Modal Assurance Criterion Research Articles

Tire mode shape categorization using Zernike annular moment and machine learning classification

This research proposes a framework for categorizing the radial tire mode shapes using machine learning (ML) based classification and feature recognition algorithms, advancing the development of a digital twin for tire performance analysis. Tire mode shape categorization is required to identify modal features in a specific frequency range to maximize driving performance and secure safety. However, the mode categorization work requires a lot of manual effort to interpret modes. Therefore, this study suggests an ML-based classification tool to replace the conventional categorization process with two primary objectives: (1) create a database by categorizing the tire mode shapes based on the identified features and (2) develop an ML-based surrogate model to classify the tire mode shapes without manual effort. The feature map of the tire mode shape is built with the Zernike annular moment descriptor (ZAMD). The mode shapes are categorized using the correlation value derived by the modal assurance criteria (MAC) with all ZAMD values for each tire mode shape and subsequently creating the appropriate labels. The decision tree, random forests, and XGBoost, the representative supervised-learning algorithms for classification, are implemented for surrogate model development. The best-performed classifier can categorize the mode shapes without any manual effort with a high accuracy of 99.5%.

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.

Compressive sensing-based construction of high-resolution mode shapes for updating bridge boundary constraints

In this study, a method of finite element model updating is proposed to quantitatively identify bridge boundary constraints using the high-resolution mode shapes of a bridge. The high-resolution mode shapes are first identified from the responses measured by few randomly distributed sensors using the compressive sensing theory, which is innovatively implemented in the spatial domain with a proposed basis matrix. To speed up finite element updating, the frequency and modal assurance criterion Kriging models are then established to approximate the implicit relation between boundary constraints and bridge modal parameters including frequencies and mode shapes, serving as surrogate models for the bridge finite element model. By adopting the surrogate models in finite element updating, the objective functions of frequencies and mode shape indicators are optimized by a multi-objective genetic algorithm. The numerical examples as well as an actual laboratory experiment have shown that the mode shapes and boundary constraints of a bridge can be identified precisely and efficiently by the proposed method, even for a continuous and variable cross-sectional bridge.

Symmetric/Asymmetric Vibrational Characteristics of Bi-Directional Functionally Graded Annular Microplates

In this study, a free vibration model of bi-directional functionally graded (BD-FG) annular microplates is established based on the modified couple stress theory (MCST) and the first-order shear deformation theory (FSDT), and the corresponding governing equations are derived from Hamilton’s principle. The annular microplates are assumed to be composed of metal and ceramic materials, and the equivalent material properties are a combination of power-law function and exponential ones. The generalized differential quadrature method (GDQM) is used to obtain the vibration frequencies and mode displacements for the C–C, S–C, C–S, and S–S (S: simply supported; C: clamped) annular microplates. The convergence and validity of the proposed model are verified through selective numerical examples. Further, the effects of gradient index, material length scale parameter, boundary conditions, and geometrical dimensions on the symmetric/asymmetric vibration frequencies of the annular microplate are explored. The modal assurance criterion is applied to estimate the influence of the radial gradient index and material length scale parameter on different-order mode displacements of the annular microplate. The results show that: (1) the vibration frequencies of the annular microplate are sensitive to changes in the geometry and boundary conditions; (2) compared with the axial gradient index, the radial gradient index not only affects the vibration frequencies of the annular microplate, but also impacts the distribution of the highest and lowest points of the vibration mode displacements as well as the vibration mode nodal lines; (3) as the material length scale parameter increases, the vibration frequencies are significantly increased, and the higher-order vibration modes of the annular microplate also change.

An improved lump mass stick model of a nuclear power plant based on the Kriging surrogate model

This paper focuses on an improved lump mass stick model of the AP1000 nuclear power plant (NPP). The conventional method is used to calculate the parameters of the lump mass stick (LMS) model of the AP1000 NPP, which has great differences between the LMS model and the finite element (FEM) model in terms of frequency and vibration mode. Therefore, with optimizing the mass condensation size of a shear wall without a floor as a goal, the improved lump mass stick (I-LMS) model based on the Kriging surrogate model is established. The results illustrate that: (i) compared with the LMS model, the relative error of the I-LMS model and the FEM model, the maximum error of the frequency is reduced from 23.04% to 6.57% with nine order frequencies; (ii) the frequencies of the Kriging surrogate model and the I-LMS model are very close, with the largest error being only 1.45%, indicating that the Kriging surrogate model has obtained better correction accuracy; (iii) the modal assurance criterion (MAC) value of the I-LMS model for the same vibration mode is increased from 0.75 to 0.95 to 0.88–0.96, and the MAC values of different vibration modes are closer to 0; and (iv) comparison of the structural dynamic response under basic design earthquake to the FEM model shows that the I-LMS model has good calculation accuracy and obvious advantages in calculation efficiency.

Identification Uncertainties of Bending Modes of an Onshore Wind Turbine for Vibration-Based Monitoring

This study considers the identification uncertainties of closely spaced bending modes of an operating onshore concrete-steel hybrid wind turbine tower. The knowledge gained contributes to making mode shapes applicable to wind turbine tower monitoring rather than just mode tracking. One reason is that closely spaced modes make it difficult to determine reliable mode shapes for them. For example, the well-known covariance-driven stochastic subspace identification (SSI-COV) yields complex mode shapes with multiple mean phases in the complex plane, which does not allow error-free transformation to the real space. In contrast, the Bayesian Operational Modal Analysis (BAYOMA) allows the determination of real mode shapes. The application of BAYOMA presents a further challenge when quantifying the associated uncertainties, as the typical assumption of a linear, time-invariant system is violated. Therefore, validity is not self-evident and a comprehensive investigation and comparison of results is required. It has already been shown in a previous study that the significant part of the uncertainty in the mode shapes corresponds to their orientation in the mode subspace (MSS). Despite all the challenges mentioned, there is still a great need to develop reliable monitoring parameters (MPs) for Structural Health Monitoring (SHM). This study contributes to this by analysing metrics for comparing mode shapes. In addition to the well-known Modal Assurance Criteria (MAC), the Second-Order MAC (S2MAC) is also used to eliminate the alignment uncertainty by comparing the mode shape with a MSS. In addition, the mode shape identification uncertainties of BAYOMA are also considered. Including uncertainties is also essential for the typically used natural frequencies and damping ratios, which can be more appropriately used if the identification uncertainty is known.

Monitoring system framework design for floating wind turbine using the deep learning technology and tower response identification considering sensor optimization

Comparing with the fixed wind turbines, the dynamic characteristics of floating wind turbines (FWTs) are more complex and resulting in distinctions in the monitoring system for structural responses. An integrated monitoring system framework concept design for FWT is proposed combing the dynamic responses correlations of different structural parts and the deep learning technology, in which the intact and partial sensor failure operation modes are considered separately. The monitoring system consists of four vital structural components, including the rotor and nacelle, tower, floating foundation, and mooring system. In order to improve the tower response identification accuracy, a new method for the sensor optimization is proposed to utilize more structural information of the structure based on the effective independence method (EIM) and modal assurance criteria (MAC) methods. A multi-perception (MLP) neural network model based on the input-output coupling mechanism is established to identify the acceleration responses at the tower top and forces at tower root. The optimized identification model can greatly improve the identification accuracy of critical sensors by more than 50%, especially for bending moments.

Vibration frequency and mode localization characteristics of strain gradient variable-thickness microplates

Based on the modified strain gradient theory and Kirchhoff–Love assumptions, a free vibration model is established for variable-thickness microplates with three material length scale parameters, and the corresponding Euler–Lagrange equation is derived. Keeping the microplate volume constant, three kinds of thickness variations along the X-direction are considered: linear, parabolic, and cubic variations. Further, a C2-type four-node 36-degree-of-freedom variable-thickness differential quadrature finite element is developed to solve the resulting variable-coefficient boundary value problem by combining the Gauss–Lobatto and differential quadrature rules. Galerkin approximate solution for fully simply supported microplates is provided as a benchmark for numerical method verification. The convergence and accuracy of the model are verified through several examples. Finally, the vibration frequencies of the microplates under different thickness variation types, taper ratios, thickness ratios, material length scale parameters, and boundary conditions are examined through parametric analysis. Also, the influence of each factor on the mode localization of the microplates is quantitatively characterized by the modal assurance criterion (MAC) for the first time. The numerical results show that the thickness variation has a minor effect on the vibration frequency but a significant influence on the mode shape when the volume of the microplate is constant. The strain gradient, taper ratio, and discontinuous boundary have a remarkable effect on the distribution of higher-order mode shape contour lines and the regions where vibration localization occurs.

An optimal sparse sensing approach for scanning point selection and response reconstruction in full-field structural vibration testing

Non-contact vibration measurements, such as 3D scanning laser Doppler vibrometry (3D SLDV), are becoming more prevalent in testing next-generation lightweight aerospace structures. This approach reduces the impact of attached sensors and improves measurement reliability. Acquiring precise measurement data for the whole area is feasible, albeit it would demand a considerable amount of time and storage space for testing. The concept of compressed sensing has been recently approved as an effective way to exploit signal sparsity and achieve full response reconstruction with very few measurements. The objective of this work is to enhance the efficiency of non-contact vibration testing by utilizing the state-of-the-art compressive sensing approach. In contrast to conventional sensor placement methods that rely on effective independence, modal kinetic energy, or modal assurance criterion matrix as targets, this paper proposes a novel sensor placement methodology from the perspective of dynamic response reconstruction. The scanning points are chosen with a minimal number to reduce testing time and are well-placed such that full-field vibration responses of the test structure can be reconstructed accurately. This allows for the spatially-detailed vibration responses to be obtained efficiently and accurately with optimal sparse sensing placement and effective response reconstruction through ℓ1 algorithm. Two case studies will be presented in this work to demonstrate and validate the methodology. The first case study is focused on a simplified cantilever beam using the numerical data from the FE analysis to demonstrate the methodology. The second case study is focused on using 3D SLDV experimental testing data from a full-scale industrial fan blade. Based on the results, it is evident that the proposed approach can significantly decrease the scanning points required for a full-field dynamic response reconstruction during full-field vibration testing.

Heteroscedastic Gaussian processes for data normalisation in probabilistic novelty detection of a wind turbine

This study investigates the data normalisation of modal parameters of an operating concrete–steel hybrid onshore wind turbine tower considering also the identification uncertainty. In order to take into account the Environmental and Operational Condition (EOC)-dependent variance, sparse heteroscedastic Gaussian processes (GPs) are used for the data normalisation. Following a typical vibration-based Structural Health Monitoring (SHM) scheme, data normalisation of the natural frequencies and the mode shapes is performed first. Subsequently, a metric is defined which takes into account both the identification uncertainty and the operation-dependent uncertainty in order to enable novelty detection.The data normalisation methods must be able to handle uncertainties of different magnitudes due to EOCs in the data. In this context, GPs can be a suitable tool. However, standard GPs assume homoscedasticity, which is an unrealistic assumption in the case of EOC-dependent variance. Using a heteroscedastic GP instead, the variance of the data is better mapped and allows comparison with the identification uncertainties of Bayesian operational modal analysis (BAYOMA), taking into account the specifics of closely spaced modes of the tower structure. This leads to a better interpretation of the data and enables the introduction of a probabilistic novelty metric.This data normalisation approach, taking into account EOC-dependent uncertainties using heteroscedastic GPs, is being applied for the first time to a tower of a full scale 3.4 MW wind turbine in operation. Following this approach, it is possible to detect smaller changes in natural frequencies and second-order modal assurance criterion (S2MAC) compared to the assumption of homoscedasticity within the GP. In addition, a novelty was detected using the S2MAC during the period under study. Therefore, it can be illustrated that mode shape-based metrics tend to be more sensitive than purely frequency-based ones. However, it is difficult to assess the significance of such changes for structural integrity without further information.

Identification of damages in a concrete beam: a modal analysis based method

Structural Health monitoring (SHM) strategies can play a pivotal role in the perspective of enhancing structures and infrastructures life cycle and maintenance operations. A plethora of sensors and technologies can be employed in this field; in a seismic context, vibrational tests are particularly relevant, being able to give an insight on the dynamic characteristics of the structure itself. In particular, modal parameters can be considered in order to detect damages. A comparison between a certain test time and 0 test time (i.e., undamaged structure) is commonly performed; to this aim numerical models result particularly useful to provide baseline data (often unavailable in pre-existing structures), but they need to be validated before use. Non-contact techniques, like scanning laser Doppler vibrometry, can be exploited to do this. In this paper a numerical model of a scaled concrete beam is realized and validated through LDV data, then it is used to design load tests for progressive damages generation. Modal analysis is conducted after different load trials to evaluate changes of modal parameters in relation to the damage occurred; also, damage-related indices are proposed. The results confirmed the suitability of LDV for dynamic analyses of cement-based structures and this can be particularly useful when big structures (e.g., bridges) have to be monitored in-field. The numerical model was validated with acceptable absolute errors in terms of natural frequencies (between 26 Hz and 131 Hz) and high Modal Assurance Criterion (MAC) values (0.85-0.93). Moreover, the proposed methodology allows to detect damages also in a concise way through synthetic indices (with changes >50% in damaged vs undamaged conditions) and early warnings could be generated according to their values, hence supporting decision-making procedures in the building management scenario.

Fast flow field prediction of three-dimensional hypersonic vehicles using an improved Gaussian process regression algorithm

Conducting large-scale numerical computations to obtain flow field during the hypersonic vehicle engineering design phase can be excessively costly. Although deep learning algorithms enable rapid flow field prediction with high-precision, they require a significant investment in training samples, contradicting the motivation of reducing the cost of acquiring flow field. The combination of feature extraction algorithms and regression algorithms can also achieve high-precision prediction of flow fields, which is more suitable to tackle three-dimensional flow prediction with a small dataset. In this study, we propose a reduced-order model (ROM) for the three-dimensional hypersonic vehicle flow prediction utilizing proper orthogonal decomposition to extract representative features and Gaussian process regression with improved automatic kernel construction (AKC-GPR) to perform a nonlinear mapping of physical features for prediction. The selection of variables is based on sensitivity analysis and modal assurance criterion. The underlying relationship is unveiled between flow field variables and inflow conditions. The ROM exhibits high predictive accuracy, with mean absolute percentage error (MAPE) of total field less than 3.5%, when varying altitudes and Mach numbers. During angle of attack variations, the ROM only effectively reconstructs flow distribution by interpolation with a MAPE of 7.02%. The excellent small-sample fitting capability of our improved AKC-GPR algorithm is demonstrated by comparing with original AKC-GPRs with a maximum reduction in a MAPE of 35.28%. These promising findings suggest that the proposed ROM can serve as an effective approach for rapid and accurate vehicle flow predicting, enabling its application in engineering design analysis.

Study and Quantitative Analysis of Mode Localization in Wind Turbine Blades

The study of damage mechanisms for wind turbine blades is important. Generally, modal localization tends to accelerate structural damage. This is a new approach to studying these damage mechanisms for wind turbine blades through modal localization theory. Therefore, this paper investigates whether modal localization phenomena exist in wind turbine blades, as well as the impact of different forms of detuning on modal localization. Based on perturbation theory, a mechanism for mode localization is described quantitatively using the degree of detuning, the degree of mode density, and the mode assurance criterion. A finite element model for wind turbine blades was established using ANSYS software (R15.0), and three detuning cases were simulated by changing the density, elastic modulus, and installation angles of the blades. Moreover, an improved mode localization factor is proposed to quantitatively evaluate the degree of mode localization in wind turbine blades. The numerical results indicate that the degree of modal localization increases with an increasing degree of detuning, but the increase in modal localization gradually slows. Finally, the detuning modal shape composition, which includes harmonic components, is analyzed. The results show that the closer the composition of the detuning modes is, the stronger the degree of mode localization.

Experimental Verification of Dynamic Properties of a Hollow Aluminum Beam

In this study, analytical and computational analyses are performed to determine the dynamic properties of an aluminum hollow beam and an experimental analysis is also performed. The experimental model is taken as a reference model and the computational model is updated accordingly using model updating tools. The damping behavior inherent in all physical structures is measured experimentally. According to the results of the cross-correlation modal assurance criterion, the experimental and computational results match well. The average error between the computational and experimental results for the first five damped natural frequency values is 1.5%.

On the Generation of Digital Data and Models from Point Clouds: Application to a Pedestrian Bridge Structure

This study investigates the capture of digital data and the development of models for structures with incomplete documentation and plans. LiDAR technology is utilized to obtain the point clouds of a pedestrian bridge structure. Two different point clouds with varying densities, (i) fine (11 collection locations) and (ii) coarse (4 collection locations), collected via terrestrial LiDAR, are analyzed to generate geometry and structural sections. This geometry is compared to the structural plans, which are then converted into numerical models (finite element—FE model) based on the point cloud data. Point cloud-based FE models (based on fine and coarse data) are compared with the structural plan-based FE model. It is observed that the static and dynamic responses are comparable within an acceptable range of a maximum difference of 5.5% for static deformation and an 8.23% frequency difference, with an average difference of less than 5%. Additionally, the dynamic properties of the fine and coarse point cloud FE models are compared with the operational modal analysis data obtained from the bridge. The fine and course point-cloud-based FE models, without model calibration, achieve an average accuracy of 8.76% and 9.94% for natural frequencies and a 0.89 modal assurance criterion value. The research found that the digital data generation yields promising results in this case for a bridge if documentation or plans are unavailable. With recent technologies and approaches such as digital twins, the connection between physical and virtual entities needs to be established by fusing digital models, sensorial information, and other data forms for better infrastructure management. Models such as those investigated and discussed in this paper can assist engineers with structural preservation in conjunction with monitoring data and utilization for digital twins.

Numerical Simulation of the Response of an Unreinforced Brick-Masonry Cross Vault Subjected to Seismic Loading

ABSTRACTThis paper presents the numerical evaluation of the seismic response of a masonry cross vault using the Discrete Macro-Element Method (DMEM). The case study corresponded to a full-scale unstrengthened cross vault that was experimentally investigated within the scope of the SERA Project — Seismic Response of Masonry Cross Vaults: Shaking table tests and numerical validations. The cross vault was subjected to repeated shaking table and dynamic identification tests until reaching significant damage. The numerical simulations involved the calibration of the Young’s modulus of the masonry material aiming at reproducing the cross vault’s experimental natural frequencies and mode shapes. The comparison of frequencies was carried out by estimating the difference between experimental and numerical results, whereas the correspondence between mode shapes was studied using the Modal Assurance Criterion. Subsequently, a sensitivity analysis was performed to identify the influence of nonlinear properties on the seismic response of the cross vault (displacement and acceleration time histories and failure mechanism). The accuracy of the numerical time histories was evaluated by estimating magnitude and phase discrepancies. The results aimed at demonstrating the applicability of the DMEM for assessing the seismic response of masonry cross vaults with an acceptable degree of accuracy and low computational cost.

Noninvasive identification of directionally-dependent elastic properties of soft tissues using full-field optical data

This paper introduces an innovative approach for elastic property characterization of soft tissues, having directional-dependent material behavior, via their vibration response measurement and interpretation. The full-field time-dependent surface displacements as a result of externally excited soft tissues are collected through digital image correlation (DIC). A developed analytical model, capturing the low-amplitude vibration behavior of anisotropic layered human skin with the incorporation of the influence of subcutaneous elasticity and inertia, is employed to accurately predict its resonant frequencies and pertaining displacement field images. An efficient solution approach for the model is implemented into an inverse algorithm to rapidly characterize the anisotropic elastic properties based on importing the vibration characteristics. To show the merit of the approach, a 3-D finite element (FE) simulation model was used to generate full-field data, detected and matched with a set of specific vibration modes via modal assurance criterion (MAC). The validity of the model implemented into the inverse characterization algorithm is demonstrated through a comparison of predicted vibration frequencies and mode-shapes simulated via the 3-D FE model for different cases with anisotropic elastic properties in different layers of the skin. It is shown that modes are influenced differently when anisotropic properties are introduced to the model. Thus, the established inverse characterization algorithm is capable of rapidly predicting the elastic material properties of anisotropic soft sheets with adequate accuracy.

Evaluation of full-sized and thick cross-laminated timber using in-line non-destructive techniques

ABSTRACT Advancements in non-destructive evaluation systems for predicting mechanical properties of cross-laminated timber appear to have been limited to laboratory scale, reduced sample sizes, or difficult practical solutions for industry implementation. This study has developed classical vibration analysis methods for industry adoption in large-scale, rapid panel characterisation through frequency analysis. The non-destructive method allowed for the prediction of the elastic moduli in both axial directions (Ex and Ey) and shear moduli (Gxz, Gyz, and Gxy) for thin or thick plates. The comparison with the static reference method and non-destructive technique showed a good consistency for predicting the elastic and shear moduli of the cross-laminated timber with mean percentage differences for Ex, Ey, and Gxy of 5.2%, 7.9%, and 18.9%, respectively. An observation was made that the accurate determination of the mechanical properties required enough correctly identified frequencies/modes. Mode shapes generated from experimental data through modal assurance criterion were compared with finite element analysis to confirm the assessment method yielded frequencies specific to the panel, rather than other contributing effects (environment, boundary conditions, panel variability, mesh resolution).

Multiscale topology optimization framework for natural frequency maximization of multi-morphology lattice structures

This paper proposes a multiscale topology optimization framework for maximizing the natural frequency of multi-morphology lattice structures (MMLSs). The proposed framework addresses the challenges of computational efficiency, design space, numerical convergence, and compatibility between adjacent microstructures in multiscale topology optimization for natural frequency problems. The macrostructural topology, the morphologies categories, distribution regions, volume fractions of different lattice materials (LMs), and the relative densities of lattice unit cells (LUCs) are simultaneously optimized to enhance the structural natural frequency. Specifically, level set functions are utilized to generate prototype LUCs, enabling obtaining graded LUCs by configuration interpolation. Multi-morphology LUCs with smooth characteristics are achieved using the Kriging-assisted morphological post-process and sigmoid function (SF) based hybrid transition strategy. Kriging metamodel-assisted Uniform Multiphase Materials Interpolation (KUMMI) schemes are constructed for the mechanical properties estimation of macro elements to promote the multiscale topology optimization procedure. Distinct processing methods for LUCs' elasticity tensor and density are incorporated within the KUMMI schemes, by which the local mode problem is avoided. The objective order natural frequency is accurately optimized with the modal assurance criterion (MAC) based mode-tracking technique. Numerical examples demonstrate that the developed design framework can efficiently maximize the natural frequency of MMLSs, while also ensuring microstructural connectivity.

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.