Structural Modal Parameter Identification Research Articles

Automated identification and long-term tracking of modal parameters for a super high-rise building

Structural modal parameter identification plays an important role in wind resistance design, damage identification, and health monitoring. At present, the modal identification process still suffers from low automation and low computational efficiency, which are not conducive to the continuous processing of monitoring data. To address this, an automated modal parameter identification approach is proposed by introducing the fast density and grid based (DGB) clustering, and applied to the Shanghai Tower, which is the tallest building in China. Moreover, in order to determine the optimal model order of the stochastic subspace identification (SSI), the trend of the logarithmic reduction rate for singular values is extracted by empirical mode decomposition (EMD). The numerical simulation of a cantilever beam and the field measurement of Shanghai Tower under the influence of Typhoon In-Fa are conducted to validate the effectiveness of the proposed approach. Results demonstrate that the approach can obtain modal parameters without human intervention and has the advantages of simple process, fast computation and high precision. Furthermore, based on the data collected from the structural health monitoring system of the Shanghai Tower over a period of 5.5 years, the approach is applied to analyze the correlation between natural frequencies and ambient temperature, as well as the long-term evolution law of modes, discovering that multi-order frequencies show a decreasing trend over time. The finite element analysis suggests that this fact might be attributed to the increase in structural mass caused by the rising usage rate and the degradation in material properties.

Fast Bayesian modal identification with known seismic excitations

AbstractFast and accurate identification of structural modal parameters after an earthquake is crucial for assessing structural conditions and facilitating repair. With the development of modern earthquake observation techniques, the recorded ground motion can be leveraged as extra input information for modal identification, enabling the experimental modal analysis applicable. This study develops a Bayesian modal identification algorithm that aims at estimating the most probable value (MPV) of modal parameters and their identification uncertainty. Incorporating the recorded seismic input, the algorithm utilizes with the structural equation of motion in the frequency domain to formulate the likelihood function and adopts a constrained Laplace method for Bayesian posterior approximation of modal parameters. With the aid of complex matrix calculus, an iterative scheme is developed, allowing a fast search of the MPV of modal parameters and an analytical evaluation of the posterior covariance matrix. The performance of the proposed algorithm is validated by examples with synthetic, laboratory and field data, respectively. In addition, its effectiveness on predicting structural responses under a future earthquake is illustrated, showing its potential for various downstream applications in seismic structural health monitoring.

A deep learning-based method for structural modal analysis using computer vision

Structural modal analysis aims to determine a structure's natural frequency, damping ratio, and mode shape, helping with structural condition assessment and maintenance. In this study, a computer vision-based framework for the identification of structural modal parameters is developed, which consists of two main procedures: First, the one-dimensional (1D) vibration signals of edge pixels on the structure in the video are extracted via edge detection and optical flow theory. Second, a 1D convolutional neural network (CNN) coupled with long short-term memory (LSTM) is generated to extract structural modal parameters from the input 1D signal. The framework's performance has been validated through comparison with baseline values, which were obtained from contact sensors. Additionally, the model's robustness and extrapolability has been analyzed. The good performance of the computer vision-based approach confirms its potential for precise and dependable contact-free modal analysis.

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.

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.

A new approach of ensemble learning in fully automated identification of structural modal parameters of concrete gravity dams: A case study of the Koyna dam

This study proposes a new automatic modal identification algorithm that identifies the system's modal parameters based on output-only data. The identification process is based on a stochastic subspace algorithm. Stochastic subspace algorithms only need the model degree to identify the modal parameters of the system. A model degree is an appropriate degree of the state-space model and it is estimated by using the Singular Value Criterion. Several clustering algorithms with different approaches have been used. The most powerful data fusion algorithm, which is called Dempster-Schaffer Theory is applied for integrating the results of the algorithms and preventing divergence of results. Furthermore, it focused on measuring the uncertainty of the identified modal parameters. In the proposed modal identification algorithm, only one data set is used for identification. In this situation, the variety of data is small and limited, and statistical resampling methods seem to be a good option. Establishing the above cycle enables the identification algorithm to identify modal parameters and quantify their uncertainty based only on a data set. This algorithm uses many fields, such as data collection, signal processing techniques, model reduction, feature extraction, clustering and data fusion. The Koyna gravity dam is selected as a case study to evaluate the performance of the developed algorithm. In the first step, a comparative study is carried out to verify the developed finite element model of the Koyna dam. Afterwards, the dam is excited by the Koyna earthquake, and dynamic responses of the dam are collected from the minimum number of points required for system identification. It is noteworthy the number of modes that are identified in this work is equal to 4 vibration modes. The maximum difference between the natural frequencies identified by the present algorithm and the finite element model does not exceed 4.33%. Also, the average difference is less than two percent, which indicates the high accuracy of the system identification algorithm. Also, all the vibration modes in the desired frequency range have been correctly identified. The results indicate that modal parameters with remarkable precision have been extracted by the modified algorithm.

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.

Automatic identification of structural modal parameters based on density peaks clustering algorithm

Automatic identification of structural modal parameters based on density peaks clustering algorithm

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.

A Hybrid Method for Structural Modal Parameter Identification Based on IEMD/ARMA: A Numerical Study and Experimental Model Validation

This article presents a hybrid method of structural modal parameter identification, based on improved empirical mode decomposition (EMD) and autoregressive and moving average (ARMA). Special attention is given to some implementation issues, such as the modal mixing, false modes, the judgment of the real intrinsic mode function (IMF) of classical EMD, and the difficulty of fixing the order of ARMA. To resolve the existing defects of EMD, an improved EMD (IEMD) that combines frequency band filtering and cluster analysis is proposed in this paper, where frequency band filtering divides the signal into several narrowband signals before the EMD process, and cluster analysis is used to determine the real IMFs. Euclidean distance is used to cluster the decomposition results, with no need to adjust any indexes or thresholds, and only by means of using the nearest distance to efficiently determine the real IMF. Moreover, IEMD is used as a pre-processing tool for ARMA, to resolve the difficulty of fixing its order. The capabilities of the proposed method were compared and assessed using a numerical simulation and an experimental model. The numerical simulation and experimental results showed that the improved method could resolve the modal mixing and false modal problems in the classical EMD process and could automatically identified the real IMFs, while the proposed IEMD was combined with ARMA to successfully identify the frequency and mode shape of the structure. Additionally, since each IMF is a single component signal, it is easy to determine the order of the ARMA model.

Identification of Structural Parameters Based on HHT and NExT

Signal processing approaches are widely used in the field of earthquake engineering, especially in the identification of structural modal parameters. Hilbert-Huang Transformation (HHT) is one new signal processing approach, which can be used to identify the modal frequency, damping ratio, mode shape, even the interlayer stiffness of the shear-type structure, incorporating with Natural Excitation Technique (NExT) method to take information from the response records of the structure. The stiffness of the structure is of great importance to judge the loss of its bearing capacity after earthquake. However, all of modal parameters are required to calculate the stiffness of the structure by use of HHT and NExT, which means that the response records shall contain all of modal information. However, it has been found that the responses of the structure recorded only contain the former order modal information; even it is excited by earthquake. Therefore, it is necessary to found a formula (formulas) to calculate the stiffness only using limited modal parameters. In this paper, the calculation formulas of the interlayer stiffness of shear-type structure are derived by using of the flexibility method, which indicate that all of interlayer stiffnesses could be worked out as long as any one set of modal parameters is obtained. After that, Taking Sheraton-Universal Hotel subjected to North Bridge earthquake in 1994 as an example, HHT and NExT are used to identify its modal parameters, the derived formulas are used to calculate the interlayer stiffnesses, and their applicability and accuracy are verified.

The effect of sensor noise on structural modal parameter identification

When errors occur in the sensor networks, there are noise in the acquired data. In this paper, based on the response correlation function between two points of the structure, the least squares complex exponential method is used to identify the influence of noise on the structural modal parameters. Through the construction of the steel beam platform experiment, the experiment verifies the influence of the noise in the collected data on the recognition of modal parameters. The results show that when there is noise in the collected response data, the noise component will cause errors in the identification of structural modal parameters, and the lower the modal order, the more sensitive the noise level.

Output-only modal parameter identification of structures by vision modal analysis

Testing of structures by non-contact and possibly-remote video camera measurement has emerged as a promising topic in engineering fields. This paper develops a vision modal analysis framework for output-only structural modal parameter identification using vision measurement. The establishment of this framework is mainly twofold. On the one hand, the vision data as the intensities of some selected pixels on a vibrating structure is elaborately derived upon the optical flow theory to possess the vision modal decomposition. Under small motion and proper smoothness assumptions, such a decomposition is similar to the conventional structural modal decomposition, indicating that the structural modal parameters are directly implicated in the vision data. While in the case of finite motion or a non-smoothing video, additional higher-order harmonics as combinations of basic frequencies may arise. On the other hand, with the vision modal decomposition, the frequency domain decomposition is utilized to identify the vision modal parameters from the vision data and then, the structural mode shapes are recovered from the vision modal shapes by some motion extraction processing. Numerical examples and an experimental case are studied to see the feasibility and accuracy of the proposed vision modal analysis.

Modal Parameter Identification Based on Hilbert Vibration Decomposition in Vibration Stability of Bridge Structures

Modal parameters are important parameters for the dynamic response analysis of structures. An output‐only modal parameter identification technique based on Hilbert Vibration Decomposition (HVD) is developed herein for structural modal parameter identification to (1) obtain the Free Decay Response (FDR) of a structure through free vibration or ambient vibration tests, (2) decompose the FDR into modal responses using HVD, and (3) calculate the instantaneous frequencies and instantaneous damping ratios of the modal responses to obtain the modal frequencies and modal damping ratios. A series of numerical examples are examined to demonstrate the efficiency and highlight the superiorities of the proposed method relative to the empirical model decomposition‐based (EMD‐based) method. The robustness of the proposed method to noises is also investigated and proved to be positive effect. The proposed method is proved to be efficient in modal parameter identification for both linear and nonlinear systems, with better frequency resolution, and it can be applied to systems with closely spaced modes and low‐energy mode.

Automatic identification of modal parameters for structures based on an uncertainty diagram and a convolutional neural network

A novel method for automatic identification of structural modal parameters is proposed, based on new developments in both uncertainty quantification for stochastic subspace identification and deep learning. An uncertainty diagram is first constructed to visualize uncertainty estimates, for clearly distinguishing spurious modes. Because the uncertainty of spurious modes is significantly larger than that of the real ones, a convolutional neural network (CNN) is adopted to automatically analyse the uncertainty diagram and efficiently determine the physical structural modes. The method is then applied to identify modal parameters for a six-degree-of-freedom spring–mass model, the Heritage Court Tower building in Canada, and the Ting Kau Bridge in Hong Kong. Results indicate for all three structures that the constructed CNN is effective for analysing the uncertainty diagram and can automatically and accurately obtain the real modes.

Comparison and application of two time domain methods analysis to modal parameter identification of Songhuajiang River highway-railway bridge

In this paper, comparison and application of two time domain modal parameter identification methods of ERA and SSI in a steel truss bridge is discussed. Firstly, multidirectional comparison and analysis of structural modal parameter identification under environment excitation to the bridge are carried out. Then finite element model of the Songhuajiang River highway-railway bridge is established by MIDAS CIVIL, and the modal analysis of the structure is carried out. The first ten order modes of the structure are obtained, and some characteristics of the first ten order modes are analyzed and compared. And combining the partial trend of the finite element modal analysis, the vibration experiment of the Songhuajiang River highway-railway steel bridge under the environmental excitation is tested. Then the modal parameters of the structure are calculated, analyzed and compared through the ERA method and SSI method based on the state space model. Finally the accuracy of the two modal parameter identification methods is tested, and the feasibility of the two methods applied in the steel truss bridge structural analysis is verified.

Investigation of Snow Load Effects on Modal Parameters of a Steel Structure Roof

Snowfall is one of the environmental factors that can cause effects on the identification of structural modal parameters. For the steel structure roof of the Harbin Railway Station, effects of snow load to the modal parameters were investigated. A single‐span simply supported beam was analysed from the theoretical perspective to study the principles. FEM‐based analyses were conducted for the steel structure roof to illustrate the significance of the snow load effects to modal parameters. Uniformly and nonuniformly distributed snow loads were regarded as the essential factors influencing modal frequencies and mode shapes. Monitoring response data are collected and analysed to confirm the accuracy of analytical results. It is concluded that snowfall‐induced variations on structural stiffness and mass matrices reduce the modal parameters and alter the mode shapes. The differences between the change regulations of the various modes are closely related to the distributions of snow loads. The theoretical and numerical analytical results are validated to be feasible and credible using temperature, axial strain, and acceleration measurements from the Harbin Railway Station field monitoring system.

Quantum-Behaved Particle Swarm Optimization-Based Structural Modal Parameter Identification Under Ambient Excitation

Under ambient excitation of white noise, structural modal parameters can be identified from cross-power spectrum calculated from structural outputs, without known input. The minimization of difference between theoretical value and test value of cross-power spectrum — the former is an equation including modal parameters to be identified, and the latter is computed based on the output-only data of structure — is adopted as an objective function for optimization. The optimal objective function value can be obtained through optimal modal parameter search. Quantum-behaved particle swarm optimization (QPSO) — swarm intelligence optimization algorithm based on particle swarm optimization (PSO) — is used for optimization to identify the modal parameters of structure under the ambient excitation. Then, the modal parameter identification method based on QPSO presented herein had been demonstrated by a numerical simulation of three-span continuous beam and experimental results of a three story structure. The computed results indicated that QPSO can be effectively used in the structural modal parameter identification under ambient excitation.

Improved independent component analysis based modal identification of higher damping structures

Structural modal parameter identification under ambient excitation has strong engineering value and theoretical significance. As the most popular tool for solving Blind Source Separation (BSS) problems, Independent Component Analysis (ICA) is able to directly extract the time-domain modal parameters, including frequencies, damping ratios and modal shapes. ICA, however, has a fatal flaw of failing to identify structures with higher damping. To overcome the flaw above, the paper proposes a new method named “ICA+IDT”. Firstly, free vibration response of a structure is obtained from structural outputs under ambient excitation. Inverse damping transfer (IDT) is employed to turn a highly damped signal into a low damping response signal without changing of frequencies and mode shapes. Then, structural modal parameters are extracted from the low damping response signal by ICA. Finally, the identified damping ratios are adjusted to eliminate the impact of IDT. To verify the effectiveness and applicability of IDT+ICA proposed herein, two numerical simulations—mass-spring model and simply supported concrete beam—and an experiment model of three-story steel frame are built, and the analysis results reveal that presented method can identify structures with higher damping effectively.