Structural Modal Identification 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.

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.

Developing and Testing High-Performance SHM Sensors Mounting Low-Noise MEMS Accelerometers.

Recently, there has been increased interest in adopting novel sensing technologies for continuously monitoring structural systems. In this respect, micro-electrical mechanical system (MEMS) sensors are widely used in several applications, including structural health monitoring (SHM), in which accelerometric samples are acquired to perform modal analysis. Thanks to their significantly lower cost, ease of installation in the structure, and lower power consumption, they enable extensive, pervasive, and battery-less monitoring systems. This paper presents an innovative high-performance device for SHM applications, based on a low-noise triaxial MEMS accelerometer, providing a guideline and insightful results about the opportunities and capabilities of these devices. Sensor nodes have been designed, developed, and calibrated to meet structural vibration monitoring and modal identification requirements. These components include a protocol for reliable command dissemination through network and data collection, and improvements to software components for data pipelining, jitter control, and high-frequency sampling. Devices were tested in the lab using shaker excitation. Results demonstrate that MEMS-based accelerometers are a feasible solution to replace expensive piezo-based accelerometers. Deploying MEMS is promising to minimize sensor node energy consumption. Time and frequency domain analyses show that MEMS can correctly detect modal frequencies, which are useful parameters for damage detection. The acquired data from the test bed were used to examine the functioning of the network, data transmission, and data quality. The proposed architecture has been successfully deployed in a real case study to monitor the structural health of the Marcus Aurelius Exedra Hall within the Capitoline Museum of Rome. The performance robustness was demonstrated, and the results showed that the wired sensor network provides dense and accurate vibration data for structural continuous monitoring.

Towards vision-based structural modal identification at low frame rate using blind source separation

With increasing availability of cost-effective and high-resolution cameras, their use as a non-contact sensing tool has rapidly progressed for structural health monitoring. The cameras offer unique capabilities to provide full-field measurement with high spatial density at low cost. However, extracting high-density temporal data is challenging, as a high-speed camera increases the monitoring cost with high-rate data processing. Recently, motion magnification (MM) has shown significant success in analyzing low-amplitude motion of structural systems. However, previous studies observed that MM methodology performs poorly at low frame rates for modal identifications. In this paper, the influence of low frame rate on phased-based motion magnification (PMM) has been investigated. A novel technique is proposed by combining PMM with zero mean-normalization cross-correlation tracker to determine vibrational responses, and then the spatial Wigner-Ville spectrum-based time-frequency blind source separation method is explored for modal identification using the extracted vibrational responses obtained from the video data. The experimental data of a lumped mass experimental model and a steel bridge is used to test the accuracy of the proposed method. The original and motion-magnified image response data is compared with accelerometer data for modal identification. The proposed method is able to extract the modal parameters with high accuracy for motion-magnified images, even for low frame rates.

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.

Interval Pareto front-based multi-objective robust optimization for sensor placement in structural modal identification

Considering the multi-performance development of complex systems and the requirement of structural modal identification with typical uncertainties, the nominal single-objective optimization method is not suitable for sensor placement. Therefore, by combining conventional optimal sensor placement with non-probabilistic theory, this study proposes an uncertainty-oriented multi-objective robust optimization method for optimal sensor placement. The Fisher information matrix and ill-posedness comprise one eigenvalue-based optimization objective, and the mean and minimum off-diagonal values in the modal assurance criterion comprise another. Considering the high-cost limitation of the statistical method for handling uncertainties, uncertainty propagations are realized by a dimension-wise analysis with better accuracy and efficiency, thus avoiding the overestimation incurred by the classical Taylor expansion method. The multi-objective robust optimization is established by uncertain eigenvalue- and eigenvector-based indices with interval numbers and solved using the multi-objective optimization algorithm. Considering the solution sets located at the Pareto front, an interval possibility was developed using interval Pareto fronts to determine the optimal number of sensors. A numerical example demonstrated the validity of the proposed method with an optimal number of sensors and corresponding configurations.

Structural Modal Parameters Identification Under Ambient Excitation Using Optimized Symplectic Geometry Mode Decomposition

In the process of structural modal parameters identification under environmental excitation, the employed measured dynamic response signal is usually non-stationary and contains noise. As a novel signal analyzed method, symplectic geometry mode decomposition (SGMD) has been proven to be effective for dealing with non-stationary and noisy signals. However, the traditional SGMD may treat noise as modal information, which inevitably undermines the accuracy of modal identification. To overcome this problem, this paper proposes an optimized SGMD algorithm for structural modal parameter identification. First, the SGMD algorithm is refined with the Hankel matrix, Kurtosis theory, Pearson correlation coefficient, and energy entropy theory. Then, the natural frequencies and damping ratios are identified using the proposed method, which consists of the optimized SGMD algorithm, natural excitation technique (NExT), direct interpolating method, and curve-fitting function. Finally, the applicability of the proposed method under environmental excitation is investigated by two examples: a two-story frame structure and an 88-story office tower. The results demonstrate that the proposed method is effective for identifying the civil structural modal parameters from non-stationary dynamic responses.

Extracting high-precision full-field displacement from videos via pixel matching and optical flow

Accurate sensing of full-field displacements plays a significant role in dynamic testing for structural health monitoring (SHM). Recently, video camera has become a more promising tool in displacement sensing due to advantages such as low price, agility, simultaneous measurement, and high spatial sensing resolution. Traditional target tracking approaches (e.g., digital image correlation, template matching, etc.) typically require clear targets on the structure surface and thus only provide sparse displacement. Phase-based motion extraction enables full-field displacement measurement at subpixel precision without the need of markers as tracking targets, which has achieved great success in structural modal identification among many other SHM applications. However, the phase-based approach in a Eulerian framework fails to deal with large motions. To tackle these challenges, an enhanced phase-based method, that synergistically combines the developed local amplitude supplemented pixel matching algorithm and optical flow processing, is proposed for full-field displacement sensing with subpixel precision meanwhile capable of dealing with large motions. In particular, the pixel matching estimates the integer-pixel motion vectors of pixels which have sufficient texture contrast determined by local amplitude. The optical flow, represented by the first order Taylor series, is then employed to approximate the rest subpixel motion associated with the integer-pixel motion vectors. The proposed technique is validated by processing a field-test videos with LVDT reference and then applied to other several lab/field recorded videos of different vibrational objects for displacement extraction and modal identification.

Structural modal identification and damage detection with incomplete data utilized by genetic algorithm optimization

This research presented a procedure to automatically identify the modal characteristics of structures to detect and quantify any localized damage of structures in frequency domain. This process uses the acceleration frequency response of the selected degree of freedoms, some natural frequency of the damaged structure and mode shapes of the undamaged Finite Element (FE) model to identify the structural stiffness of the damaged structure containing the damping ratio. The incomplete data in the unmeasured degree of freedom will be updated using a genetic optimization algorithm. The accuracy and efficiency of the proposed method have been tested on a 25 elements truss subjected to a harmonic load with sweep frequency. Optimization results demonstrated that the proposed method is capable of precisely identifying the modal characteristics and stiffness reduction factor of the damaged structure using genetic optimization algorithm along with 5% noise in the input force and response of the system in all studied cases.

Structural modal identification and enhancement of low-energy modes by successively variational extraction of high-energy modes

Accurate identification of modal properties for as much as possible modes from structural monitoring responses is an important part for structural health monitoring systems. Limited by the energy of external excitations, or influenced by the heavy noise, the energies of some modal components may be weak or buried in the energy of noise, giving rise to the difficulty for accurate modal identification. Variational mode decomposition method is a non-recursive decomposing procedure to decompose a signal into narrow-band sub-components. However, the difficulty for the decomposition of low-energy mode is determining the corresponding initial center frequencies. In this study, a new method for low-energy mode identification is proposed using the idea of locating, identifying, and subtracting the high-energy component to gradually enlarge the relative energy level of low-energy mode by substituting the original signal with residual signal repeatedly. First, the initial center frequency of the mode with maximum energy is determined by autoregressive power spectrum; second, the modal parameters including frequency, damping ratio and mode shape are identified by the singular value decomposition of Hankel matrix with low system order; third, vibrational mode extraction method is proposed to extract the modal component with maximum energy; subsequently, the modal component with maximum energy is subtracted from the original signal to construct the residual signal for the identification of next maximum energy component. The relative energy level of low-energy mode is enlarged gradually by repeating the subtraction of high-energy modal component. Then, the accuracy of low-energy mode identification is improved. The effectiveness of the proposed method is verified by the simulated structures under ambient and earthquake excitations with high-level noises. Besides, the capability for the application of practical structure is verified by the experimental data of a real bridge.

Modal identification of structures with a dynamic behaviour characterised by global and local modes at close frequencies

Identification of modal parameters of a space frame structure is a complex assignment due to a large number of degrees of freedom, close natural frequencies, and different vibrating mechanisms. Research has been carried out on the modal identification of rather simple truss structures. So far, less attention has been given to complex three-dimensional truss structures. This work develops a vibration-based methodology for determining modal information of three-dimensional space truss structures. The method uses a relatively complex space truss structure for its verification. Numerical modelling of the system gives modal information about the expected vibration behaviour. The identification process involves closely spaced modes that are characterised by local and global vibration mechanisms. To distinguish between local and global vibrations of the system, modal strain energies are used as an indicator. The experimental validation, which incorporated a modal analysis employing the stochastic subspace identification method, has confirmed that considering relatively high model orders is required to identify specific mode shapes. Especially in the case of the determination of local deformation modes of space truss members, higher model orders have to be taken into account than in the modal identification of most other types of structures.

Recursive variational mode decomposition enhanced by orthogonalization algorithm for accurate structural modal identification

Modal identification is critical for structural condition monitoring. Variational mode decomposition (VMD) has been widely applied to identify modal parameters and has achieved excellent performance. It is crucial for VMD to predefine the decomposition parameters, that is, the mode number and balance factor. However, in practical engineering, abnormal impulses and heavy noise render it difficult to preset the mode number and balance factor. Therefore, a novel method, termed orthogonal and recursive VMD (ORVMD), is proposed to overcome the difficulty of setting decomposition parameters in advance. ORVMD consists of two components: recursive VMD (RVMD) and a rough-to-precise decomposition scheme based on an orthogonal algorithm. RVMD is an iterative method of VMD that is used to circumvent the difficulty of predefining the mode number. A rough-to-precise decomposition scheme based on an orthogonal algorithm is proposed to address the difficulty of setting the balance factor. Furthermore, the proposed ORVMD in combination with the Hilbert transform (HT) is employed to estimate the modal parameters of the structures. The raw signals are pre-processed by using the random decrement technique (RDT) to obtain its random decrement signature (RDS) and then the proposed method is applied to the RDS to identify the modal parameters of a simulated system and a real arch bridge. The obtained results show that the proposed method outperforms other existing methods in separating multicomponent signals; thus, it is an efficient method for identifying the natural frequencies and damping ratios of structures.

Structural modal identification using a portable laser-and-camera measurement system

Vision-based techniques for modal analysis of full-scale civil infrastructure have been constrained by the challenge of collecting measurements of all points on a large structure using limited-resolution video devices. This paper proposes a portable, simple-to-assemble laser-and-camera (LAC) system capable of measuring multipoint displacements at a low cost. An efficient video processing flow with an improved binarization strategy for pinpointing the laser spot's center is provided to extract the displacement from the video collected by LAC devices. In addition, the laser-assisted vision-based measurement technique is implemented for structural modal identification for the first time. To evaluate the performance of LAC devices in displacement measurement and structural modal identification, an error analysis test, a measurement accuracy test, and a scaled bridge model experiment are conducted in succession. The results with different types of laser receiving panels and under variable light environments demonstrate the feasibility and application potential of the proposed LAC system and approach for structural health monitoring.

Developing a method for determining the natural frequency of a structure using multiple combined measurements in the frequency domain

Modal identification of structures using vibration measurement data has attracted considerable attention. Current identification methods can be divided into several groups: single-degree-of-freedom and multi-degrees-of-freedom methods; time domain identification, frequency domain identification. In which, the simultaneous determination of many natural frequencies of the structure from a single measurement data remains a complicated problem, in particular in the presence of noise. The article develops the rational fraction polynomial method using combined measurements in the frequency domain to identify the natural frequencies of structures. The effectiveness of the proposed method is validated by numerical simulations and experimental tests of steel beam.

Structural modal parameter identification based on 2D spectral analysis

This paper proposes a 2D spectral analysis method based on damped Capon (dCAPON) and damped APES (dAPES) for structural modal parameter identification. The frequency and damping are estimated from the 2D dCAPON energy spectrum first, and then the amplitude (to construct the modal shape) corresponding to the frequency-damping point is calculated by the dAPES. The raw evenly-spaced computing grid is optimized into a banded hierarchically-refined one, greatly improving the computational efficiency. The performance of the proposed method is studied and it is investigated through the numerical and experimental data of a benchmark structure. The proposed method provides a simple and direct approach to estimating structural modal parameters, particularly for frequency and damping ratio.

Structural Modal Parameter Identification Method Based on the Delayed Transfer Rate Function under Periodic Excitations

The dynamic response transfer rate function (TRF) is increasingly used in the field of structural modal parameter identification because it does not depend on the white noise assumption of the excitation. In this paper, the interference of periodic excitation on structural modal parameter identification using TRF is analyzed theoretically for a class of civil engineering structures with obvious periodic components in excitation, and then an identification method of structural real modal parameters is proposed. First, a delayed TRF is constructed, and the pseudo-frequency response function is further obtained to identify the periodic spurious poles of the whole system. Then, the effective identification of the real modal parameters of the structure is achieved by comparing the system poles identified via conventional TRF. Finally, the feasibility and robustness of the proposed method were verified using a calculation example with four-degrees-of-freedom system. In addition, the modal parameters of a structure under periodic excitation were effectively identified by taking a pumping station as an example, and the results show that the method accurately identified the structural modal parameters when the excitation contained periodic components, which has wider prospects for technical applications.

Transfer learning-based data anomaly detection for structural health monitoring

The structural health monitoring (SHM) data of civil infrastructure are inevitably contaminated due to sensor faults, environmental noise interference, and data transmission failures. Anomalous data severely disturb the subsequent structural modal identification, damage identification, and condition assessment. Therefore, it is critical to detect and clean SHM data before data analysis. This paper proposes a novel approach for data anomaly detection based on transfer learning, that makes full use of the similarity of the anomalous patterns across different bridges and shares the knowledge incorporated in a deep neural network to achieve high-accuracy data anomaly identification for bridge groups. In the proposed approach, first, a multivariate database for a source bridge is built by plotting and labeling the raw sequential data. Then, a convolutional neural network (CNN) for data anomaly classification is designed and trained with the database in different conditions. The original CNN with the highest accuracy is transferred to a new bridge with enhancement training using a small part of the target bridge data. To validate the performance of the proposed method, the multivariate SHM data for two real long-span bridges are employed, including the acceleration, strain, displacement, humidity, and temperature data. The results demonstrate that transfer learning leads to a better classification capacity for the case of scarce labeled training data compared with the original network.

An improved NExT method for modal identification with tests validation

The Natural Excitation Technique (NExT) is widely used in structural modal parameter identification. However, the cross-correlation function is susceptible to the mode shape of each order, which is obtained by the traditional NExT method combined with other modal identification methods between the two measuring points, resulting in large errors of the identified frequency and damping ratio of various modes. Therefore, in this study, to obtain the modal responses of the target order correctly and eliminate interaction of various modes, a new combined NExT method with improved Empirical Mode Decomposition (EMD) method is developed. The improved NExT method is introduced firstly, then, the structural modal parameters are identified by five different methods, which are Ibrahim Time Domain Technique, Sparse Time Domain Algorithm, Autoregressive Moving Average timing method, Least Square Complex Exponential and Eigensystem Realization Algorithm respectively. The correction and improvement of the new method are verified through a simple-supported beam experiment and a shaking table test of a 12-story benchmark tall building at Tongji University. The structural modal parameters are identified and compared through adopting traditional NExT method and the proposed new NExT algorithm. Results illustrate that the improved NExT algorithm in this paper has a higher accuracy and effectiveness than the traditional one in structural modal parameter identification.

Machine learning-based stochastic subspace identification method for structural modal parameters

Machine learning brings a new paradigm to the traditional structural modal parameter identification problem. In this study, we propose a novel machine learning method for stochastic subspace identification (SSI) problem. The proposed method embeds the mathematical characteristics of modal identification into a neural network and formalizes the modal identification into optimization problem of deep neural networks (DNN). The network optimization process is the process of obtaining modal parameters, which can be implemented in a relatively autonomous manner with little manual intervention. The designed modal identification network includes two sub-neural-networks: a model order determination neural network and modal identification neural network. In the model order determination neural network, the singular values of the Toeplitz matrix, which is constructed by output covariance matrices are fed into the network, and the designed network can automatically determine the model order by the designed loss function. In the modal identification neural network, the SSI principles are informed into the neural network, and the designed network is used to identify the modal parameters which optimizes the designed loss function to obtain the system matrix and output matrix. The examples of a numerical simulation and two actual bridges are used to illustrate the ability of the proposed method. Results show that the proposed method is capable of operating automatically to extract modal information from structural responses with stronger anti-interference ability and the identified number of accurate modes are obviously increased.

Modal Identification of Structures by Eliminating the Effect of the High Ocean Wind

Tropical cyclone is a rapidly rotating storm system with severe excitation such as high wind. This severe excitation may change the performance of structures, such as bridges, wharves and wind turbine structures. It is very necessary to monitor this important change. Modal parameters are the ones to reflect the structural instinct behavior. However, many identification methods assume that the excitation is white noise, which is not the truth during high ocean wind excitation. Therefore, the modal identification method to deal with severe ocean wind excitation should be investigated. This paper proposes an innovative method to eliminate the effect of high ocean wind on modal identification. The formulation to generate an impulse response is described, where the effect of high wind is pointed. Then the elimination method is derived using the wind velocity spectrum and correlation function. After the wind field is simulated, the wind velocities and spectra at all accelerometer positions are obtained. The real impulse response form is obtained. Then, modal identification using the real impulse response is performed. Finally, a practical cable-stayed bridge is employed and modal identification is performed. The results show that the identified modes can reflect structural real behavior.