System identification of timber masonry walls using shaking table test

This paper addresses delamination detection of concrete slabs by analyzing vibration data from dynamic tests. Four concrete decks with different delamination sizes were constructed and experimental tests were conducted on these concrete slabs. Traditional peak-picking (PP), frequency domain decomposition (FDD) and stochastic subspace identification (SSI) methods were applied in the modal identification from real measurements of dynamic velocity responses. The modal parameters identified by these identification methods matched very well. The changes in modal frequencies, damping ratios, and mode shapes that were extracted from dynamic measurements were correlated to delamination size and can indicate presence and severity of delamination. Finite element (FE) models of reinforced concrete plates with different delamination sizes and locations were established. The modal parameters computed from FE models were compared to those obtained from real measurements and FE models were validated.KeywordsMode ShapeDynamic TestConcrete SlabModal IdentificationConcrete DeckThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Modified frequency and spatial domain decomposition method based on maximum likelihood estimation

A comprehensive monitoring system is installed and currently in operation on the Bergsøysund Bridge, an end-supported floating pontoon bridge, collecting data on accelerations, displacements, waves, and wind. Using covariance-driven stochastic subspace identification (Cov-SSI), data-driven stochastic subspace identification, and frequency domain decomposition, the modal parameters of the structure are estimated to investigate its dynamic behaviour. Aspects regarding the selection of good parameters for the Cov-SSI analyses are highlighted, and the clarifying effect of applying stabilization criteria on multiple orders of output is discussed. The effects of the significant wave height on the modal parameters are investigated based on an automatic selection of stable poles from stabilization plots produced by the Cov-SSI method.

<div class="htmlview paragraph">Operational Modal Analysis also known as Output Only Modal Analysis has in the recent years been used for extracting modal parameters of civil engineering structures and is now becoming popular for mechanical structures. The advantage of the method is that no artificial excitation needs to be applied to the structure or force signals to be measured. All the parameter estimation is based upon the response signals, thereby minimising the work of preparation for the test. This test case is a controlled lab set-up enabling different parameter estimation methods techniques to be used and compared to the Operational Modal Analysis. For Operational Modal Analysis two different estimation techniques are used: a non-parametric technique based on Frequency Domain Decomposition (FDD), and a parametric technique working on the raw data in time domain, a data driven Stochastic Subspace Identification (SSI) algorithm. These are compared to other methods such as traditional Modal Analysis. In the paper the method is illustrated by practical examples.</div>

The paper presents how to identify natural frequencies and mode shapes of structures by Operational Modal Analysis (OMA) technique, in which the Frequency Domain Decomposition (FDD) method is used. This method is an experimental method only base on the data of measuring the dynamic response of the structures under the excitation due to ambient forces and operational loads to determine the vibration characteristics. Measure vibration (acceleration) and determine spectral density matrix, using the singular values decomposition method of spectral density matrix to determine the natural frequencies and mode shapes of structures. The calculation results show that the natural frequencies, the mode shapes form determined by the OMA technique is consistent with the calculation results according to the theory and show the reliability of the method.KeywordsNatural frequencyMode shapeIdentifyEMAOMAFDD

SummaryShanghai Tower is the tallest building in China with a height of 632 m. This study aims to investigate the wind characteristics and its impact on Shanghai Tower so as to provide useful information for the wind‐resistant design of 600 m+ super‐tall buildings. By analyzing the data of wind speed during the occurrence of DeHong in June 2017, the relationship between turbulence intensity and mean wind speed is verified, and the correlation between gust factor and turbulence intensity is confirmed. Apart from that, it is also found that the von Karman spectrum fits well with the measured fluctuating wind speed spectrum. In addition, the 83rd and 117th acceleration data are analyzed to obtain the natural frequency by peak‐picking, frequency domain decomposition, stochastic subspace identification, and fast Bayesian fast Fourier transform methods. The amplitude‐dependence dynamic parameters of Shanghai Tower on the basis of the field measurements are studied as well. Finally, the wind‐induced vibration is investigated based on the acceleration data and wind speed data, which verifies that the responses along two main axes having a similar amplitude under wind effects. The occurrence of DeHong demonstrates that a gale equivalent to a typhoon may occur in urban areas without any urban warning.

Right after its invention in the late nineties, the Frequency Domain Decomposition (FDD) identification technique became very popular in the operational modal analysis community due to its simplicity and robustness. The underlying idea of this technique consists of computing the singular value decomposition of the Power Spectral Densities (PSDs) estimated from the measured vibration responses with the periodogram (also known as “Welch’s”) approach to identify the natural frequencies and mode shape vectors of the tested structural system. When dealing with multi-dataset output-only modal analysis, the classic approach for extracting the global mode shape vectors from all the measured datasets consists of estimating the mode shape parts corresponding to each dataset, and then scaling the different parts with the aid of the reference sensors. In this paper, two new merging approaches are proposed to scale the different mode shape parts. The first consists of (i) re-scaling the different PSDs prior to the identification; (ii) forming a global matrix containing all the re-scaled PSDs; and (iii) applying the FDD approach to the global PSD matrix to estimate the global mode shape vectors. The second merging strategy consists of (i) forming a global matrix containing all the PSDs without any prior re-scaling; (ii) applying the FDD approach to the PSD matrix to estimate the global mode shape vectors; and (iii) re-scaling the different mode shape parts by making use of the reference singular vectors. In order to illustrate the benefits of the two proposed merging approaches with regards to their classic counterpart from a practical perspective, a real-live application example is presented as the last part of the paper.

The accuracy of modal parameter estimates from estimation methods built in the framework of experimental modal analysis (EMA) can be assessed by several methods provided the information of input loadings and output responses. However, a deeper investigation is necessary for estimation methods built in the operational modal analysis (OMA) framework to establish confidence boundaries for the modal parameter estimates. This paper aims to estimate uncertainties of the modal parameter estimates by testing the sensitivity of the damped natural frequencies, damping ratios, and mode shapes to the choice of the estimation method and data acquisition settings used in this method. The uncertainty estimates of the modal parameter estimates are tested for changes in the boundary conditions. The tests provide insights into tendencies for the accuracy of the modal parameter estimates when the boundary conditions provide a different set of “true” modal parameter values. A simple cantilever beam experimental setup is used to obtain benchmark modal parameter estimates from EMA that are used to estimate the accuracy of the modal parameter estimates from OMA. The method’s robustness in estimating uncertainties and accuracies for modal parameter estimates is tested for several independent experiments. The boundary conditions for the cantilever beam are changed to test the influence of altering modal parameter estimates on the estimated uncertainties and accuracies. The boundary conditions are changed using materials with different elastic properties and the connection pressure between the clamping device and beam. A method presented in Paulsen et al. (Proceedings of the 9th International Operational Modal Analysis Conference, IOMAC, 2022) calculates a representative modal parameter estimate from a set of modal parameter estimates based on weightings obtained from the modal assurance criterion. The method’s ability to reduce uncertainties and increase accuracies of the representative estimate is demonstrated by repeating a test setup ten times. The results present simultaneously a reduction of uncertainties and an increase of accuracies for the representative modal parameter when the weighting method is used. An evaluation of dependencies between the estimated uncertainties and accuracies finds a proportional relation for the damped natural frequency when the uncertainties are described as a relative standard deviation. The analysis presents higher accuracy for the damped natural frequency and mode shape estimates compared to the damping factor, and the accuracy of the damping factor is dependent on the actual value of the damping factor. These phenomena for accuracy are well known and indicate that the uncertainties of modal parameter estimates can be assessed through a sensitivity test of estimation methods and data acquisition parameters.

In this paper, system identification of a cable-stayed bridge in Korea, the Hwamyung Bridge, is performed using vibration responses measured by a wireless sensor system. First, an acceleration based-wireless sensor system is employed for the structural health monitoring of the bridge, and wireless sensor nodes are deployed on a deck, a pylon and several selected cables. Second, modal parameters of the bridge are obtained both from measured vibration responses and finite element (FE) analysis. Frequency domain decomposition and stochastic subspace identification methods are used to obtain the modal parameters from the measured vibration responses. The FE model of the bridge is established using commercial FE software package. Third, structural properties of the bridge are updated using a modal sensitivity-based method. The updating work improves the accuracy of the FE model so that structural behaviors of the bridge can be represented better using the updated FE model. Finally, cable forces of the selected cables are also identified and compared with both design and lift-off test values.

In this study, the strain based monitoring method to evaluate the lateral structural response of buildings is presented and an applicability of the proposed method is confirmed through the numerical study. It is assumed that the fiber Bragg grating(FBG) strain sensor is employed to measure the strain response of members due to the excellent properties such as multiplexing, and higher sampling frequency. These properties of FBG sensors is proper for buildings the a lot of sensors are required to monitor the reponses of those. FBG sensors measure the strain response of vertical members and are employed to calculate the curvatures of members using the measured strain responses. Then the lateral displacement, and lateral acceleration is evaluated based on the curvatures of vertical members. Additionally, these dynamic responses of buildings are used to evaluate the dynamic properties of buildings such as the natural frequencies and mode shapes using the frequency domain decomposition(FDD) method. Through the application of nine-story steel moment frame example structure, it is confirmed that the proposed method is appropriate to evaluate the lateral structural responses and dynamic properties of buildings.

En esta investigación se realizó un análisis espectral de la respuesta estructural de dos edificios de concreto reforzado, de 18 m y 56 m de altura y con distintos niveles de irregularidad en planta, al ser sometidos a vibraciones ambientales. Específicamente, se han usado el método básico (BFD) y de descomposición en el dominio de la frecuencia (FDD) sobre registros de vibración ambiental adquiridos mediante tres acelerómetros triaxiales para la identificación de las frecuencias y los modos naturales de vibración. Para cada edificio se identificaron al menos tres modos de vibración en un rango de frecuencias comprendido entre 1,0 Hz y 6,0 Hz. Los modos con mayor densidad espectral fueron exhibidos entre las frecuencias de 1,0 Hz y 3,0 Hz. De las formas modales, se evidenció que, entre más irregularidad en planta, mayor será la presencia de modos de torsión y el acoplamiento de estos con modos de flexión.

The purpose of this study is to identify modal parameters of an elevator car by operational modal analysis, and to estimate the stiffness parameters of the elevator car based on the obtained modal parameters. It is assumed that the inertia properties such as mass, the center of gravity and the moment of inertia are well predicted based on the design condition. However, it is difficult to predict the stiffness parameters of an elevator car especially in the operating condition. Therefore, the stiffness coefficients are estimated based on the operational modal analysis in this study. The frequency range of interest is up to 4 Hz, where the assumption that the car behaves rigidly is satisfied. In order to check the assumption the Rigidity Indicator Function (RIF) is introduced as a function of frequency. Frequency Domain Decomposition (FDD) method is used for the operational modal analysis. The stiffness parameters are estimated by minimizing the sum of the errors of natural frequencies and the errors of mode shape vectors between the experimentally identified modal model and the analytical model.

Structural identification of a cantilever beam with multiple cracks: Modeling and validation

Mobile sensing has emerged as an economically viable alternative to spatially dense stationary sensor networks, leveraging crowdsourced data from today's widespread population of smartphones. Recently, field experiments have demonstrated that using asynchronous crowdsourced mobile sensing data, bridge modal frequencies, and absolute mode shapes (the absolute value of mode shapes, i.e., mode shapes without phase information) can be estimated. However, time‐synchronized data and improved system identification techniques are necessary to estimate frequencies, full mode shapes, and damping ratios within the same context. This paper presents a framework that uses only two time‐synchronous mobile sensors to estimate a spatially dense frequency response matrix. Subsequently, this matrix can be integrated into existing system identification methods and structural health monitoring platforms, including the natural excitation technique eigensystem realization algorithm and frequency domain decomposition. The methodology was tested numerically and using a lab‐scale experiment for long‐span bridges. In the lab‐scale experiment, synchronized smartphones atop carts traverse a model bridge. The resulting cross‐spectrum was analyzed with two system identification methods, and the efficacy of the proposed framework was demonstrated, yielding high accuracy (modal assurance criterion values above 0.94) for the first six modes, including both vertical and torsional. This novel framework combines the monitoring scalability of mobile sensing with user familiarity with traditional system identification techniques.

This paper reports the step-by-step procedures of a full-scale ambient vibration test and the corresponding modal identification and Bayesian structural model updating of a coupled building. The building is characterized as a combination of a main part and a complementary part connected together by corridors in between. Compared with the main part, the volume of the complementary part is much smaller. Therefore, the influence on the dynamic properties of the complementary part from its counterpart is expected. To capture the dynamic properties of the coupled building, a 21-setup ambient vibration test was designed to cover all the degrees of freedom (DOFs) of interest. The modal parameters of each setup were identified following the frequency domain decomposition (FDD) method and the partial mode shapes from different setups were assembled following a least-squares method. To determine the stiffness of the linkage between the two parts, the coupled building was simulated with two linked shear buildings and updated utilizing the Markov chain Monte Carlo (MCMC)-based Bayesian model updating method. The identified modal parameters revealed interesting features about the coupled effects between the main part and complementary part and were discussed in detail. The good match between the model-predicted and identified modal parameters verified the validity of proposed shear building model. This study provides valuable experience in the area of structural model updating and structural health monitoring.