Modal Identification Method Research Articles

Automated method for structural modal identification based on multivariate variational mode decomposition and its applications in damage characteristics of subway tunnels

This paper introduces a fully automated modal identification algorithm based on the Multivariate Variational Mode Decomposition (MVMD) of free vibration responses to determine structural modal parameters. Addressing the challenge of setting MVMD parameters, we introduce a fusion parameter combining power spectral cross-entropy with reconstruction error as an adaptive fitness function in the optimization algorithm, enabling optimal parameter selection. Then, modal frequencies, damping ratios, and shapes of structures can be extracted from autonomously decomposed Intrinsic Mode Functions by employing the principle of modal superposition and least squares fitting without manual parameter adjustments. Validated by a four-degree-of-freedom numerical model, the method demonstrated accurate, automatic modal parameter identification. The method was further applied to a subway tunnel structure model experiment. Comprehensive modal identification was conducted on tunnel structures under varying degrees of damage. The results validate the proposed method’s effectiveness and reveal the damaged segment structure’s multimodal parameter variation patterns and surrounding soil.

Structural acceleration response reconstruction based on BiLSTM network and multi-head attention mechanism

The effectiveness of structural health monitoring often relies on the precise analysis of structural response data, with data completeness directly impacting the performance of monitoring systems. Addressing the common issue of data loss in structural health monitoring systems, this study proposes a Bidirectional Long Short-Term Memory (BiLSTM) network based on a multi-head attention mechanism for the reconstruction of missing structural acceleration responses. Firstly, employing a two-layer BiLSTM network to establish an encoder-decoder framework for extracting spatio-temporal correlation features among sensor data. Subsequently, innovatively embedding a multi-head attention mechanism into the network framework enhances the modeling capability of long-distance input elements and establishes dependencies among different sensors, thereby enabling the network to better capture the global features of input information. The proposed method undergoes validation through a numerical example of a simply supported beam, practical monitoring data on the Hardanger Bridge from the Norwegian University of Science and Technology, and an experimental study of steel frame structure from our laboratory. These validations are compared with alternative response reconstruction models. The experimental results make obvious that the proposed method demonstrates superior accuracy in response reconstruction. Additionally, the suitability of this method for modal identification is validated. Through the utilization of reconstructed responses, the method effectively discerns the structural natural frequencies with accuracy.

A hybrid method for intercity transport mode identification based on mobility features and sequential relations mined from cellular signaling data

A hybrid method for intercity transport mode identification based on mobility features and sequential relations mined from cellular signaling data

High-resolution frequency domain decomposition for modal analysis of bridges using train-induced free-vibrations

Modal parameters are structural inherent characteristics that can be applied for revealing performance of railway bridges. Free vibration signals generated by a passage of train are commonly utilized to estimate the modal parameters of railway bridges due to their higher signal-to-noise ratios compared to random vibrations caused by ambient loads. However, since free vibration signals rapidly decay over time, the available free-vibration data is typically short-time. When using the fast Fourier transform-based spectral estimation method for modal identification from short-time vibration data, a phenomenon known as spectral leakage occurs, leading to miss-identification of some structural modes. In this study, the classical frequency domain decomposition (FDD) is improved for modal identification of railway bridges, in which the higher resolution auto-power spectral density (PSD) and cross-PSD functions are calculated through the autoregressive (AR) model-based method. The AR model-based method improves both the smoothness and resolution of the PSD functions compared to the fast Fourier transform technique. These AR model-based PSD functions are then employed in the FDD process to facilitate frequency and mode shape identification while avoiding spurious noise modes. The proposed eigenvalue fitting technique is subsequently utilized to estimate damping ratios. Numerical simulation data as well as vibration data from an actual bridge are analyzed to validate the proposed method, with a comparison made to the Welch’s PSD-based method. The results demonstrate that the modified FDD approach enables more effective identification of structural modes, even in the presence of closely-spaced modes.

A mechanics-informed neural network method for structural modal identification

Modal identification is one of the core topics within the realm of structural health monitoring (SHM). In this study, we summarize four modal mechanical properties and propose a mechanics-informed neural network (MINN) method for structural modal identification. The proposed MINN method incorporates the sparsity of the data in the time–frequency domain and cross-correlation minimization in the time domain into the neural network to obtain modal parameters, which uses sparsity constraint and cross-correlation minimization constraint to obtain the accurate modal responses and mode shapes. Subsequently, modal frequencies and damping ratios can be derived from the modal responses. The proposed MINN method is verified by numerical simulations and two actual suspension bridges. Compared with traditional methods, the proposed MINN method has two major advantages. Firstly, the proposed MINN method presents explicit mathematical equations to distinguish the modes and the spurious modes, which obviates the necessity for priori information such as model order or time-consuming manual intervention to distinguish the modes and the spurious modes. Therefore, it can be implemented adaptively to determine the modal order and obtain the modal parameters. Secondly, the proposed MINN method can obtain a greater number of accurate modal parameters than traditional methods and achieves an increase of 102.6%, 43.4%, and 31.5% in the number of accurate results when compared to covariance-driven stochastic subspace identification (SSI-COV), data-driven stochastic subspace identification (SSI-DATA) and the natural excitation technique and the eigensystem realization algorithm (NExT-ERA), respectively. Therefore, the proposed MINN method provides an adaptively modal identification method that has clear modal mechanical properties to distinguish the modes and the spurious modes and can obtain a greater number of accurate results.

Application of a Modal Parameter Identification Method Based on Variational Mode Decomposition in Flight Flutter Testing

Signals of flight flutter testing exhibit non-stationary characteristics, closely spaced modes, and low signal-to-noise ratio, presenting challenges in data processing. In recent years, the variational mode decomposition (VMD) method has emerged as a promising approach to mitigate mode mixing and exhibit robust noise resistance. Therefore, a novel time-frequency domain modal parameter identification method based on VMD is proposed to process impulse response signals in flight flutter testing. The modal frequency and damping ratio are determined through a three-step process: VMD analysis, Hilbert transform, and least square fitting. The efficacy of the proposed method in identifying closely spaced modes and resisting noise is validated through a numerical example. Furthermore, this method is applied to analyze two types of pulse excitation signals in actual flight flutter testing: one induced by the pilot’s shaking stick and the other induced by small rocket excitation. The obtained modal parameters are compared with those from ground vibration tests and specialized software, respectively, to showcase the effectiveness and superiority of the proposed method.

Intercity Traffic Travel Mode Identification Method Based on Mobile Signalling Data

With the popularity of mobile devices, the signalling data generated by them provides significant opportunities for studying intercity travel behaviour in terms of data scale and information continuity. However, due to the low quality of the data in spatial accuracy, temporal frequency, and traffic semantics, the accuracy of identifying individual travel modes is low and it is difficult to extend to complex traffic scenarios. In this paper, we propose a new framework for identifying individual intercity travel modes based on mobile signalling data. The framework includes components for data pre-processing, geo-information mapping, feature and attribute extraction, and travel mode recognition. We utilize a comprehensive detection model to identify users’ multimodal intercity transport behaviour. Using two modules, Random Forest Embedding (RFE) and Bidirectional Long Short-Term Memory (Bi-LSTM), the model can capture the spatiotemporal characteristics and complex multi-stage associations in intercity travel chains. A large-scale mobile phone dataset from Jiangsu Province, China, was used for verification. The results showed that, on average, the method was able to detect travel mode with 92% accuracy. This study provides valuable support for further research on individual travel behaviour and the enhancement of transportation planning.

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.

Nonisospectral water wave field: Fast and adaptive modal identification and prediction via reduced-order nonlinear solutions.

Real-world water wave fields exhibit significant nonlinear and nonisospectral characteristics, making it challenging to predict their evolution by relying solely on numerical simulation or exact solutions using integrable system theory. Hence, this paper introduces a fast and adaptive method of modal identification and prediction in nonisospectral water wave fields using the reduced-order nonlinear solution (RONS) scheme. Specifically, we discuss the coarse graining and mode extraction of wave field snapshots from the data-driven and physics-driven perspectives and utilize the RONS method for principle modal prediction of nonisospectral water wave fields. This is achieved by investigating the standard and nonisospectral Gardner system describing nonlinear water waves as a demonstration. Through detailed comparison and analysis, the fundamental solitary behaviors and dispersive effects in the Gardner system are discussed. Subsequently, a neighbor approximation is developed that combines the essences of symbolic precomputation and numerical computation in the RONS procedure, which exploits the locality of nonlinear interactions in water wave fields.

A bootstrap-based stochastic subspace method for modal parameter identification and uncertainty quantification of high-rise buildings

This paper proposes a bootstrap-based stochastic subspace method for modal parameter identification and uncertainty quantification of high-rise buildings. Firstly, the stochastic subspace method in combination with the bootstrap technique enables the estimation of multiple sets of modal parameters from raw data series. Then, a bootstrap-based stabilization diagram is used to extract the physical modes. Finally, the modal identification and associated uncertainty quantification results are determined via statistical analysis. Through a numerical study of high-rise buildings, the performance of the proposed method is validated, demonstrating that it can provide reliable modal parameter identification and uncertainty quantification as well as has good noise immunity. Furthermore, the developed approach is employed to identify modal parameters of a 600-m-tall skyscraper during a typhoon, proving its applicability to field measurements and structural health monitoring of high-rise buildings. This paper aims to present a novel tool for modal parameter identification and associated uncertainty quantification of high-rise buildings.

Impact force curve feature and failure mode identification method of concrete-filled steel tube members under lateral impact

A collision accident caused by derailed trains is a potential safety hazard for the structure adjacent to high-speed rail lines. Concrete-filled steel tube (CFST) columns are frequently utilized in modern high-speed railway stations, however CFST station columns may suffer severe damage from train collisions because of their high impact energy. Therefore, the method of identifying CFST members' failure modes under large impact energy was investigated in this paper. Adopting numerical simulation by LS-DYNA, the corresponding relationship between the local indentation and impact process was researched, the characteristic impact force time-history curve was proposed, and the effects of impactor and CFST specimen parameters on impact force feature were analyzed. The plateau proportion was established and quantified, then the mapping relationship between plateau proportion and failure degree was acquired. Research results indicated that local indentation developed primarily at impact force plateau stage. CFST specimens showed bending deflection when plateau proportion was below 67.5%, experienced fracture failure when it was above 77%, and exhibited crack failure when it was in between respectively. Finally, the empirical formulas for plateau proportion and maximum deflection were established, and a simplified approach for predicting the failure modes was put forward. The research provides suggestions for identifying damage patterns and strengthening CFST columns subjected to lateral impact loads.

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

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

Quasi-static testing based structural modal parameter estimation

ABSTRACT Structural modal identification is generally implemented within a dynamic framework, requiring multidisciplinary knowledge and adequate operational experience. This preliminary study attempts to explore an easy-to-handle quasi-static alternative method for dynamics-based modal identification of beam-type structures. Acceleration time-history data are replaced by quasi-static deflections induced by slow moving loads. A concept of quasi-static deflection influence surface is proposed based on the theory of influence lines and the principle of virtual work. Its analytical expression is simplified into a deflection matrix by choosing specific points on the surface according to deflection measurement coordinates. The matrix form is divided by external loads to obtain a generalised quasi-static flexibility matrix, which is used to replace the inversion of the global stiffness matrix in the modal eigenvalue equation. The lumped-mass method is also employed to establish the mass matrix. Subsequently, the eigenvalue equation is analytically solved seeking for modal frequencies and mode shapeswithout performing modal tests. The feasibility of the proposed method has been successfully verified against three experimental examples including a continuous box girder with variable cross sections. It was observed that the modal frequencies and mode shapes estimated by the proposed method were very close to those given by the dynamically modal tests.

Frequency Identification of Equal-Span Continuous Girder Bridge Based on Moving Vehicle Responses

The indirect method for bridge modal identification based on the response of moving vehicles has attracted widespread attention in recent years. However, most existing studies only focus on the simply supported bridge, while continuous girder bridges are widely used in practical engineering. Therefore, this study proposes an indirect frequency identification method for continuous girder bridges. First, the mode shape formula of the equal-span continuous beam is deduced using the three-moment equations, and the analytical solution of the vehicle vibration response is deduced via the vehicle–bridge coupled vibration theory. Second, the derived analytical solution is verified through numerical analysis results and field test results. Finally, the effects of bridge and vehicle parameters on the frequency identification accuracy are analyzed. The results show that a reasonable frequency of the trailer should be selected to avoid the resonance between the vehicle and the bridge for better performance. The research findings can provide a reference for the indirect identification of continuous girder bridges based on the response of moving vehicles.

Research on loose bolt localization technology for transmission towers

Research on loose bolt fault in transmission towers is difficult to detect, and the localization of the loose bolts has always been a challenge in the field of structural health monitoring. This article investigates the relationship between the modal frequencies and modal shapes at different levels and finds that when bolts in transmission towers become loose, the order of modal frequency changes is consistent with the order of the mode shape at the location of the loosening. Based on this, a new method for locating loose bolts in transmission towers is proposed. In the identification of mode parameters, an improved variational mode decomposition is used to extract the mode components at different orders. A modal frequency identification method based on feature set signal reconstruction is proposed, which is based on the modal correlation between the signal components from different sensors, effectively preserving and extracting the structural modal characteristics from the vibration response. At the same time, the identification of modal shapes in transmission towers is achieved through feature-level fusion based on adaptive multi-sequence signals, greatly reducing identification errors. The effectiveness of this method is validated in the finite element analysis of transmission towers, and its superiority is demonstrated through comparison with more advanced methods. The results of a 110 kV transmission tower bolt loosening test also show that this method can accurately identify the area where the bolts are loose, with high identification accuracy, providing a new approach for the localization of loose bolts in transmission towers.

Experimental and numerical studies on a glubam spherical dome

This paper explores static experiments and dynamic tests, along with structural analysis of certain glubam (glued laminated bamboo) dome models. A self-balancing lever system was employed for the static experiment, revealing mechanical performance details such as load-displacement relationships and internal axial forces in glubam dome structures. Dynamic behaviors were assessed through triaxial accelerometers on specific joints, employing the Bayesian FFT modal identification method to calculate structural modal parameters, including natural frequency and mode shape. Experimental outcomes closely aligned with results from the analytical approach using the finite element method. Overall, the paper contributes valuable insights into the static and dynamic characteristics of glubam dome structures, bridging experimental findings with analytical predictions.

Empirical Wavelet Transform Based Method for Identification and Analysis of Sub-synchronous Oscillation Modes Using PMU Data

Empirical Wavelet Transform Based Method for Identification and Analysis of Sub-synchronous Oscillation Modes Using PMU Data

Drive-by modal identification of high-speed railway bridge via CP response identification

Railway bridges are subjected to heavy operational loads and significant impact forces due to the moving trains. It is important to carry out an effective structural health monitoring to ensure the safe operation of railway bridges. Traditional online bridge monitoring methods require sensor installations on the structures that can be time-consuming and expensive making it very difficult to satisfy the huge needs of monitoring all the existing railway bridges. Therefore, this study proposes to use the drive-by method for the bridge modal identification using responses of instrumented in-service trains. The measuring sensors are installed on the train that can conduct the measurement in its normal operational states. To improve the feasibility and accuracy of drive-by bridge modal identification, the contact-point (CP) responses between the wheels and the rail track are identified from the train responses. A novel method via Bayesian expectation-maximization based augmented Kalman filter is proposed to reconstruction the CP responses and unknown states of the train simultaneously. The method is robust to the measurement noise of the train responses and the CP responses can be identified accurately. The identified CP responses successfully eliminate the dynamic components related to the train and greatly enhance the bridge dynamic information. The proposed CP response reconstruction method has great potential for drive-by bridge modal identification using the responses of train that can be further used to assess the structural condition of high-speed railway bridges.

A Novel Method of Pure Output Modal Identification Based on Multivariate Variational Mode Decomposition

A Novel Method of Pure Output Modal Identification Based on Multivariate Variational Mode Decomposition

Data-driven prediction method for shear capacity of corroded rectangular reinforced concrete shear walls under varied failure modes

The physical and mechanical properties of rectangular reinforced concrete shear walls (RRCSW) will deteriorate over time due to acidic erosion, causing changes in damage characteristics and a reduction in shear capacity under seismic loading. The aim of this paper is to develop a failure mode-based prediction method for the shear capacity of corroded RRCSW, as the existing formulas for calculating shear strength become invalid in such scenarios. Initially, a total of 2403 RRCSW samples with various corrosion levels and main design parameters were generated and simulated using the authors' previous numerical method to obtain a comprehensive database of shear capacity. Subsequently, an efficient damage mode identification method for RRCSW was established using the Random Forest algorithm, and its accuracy and applicability in identifying damage modes of corroded RRCSW were verified. Finally, the existing calculation formulas for RRCSW in flexure-shear and shear failure modes were selected and modified to consider the corrosion effect based on the shear capacity database. The comparative analysis revealed that the proposed formulas provide accurate predictions of the shear capacity of corroded RRCSW, making the results of this study invaluable for seismic design of new structures and seismic performance evaluation of existing structures.