Analysis of Modal Frequencies Estimated from Frequency Domain Decomposition Method

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

SSI-LSTM network for adaptive operational modal analysis of building structures

In order to identify time-varying transient modal parameters only from nonstationary vibration response measurement signals for slow linear time-varying (SLTV) structures which are weakly damped, a moving window differential evolution (DE) independent component analysis- (ICA-) based operational modal analysis (OMA) method is proposed in this paper. Firstly, in order to overcome the problems in traditional ICA-based OMA, such as easy to go into local optima and difficult-to-identify high-order modal parameters, we combine DE with ICA and propose a differential evolution independent component analysis- (DEICA-) based OMA method for linear time invariant (LTI) structures. Secondly, we combine the moving widow technique with DEICA and propose a moving window differential evolution independent component analysis- (MWDEICA-) based OMA method for SLTV structures. The MWDEICA-based OMA method has high global searching ability, robustness, and complexity of time and space. The modal identification results in a three-degree-of-freedom structure with slow time-varying mass show that this MWDEICA-based OMA method can identify transient time-varying modal parameters effectively only from nonstationary vibration response measurement signals and has better performances than moving window traditional ICA-based OMA.

Structural safety assessment of bowstring type RC arch bridges using ambient vibration testing and finite element model calibration

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.

Damping estimation using free decays and ambient vibration tests

The objective of this paper is to develop a novel sensing system which can conduct continuous monitoring of a building structure and generate a monitoring report. The building monitoring data will focus on the ambient vibration responses. Two servers are used in this SHM system: 1) wireless measurement server which takes care of measuring and archiving all the structural responses and environmental situation, and 2) analysis server which conducts the signal processing on the received signals. The measurement server is in charge of the collection of signals and broadcast wirelessly from all sensors to the analysis server. Dominant frequencies and mode shapes of the building will be estimated in the analysis server from the continuous monitoring of the ambient vibration data (velocity) of the building by using AR-Model, Frequency Domain Decomposition and Stochastic Subspace Identification methods. The proposed continuous monitoring system can effectively identify the building current health condition and generate a report to the owner.

Modal analysis is a fundamental and essential research direction in the field of structural engineering. The ultimate goal is to determine the modal parameters of the structures. However, the existing modal analysis algorithms often require a large number of parameter adjustments and manual intervention during operation, which cannot be fully automated. In order to realize the automatic identification of modal parameters, the automatic operational modal identification method (AOMI) is proposed based on the interpolated power spectral density estimation (IPSE). To achieve more precise spectrum analysis in the low-frequency band, IPSE is employed to perform Fourier transform on the original frequency domain segment with optimized frequency resolution. This enhances the sharpness of the obtained spectrum in the low-frequency range, making peak frequencies more discernible. Subsequently, the scale-space peak picking algorithm is used to automatically obtain the peak of the power spectral density (PSD), thus enabling the automatic identification of the natural frequency. Finally, the frequency domain decomposition method (FDD) is used to identify modal parameters based on the natural frequencies. The effectiveness of AOMI is verified through the modal identification of the old steel truss bridge and the three layer framework. Under the environmental excitation, the frequencies identified by the IPSE method is close to that of FDD, Bayesian fast fourier transform (FFT) and covariance driven stochastic subspace identification (SSI-COV). Furthermore, the PSD obtained through IPSE has sharper peak than that of FDD and the Welch’s method. The damping ratio identification accuracy and modal assurance criterion (MAC) are satisfactory in AOMI, which can improve the automatic performance.

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.

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.

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.

Signal processing of flutter flight test data enables verification of aircraft flutter design, and the signal from a flutter flight test excited by atmospheric turbulence is a particularly important form of the flutter test. Owing to the randomness of atmospheric turbulence excitation, multi-channel analysis of turbulence responses at various positions in the same component can improve the analytical accuracy of flutter signal processing. The relationship between the maximum singular value of the multi-channel turbulence response power spectral density matrix and the system self-power spectral density function is elucidated herein using a frequency domain decomposition method. However, there is a contradiction in the power spectral density function between the spectral line density and the spectral line smoothing calculated based on the periodogram of the frequency domain decomposition. By applying an autoregressive spectral model, the power spectral density function of the turbulence response is calculated to achieve spectral line smoothing and sufficient spectral line density. Additionally, the power spectral density function is then used to construct the power spectral density function matrix of the multi-channel turbulence response, and the maximum singular value curve is calculated based on the singular value decomposition of each spectral pin. Finally, the modal parameters of the turbulence response signal are estimated via multi-modal frequency domain fitting. The developed approach is validated based on simulations and flutter flight test turbulence response signals.

Structural Health Monitoring (SHM) is nowadays common in many branches of engineering since it allows to have a continuous or periodic report of the structural conditions and therefore to promptly intervene if there are incipient damages. The first step to perform a SHM is the identification of the dynamic parameters, i.e. natural frequencies, damping ratios and modal shapes, and it is a crucial step since a modification of the structural parameters can be a direct consequence of structural damages. Among the structural identification methods, Operational Modal Analysis (OMA) methods have received increasing attention from the researchers since they do not require the knowledge of the structural excitation that is due to ambient vibrations and that is usually modeled as a white noise. This aspect makes this kind of methods cheaper and simpler than the classical Experimental Modal Analysis (EMA) methods. In this paper an innovative OMA method is proposed. It is a semi - automated method that allows to identify natural frequencies, damping ratios and modal shapes of a structural system and that can be used also from users that have not knowledge in stochastic dynamics and signal analysis. First of all, the modal shapes are estimated through the use of signal filtering techniques applied on the stochastic properties of the output process and then natural frequencies and damping ratios can be estimated from the mono - component analytical signals obtained by performing a decomposition of the analytical signals matrix. The proposed method has been used to perform the dynamic identification of a real historic building situated in Palermo, i.e. Chiaramonte palace, and the results obtained have been compared with those obtained by using other OMA methods.

Operational modal analysis (OMA) is a procedure that allows the modal parameters of a structure to be extracted from the measured response to an unknown excitation generated during operation. Nonlinearity is inevitably and frequently encountered in OMA. The problem: The traditional OMA method based on linear modal theory cannot be applied to a nonlinear oscillation system. The solution: This paper aims to propose a nonlinear OMA method for nonlinear oscillation systems. The new OMA method is based on the following: (1) a self-excitation phenomenon is caused by nonlinear components; (2) the nonlinear normal modes (NNMs) of the system appear under a single-frequency harmonic excitation; and (3) using forced response data, the symbolic regression method (SR) can be used to automatically search for the NNMs of the system, whose modal parameters are implicit in the expression structure expressing each NNM. The simulation result of a three-degree-of-freedom (3-DOF) nonlinear system verifies the correctness of the proposed OMA method. Then, a disc-rod rotor model is considered, and the proposed OMA method’s capability is further evaluated.

Performing forced vibration tests on full-scale structures is the most reliable way of determining the relevant modal parameters in structural dynamics, such as modal frequencies, mode shapes, modal damping, and modal masses. This study describes the modal identification of a double-level curved cable-stayed bridge with separate deck systems for pedestrians and vehicles via forced vibration tests. The steady-state structural responses to sinusoidal excitations produced by an electrodynamic shaker are recorded under varying excitation frequencies, and the frequency response functions are established. The measured frequency response functions are curve fitted to estimate the modal parameters. The numerical simulation of frequency response function–based modal parameter identification of an elastically multi-supported continuous beam structure is carried out, and the emphasis has been placed on the evaluation of the effect of an additional shaker mass, excitation frequency step and range, multi-mode vibration, and noise on identification results. Finally, the modal parameters for the first lateral mode of a double-level curved cable-stayed bridge are identified by forced vibration experiments, and the results are compared with those from ambient vibration tests and free vibration tests. The effect of the unmeasured wind excitation on identification is discussed. It is shown that the effect of ambient vibration is minor for wind velocity of 3–5 m/s. The damping ratios identified by forced and free vibration tests are comparable, while those from ambient vibration are subject to large variations. The modal mass obtained from forced vibration tests is in good agreement with finite element prediction, which provides design basis for mass-type dampers.