode expansion. The proposed approach was demonstrated on an assembled structure consisting of an irregular plate (test model) and a simple beam (FE model). The SEREP method was used to augment the translational and rotational FRFs to the updated ASFE mode shapes. The expanded rotational FRF of the test model was validated with the measured rotational FRF obtained from a piezoelectric direct rotational accelerometer. The results showed that the proposed approach for FBS correctly predicted the experimental FRF of the assembled structure with 90% accuracy. The FBS method is no longer dependent on the experimental rotational FRF, which is very difficult to measure with the methodology presented here.

Application of Sliding Smoothing Method Denoising in Model Updating Damage Identification

The accuracy of finite element model updating for structural damage identification is easily affected by the noise in the measured modal, so the sliding smoothing method is introduced to reduce the impact of noise. In each iteration step, the sliding smoothing method denoising is applied to the difference between measured modal and simulated modal from the finite element model because the time-frequency characteristic of actual modal is different from noise modal. The modal parameters after denoising are used to construct objective function for modal updating, and the optimal question is solved to determine the stiffness in finite element model. Finally, the stiffness change can indicate the damage position and magnitude. The numerical analysis shows the proposed method can improve the robustness of finite element model updating for the structural damage identification.

Model Updating and Aeroelastic Correlation of a Scaled Wind Tunnel Model for Active Flutter Suppression Test

This article presents a modal correlation and update carried out on an aeroelastic wind tunnel demonstrator representing a conventional passenger transport aircraft. The aim of this work is the setup of a corresponding numerical model that is able to capture the flutter characteristics of a scaled aeroelastic model designed to investigate and experimentally validate active flutter suppression technologies. The work described in this paper includes different finite element modeling strategies, the results of the ground vibration test, and finally the strategies adopted for modal updating. The result of the activities is a three-dimensional hybrid finite element model that is well representative of the actual aeroelastic behavior identified during the wind tunnel test campaign and that is capable of predicting the flutter boundary with an error of 1.2%. This model will be used to develop active flutter suppression controllers, as well as to perform the sensitivity analyses necessary to investigate their robustness.

Representation of bolted joints in a structure using finite element modelling and model updating

Efficient and accurate finite element (FE) modelling of bolted joints is essential for increasing confidence in the investigation of structural vibrations. However, modelling of bolted joints for the investigation is often found to be very challenging. This paper proposes an appropriate FE representation of bolted joints for the prediction of the dynamic behaviour of a bolted joint structure. Two different FE models of the bolted joint structure with two different FE element connectors, which are CBEAM and CBUSH, representing the bolted joints are developed. Modal updating is used to correlate the two FE models with the experimental model. The dynamic behaviour of the two FE models is compared with experimental modal analysis to evaluate and determine the most appropriate FE model of the bolted joint structure. The comparison reveals that the CBUSH element connectors based FE model has a greater capability in representing the bolted joints with 86 percent accuracy and greater efficiency in updating the model parameters. The proposed modelling technique will be useful in the modelling of a complex structure with a large number of bolted joints.

High‐resolution time‐frequency representation for instantaneous frequency identification by adaptive Duffing oscillator

Time-frequency analysis of structural vibration responses provides essential information for structural system identification, modal updating, and condition assessment. However, spurious peaks introduced by the strong noise will significantly increase the false positive rate as well as compromise the sparse time-frequency signal representation. This paper proposes a high-resolution time-frequency representation approach for nonstationary signals polluted with strong noise. With a high sensitivity to detect slight frequency shift and an immunity to noise effect, the intermittent chaotic of Duffing oscillator system is introduced to accurately identify the time-varying instantaneous frequencies. Furthermore, an adaptive Duffing oscillator array is adopted to improve the instantaneous frequency identification efficiency. The feasibility and effectiveness of the proposed method are verified with numerical and experimental studies. Numerical studies are conducted on a multicomponent synthetic nonstationary signal as well as on a two-story shear building with time-varying stiffness under seismic loads. In experimental validations, the acceleration response of a laboratory bridge model under moving vehicle load is also analyzed by using the proposed approach to obtain the instantaneous frequency variations induced by the bridge–vehicle interaction. These results are compared with those obtained from a method based on empirical wavelet transform and Hilbert transform (EWT-HT), to highlight the superiority of the proposed approach in obtaining high-resolution time-frequency analysis results for nonstationary signals with strong noise.

Estimating Rotational FRFs of a Complex Structure Using FE Model Updating, Mode Expansion and FRF Synthesis Method

Estimating rotational frequency response functions (FRFs) from experimental data is very challenging, and the estimation often leads to poor FRFs due to the presence of spurious resonance peaks. In practice, special equipment is essentially required in the measurement process, unless the rotational FRFs are synthesised using measured modal data. This paper presents an alternative approach for estimating the rotational FRFs of a geometrically complex structure by using finite element modal updating, mode expansion and the FRF synthesis method. The applicability and accuracy of the proposed approach are demonstrated on a car front-end module A simplified finite element (SFE) model of the test structure is introduced and the SFE model is then updated based on the measured modal model obtained from experimental modal analysis. The mode shapes of the updated SFE model are expanded to the test model to obtain the entire translational and rotational modal vector. The rotational FRFs of the expended experimental model is derived via the FRF synthesis method. The derived translational FRF is compared with the measured counterparts for validation purposes. It was found that the derived translational and measured FRF are in a perfect match, and the derived rotational FRF has successfully estimated all the resonance peaks within the frequency of interest. The findings from this work may be useful in improving the accuracy of the experimental rotational FRFs, which are crucial for particular structural dynamics analysis.

Full-degrees-of-freedom frequency based substructuring

Abstract Dividing the whole system into multiple subsystems and a separate dynamic analysis is common practice in the field of structural dynamics. The substructuring process improves the computational efficiency and enables an effective realization of the local optimization, modal updating and sensitivity analyses. This paper focuses on frequency-based substructuring methods using experimentally obtained data. An efficient substructuring process has already been demonstrated using numerically obtained frequency-response functions (FRFs). However, the experimental process suffers from several difficulties, among which, many of them are related to the rotational degrees of freedom. Thus, several attempts have been made to measure, expand or combine numerical correction methods in order to obtain a complete response model. The proposed methods have numerous limitations and are not yet generally applicable. Therefore, in this paper an alternative approach based on experimentally obtained data only, is proposed. The force-excited part of the FRF matrix is measured with piezoelectric translational and rotational direct accelerometers. The incomplete moment-excited part of the FRF matrix is expanded, based on the modal model. The proposed procedure is integrated in a Lagrange Multiplier Frequency Based Substructuring method and demonstrated on a simple beam structure, where the connection coordinates are mainly associated with the rotational degrees of freedom.

Using experimental modal analysis to assess the behaviour of timber elements

Timber frameworks are one of the most important and widespread types of structures. Their configurations and joints are usually complex and require a high level of craftsmanship to assemble. In the field of restoration, a good understanding of the structural behaviour is necessary and is often based on assessment techniques dedicated to wood characterisation. This paper presents the use of experimental modal analysis for finite element updating. To do this, several timber beams in a free supported condition were analysed in order to extract their bending natural characteristics (frequency, damping and mode shapes). Corresponding ABAQUS finite element models were derived which included the effects of local defects (holes, cracks and wood nodes), moisture and structural decay. To achieve the modal updating, additional simulations were performed in order to study the sensitivity of the mechanical parameters. With the intent to estimate their mechanical properties, a procedure of modal updating was carried out in MatLab with a Python script. This was created to extract the modal information from the ABAQUS modal analysis results to be compared with the experimental results. The updating was based on a minimum of unconstrained multivariable function using a derivative-free method. The objective function was selected from the conventional comparison tools (absolute or relative frequency difference, and/or modal assurance criterion). This testing technique was used to determine the dynamic mechanical properties of timber beams, such as the anisotropic Young's Moduli and damping ratio. To verify the modulus, a series of static 4-point bending tests and STS04 classifications were conducted. The results also revealed that local defects have a negligible influence on natural frequencies. The results demonstrate that this assessment tool offers an effective method to obtain the mechanical properties of timber elements, especially when on-site and non-destructive techniques are needed, for example when retrofitting an existing structure.

New structural damage-identification method using modal updating and model reduction

Early prediction of damages using vibration signal is essential in avoiding the failure in structures. Among different damage-detection approaches, the finite-element model updating and modal analysis-based methods are of most importance due to their applicability and feasibility. Owing to some restrictions in nodal measurements in experimental cases, finite-element model reduction is an indispensable part of fault-detection methods. Even though model reduction of dynamic systems leads to the less complicated models, an improved convergence rate and acceptable accuracy are highly required for a successful structural health monitoring of the real complex systems. In this paper, the aim is to design a damage-detection algorithm based on a new model updating method, which has a faster rate of convergence and higher accuracy. Then the proposed method is applied on a simulated damaged beam considering different noise levels to see how capable the method is in dealing with noise-corrupted data. Finally, the experimentally extracted data from a cracked beam in a real noisy condition are used to evaluate the efficiency of the proposed method in identifying the damages in a beam-like structure. It is concluded that the identification of the damages by the proposed method is encouraging and robust to the noise compared with the traditional method. Also, the proposed method converges faster and is more accurate in identifying damage than the traditional method.

Modal Parameter Identification and Model Updating of a Continuous Steel Truss Bridge with Three Main Chords

Modal Parameter Identification and Model Updating of a Continuous Steel Truss Bridge with Three Main Chords

Recent research and applications of GPS based technology for bridge health monitoring

Today, long-span bridges are being designed to be more flexible and to resist extensive impacts from changes in temperature, severe wind gusts and earthquake tremors. Structural responses (especially displacement) of bridge structures are becoming increasingly important for the finite element (FE) modal updating, structural response prediction and safety evaluation. Methods of global displacement sensing were developed for these needs. This paper presents an overview of current research and development activities in the field of bridge health monitoring using the global positioning system (GPS). The GPS monitoring technology and its accuracy assessment method are also briefly described. Finally, existing problems and promising research efforts in the GPS based bridge health monitoring are discussed.

Full-scale measurements of dynamic response of suspension bridge subjected to environmental loads using GPS technology

Nowadays, there are many larger and taller engineering structures than in the past. These structures are commonly designed to be more flexible. Thus, they are sensitive to severe wind gust and earthquake tremor. For the dynamic response prediction, finite element (FE) modal updating and structural health monitoring, the dynamic characteristics of a structure are becoming increasingly important. The aim of this paper is to show an emerging tool-the real time kinematic (RTK) global positioning system (GPS), which is used to measure and monitor the low-frequency vibration of Dalian BeiDa Bridge, a medium span suspension bridge. The modal analysis is firstly performed on the developed three-dimensional FE model according to the original blue prints of the bridge to provide the analytical frequencies and mode shapes. The field ambient vibration tests using the accelerometers on the bridge deck are conducted just prior to the use of the GPS system in order to validate the FE model. And then, the calibration test is done to assess the dynamic displacement measurement accuracy of the GPS in three orthogonal directions. The GPS signal properties, such as the amplitude, standard deviations (STD), power spectral density (PSD), and probability density functions (PDF), are studied in details. After that, a structural health monitoring system based on the GPS is devised and installed on the bridge to provide real-time measurement of deck movement. The output-only modal parameter identification is carried out by using the Periodogram method to investigate the responses of the bridge. The result shows that the spectral densities of the displacements measured by the GPS correspond well with the results by the FEM analysis and the accelerometer vibration test. It is concluded that the GPS method is reliable and useful to clarify the ambient vibration response behaviors of the flexible structures. The integration of the GPS and accelerometer methods results in a hybrid arrangement that can help to eliminate some disadvantages of the two devices used separately.

Nonlinear Perturbation Theory for Structural Dynamic Systems

A novel nonlinear perturbation theory for structural dynamic systems is developed that can provide an exact relationship between the perturbation of structural parameters and the perturbation of modal parameters. A system of governing equations based on the developed theory is further derived, which can be utilized for general applications, such as structural reanalyses, eigendata modification, model updating, and damage identification, suitable for all types of structures including mechanical systems, framed structures, and continua. Neither model reduction nor mode shape expansion is required for modal updating and damage identification because information about incomplete measured modal data can be directly employed. The developed theory successfully avoids adopting a Taylor series expansion procedure and then the derivatives of modal parameters are not required. Computational procedures based on the derived nonlinear governing equations are presented for eigendata modification, model updating, and damage identification. The Jacobi transformation method and the accelerated modal method are introduced to make the proposed techniques particularly suitable for cases with a very large perturbation of structural parameters. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed techniques. The results show that the modified modal parameters can be predicted exactly even for cases with a large modification of structural parameters, and the analytical model can be adjusted correctly using the information about limited modal data available.

Damage Detection on Typical Aeronautical Structures

The paper pursues the exploration of the feasibility and reliability of current damage detection technologies, evaluating their detection capabilities, environmental factors effects, false alarms rate, adaptability to complex geometries, etc. The method to be used is based on finite element modal updating. Three aspects, as outlined below, are covered: testing samples will be aluminium sheets (0.6m x 0.4m x 1.6mm) strengthened with riveted L-shaped stiffeners. Data will be presented from the undamaged specimens. Secondly, the testing of the samples with damage simulated at different places by temporary removal of specific rivets, thus affecting the overall structural characteristics of the structure. The models used for damage identification methods will be fine tuned to properly detect the simulated damages. Finally, using this information, the paper resumes the capabilities of the method to detect and locate the simulated damage.

Bayesian Fast Fourier Transform Approach for Modal Updating Using Ambient Data

The problem of identification of the modal parameters of a structural model using measured ambient response time histories is addressed. A Bayesian Fast Fourier Transform approach (BFFTA) for modal updating is presented which uses the statistical properties of the Fast Fourier transform (FFT) to obtain not only the optimal values of the updated modal parameters but also their associated uncertainties, calculated from their joint probability distribution. Calculation of the uncertainties of the identified modal parameters is very important when one plans to proceed with the updating of a theoretical finite element model based on modal estimates. The proposed approach requires only one set of response data in contrast to many of the existing frequency-based approaches which require averaging. It is found that the updated PDF can be well approximated by a Gaussian distribution centred at the optimal parameters at which the posterior PDF is maximized. Examples using simulated data are presented to illustrate the proposed method.