Operational Modal Analysis Research Articles

The effect of geometric parameters on natural frequencies of Persian brick masonry arches

In this paper, several parametric studies were performed on the dynamic behaviour of seven types of Persian brick masonry arches using the finite element method. The studied parameters included the arch types, arch thickness, arch scale, support conditions, and brick arrangement. The finite element models were calibrated using experimental results obtained from operational modal analysis of an arch constructed in the laboratory. The parametric studies have shown that the type of arch significantly affects the natural frequencies. The increasing of arch thickness leads to increase of the natural frequencies. Simply supported arches exhibit reduced natural frequencies, compared to those fixed at their supports. Brick arrangement has little effect on the natural frequency. Finally, an empirical equation for estimating the fundamental frequency of the studied arches was proposed using the obtained results from finite element models. The high accuracy of the empirical equation was tested through measurements on a real full-scale arch.

Vibration Signal Evaluation Based on K-Means Clustering as a Pre-Stage of Operational Modal Analysis for Structural Health Monitoring of Rotating Machines

Rotating machines are key components in energy generation processes, and faults can lead to shutdowns or catastrophes encompassing economic and social losses. Structural Health Monitoring (SHM) of structures in operation is successfully performed via Operational Modal Analysis (OMA), which has advantages over traditional methods. In OMA, white noise inputs lead to the accurate extraction of modal parameters without taking the system out of operation. However, this excitation condition is not easy to attain for rotating machines used in power generation, and OMA can provide inaccurate information. This research investigates the applicability of machine learning as a pre-stage of OMA to differentiate adequate from inadequate excitations and prevent inaccurate extraction of modal parameters. Data from a rotor system was collected under different conditions and OMA was applied. In a training stage, measurements were characterized by statistical features and K-means was used to determine which features provided information about the excitation condition, that is, which excitation was adequate to extract the rotor’s modal parameters via OMA. In a testing stage, data were successfully classified as adequate or not adequate for OMA, achieving 100% accuracy and revealing the technique’s potential to support SHM of rotating machines. The technique is extendable to other monitoring systems based on OMA.

Enhancing second-order blind identification for underdetermined operational modal analysis through bandlimited source separation

Blind source separation (BSS) has been demonstrated to be a promising method for operational modal analysis (OMA). However, the conventional BSS-based modal identification methods can only handle the determined or overdetermined identification where the number of sensors must equal or exceed that of active modes, limiting their wider application. Furthermore, the existing methods for underdetermined BSS require sparsity assumption of sources, optimization of model parameters, or structural prior information, undermining the non-parametric and “blind” properties of BSS. This paper proposes a novel method for underdetermined OMA. Firstly, the bandlimited source separation using sinc-dictionaries is performed to efficiently transform the underdetermined problem into several determined or overdetermined ones. An improved second-order blind identification (SOBI) involving Hilbert transform and random time-lagged covariances is then applied for each bandlimited signal to recover modal responses and mode shapes. To attenuate noise, an adaptive singular spectrum analysis (SSA) can be optionally applied to the recovered modal responses for the highly noisy systems. Finally, the natural frequencies and damping ratios are estimated by the single-degree-of-freedom (SDOF) fitting technique. Several numerical examples, an experimental frame case, and a field test of a pedestrian bridge are studied to verify the effectiveness of the proposed strategy.

Improved multi-order Vold-Kalman filter for order tracking analysis using split cosine and sine terms

Order tracking analysis is an effective tool for the analysis of non-stationary vibration and acoustical signals for the purposes of machinery fault diagnosis and operational modal analysis. The second-generation Vold-Kalman filter is widely used for order tracking analysis; however, the formulation of the data equation is based on incomplete complex kernels, which introduce an imaginary part error in the cost function. In this work, the data equation of the second generation Vold-Kalman filter is re-formulated using separated cosine and sine kernels that necessarily provide a real-valued sum. Doing so will minimize the error in the data equation and offer better optimization scheme to reduce the error in the structural equation and; hence, provide smooth envelopes. Unlike Vold-Kalman method which requires high filter weighting factors to suppress envelope artifacts, the proposed method can achieve high accuracy even when using small weighting factor as deduced from the simulation and experimental investigations. The proposed method can be used to measure the envelopes of close and crossing orders, as well as orders experiencing resonance conditions or orders with high slew rate due to lower filter decay time.

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.

Vibration signature effects on damping identification of a RC bridge under ambient vibrations

Experimental tests for dynamic identification of reinforced concrete (RC) bridges by means of Operational Modal Analysis (OMA) are increasingly used in common engineering practice. Nevertheless, especially when measurements are carried out under in-service conditions (i.e. under traffic induced vibrations), some drawbacks should be carefully considered, especially in the damping-ratio quantification. As a matter of fact, the estimation is affected by several factors: i) the length of the signals, ii) the non-stationarity of the input process, and iii) the dependence on the vibration amplitude. Even if the damping ratio is a key parameter in the bridge dynamics, a major part of these aspects has not been yet fully investigated to estimate reliable values.Starting from a dynamic test program on a short-span RC bridge with half-joints in Italy, this paper investigates the issues mentioned above for the damping ratio estimation of the first two modes focusing on: i) the influence of the signal length, ii) the effects of the signals properties, and iii) their correlation with the vibration amplitude. Both the Stochastic Subspace Identification technique fed with the signal covariance (SSI-cov) and the Random Decrement technique (RD) have been used to compute the damping ratios from the collected signals. This paper shows how a convergence of the results cannot be attained by simply increasing the sample size, suggesting that the nature of the vibration itself influences the damping values. A negative, although weak, correlation between the damping ratio and the power of the signals indicates that several factors play a crucial role in the damping estimation in the short span RC bridges with half-joints.

An efficient automatic modal identification method based on free vibration response and enhanced Empirical Fourier Decomposition technique

This paper presents an efficient yet practical approach for the automatic modal identification of structures based on their free vibration response. The proposed approach relies on the Empirical Fourier Decomposition (EFD) technique. It implements a new procedure to recognize automatically the number of modal components to be extracted from noisy data in such a way to prevent both mode-mixing and mode-splitting effects. A suitable strategy is adopted to improve the segmentation of the frequency spectrum of the free vibration response, so as to identify accurately the bounds of the frequency spectrum partition corresponding to each modal component. The related modal damping ratios are estimated by means of a robust area-based approach in order to mitigate the noise-induced disturbances whereas a time-domain method based on the phase shift of the free vibration response peaks is employed to identify the mode shapes.The proposed approach is first validated through the analysis of synthetic signals that embed closely spaced components and a lowly excited vibration mode. Finally, the proposed approach is applied to two real bridges. The first case-study deals with the identification of modal frequencies and damping ratios of the cables of a stay-cabled bridge. The second case-study involves the modal identification of a steel railway bridge deck that exhibits two closely spaced vibration modes. The outcomes obtained using the proposed approach based on EFD technique are compared with the results obtained by means of the Variational Mode Decomposition (VMD) technique as well as with those computed through classical operational modal analysis techniques. The consistent estimates produced by means of the proposed approach demonstrate its accuracy and robustness.

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.

Research on online monitoring technology for transmission tower bolt looseness

Minor damages such as tower bolt looseness are difficult to detect through manual inspections. Operational modal analysis plays an important role in the online monitoring of transmission tower structure safety. However, the traditional analysis methods select feature parameters manually, and the deviation generated will directly affect the estimation accuracy of structural modal parameters. This article proposes a method for diagnosing tower bolt looseness without human intervention. This method can reduce the influence of background noise greatly through data cleaning and data fusion. Besides, the intelligent feature recognition of vibration acceleration time-domain signals based on an improved 1DCNN algorithm can improve the monitoring accuracy and speed significantly. The effectiveness of the method has been validated by conducting dynamic response tests on a 110KV transmission tower under different bolt loosening conditions. In the end, an online monitoring technology for transmission towers bolt looseness has been developed and successfully applied to the Guangdong power grid. The results show that this method has high identification accuracy and provides a new approach for online monitoring of tower bolt looseness.

Iterative hierarchical clustering algorithm for automated operational modal analysis

Recent developments in sensors and data processing made the structural health monitoring (SHM) sector expanding to big-data field, particularly when continuous long-term strategies are implemented. Nevertheless, main shortcomings are due to the identification and extraction of modal features. In fact, although machine learning methods have been implemented to automate modal identification processes, intense user interaction and time-consuming procedures are still required, limiting the extensive use of these techniques. In order to provide a fully automated procedure capable of identifying and extracting modal properties from covariance driven SSI analyses, an innovative and flexible algorithm for Iterative Hierarchical Clustering Analysis (IHCA) is proposed. To evaluate the stability and robustness of the IHCA method, a Variance-Based Global sensitivity Analysis (VBGA) was performed considering a numerical and experimental case study. The outcomes demonstrated that the IHCA is stable in clustering the physical structural modes and selecting the most representative modal features.

Modal and Structural Identification of Historic Bell Tower in Čuntić, Croatia Using Ambient Vibration Testing

In this study, modal and structural identification of a historic masonry bell tower in Čuntići, Croatia, damaged during the recent Petrinja earthquake, was performed. The results of the ambient vibration tests (AVT) and operational modal analysis (OMA) were used to update the finite element numerical model of the bell tower. Three modes were experimentally determined: the first two were bending modes (f1 = 4.395 Hz and f2 = 4.639 Hz), and the third was a torsional mode (f3 = 10.303 Hz). The experimentally determined and the originally calculated (preliminary NM) modal shapes agreed well, but in terms of modal frequencies, the correlation was poor. After model updating, some structural parameters were identified, and a reliable finite element numerical model was established. The proposed method can provide a reliable evaluation of the structural parameters of historic masonry buildings.

Moving window incremental multidimensional scale analysis-based operational modal analysis for linear slow time varying structure

Moving window incremental multidimensional scale analysis-based operational modal analysis for linear slow time varying structure

Counter-checking uncertainty calculations in Bayesian operational modal analysis with EM techniques

Bayesian operational modal analysis makes inference about the modal properties (e.g., natural frequency, damping ratio) of a structure using ‘output-only’ ambient vibration data. With sufficient data in applications, the posterior probability density function (PDF) of modal properties can be approximated by a Gaussian PDF, whose covariance matrix is given by the inverse of the Hessian of negative log-likelihood function (NLLF) at the most probable value. Existing methodologies for computing the Hessian are based on semi-analytical formulae that offer an efficient and reliable means for applications. Inevitably, their computer coding can be involved, e.g., a mix of variables with different sensitivities, singularity of Hessian due to constraints. In the absence of analytical or numerically ‘exact’ result for benchmarking, computer code verification during development stage is also non-trivial. Currently, finite difference method is often used as the only and last resort for verification, although there are also difficulties in, e.g., the choice of step size, and criterion for comparison/convergence. Motivated by these, this work explores an identity in the theory of Expectation-Maximisation (EM) algorithm to provide an alternative means for evaluating the Hessian of NLLF. Such identity allows one to evaluate the Hessian by means of Monte Carlo simulation, averaging over random samples of hidden variables. While the existing semi-analytical approach is still preferred for Hessian calculations in applications for its high definitive accuracy and speed, the proposed Monte Carlo solution offers a convenient means for counter-checking during code development. Theoretical implications of the identity will be discussed and numerical examples will be given to illustrate implementation aspects.

A novel demodulation method with a reference signal for operational modal analysis and baseline-free damage detection of a beam under random excitation

A novel demodulation method with a reference signal is developed for operational modal analysis and damage detection of a beam structure under random excitation. The novel demodulation method can process measurements of the beam by a continuously scanning laser Doppler vibrometer (CSLDV) system and measurements of a reference point on the beam by a single-point laser Doppler vibrometer to estimate its modal parameters, such as damped natural frequencies and undamped mode shapes. Damped natural frequencies of the beam are estimated from fast Fourier transforms of measurements of the CSLDV system. A cross-correlation function between a measurement of the CSLDV system and a measurement of a single-point laser Doppler vibrometer is calculated, and the cross-correlation function is multiplied by a sinusoidal signal whose frequency is an estimated damped natural frequency of the beam. The processed cross-correlation function is filtered by a low-pass filter to obtain the undamped mode shape of the beam that corresponds to the estimated damped natural frequency of the beam. Smooth polynomials are used to fit estimated undamped mode shapes, which can be considered as undamped mode shapes of an undamaged beam. Curvatures of estimated undamped mode shapes and polynomials are compared by curvature damage indices to determine the location of a damage in the beam. The novel demodulation method with a reference signal is investigated for baseline-free damage detection from both finite element simulation and experiment. Modal parameters of a finite element model of the damaged beam and a damaged beam specimen, which are under random excitation, are successfully estimated, and locations of damages in the beam model and beam specimen are accurately determined.

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

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

Behavior factor estimation for seismic design of unreinforced masonry buildings

The use of new geo-sourced construction materials in seismic areas requires the assessment of the structure ductility in order to properly design the building. This research aims to propose a procedure for behavior factor estimation in case of using a new construction material. In particular, in this paper, the proposed methodology is applied to an unreinforced masonry building in an average-risk seismic zone. Before application for seismic design, the reliability of the selected equivalent frame modeling approach is validated by comparison of dynamic features obtained from both numerical and operational modal analysis. An existing stone masonry building is selected as case study to validate the modeling approach. A measurement campaign provides the structural response to ambient vibrations and structural damping. After validating the model in elastic conditions, the building ductility capacity is estimated using a numerical pushover analysis, for different load combinations and distributions, according to the European design code, under the assumption of perfect plasticity. The proposed procedure provides a behavior factor obtained specifically for the analyzed building, using a relationship between ductility demand and behavior factor deduced from dynamic analysis. The average ductility demand is estimated numerically, for a set of synthetic acceleration signals compatible with the Eurocode elastic response spectrum and a given behavior factor. Finally, it is suggested to verify the near collapse limit state of the building structure not only in terms of target to capacity displacement ratio but also in terms of load ratio, since it can be more restrictive in some instances.

Investigation of the concrete parameters of existing RC buildings by operational modal analysis

Investigation of the concrete parameters of existing RC buildings by operational modal analysis

Monopile Foundation Stiffness Estimation of an Instrumented Offshore Wind Turbine through Model Updating

Rapid development of offshore wind foundation models has resulted in a large number of built structures with generally underestimated foundation stiffness properties and a need to update and validate both the individual structural models and the underlying foundation design frameworks. This paper outlines a structural health monitoring approach, based on the combination of output only structural health monitoring methods and model updating, to estimate foundation stiffness parameters using field monitored data. Field monitoring data from an offshore wind turbine under idling conditions, over a large monitoring period, are presented and operational modal analysis is applied to estimate the modal parameters. Those are compared to modal properties predicted by finite element models, employing either old (API/DNVGL) or new (PISA) foundation design properties, which are calibrated using geotechnical site investigation data. A new approach to interpret seabed level statically equivalent foundation stiffness, in terms of effective lateral and rotational stiffness against load eccentricity, is presented. Seabed level statically equivalent foundation properties are updated by comparison against the observed modal behaviour and the optimised foundation parameters are presented, demonstrating a close match to the predictions of the PISA method.

An edge-computing framework for operational modal analysis of offshore wind-turbine tower

With massive construction of offshore wind turbines (OWT), structural health monitoring (SHM) techniques have been applied to estimate the working conditions and provide early warnings of structural damage. This study proposes an edge-computing-based SHM system for operational modal analysis (OMA) of an OWT. ThssCe system comprised an open-source data acquisition (DAQ) device, a Raspberry Pi single-board computer, and associated drivers, protocols, and algorithms. The DAQ device can measure the acceleration response of an operating OWT subjected to environmental excitation and transmit raw signals to the Raspberry Pi according to the UDP protocol. The data are further processed to obtain the first-order frequency via an OMA algorithm developed by combining Kalman filtering, the random decrement technique (RDT), and the stochastic subspace identification (SSI) method. The proposed SHM system was implemented in a scaled OWT model to verify its feasibility for field use. The experimental results indicate that (1) the edge-computing-based SHM system can accurately measure the response of the OWT; (2) the proposed algorithm can estimate the modal information of the OWT during operation; (3) the variation in the first-order frequency induced by lateral loads can be identified by the SHM system. Unlike a centralized SHM system, the proposed edge-computing-based SHM system does not require massive data transmission, making it promising for offshore environments.

An Automated Procedure for Continuous Dynamic Monitoring of Structures: Theory and Validation

IntroductionStability diagrams are a helpful tool for operational modal analysis to obtain the physical modes of a structure. These modes can be defined by visualizing stable columns formed by consistently identified modes over a range of model orders. Extracting these modes manually becomes an obstacle if continuous identification of modal parameters is required.Materials and methodsIn this paper, a procedure is configured to automatically interpret the stability diagrams constructed with the identification results of the SSI-COV/ref algorithm. This procedure is based on some methodologies found in the literature, which follow three stages. First, a stability diagram cleaning stage is defined where modal validation criteria and partitioning clustering algorithms are used to detect spurious modes. Second, a mode grouping stage based on a hierarchical clustering algorithm is implemented to form sets of modes that share similar modal information. Finally, a selection stage is applied to define representative modal parameters from the set of physical modes.ResultsThe proposed procedure is validated by simulating a beam-type structural model with ten degrees of freedom affected by ambient temperature functions. Natural frequencies computed for the DT140 and DT220 datasets collection with the frequency-domain decomposition method agree with the computed ones with the proposed procedure, presenting MAC coefficients higher than 0.97. A total of 192 datasets are simulated, and the acceleration responses are polluted with two noise levels, SRN = 40 [dB] and SNR = 20 [dB].ConclusionsFor the analyzed beam, the modal tracking results showed that the procedure could perform continuous identification automatically. The variations in the natural frequencies are correlated to the variations in the ambient temperature functions.