Modal Parameters Of Structure 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.

Evaluation of the Modal Parameters of a Unidirectional Carbon-Based Composite Structure Using the Influential Factor of Static Loading.

Static loading can significantly alter the dynamics of unidirectional carbon-based composites (UCBCs), with modal parameters varying depending on the orientation of the carbon fibers. In this study, the sensitivity of modal parameters of UCBC structures under uniaxial static loading was investigated. The theoretical static load influential factor was derived from a linearized UCBC model and corresponded to the transformed decoupled response over the mass-normalized static load. Three rectangular UCBC specimens (carbon fiber orientation of 0°, 45°, and 90°) were prepared under fixed-fixed boundary conditions using a jig fixture. Uniaxial static loads between 0 N and 1000 N were applied, and the first three modes of the UCBC specimens were analyzed. An isotropic SUS304 specimen was used as a reference. The linearization assumption about the UCBC structure was preliminarily validated with the Modal Assurance Criterion (MAC). A high influential factor was found for the UCBC specimen when carbon fibers were aligned with the static load direction at the first two resonance frequencies. Therefore, the proposed influential factor is an efficient indicator for determining the sensitivity of the dynamic response of a UCBC structure over a static load case. The variations in the influential factors for the UCBC specimens were more pronounced than for the isotropic specimens.

Modal Parameter Recursive Estimation of Concrete Arch Dams under Seismic Loading Using an Adaptive Recursive Subspace Method.

Modal parameter estimation is crucial in vibration-based damage detection and deserves increased attention and investigation. Concrete arch dams are prone to damage during severe seismic events, leading to alterations in their structural dynamic characteristics and modal parameters, which exhibit specific time-varying properties. This highlights the significance of investigating the evolution of their modal parameters and ensuring their accurate identification. To effectively accomplish the recursive estimation of modal parameters for arch dams, an adaptive recursive subspace (ARS) method with variable forgetting factors was proposed in this study. In the ARS method, the variable forgetting factors were adaptively updated by assessing the change rate of the spatial Euclidean distance of adjacent modal frequency identification values. A numerical simulation of a concrete arch dam under seismic loading was conducted by using ABAQUS software, in which a concrete damaged plasticity (CDP) model was used to simulate the dam body's constitutive relation, allowing for the assessment of damage development under seismic loading. Utilizing the dynamic responses obtained from the numerical simulation, the ARS method was implemented for the modal parameter recursive estimation of the arch dam. The identification results revealed a decreasing trend in the frequencies of the four initial modes of the arch dam: from an undamaged state characterized by frequencies of 0.910, 1.166, 1.871, and 2.161 Hz to values of 0.895, 1.134, 1.842, and 2.134 Hz, respectively. Concurrently, increases in the damping ratios of these modes were observed, transitioning from 4.44%, 4.28%, 5.42%, and 5.56% to 4.98%, 4.91%, 6.61%, and 6.85%%, respectively. The correlation of the identification results with damage progression validated the effectiveness of the ARS method. This study's outcomes have substantial theoretical and practical importance, facilitating the immediate comprehension of the dynamic characteristics and operational states of concrete arch dam structures.

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.

Identification Methods for Modal Parameters of Track Structures and Their Application Status and Prospects

Rail transit’s wheel–rail system periodically encounters defects such as wheel polygons, rail corrugation, and rail fastener failure, which are intricately linked to the modal parameters of track structures. Identifying these modal parameters is essential for refining wheel–rail dynamics models, understanding track defect mechanisms, and defect detection. This study reviews the current methodologies for identifying track structure modal parameters, emphasizing their significance in track engineering. It categorizes various identification techniques, examines their development, and highlights their application in updating track dynamics theoretical models. The relationship between track modal parameters and wheel–rail defects is discussed, alongside a summary of modal parameter-based defect remediation strategies globally. The paper also evaluates the current state of defect identification research utilizing track modal parameters. In the “prospects” section, three forward-looking research avenues are proposed. These approaches are poised to streamline and improve the efficiency of modal parameter extraction, marking potential breakthroughs in the field.

Transmissibility-based operational modal analysis: A unified scheme and uncertainty quantification

The transmissibility-based Operational Modal Analysis (OMA) technique has attracted substantial research interest over the past two decades due to its capability to extract structural modal parameters in the presence of non-white excitation. The transmissibility function used in OMA can be categorized as Response Transmissibility (RT) and Power Spectral Density Transmissibility (PSDT). Modal parameters can be identified by combining RTs from multiple load cases or PSDTs from multiple transfer outputs. Nevertheless, the mathematical formulations and implementation procedures of the various RT-based and PSDT-based methods exhibit significant differences. Furthermore, the uncertainty associated with modal parameter estimates is rarely assessed in these methods. This work aims to propose a scheme that unifies various transmissibility-based OMA algorithms through a consistent parametric formulation. Within this scheme, a universal parametric model and a standardized implementation procedure are developed to accommodate two types of transmissibility in both time and frequency domains and six OMA algorithms; additionally, a generalized framework for quantifying the uncertainties associated with modal parameter estimates is provided. The proposed scheme is finally validated using a planar truss structure.

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.

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.

An Output-Only, Energy-Based, Damage Detection Method Using the Trend Lines of the Structural Acceleration Response

Using the trendlines of an acceleration response as a tool to decompose a structural response is a new topic that was proposed by authors in 2020. This paper provides a numerical/experimental investigation of using a Savitzky–Golay filter (SGF) in a method to calculate the trendline and decompose building acceleration responses when subjected to a seismic load. Hence, this paper proposes an output-only, energy-based, damage detection method in which the trend lines of a building’s structural acceleration responses are used to locate the damage. For this purpose, an adjusted SGF is utilized to calculate an especial trend line for each floor’s acceleration response of the building structural model. The energy of these trend lines is then calculated and normalized. Two damage indices are used, of which, the second one is being proposed for the first time in this paper. The accuracy of the proposed method is numerically and experimentally investigated using a five-floor building structural model subjected to white noise excitation through a shake table. The results prove that the proposed method is capable of accurately locating and quantifying structural damages with a severity of more than 10% in a noisy environment. In view that the proposed method locates the damage with no need of determining the structural modal properties or parameters, it can be categorized as an online and quick structural damage detection method.

Modal Identification of Aircraft Time-varying Structure Based on Fiber Grating Measurement

To meet the increasing mission requirements, the time-varying characteristics of the aircraft structural system have been increasingly considered and utilized. Therefore, it is significant to obtain the structural modal parameters during the mission of the aircraft. However, the traditional electrical sensors have many limitations in the online measurement of spacecraft structure, and fiber grating sensors are expected to better adapt to the requirements. The online modal parameter identification methods of time-varying structures also lack sufficient research. The traditional modal parameter identification methods include non-parametric method and parametric method. However, the rapid development of neural networks in recent years makes them an effective tool for modal parameter identification. In this paper, a moving mass beam simulation model is established to simulate the time-varying characteristics of the structure, and the modal parameters of the dynamic strain signal are identified. The comparison results of three identification methods are obtained.

Correlation Analysis of Large-Span Cable-Stayed Bridge Structural Frequencies with Environmental Factors Based on Support Vector Regression

The dynamic characteristics of bridge structures are influenced by various environmental factors, and exploring the impact of environmental temperature and humidity on structural modal parameters is of great significance for structural health assessment. This paper utilized the Covariance-Driven Stochastic Subspace Identification method (SSI-COV) and clustering algorithms to identify modal frequencies from four months of acceleration data collected from the health monitoring system of the Jintang Hantan Twin-Island Bridge. Furthermore, a correlation analysis is conducted to examine the relationship between higher-order frequency and environmental factors, including temperature and humidity. Subsequently, a Support Vector Machine Regression (SVR) model is employed to analyze the effects of environmental temperature on structural modal frequencies. This study has obtained the following conclusions: 1. Correlation analysis revealed that temperature is the primary influencing factor in frequency variations. Frequency exhibited a strong linear correlation with temperature and little correlation with humidity. 2. SVR regression analysis was performed on frequency and temperature, and an evaluation of the fitting residuals was conducted. The model effectively fit the sample data and provided reliable predictive results. 3. The original structural frequencies underwent smoothing, eliminating the influence of temperature-induced frequency data generated by the SVR model. After eliminating the temperature effects, the fluctuations in frequency within a 24 h period significantly decreased. The data presented in this paper can serve as a reference for further health assessments of similar bridge structures.

Operational modal identification of structures based on improved empirical wavelet transform

When empirical wavelet transform (EWT) is used to identify the modal parameters of civil engineering structures, the frequency band division is generally not accurate due to the noise effect on the Fourier spectrum. This phenomenon will lead to modal mixing and false modes in the analysis results. Therefore, this article establishes a signal frequency band division method by taking advantages of maximal spectrum technique and spectral skewness index. Combining the random decrement technique (RDT) and the least square method of single component modal parameter identification, an adaptive approach based on the improved EWT for operational modal parameter identification of civil engineering structures under stationary environmental excitations is proposed. The traditional frequency band division method based on EWT can not completely and effectively divide the meaningful frequency bands. While the proposed frequency band division technology based on the spectral skewness index can prevent the phenomenon of insufficient division and excessive division and realize adaptive frequency band division. The effectiveness of the proposed approach is validated by a numerical three-story frame and a field three-span concrete box girder bridge under ambient vibrations. The modal identification results from both numerical and experimental validations demonstrate that the proposed approach can effectively and accurately decompose the vibration responses and identify the structural modal parameters under operational conditions.

Fully automated operational modal identification of regular and irregular buildings with ensemble learning

Modal identification, a type of system identification that employs modal analysis, can be automated to reduce user interference in extracting modal parameters. Modal analysis is a valuable tool for obtaining a structure's modal parameters, which define its dynamic characteristics. Operational modal identification is a specific type of modal analysis that uses only system outputs to extract modal parameters. The present study aims to introduce a fully automated modal identification algorithm to identify modal parameters for an unknown system based on its output information. The algorithm uses a stochastic subspace algorithm to extract modal parameters, requiring only the appropriate degree of the state-space model estimated using the Singular Value Criterion. Several features are used to create a feature space that separates physical and spurious modes. The Improved Distance Evaluation algorithm selects appropriate features, making the identification process more accurate and flexible. The identification algorithm employs clustering algorithms with different approaches and the Dempster-Shafer data fusion algorithm to integrate clustering algorithm results and avoid divergence among them. Due to limited data diversity for identification in cases where only one dataset is available, statistical resampling methods are used as an alternative. The proposed algorithm can identify modal parameters using only one dataset of the building structure. Signal processing, data collection, clustering, feature extraction, model reduction, and data fusion are all aspects of this algorithm. To assess its performance, four regular and irregular buildings are considered as case studies. The presented modal identification algorithm is highly accurate and robust with the repeatable result as compared to similar algorithms, with extracted modal parameters demonstrating high stability.

Damage detection of offshore jacket structures using structural vibration measurements: Application of a new hybrid machine learning method

The artificial intelligence (AI) technologies, such as meta-heuristic computing and deep learning, have provides solid technical support for structural health monitoring (SHM) of offshore jackets. In this paper, a physics-enhanced AI method based on the parametric damage identification is developed for SHM of the offshore jacket structures. In this new method, a hybrid kernel function-based kernel extreme learning machine (HKELM) is proposed to construct an AI structure to enhance the SHM detection capacity on the structural modal parameters extracted by the parametric damage identification technique. Simulation analysis is carried out to verify the feasibility of the HKELM-based method using the response signals of a jacket structure under impact force, and the result demonstrates good damage location capability of the proposed method. Furthermore, to select proper parameters for the HKELM, the whale optimization algorithm (WOA) is applied to optimize the values of the regularization coefficient and kernel parameter array. Then, the wavelet denoising (WD) is introduced to preprocess the vibration signals to improve the damage detection ability of the WOA-HKELM. Lastly, experimental tests are performed to validate the effectiveness of the proposed method in utilizing the structural modal parameters for identifying the structural damage. The analysis results illustrate that the proposed method produces satisfactory damage location ability under the influence of actual noise in the vibration signals. Meanwhile, this method has broad application prospects in the SHM of other offshore structures.

Research on online monitoring technology for transmission tower bolt looseness

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

A lightweight stochastic subspace identification-based modal parameters identification method of time-varying structural systems

The application of stochastic subspace identification (SSI) on identifying structural time-varying modal parameters suffers from the shortcomings of poor computational efficiency and susceptibility to spurious modes. This work overcomes the shortcomings by the following procedures based on existing covariance-driven SSI. First, the covariance-driven SSI is embedded with techniques of randomized singular value decomposition and subspace iteration for reducing computation cost and avoiding accuracy loss, forming the lightweight SSI (lwSSI). Then, the lwSSI is combined with the technique of sliding window for eliminating spurious modes and continuously identifying time-varying modal parameters. The proposed lwSSI-based identification method is applied on the simulation of a gravity dam, and the identified time-varying modal parameters show the same trend as the assumed time-varying elastic modules. Furthermore, the characteristics of the lwSSI-based identification method, including noise resistance, computational efficiency, and identification accuracy, are investigated. Finally, the identification of a steel cantilever beam with the time-varying modal parameters caused by the mass distribution experimentally validates the effectiveness of the proposed lwSSI-based identification method.

Experimental method for modal parameter identification of civil engineering structures based on improved wavelet transform

With the continuous acceleration of the global construction industry, many structural infrastructure structures in China have been put into use for decades. They are very prone to damage due to fatigue. The modal parameter identification of civil engineering construction can evaluate the safety status of infrastructure structures. In view of this, an identification system of civil engineering structure modal parameters is proposed based on improved wavelet transform. In the process, the mode shape was chosen as the method of wavelet transform. The data was discretized by selecting the actual data of a high-speed railway station combined with sensors and wavelet transform. Finally, the correct identification of the modal parameters of civil engineering structures is realized. The data shows that under normal conditions where there is only white noise interference, the waveform of the structure is relatively stable, and the amplitude fluctuation is in the [-2,3] interval. At the same time, the average amplitude of the structure is in the [2.2, −1.5] interval under normal conditions. In addition, the positive and negative extreme points are 3.7 and −2.3, respectively. This indicates that the structure amplitude fluctuation is in a dynamic and stable state under normal circumstances. The optimized wavelet transform method identifies a total of four orders in the first six natural frequencies. The minimum error is 0.11%, the maximum error is 1.50%, and the average error of the first four natural frequencies is 0.578%. In addition, based on the comparison of theoretical and identification values of longitudinal vibration shapes, the proposed method can successfully detect abnormal values at the 10th and 18th nodes. From the above results, it shows that the wavelet transform method has high accuracy and small error in frequency identification. It meets the requirements of identifying the natural frequency parameters of the structure. From the calculation, the method proposed in the experiment can realize the real-time health detection of the structure, which is of great significance.

Analysis of Vibration and Acoustic Radiation Characteristics of Reinforced Laminated Cylindrical Shell Structure

This paper investigates the acoustic radiation characteristics of reinforced laminated cylindrical shell structures in the medium-low frequency range (1~1000 Hz) of aircrafts, submarines, and deepwater thrusters by combining simulation analysis and experimental testing. The research focuses on reinforced laminated plates, where experimental setup is established to measure structural modal parameters and structural acoustic power, and a finite element model is developed to verify the reliability of the finite element modeling method through comparison with experimental and simulation results. Simultaneously, a finite element model of the reinforced laminated cylindrical shell structure is established, and finite element simulation analysis is conducted to investigate the effects of different reinforcement methods, reinforcement quantities, reinforcement lengths, and reinforcement thicknesses on the acoustic radiation characteristics of the structure. The results indicate that in the frequency range of 1~1000 Hz, ribbed reinforcement exhibits better performance in reducing structural noise radiation compared to longitudinal reinforcement. With the increase in reinforcement quantity and thickness, the structural acoustic radiation decreases. Meanwhile, with the increase in reinforcement length, the overall sound power level of the structure shows a trend of first increasing and then decreasing.

A modal estimation method of rotating blade based on compressed sensing and blade tip timing

Structural modal estimation has consistently remained one of the most crucial areas of research in mechanical vibration analysis and signal processing. It is imperative to accurately monitor the vibration signals of rotor blades and their corresponding structural modal parameters. Blade tip timing (BTT) is a promising approach used to measure vibration and monitor the health of blades. However, most existing BTT methods focus on frequency accuracy, neglecting damping, a key physical quantity that represents the strength of the structure. This research focuses on damping modal estimation of blade vibration and proposes a sparse reconstruction algorithm based on a two-dimensional Laplace wavelet family, which addresses the inherent under-sampled problem of BTT technology while enabling estimations of both the structural modal frequency and modal damping of the blades. Firstly, the proposed algorithm is achieved by designing a Laplace wavelet dictionary based on prior information and using a convex optimization objective function with a regularization term. Secondly, Laplace wavelet dictionary matches the signal better than the traditional Fourier dictionary based on the similarity between the damped vibration signal and the Laplace wavelet, then a sparser representation vector can be obtained. Moreover, the research object is not limited to a single blade, but can be easily expanded to multiple stages and multiple rotating blades monitored simultaneously. Finally, the simulation and physical test results indicate that the proposed method exhibits high reconstruction accuracy, reliability, and anti-noise abilities.

Long-term continuous automatic modal tracking algorithm based on Bayesian inference

Modal tracking plays a vital role in structural health monitoring since changes in modal parameters help us understand a structure’s dynamic characteristics and may reflect the potential deterioration of structural performance. Although numerous modal parameter estimation (MPE) methods exist, it is not guaranteed that an MPE process will exclude all spurious modes and not lose any physical modes every time over a long-term monitoring period. Relatively large damping of a structure, poor data quality, and significant changes in structural modal parameters may make the estimated modal parameters spurious, missing, or misclassified. It makes long-term modal tracking semiautomated or manual, which constrains timely downstream applications such as anomaly detection, condition assessment, and decision making. This research aims to propose a long-term continuous automatic modal tracking algorithm based on Bayesian inference even when the modal parameters, damping, and data quality change significantly. Bayesian inference is used to determine the physical modes from the results of existing MPE methods. Both the modes identified from the most recent response set and the modal probability model from multiple previous response sets are considered in the Bayesian model to better determine the physical modes from the results of MPE. Moreover, the proposed algorithm requires only three extra hyperparameters compared to general modal tracking algorithms, and they can be quickly determined by a grid search method. The performance of the proposed algorithm is verified by a numerical example and a real-world civil structure Z24 Bridge benchmark.