Operational Modal Identification Research Articles

Fully automated operational modal identification based on scale-space peak picking algorithm and power spectral density estimation

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.

Performance evaluation of a seismic strengthening applied on a masonry school building by dynamic analyses

With its unreinforced masonry structural system, Münevver Şefik Fergar Primary School has been analyzed and retrofitted by the Istanbul Project Coordination Unit, IPKB in Istanbul. The applied strengthening is mainly composed of the addition of reinforced concrete layers to the masonry walls by shotcreting. This study is performed to monitor the variation of the dynamic properties of the building through the constructional works and evaluate the effects of the performed retrofitting. For this aim, six sets of operational modal analysis type dynamic identification, starting from the original building and ending with the retrofitted building, were performed to extract the dynamic properties of the building. To discuss the effectiveness of retrofitting efficiently, numerical analyses have also been conducted. The original and retrofitted form of the building has been modeled by finite element modeling technique and Eigenvalue analyses were performed to obtain the dynamic properties of the building numerically for both phases. The comparison of the dynamic characteristics of the original and retrofitted building enabled the assessment of the efficiency of the applied seismic strengthening. Moreover, the experimentally and numerically obtained results were compared. It is seen that, while both experimental and numerical results proved the effectiveness of the performed retrofitting to increase the dominant frequencies of the building, the difference in their quantity was worth noting and should be accounted for seismic analysis of similar structures.

An extended modal approach for modal parameter identification of structure under the existence of harmonic excitations

The existing operational modal analysis (OMA) methods for the structure subjected to white noise and harmonic combined excitations have some limitations such as easy misjudgment of true and spurious modes and slow identification speed. Through expressing the system response with the extended modal matrix (EMM) and the extended modal response (EMR) vector, a novel operational modal parameter identification approach called the extended modal approach is proposed to obtain structural true modes under the existence of multiple harmonic excitations. The EMRs consist of the true modal responses and the spurious modal responses, and each of the former is random while each of the latter is harmonic. It is also proved theoretically that the EMM can be identified using the power spectrum density transmissibility (PSDT) method. Therefore, the extended modal approach includes three steps: (1) Using the PSDT to identify the EMM; (2) Utilizing the least squares reconstruction method to obtain the EMRs from the underdetermined extended modal equation; (3) Judging each of the EMRs to be true or spurious according to its empirical density function. Structural true modes can be ultimately obtained by removing all spurious modes from the identified results. The new approach is numerically verified through the OMA of two multiple-degree-of-freedom systems and then experimentally verified through the OMA of a test beam. The results in numerical simulation and experiments all show that the extended modal approach can identify accurately and quickly structural true modes under multiple harmonic excitations. Besides, the approach has good robustness against noise contamination.

A Novel Operational Strain Modal Identification Method Based on Strain Power Spectrum Density Transmissibility (SPSDT)

Compared with conventional displacement modal analysis, the strain modal analysis has remarkable advantages in structural damage detection. Identifying the operational strain modal parameters directly from only dynamic strain time–history response measurements of a structure under operational conditions is a challenging issue. In this paper, the strain power spectrum density transmissibility (SPSDT)-based approach is presented to identify the operational strain modal parameters. The SPSDT is first defined by selecting a strain response measurement point as a reference. It is then theoretically proved that the defined SPSDT converges to the ratio of strain mode amplitudes at the system poles. Based on this unique property, the SPSDT matrix is constructed by selecting different strain response measurement points as the references. Singular value decomposition (SVD) is implemented in the matrix at the system pole. The first left singular vector is used to estimate strain mode shape. A simulated three-span continuous beam, a simply supported beam model tested in the laboratory and a full-size arch bridge tested in field are employed to verify the applicability and effectiveness of the proposed SPSDT-based operational strain modal identification method. The obtained results are compared with those of other available methods. It is found that a good agreement is achieved. It is demonstrated that the proposed SPSDT-based method is capable of identifying the operational strain modal parameters of a structure where only the dynamic strain time–history responses are measured. The proposed SPSDT-based method does not need white noise assumption under a single load condition.

Operational modal identification of structures based on improved empirical wavelet transform

When empirical wavelet transform (EWT) is used to identify the modal parameters of civil engineering structures, the frequency band division is generally not accurate due to the noise effect on the Fourier spectrum. This phenomenon will lead to modal mixing and false modes in the analysis results. Therefore, this article establishes a signal frequency band division method by taking advantages of maximal spectrum technique and spectral skewness index. Combining the random decrement technique (RDT) and the least square method of single component modal parameter identification, an adaptive approach based on the improved EWT for operational modal parameter identification of civil engineering structures under stationary environmental excitations is proposed. The traditional frequency band division method based on EWT can not completely and effectively divide the meaningful frequency bands. While the proposed frequency band division technology based on the spectral skewness index can prevent the phenomenon of insufficient division and excessive division and realize adaptive frequency band division. The effectiveness of the proposed approach is validated by a numerical three-story frame and a field three-span concrete box girder bridge under ambient vibrations. The modal identification results from both numerical and experimental validations demonstrate that the proposed approach can effectively and accurately decompose the vibration responses and identify the structural modal parameters under operational conditions.

Output-only modal identification with recursive dynamic mode decomposition for time-varying systems

The time-varying modal identification is a prominent analytical means but challenging task to grasp the dynamic characteristics of time-varying systems, which is important guarantee for real-time control and on-line health monitoring of many engineering structures. In this paper, a data-driven approach for time-varying modal identification without requiring parametric modeling about underlying system is presented. Firstly, the fundamental theory for Dynamic Mode Decomposition (DMD) is reviewed combining the Koopman operator. Subsequently, the DMD incorporated into operational modal identification is examined from the perspective of linear system, and the inner connection between modal parameters of vibration system and eigenvalues and eigenmodes of DMD is established. On the basis of that, a weighted recursive strategy integrated with DMD is employed to investigate the capability of time-varying modal identification, and the main identification procedures are elaborated. Finally, the effectiveness and practicability of the proposed method in extracting modal properties of time-varying systems are investigated by a numerical and experiment example. The results demonstrate that, compared to other methods, the proposed approach has high computational efficiency while ensuring the identification accuracy, exhibiting a good engineering application prospect.

Fully automated operational modal identification of regular and irregular buildings with ensemble learning

Modal identification, a type of system identification that employs modal analysis, can be automated to reduce user interference in extracting modal parameters. Modal analysis is a valuable tool for obtaining a structure's modal parameters, which define its dynamic characteristics. Operational modal identification is a specific type of modal analysis that uses only system outputs to extract modal parameters. The present study aims to introduce a fully automated modal identification algorithm to identify modal parameters for an unknown system based on its output information. The algorithm uses a stochastic subspace algorithm to extract modal parameters, requiring only the appropriate degree of the state-space model estimated using the Singular Value Criterion. Several features are used to create a feature space that separates physical and spurious modes. The Improved Distance Evaluation algorithm selects appropriate features, making the identification process more accurate and flexible. The identification algorithm employs clustering algorithms with different approaches and the Dempster-Shafer data fusion algorithm to integrate clustering algorithm results and avoid divergence among them. Due to limited data diversity for identification in cases where only one dataset is available, statistical resampling methods are used as an alternative. The proposed algorithm can identify modal parameters using only one dataset of the building structure. Signal processing, data collection, clustering, feature extraction, model reduction, and data fusion are all aspects of this algorithm. To assess its performance, four regular and irregular buildings are considered as case studies. The presented modal identification algorithm is highly accurate and robust with the repeatable result as compared to similar algorithms, with extracted modal parameters demonstrating high stability.

Cross-correlation-guided operational modal identification of bridge considering asynchronous signals

The accurate identification of modal parameters is crucial for bridge health monitoring. In practical scenarios, there is often an asynchronization in the multi-channel vibration signals obtained from wireless sensors or offline measurements without temporal data. This asynchronization can lead to significant bias in the mode shapes when using the classical operational modal identification method. To address this issue, a new cross-correlation (CC) coefficient-based time lag detection is proposed. This technique aims to determine whether the multi-channel signals are synchronous and to prepare the reliably synchronous signals for modal identification. Because this detection technique specifically focuses on detecting the time lag between single degree-of-freedom (DOF) asynchronous signals, a multivariate variational mode decomposition (VMD) technique is developed to handle the multiple DOF signals of a bridge. To ensure that the decomposed components are not distorted or mixed, the penalty parameter in the multivariate VMD is optimized by minimizing the proposed similarity index. The proposed time lag detection process is validated using numerical and actual bridge examples. The results demonstrate that the new CC coefficient-based method is more effective than the classical CC coefficient or phase-based method, regardless of the employed mode or the amount of time lag present.

One year monitoring of an offshore wind turbine: Variability of modal parameters to ambient and operational conditions

This paper presents the variation of identified modal parameters of an offshore wind turbine (OWT) over one year of continuous monitoring. The considered OWT is a Haliade 150–6 MW GE turbine on a jacket substructure at the Block Island Wind Farm in Rhode Island, U.S. The turbine was instrumented with a monitoring system including accelerometers, strain gauges, inclinometers, and a data acquisition system with automatic data transfer to cloud storage. Continuous vibration measurements of the OWT have been collected over one year from April 2021 to April 2022. An automated output-only operational modal identification approach is developed to extract modal parameters of the OWT over this one-year period using windows of 10-min data. The identified modal parameters of the first few vibration modes show variability and correlation with several ambient and operational conditions. It is observed that the identified natural frequencies and damping ratios of the first side-to-side (SS) mode are stable over time and have very small variation, but those of the first fore-aft (FA) mode show significant variability. The second FA/SS modes can only be identified with reasonable accuracy when the turbine is in idle condition. Similar to the first FA/SS modes, the second FA mode has larger variability in frequencies and damping ratios than the second SS mode because of the aerodynamics effects. The system identification results over one full year verify the effectiveness and robustness of the proposed approach for long-term monitoring of this OWT and serve as the reference database.

Propeller's operational modal parameters identification based on Fiber Bragg Grating sensing

The propeller will generate a lot of harmful vibration and noise underwater. In order to effectively solve the problem of vibration and noise, it is of great significance to accurately obtain the modal parameters of propeller for the design and optimization of the propeller structure. Since it is difficult to measure the load of propeller when it is running underwater, only operational modal analysis (OMA) method can be used to identify the operational modal parameters of propeller. This paper is aimed at solving this problem by taking the metal propeller as the research object, an open-water test platform was built, and the Fiber Bragg Grating (FBG) sensors were used to obtain the underwater strain information of the propeller. Finally, the operational modal parameters of propeller are identified by the Stochastic subspace identification (SSI) method. In addition, the modal simulation analysis of propeller was carried out by using finite element simulation software, and the experimental results were compared with the simulation results. The results show that the stochastic subspace identification method can accurately identify the operational modal parameters of propeller.

A novel instantaneous frequency estimation method for operational time-varying systems using short-time multivariate variational mode decomposition

Operational modal identification of time-varying systems plays a crucial role in assessing the health condition and controlling the dynamic properties of engineering structures. However, only the response is measurable, making it challenging. Based on the variational mode decomposition (VMD) theory, this paper presents a short-time multivariate or multi-channel VMD (STMVMD) method for instantaneous frequency (IF) identification of time-varying structures in the case of output-only measurements. The idea of short-time windows overcomes the shortcoming of many VMD-based methods that employ the narrowband assumption of intrinsic mode functions (IMFs) and cannot decompose non-stationary signals involving closely-spaced wideband IMFs. After obtaining the multivariate IMFs by STMVMD, an average scheme is employed to estimate IFs, reducing the noise sensitivity of Hilbert Transform. Moreover, by tracking the center frequencies of STMVMD at different moments, another more noise-robust IF estimation method is also presented. A series of numerical and experimental examples illustrate the advantages of the proposal.

Rapid Safety Assement and Experimental Derivation of Damage Indexes for In-Service Glass Slabs

The mechanical performance of pedestrian structures attracts the attention of several studies, especially with respect to unfavourable operational conditions or possible damage scenarios. In terms of vibrations, for example, specific customer comfort levels must be satisfied, depending on the class of use, the structural typology, the involved materials, in addition to basic safety requirements. A special consideration should be given to in-service systems that are possibly affected by degradation or even damage, and thus potentially unsafe for pedestrians. In this regard, the availability of standardized non-destructive protocols for a reliable and rapid structural safety assessment may result in efficient support for diagnostic analyses. In this paper, 3 different laminated glass (LG) modular units belonging to 2 different indoor in-service pedestrian systems located in Italy are investigated. Operational Modal Analysis (OMA) procedures and dynamic identification techniques are used to quantify the residual capacity of the examined systems, including damage and material degradation, based on a single triaxial Micro Electro-Mechanical System (MEMS) accelerometer. The experimentally derived performance indicators and calibrated mechanical parameters for the examined structural system are assessed towards traditional design procedures, and further quantified with the support of Finite Element (FE) numerical model updating. A comparative analysis is carried out to explore the structural performance and safety levels of in-service LG slabs in regards to vibration comfort, deflection control and stress analysis.

Bayesian Operational Modal Analysis with Genetic Optimization for Structural Health Monitoring of the Long-Span Bridge

Modal parameters, including natural frequencies, damping ratios, and mode shapes, are vital for evaluating the in-service condition of long-span bridges subjected to performance degradation or damages. Operational modal identification techniques requiring only ambient vibration responses are usually utilized to identify the modal parameters of in-service bridges. Due to the measurement incompleteness and modeling errors, uncertainties would inevitably be involved in the identification. The changing operational loads of long-span bridges, e.g. vehicles and winds, could also increase uncertainties. These uncertainty factors could decrease the precision of the operational modal identification and undermine the reliability of structural health monitoring (SHM) for long-span bridges. This study introduces an improved Bayesian modal identification approach using the scaled Fast Fourier Transform data for uncertainty quantification. The proposed method integrates the genetic optimization with the posterior probability density function of modal parameters to ensure the accuracy and robustness of the iteration process. Additionally, an asymptotic estimate interval with the assumption of a high signal-to-noise ratio is defined to improve the computational efficiency. The acceleration responses from a numerical example and a full-scale long-span bridge are adopted to validate the performance of the proposed method. Results show that the improved Bayesian approach can accurately identify the modal parameters and efficiently quantify the uncertainties. The method enhances the reliability of modal tracking for SHM of operational long-span bridges.

Operational modal identification of ultra-precision fly-cutting machine tools based on least-squares complex frequency-domain method

Operational modal identification of ultra-precision fly-cutting machine tools based on least-squares complex frequency-domain method

Research on the Operational Modal Prediction of Dry Gas Seal System Based on Response Surface Method

The cross power spectrum function is used to realize the operational modal analysis and identification of the dry gas seal device system through the multi-reference point least squares complex frequency domain method. The steady state diagram and mathematical indicators MAC, MPD, MPC, MOV and MIF are used to verify the modal results. At the same time, based on the response surface method, with two different operating conditions of medium pressure and rotating speed, modal direction and modal order as the response surface variables, a time-varying modal recognition model is established. Through the Full Factorial experiment design, Box-Behnken experiment design and Central Composite experiment design, the suitable variable sample points are formed. A complete quadratic polynomial response surface model of the system operational modal parameters is established. The complex correlation coefficient, the modified complex correlation coefficient and the root mean square error are used to verify the effectiveness of the response surface model. It provides new method and technical support for realizing time-varying modal identification in this paper.

Fully Automated Operational Modal Identification Using Continuously Monitoring Data of Bridge Structures

AbstractStructural modal identification for providing dynamic properties, including frequencies, damping ratios, and mode shapes, plays an important role in structural health monitoring and safety ...

Operational modal identification based on parallel factor decomposition with the presence of harmonic excitation

One of the main difficulties of the operational modal analysis is to deal with underdetermined problems inwhich the number of sensors is less than the number of active modes. In the last decade, methods based on the PARAllel FACtor (PARAFAC) decomposition have attracted a lot of attention in the field of modal analysis because it has been proven that these methods can deal with underdetermined cases, as well as the presence of harmonic excitations. Moreover, in combination with kurtosis value as a harmonic indicator, this makes them more efficient in distinguishing between harmonic and structural components. However, it can lead to distorted results as it does not take into account the variation in the length of the covariance functions of the modal coordinates. Since the kurtosis values are estimated from these covariance functions, the length of the latter directly affects the kurtosis. To overcome this limit, the present study proposes to introduce the choice of the length of these functions based on their frequency and damping coefficient. This change improves the existing method by more efficient separating between harmonics and modal components. The proposed procedure is validated using numerical simulations, followed by ambient vibration measurements. © 2021 Academie des sciences, Paris and the authors.

Tensor-based approach for underdetermined operational modal identification

During these years, blind source separation (BSS) techniques have been demonstrated as a promising tool for operational modal identification of large-scale engineering structures only from output responses. However, plenty of BSS identification approaches are based on the assumption that the sources are sparse or statistically independent, limiting their application scopes. Furthermore, it has been challenging to perform operational modal identification in underdetermined cases where the number of observed sensors is less than the number of active modes. In allusion to the problems above, a novel tensor-based approach for operational modal identification with limited sensors is proposed, in which the low-rank characteristics of vibration measurements is utilized. This paper reveals the intrinsic connection between tensor decomposition and modal expansion. Firstly, a third-order tensor is constructed through a set of generated matrices, in which each observed signal is reshaped into a matrix by segmentation operation. Then, the tensorial observed signals are decomposed into multilinear rank-Lr,Lr,1 terms by block-termed decomposition (BTD). And a collection of sub-tensors that correspond to the mode shapes matrix and modal responses can be obtained, from which the modal parameters are estimated. Finally, the effectiveness of the proposed method is validated with a series of numerical studies and experimental investigations, even in closely-spaced modes. The simulation and experimental results indicate that the proposed method can identify the modal parameters accurately and robustly in both determined and underdetermined situations.

A two-stage framework for automated operational modal identification

Automated operational modal analysis (OMA) is attractive and has been extensively used to replace traditional OMA, which requires much empirical observation and engineers’ judgment. Still, the uncertainties on modal parameters and spurious modes are challenging to estimate under the field conditions. For addressing this challenge, this research proposed an automated modal identification approach. The proposed approach consists of two steps: (1) modal analysis using covariance-driven stochastic subspace algorithm; (2) automated interpretation of the stabilization diagram. An additional uncertainty criterion is employed to initially remove as many spurious modes as possible. A novel threshold calculation for clustering is proposed with incorporating uncertainty of modal parameters and the weighting factor. An improved self-adaptive clustering with new distance calculation is used to group physical modes, followed by the final step of robust outlier detection to select outlying modes. The proposed automated approach requires minimum human intervention. Two field tests of the footbridge and a post-tensioned concrete bridge are used to verify the proposed approach. A modal tracking was used for continuously measured data for demonstrating the applicability of the approach. Results show the proposed approach has fairly good performance and be suitable for automated OMA and long-term health monitoring.

Modal identification of concrete arch dam by fully automated operational modal identification

Modal identification is a type of system identification, which studies on the modal parameters of systems by using modal test. In the case of using operational or ambient modal analysis, there is no need to measure excitation, and the system output data are adequate for identification purposes. These modal parameters of system are of great importance from the engineering point of view particularly in the area of system identification, damage detection, and condition monitoring. In a fully-automated identification approach, the modal parameters are extracted without intervention of a specialized user. In this study, a Fully Automated Operational Modal Identification algorithm is developed to identify modal parameters of an arch dam. For this purpose, Morrow point arch dam is selected, and a 3-D finite element of the dam is established. In the first step, the computed natural frequencies of the dam based on the forced vibration tests are utilized to verify the developed finite-element model of the dam. Afterwards, the dam is excited by El-Centro earthquake, and its seismic response is recorded. The collected signals are presented to the proposed identification algorithm. The proposed algorithm presents a methodology to classify the physical mode shapes from spurious modes using the Stochastic Subspace framework. The results indicate acceptable identification via the proposed algorithm using a dataset and non-repetitive data acquisition. Moreover, the identification process is automated and it does not require any user interaction. It is noteworthy to state that the algorithm can identify any dam with any number of mode shapes, and it is practical and straightforward to apply.