Operational Modal Analysis Method Research Articles

Automated operational modal analysis for supertall buildings based on a three-stage strategy and modified hierarchical clustering

Several automated operational modal analysis (AOMA) methods have been developed to evaluate the dynamic characteristics of large-scale structures in real-time under environmental and operational variations. Typically, these methods need to manually set some thresholds to achieve automatic identification. However, there is a lack of uniform standards for setting these thresholds, which may result in the adoption of inappropriate settings in AOMA, thereby introducing errors in modal identification. To address this issue, this paper proposes a novel AOMA framework to automatically identify modal parameters, which mainly involves three steps. Firstly, the covariance-driven stochastic subspace identification (Cov-SSI) algorithm is employed to perform modal estimation based on measured ambient vibration records. Then, a three-stage strategy, including hard validation criteria, Gaussian mixture model clustering-driven soft validation criteria, and the local outlier factor algorithm, is presented to remove spurious modes and determine real physical modes. Finally, a modified hierarchical clustering based on the k-nearest neighbor information is applied to group the determined physical modes to achieve automatic modal identification. The effectiveness of the proposed AOMA framework in automatically identifying modal parameters is validated through a numerical simulation study for a five-floor frame structure. Furthermore, the proposed framework is applied to evaluate the modal properties of a 600 m high supertall building based on long-term monitoring records. The results show that the AOMA framework can effectively remove spurious modes and group physical modes, thus identifying the modal parameters with high accuracy. In short, the proposed AOMA framework is an effective tool for modal identification applied in field measurements or structural health monitoring.

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.

Stochastic Subspace Identification-Based Automated Operational Modal Analysis Considering Modal Uncertainty

An automated operational modal analysis (AOMA) method that considers the uncertainty in modal parameters is presented and data acquired from actual bridges are used to validate it. The proposed method processes stepwise, from SSI to pre-cleaning, clustering and the removal of outliers. The stochastic subspace identification (SSI) step also calculates the uncertainty of the modal parameters. In this step, the MAC (modal assurance criterion) index and its variability are additionally calculated by exploiting the alteration of the mode shapes. The pre-cleaning stage sorts out the spurious modes by means of the frequency, the coefficient of variation related to the frequency and the damping ratio, as well as the MAC index and its standard deviation. Under the assumption of normal distributions for the frequency and the MAC index, the clustering stage constructs clusters of identical modes with reference to the uncertainty of each mode. The outliers that may be contained in each of these clusters are then removed based upon the frequency, the MAC index and the damping ratio. Values for the parameters that make the proposed method applicable are suggested and are applied unilaterally to three instrumented bridges of different types. The results show that the proposed AOMA method provides accurate mode identification regardless of the bridge type.

Automated operational modal analysis for civil engineering structures with compressed measurements

Introducing compressive sensing (CS) to modal analysis enables modal identification approaches to process compressed measurements, which enhances the efficiency in both data transmission and analysis for long-term monitoring of civil engineering structures. Nevertheless, the existing methods normally require users’ judgment in mode selection, and thus they cannot realize automated modal analysis. To bridge this gap, this study proposes an automated CS-based operational modal analysis (OMA) method, namely Automated Sparse Decomposition (ASD). A mode selection strategy is proposed to gradually eliminate noise and false modes and thus realize automated modal identification based on compressed measurements. A search strategy with both extensive and intensive search stages is proposed to realize higher frequency search resolution with low computational costs. Additionally, an automated mode shape identification process is designed to enhance accuracy. To demonstrate the effectiveness of the proposed method, experimental data on an offshore wind turbine model and real-world monitoring data from an in-service cable-stayed bridge are analyzed. The results show that the identification accuracy of the proposed ASD is comparable to state-of-art CS-based methods. Due to its superior performance in both efficiency and accuracy, the proposed method has the potential to become a promising online modal analysis tool.

Intelligent automatic operational modal analysis

Operational modal analysis methods have been proven especially useful to identify existing structures and infrastructures under serviceability conditions. However, the installation of sensing systems for monitoring continuously an ever larger number of existing constructions has motivated significant efforts towards the automation of the available methods.Within this framework, the present paper introduces a new paradigm for the automatic output-only modal identification of linear structures under ambient vibrations, namely the intelligent automatic operational modal analysis (i-AOMA). It exploits the covariance-based stochastic subspace (SSI-cov) algorithm for the output-only identification of the modal parameters and its workflow consists of two main phases. Initially, quasi-random samples of the control parameters for the SSI-cov algorithm are generated. Once the SSI-cov algorithm is performed for each sample, the corresponding stabilization diagrams are processed in order to prepare a database for training the intelligent core of the i-AOMA method. This is a machine learning technique (namely a random forest algorithm) that predicts which combination of the control parameters for the SSI-cov algorithm is able to provide good modal estimates. Afterward, new quasi-random samples of the control parameters for the SSI-cov algorithm are generated repeatedly until a statistical convergence criterion is achieved. If the generic sample is classified as feasible by the intelligent core of the i-AOMA method, then the SSI-cov algorithm is performed. Finally, stable modal results are distilled from the stabilization diagrams and relevant statistics are computed to evaluate the uncertainty level due to the variability of the control parameters.The proposed i-AOMA method has been applied to identify the modal features of the Al-Hamra Firduos Tower, an iconic 412.6 m tall building located in Kuwait City (Kuwait). The final results well agree with a previous experimental study, and it was also possible to identify two new vibration modes of the structure. The implemented open-source Python code is made freely available.

An Interpretable Method for Operational Modal Analysis in Time-Frequency Representation and Its Applications to Railway Sleepers

Operational modal analysis (OMA) enables the identification of modal characteristics under operational loads and conditions. Traditional frequency-domain methods cannot directly capture modal changes over time, while existing time-frequency representations are not sufficiently interpretable due to spurious modes and implicit parameter design. This paper develops a new OMA method in time-frequency representation based on frequency-domain decomposition (FDD). Short-time FDD and a convolution-based strategy are proposed to obtain singular values and local mode shape similarity, respectively, which are further fused into mode indicators by a fuzzy-based strategy mimicking the modal assurance criterion. The method provides not only a global view of the modal characteristics over time and frequency but also estimates of the modal parameters. It is applicable to strongly nonstationary responses under time-varying loads and conditions. All the parameters explicitly affect the time-frequency representation, and the interpretability is enhanced by including physical information from the user’s prior knowledge in selecting parameters and peak bands. The proposed method is validated based on a study of railway sleepers under train passage. The rigid-body motions and bending modes are identified at frequencies up to 6,500 Hz in laboratory tests and 4,500 Hz in field tests at speeds up to 200 km/h. The identified natural frequencies and mode shapes agree with experimental modal analysis (EMA). The proposed method outperforms EMA in terms of broad frequency range and low measurement cost and can be potentially applied to structural health monitoring under operational conditions.

UAV-based operational modal analysis method using improved homography-based perspective rectification method

In this paper, a new dynamic photogrammetry method using an unmanned aerial vehicle (UAV) is proposed and the UAV-based operational modal analysis method is established. The presented dynamic photogrammetry method can measure the dynamic displacements of structure using one or two cameras. However, it is difficult to use fixed cameras or handheld cameras to measure the dynamic responses for some outdoor structures, because it is hard to reach for measurement or maintenance sometimes. Therefore, UAV is an effective alternative and the homography-based perspective rectification method can be used to correct the UAV images. However, the presented methods use only four calibration points. Additionally, there is still obvious signal drift in the extracted dynamic responses. In this paper, a new time varying homography matrix, calculated using n calibration points, is proposed here for the first time to correct the perspective distortion for image at different time and the relative displacements are used to eliminate the influence of UAV in-plane motion. The influence analysis of UAV vibration and the method to eliminate the UAV vibration are the novelty of this paper. And then, the UAV-based operational modal analysis method is proposed. The proposed method is verified using a plane frame structure in laboratory. The results show that the proposed method can effectively eliminate the vibration of UAV and identify the structural modal parameters. Under the impulse excitation and white noise excitation, when the calibration points n is larger than 60, the relative errors of natural frequency and damping ratio are less than 0.4% and 5.45%, respectively. And the MAC values are all greater than 0.99. Meanwhile, the influence of the number of adopted calibration points on modal parameters identification is considered in the experiment and the advised value is given.

Influence of system changes on closely spaced modes of a large-scale concrete tower for the application to structural health monitoring

AbstractConcrete steel towers are increasingly being used for onshore wind turbines. The lower part consists of separated segmented concrete rings connected with dry joints. Due to slight deviations from the axisymmetric cross-section, closely spaced modes occur. Therefore, the influences of small system changes on closely spaced modes, particularly the mode shapes, should be investigated to enable reliable vibration-based monitoring. In this context, the influence of imperfections due to the waviness of the dry joints requires attention. As no acceleration measurements on concrete towers considering small system changes have been performed so far, this has not yet been investigated. Therefore, an experiment is carried out using a large-scale laboratory model of a prestressed concrete segment tower. The system modifications are introduced by changing the preload. This changes the influence of imperfections of the surfaces of the horizontal dry joints, estimated by measuring strain and displacement at the lowest joint. An increasing preload causes the first two pairs of bending modes to move closer together. This enables to study the effect of the closeness of natural frequencies on the related mode shapes based on the same structure. Thus, the known effects of increasing uncertainty of the alignment and a rotation of the mode shape in the mode subspace with closer natural frequencies can be shown experimentally. In this work, the operational modal analysis (OMA) methods Bayesian-OMA (BAYOMA) and Stochastic Subspace Identification (SSI) are used. Local imperfections can significantly affect modal parameters, so these should be considered for vibration-based monitoring.

A new OMA method to perform structural dynamic identification: numerical and experimental investigation

Operational modal analysis (OMA) methods are nowadays common in civil, mechanical and aerospace engineering to identify and monitor structural systems without any knowledge on the structural excitation provided that the latter is due to ambient vibrations. For this reason, OMA methods are embedded with stochastic concepts and then it is difficult for users that have no-knowledge in signal analysis and stochastic dynamics. In this paper an innovative method useful for structural health monitoring (SHM) is proposed. It is based on the signal filtering and on the Hilbert transform of the correlation function matrix. Specifically, the modal shapes are estimated from the correlation functions matrix of the filtered output process and then the frequencies and the damping ratios are estimated from the analytical signals of the mono-component correlation functions: a complex signals in which the real part represents the correlation function and the imaginary part is its Hilbert transform. This method is very simple to use since requires only few interactions with the users and thus it can be used also from users that are not experts in the aforementioned areas. In order to prove the reliability of the proposed method, numerical simulations and experimental tests are reported also considering comparisons with the most popular OMA methods.

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

Various operational modal analysis (OMA) methods have been developed to identify the modal parameters of buildings in use. Recently, efforts have been expended to solve the existing problems associated with accuracy and computational time of OMA methods using deep learning algorithms of convolution neural network (CNN) and deep neural network (DNN). Considering that the result of modal parameters involves a process associated with the extraction of the dynamic characteristics by separating the periodic modes based on a complex ambient vibration response, the neural network technique, whereby the outputs of the past and present data are independent and static, may not be suitable for application in OMA. In this study, an adaptive, stochastic subspace identification long-short term memory (SSI-LSTM) method is proposed to evaluate the variations of the modal parameters as an indicator of the dynamic characteristics of a structure in the time history data of the structural response measured in real-time. Both past and present responses can be considered in the adaptive SSI-LSTM method and can estimate the natural frequency that changes with aging and damage to buildings. Simultaneously, as the deep learning method is basically used, the problems of accuracy and computational time continuously raised in the OMA method can be solved. The proposed method can configure the OMA method using the modal parameter results from the ambient vibration response and SSI for direct network learning. The covariance-driven SSI (SSI-COV) method is used to construct the training data for the proposed adaptive SSI-LSTM method. The proposed SSI-LSTM method is verified by applying it to a simulation model with four degrees-of-freedom and a three-story experimental model. Lastly, the practicality of the proposed method is validated using the response obtained from a 55-story high-rise building.

Modal identification of building structures under unknown input conditions using extended Kalman filter and long-short term memory

Various system identification (SI) techniques have been developed to ensure the sufficient structural performance of buildings. Recently, attempts have been made to solve the problem of the excessive computational time required for operational modal analysis (OMA), which is involved in SI, by using the deep learning (DL) algorithm and to overcome the limited applicability to structural problems of extended Kalman filter (EKF)-based SI technology through the development of a method enabling SI under unknown input conditions by adding a term for the input load to the algorithm. Although DL-based OMA methods and EKF-based SI techniques under unknown input conditions are being developed in various forms, they still produce incomplete identification processes when extracting the identification parameters. The neural network of the developed DL-based OMA method fails to extract all modal parameters perfectly, and EKF-based SI techniques has the limitations of a heavy algorithm and an increased computational burden with an input load term added to the algorithm. Therefore, this study proposes an EKF-based long short-term memory (EKF-LSTM) method that can identify modal parameters. The proposed EKF-LSTM method applies modal-expanded dynamic governing equations to the EKF to identify the modal parameters, where the input load used in the EKF algorithm is estimated using the LSTM method. The EKF-LSTM method can identify all modal parameters using the EKF, which is highly applicable to structural problems. Because the proposed method estimates the input load through an already trained LSTM network, there is no problem with computational burden when estimating the input load. The proposed EKF-LSTM method was verified using a numerical model with three degrees of freedom, and its effectiveness was confirmed by utilizing a steel frame structure model with three floors.

Towards minimal empirical uncertainty bounds of damping estimates of an offshore wind turbine in idling conditions

Structural damping is a critical quantity for condition assessment and fatigue lifetime prediction in wind energy. Its estimation from operational vibration data comes with a considerable amount of uncertainty, derived from environmental and operational variability and from the quality of the estimation process itself. In this paper, we aim to determine experimentally the damping values and their least possible uncertainty bounds for the first two modes of an idling offshore wind turbine. For this purpose, we use field measurements from a 3.6 MW offshore wind turbine located at the DanTysk wind farm. We select a subset of cases from the wind turbine on idling conditions for a confined interval of environmental and operational conditions, in an attempt to minimize operational variability in the damping estimates. In addition, we make a study on the adjustment parameters of the automated operational modal analysis method, aiming at obtaining the most consistent damping estimates. As a result of the proposed methodology, it is possible to confine the 90% confidence intervals of the damping ratio estimates of the first two tower modes within 0.8 and 1.1 percentual points in the fore-aft and the side-to-side direction, respectively.

Health Monitoring of Serial Structures Applying Piezoelectric Film Sensors and Modal Passport.

Health monitoring of critical structures, that form parts of serial operating objects, is a pressing task. The Operational Modal Analysis (OMA) techniques could be the optimal solution. An inexpensive measurement system, such as the OMA, uses a lot of sensors for structural response assessment. The health monitoring of serial structures has to also consider possible deviations between samples. A solution providing the OMA application includes the compact measurement system based on piezoelectric film sensors and modal passport (MP) techniques. For validation of the proposed approach, a series of five similar composite cylinders, with a network of piezoelectric film sensors, was used. Applying modal tests on the specimens, and using OMA with MP methods, the set of typical modal parameters was determined and analyzed. The results of the study confirmed the feasibility of the sensor network and its applicability for structural health monitoring of serial samples using OMA methods. The proven effectiveness of OMA/MP techniques, combined with a sensor network, provides a prototype of intelligent sensor technology, which can be used for health monitoring of structures, including those that are part of an operating facility.

Distributed fiber mountain seismic monitoring and steady-state analysis under natural earthquakes.

Mountain dynamic response monitoring plays important roles in geological disaster evolution monitoring and warning. A distributed mountain seismic monitoring and steady-state analysis method is demonstrated with distributed acoustic sensing (DAS) and a natural earthquake stimulus. In the field test, the seismic detection capability is first verified by comparing the recorded seismic waveforms from DAS and existing seismic stations. The vibration signal difference between steady-state and unsteady-state mountain parts is apparent; the operational modal analysis method is utilized to extract the response difference and to monitor the disaster evolution process. The proposed method has many advantages, including being easy to deploy, all-weather online monitoring, etc. It is believed that the proposed method will broaden the DAS application scope and promote the development of geological disaster early warning such as landslides and collapses.

Modal parameter identification and seismic assessment of historical timber structures under near-fault and far-fault ground motions

Timber, one of the oldest structural materials, is an essential material in the construction of traditional structures due to its undeniable advantages. However, wood is sensitive to environmental effects, and hence, historical timber structures experience various degradations and destructions during their service life. This highlights the necessity of investigating the structural responses of such structures using experimental techniques and calibrated finite element models. This paper presents vibration-based system identification of two historical timber structures and an in-depth comparison of the effects of near-fault and far-fault ground motions on seismic responses. Ambient vibration tests were carried out using the operational modal analysis method. Enhanced Frequency Domain Decomposition and Stochastic Subspace Identification methods were used for experimental modal parameters estimation. Also, the initial finite element models were calibrated considering the ambient vibration test results to correctly assess the seismic responses of the selected structures under near-fault and far-fault ground motions. The distributions of maximum amplitudes (displacements, internal forces, and absolute accelerations) under earthquake records with near-fault and far-fault are comparatively presented. All numerical results indicated that both near-fault ground motions and their far-fault counterparts played major roles in terms of the seismic responses of selected historical timber structures. In addition, these results illustrate that both had the potential to increase displacements and, internal forces at load-bearing elements, and leading to notable structural responses and destructive effects.

An unsupervised learning algorithm for computer vision-based blind modal parameters identification of output-only structures from video measurements

Operational modal analysis (OMA) is required to maintain large-scale and necessary civil infrastructures. The non-contact method of OMA using digital image correlation and point tracking algorithms requires a speckle pattern placed on the structure. Alternatively, advanced computer vision methods like optical flow and phase-based video motion magnification (PBVMM) techniques are used to measure modal parameters. Despite the importance of PBVMM, the users should know the range of frequencies in which the natural structure frequency lies. A methodology based on an unsupervised machine learning technique is developed to extract the modal parameters blindly from its recorded digital video. The proposed methodology uses complex steerable pyramids and an unsupervised machine learning technique, also known as principal component analysis, and analytical mode decomposition with a random decrement technique to blindly extract the modal parameters of a structure. This study validated the proposed methodology using a multi-degree of freedom (DOF) numerical model. The results are compared with theoretical and estimated values and are in good agreement. Furthermore, it is implemented on a laboratory benchmark SDOF, MDOF, and real-time videos of the London Millennium and Tacoma Narrows bridges for blindly extracting the modal frequencies and damping ratios.

Fully automatic operational modal analysis method based on statistical rule enhanced adaptive clustering method

Timely monitoring of modal parameters is commonly adopted to keep in-service bridges safe. For fulfilling the demand, plenty of operational modal analysis (OMA) methods were developed in which only the structural response needs to be measured. However, when utilizing these methods, there are still some deficiencies, like mingled spurious modes and the hyper-parameters needing manual tuning. Although many studies have utilized clustering algorithms to solve these issues and promote the automatic level of the OMA method, some new hyper-parameters belonging to these algorithms would be introduced as well, which also need manual maneuvering. Meanwhile, the performance of various clustering algorithms on this issue also shows variety due to their distinct inductive biases. As a result, the prerequisite of relevant expertise still hinders the common users in their extraction and tracking of the bridge’s modal information. Under these circumstances, after conducting a comparison among representative clustering algorithms, this study proposed an applicable fully automatic OMA method by an adaptive clustering method, “K-average nearest neighbor density-based spatial clustering of applications with noise (KANN-DBSCAN)” enhanced by the five-number summary. This method’s performance was investigated via numerical analyses and the measured data from an actual bridge. The results illustrated that this method functions well in the tested scenarios and has the potential for wide application in actual engineering.

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.

Removal of transfer function effects from gear vibration signals under constant and variable speed conditions

Gear faults generally cause changes to the forcing functions of the system, which are usually hard to measure. Vibration is a common tool for gear condition monitoring, it being generated by a forcing function exciting responses through a transmission path from the excitation to the measurement point. The diagnostic information in the vibration measurements is often distorted by transfer function effects, in particular for local faults, such as cracks, where the waveform is important. In such cases, more direct diagnostic information can be extracted by removing the transfer function effects. However, a very limited amount of research has been carried out to reconstruct the time-domain waveforms of the forcing functions, except some making the assumption that the forcing functions are impulsive. A method was previously developed to identify and remove the transfer function effects from transmission error (TE) measurements at constant speeds to reconstruct the excitations, utilising a cepstrum-based operational modal analysis (OMA) method. In the current paper, this method is extended to vibration signals under constant and variable speed conditions. Since vibration has more complex transfer functions than TE, this paper establishes an additional pre-processing procedure, which removes the deterministic components in order to facilitate the OMA process. After removing the transfer function effects from measured vibration signals, the proposed technique reconstructs forcing functions that are much more clearly indicative of the faults at all speeds and which approximate the meshing forces at the gear teeth. The fault features are effectively enhanced and localised in the forcing functions, and the importance of phase modification to the reconstruction of forcing function waveforms is demonstrated. The technique was validated using vibration measurements obtained from a single stage spur gear box with a tooth root crack.

An Innovative Structural Dynamic Identification Procedure Combining Time Domain OMA Technique and GA

In this paper an innovative and simple Operational Modal Analysis (OMA) method for structural dynamic identification is proposed. It combines the recently introduced Time Domain–Analytical Signal Method (TD–ASM) with the Genetic Algorithm (GA). Specifically, TD–ASM is firstly employed to estimate a subspace of candidate modal parameters, and then the GA is used to identify the structural parameters minimizing the fitness value returned by an appropriately introduced objective function. Notably, this method can be used to estimate structural parameters even for high damping ratios, and it also allows one to identify the Power Spectral Density (PSD) of the structural excitation. The reliability of the proposed method is proved through several numerical applications on two different Multi Degree of Freedom (MDoF) systems, also considering comparisons with other OMA methods. The results obtained in terms of modal parameters identification, Frequency Response Functions (FRFs) matrix estimation, and structural response prediction show the reliability of the proposed procedure.