Modal Parameter Identification Research Articles

Modal frequency identification using the predictor subspace approach for a space solar power station

The system’s modal frequency parameters are determined by using a technique known as predictor-based subspace identification (PBSID), which is based on the dynamic properties of space solar power stations’ huge size and low frequency. First, the dynamic equation for the space solar power station with an Abacus configuration’s attitude-vibration coupling is developed. Additionally, the PBSID approach is used to build the relevant parameter matrix, and singular value decomposition (SVD) is chosen to evaluate the system’s structural frequency parameters. The right input signals are created via numerical simulation, and the best sensor placement technique yields the associated vibration response signals. The computing results then demonstrate that the modal frequency characteristics of the space solar power station may be successfully identified by the PBSID method, which is based on SVD. Additionally, the findings demonstrate the superior noise immunity capabilities of the PBSID algorithm when compared to the standard modal parameter identification approaches.

The Determination of Effective Modes of Wind-Bridge Coupling System Based on Stabilization Clustering Method

Modal identification is the core content of the full-bridge aeroelastic model wind tunnel test. Modal consistency is the most direct and effective basis to ensure that the model and the real bridge meet the similarity criteria. Accurate, simple and fast identification of modal parameters has very important practical significance for the evaluation and correction of aeroelastic models. In this paper, the eigensystem realization algorithm (ERA) and stochastic subspace identification (SSI) is improved, and the automatic identification theory of effective modes of bridge aeroelastic model based on stable clustering method is proposed. The stable diagram eliminates the unstable modes by comparing the results of different system orders, and the pedigree clustering further polarizes the stable modes to obtain multi-order and high-precision system modes. Numerical simulation examples and wind tunnel engineering examples show that the method has high accuracy and good adaptability, and can solve the problem of unstable damping identification results to a certain extent. In the wind tunnel test, the stable clustering method is one of the effective methods to identify the modal of the bridge aeroelastic model excited by the wind environment.

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.

Modal Parameter Identification of a Structure Under Earthquake via a Wavelet-Based Subspace Approach

This paper introduces a novel wavelet-based methodology for identifying the modal parameters of a structure in the aftermath of an earthquake. Our proposed approach seamlessly combines a subspace method with a stationary wavelet packet transform. By relocating the subspace method into the wavelet domain and introducing a weighting function, complemented by a moving window technique, the efficiency of our approach is significantly augmented. This enhancement ensures the precise identification of the time-varying modal parameters of a structure. The capacity of the stationary wavelet packet transform for rich signal decomposition and exceptional time-frequency localization is harnessed in our approach. Different subspaces within the stationary wavelet packet transform encapsulate signals with distinct frequency sub-bands, leveraging the fine filtering property to not only discern modes with pronounced modal interference, but also identify numerous modes from the responses of a limited number of measured degrees of freedom. To validate our methodology, we processed numerically simulated responses of both time-invariant and time-varying six-floor shear buildings, accounting for noise and incomplete measurements. Additionally, our approach was applied to the seismic responses of a cable-stayed bridge and the nonlinear responses of a five-story steel frame during a shaking table test. The identified modal parameters were meticulously compared with published results, underscoring the applicability and reliability of our approach for processing real measured data.

An extended modal approach for modal parameter identification of structure under the existence of harmonic excitations

The existing operational modal analysis (OMA) methods for the structure subjected to white noise and harmonic combined excitations have some limitations such as easy misjudgment of true and spurious modes and slow identification speed. Through expressing the system response with the extended modal matrix (EMM) and the extended modal response (EMR) vector, a novel operational modal parameter identification approach called the extended modal approach is proposed to obtain structural true modes under the existence of multiple harmonic excitations. The EMRs consist of the true modal responses and the spurious modal responses, and each of the former is random while each of the latter is harmonic. It is also proved theoretically that the EMM can be identified using the power spectrum density transmissibility (PSDT) method. Therefore, the extended modal approach includes three steps: (1) Using the PSDT to identify the EMM; (2) Utilizing the least squares reconstruction method to obtain the EMRs from the underdetermined extended modal equation; (3) Judging each of the EMRs to be true or spurious according to its empirical density function. Structural true modes can be ultimately obtained by removing all spurious modes from the identified results. The new approach is numerically verified through the OMA of two multiple-degree-of-freedom systems and then experimentally verified through the OMA of a test beam. The results in numerical simulation and experiments all show that the extended modal approach can identify accurately and quickly structural true modes under multiple harmonic excitations. Besides, the approach has good robustness against noise contamination.

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.

An Improved MP Algorithm for Power System Mode Identification

An improved matrix pencil (MP) algorithm for power system mode identification has been proposed in this paper. Aiming at the problem of inaccurate order determined by the singular value decomposition (SVD) step in traditional MP algorithms and the lack of Hankel structure in the reconstructed matrix, which leads to inaccurate identification under low signal-to-noise ratio (SNR) condition, singular entropy order determination is introduced. An iterative algorithm is proposed to calculate a reconstructed matrix with both Hankel structure and rank-deficient attributes. This reconstruction matrix has a better approximation effect and improves the identification accuracy of the MP algorithm under low SNR. The effectiveness of the proposed algorithm was verified by modal parameter identification of numerical signals and oscillation signals of the 4-machine and 2-area systems. The algorithm proposed in low SNR has higher accuracy than the traditional MP algorithm, and the reconstructed signal has a better fitting effect.

Identification of bridge modal parameters from GNSS data by integrating IEWT and robust ICA algorithm

Empirical wavelet transform is often used to process global navigation satellite system (GNSS) bridge deformation monitoring data, but it leads to inaccurate band division and too many spurious modes. To address these problems, this study proposes an improved algorithm to identify bridge modal parameters, which combines improved empirical wavelet transform and robust independent component analysis (ICA). The proposed method adopts the autoregressive power spectrum of an improved covariance algorithm, instead of the Fourier spectrum, for band division. Additionally, it performs noise reduction and reconstruction of multi-channel GNSS monitoring data. The reconstructed signal is inputted as multi-channel observation signal into robust ICA to extract features of the source signal. Finally, the natural excitation technique and Hilbert transform are used to solve the self-oscillation frequency and damping ratio of the structure. The proposed method is validated using both simulation data and the GNSS monitoring data of the Wilford suspension bridge. The results show that the proposed method can effectively reduce the measurement noise and successfully identify the first-order vibration frequencies and damping ratios of bridge. This algorithm can also be applied in the parameter identification of other engineering structures from GNSS data.

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.

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.

Optimal viscoelastic properties for passive damping treatments

In the context of noise and vibration control, constrained viscoelastic materials can be used to reduce structure-borne noise of vibrating structure. This passive damping treatment finds many applications due to its robustness and low cost. While several approaches are proposed in the literature to optimise the placement of constrained viscoelastic patches, few studies has been dedicated to the optimisation of the viscoelastic material's properties. The difficulty stems from their frequency-dependency. In this work, a fractional derivative model is used to describe the complex frequency-dependent viscoelastic properties. This study illustrates the effectiveness of using surrogate modeling to predict the damping performance of viscoelastic patches. A multi-model reduction method combined with a modal parameter identification method is used to build a surrogate model at a reasonable computational cost. Once trained, this metamodel is explored to optimise the parameters of the fractional derivative model, thus allowing the design optimisation of viscoelastic properties. This approach could be extended to optimise the material properties of viscoelastic foams in the low frequency range.

Experimental Investigations of Damage Identification for Aluminum Foam Sandwich Beams Using Two-Step Method

In the experiment, strain gauges and dynamic signal acquisition instruments are used to collect and record data, and the stochastic subspace algorithm is used to extract the first three strain modal parameters of each case. The damage amount identified by the second natural frequency based on the modified Timoshenko beam theory is more in line with the actual situation. The damage depth of case 2 and case 4 is 2 mm, and the identified damage amount is 10% and 9%, respectively. The damage depth of case 3 and case 5 is 4 mm, and the identified damage amount is 16% and 23%, respectively. The damage location information of case 6 is well identified by using the normalized strain modal shape difference index and the enhanced strain modal shape difference index. Taking the strain response signal of case 6 as an example, it is proved that the stochastic subspace strain modal parameter identification algorithm has strong anti-interference ability under the action of 1.5 times, 4 times, and 9 times noise. In addition, the method is verified by theoretical calculation and numerical simulation, and the damage law has a high degree of coincidence with the test. The experimental results show that this method expands the theoretical basis of foam metal damage degree information identification and improves the accuracy of damage location information identification and the anti-interference of parameter identification.

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.

Cross-correlation-guided operational modal identification of bridge considering asynchronous signals

The accurate identification of modal parameters is crucial for bridge health monitoring. In practical scenarios, there is often an asynchronization in the multi-channel vibration signals obtained from wireless sensors or offline measurements without temporal data. This asynchronization can lead to significant bias in the mode shapes when using the classical operational modal identification method. To address this issue, a new cross-correlation (CC) coefficient-based time lag detection is proposed. This technique aims to determine whether the multi-channel signals are synchronous and to prepare the reliably synchronous signals for modal identification. Because this detection technique specifically focuses on detecting the time lag between single degree-of-freedom (DOF) asynchronous signals, a multivariate variational mode decomposition (VMD) technique is developed to handle the multiple DOF signals of a bridge. To ensure that the decomposed components are not distorted or mixed, the penalty parameter in the multivariate VMD is optimized by minimizing the proposed similarity index. The proposed time lag detection process is validated using numerical and actual bridge examples. The results demonstrate that the new CC coefficient-based method is more effective than the classical CC coefficient or phase-based method, regardless of the employed mode or the amount of time lag present.

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.

Recurrence rate spectrograms for impact localization in wood

Characteristics like cellular grain structure, inhomogeneous density, aging, and altering environmental conditions (moisture, temperature) give wood highly anisotropic viscoelastic properties and non-linear vibrational wave propagation properties. Nonlinearity limits the use of linear methods, such as modal analysis and parameter identification via transfer functions. Acoustic localization of natural damage to wood, like crack growth, is of general interest in structural health monitoring of timber structures. Time-difference of arrival or energy attenuation is commonly used for localization, which are prone to boundary reflections or require the frequency response function. Recent advancements in machine learning-based classification of non-linear signals can achieve a much higher accuracy when recurrence rate-based spectrograms are used compared relative to conventional short-time Fourier transforms, especially in the presence of noise. Hence, in this work, multi-sensor measurements of impulse induced vibration in wood beams are classified by their distance to the excitation, based on their time series, avoiding a priori knowledge of a transfer function for the localization. The machine learning model is trained across various widths and thicknesses of samples, giving a localization estimate independent of beam dimensions. This research will contribute to early detection of damage in the field of vibration-based structural health monitoring of wood.

Optimization of machining performance in deep hole boring: A study on cutting tool vibration and dynamic vibration absorber design

In the realm of precision engineering, particularly in deep hole boring processes, tool vibration emerges as a critical determinant of machining performance. This investigation elucidates the genesis of self-excited vibrations within deep hole boring operations and delineates the underlying mechanisms of cutting tool vibration. A focal point of this study is the optimal alignment of the boring bar to mitigate vibrational impacts, thereby enhancing surface finish quality and extending tool longevity. Central to this analysis is the employment of a Dynamic Vibration Absorber (DVA) aimed at attenuating cutting tool vibration. The deployment of DVA necessitates precise identification of modal parameters, namely the equivalent stiffness (K) and mass (M) of the cutting tool. This research juxtaposes various scholarly methodologies to amalgamate theoretical calculations with simulation approaches, thereby acquiring accurate modal parameters. Utilizing Matlab software, the vibration amplitude of the boring bar under varying spring stiffness scenarios was examined. Results indicate a direct correlation between increased stiffness and reduced amplitude, particularly when the frequency ratio 'g' ranges between 0.5 and 1.1. Consequently, a stiffer DVA configuration is posited as more effective in vibration reduction. Furthermore, the study conducted frequency sweep experiments on a damping boring bar, utilizing a vibration excitation platform. These experiments revealed the existence of an optimal stiffness value for the DVA, thereby underscoring the significance of stiffness matching in vibration mitigation strategies.

Effect of Support Stiffness Nonlinearity on the Low-Frequency Vibro-Acoustic Characteristics for a Mechanical Equipment—Floating Raft—Underwater Cylindrical Shell Coupled System

The low-frequency vibro-acoustic characteristics of a mechanical equipment—floating raft—cylindrical shell—underwater acoustic field coupled system with nonlinear supports are studied in this paper. Firstly, the state space equations were established by a modal superposition theory for the coupled system, and a modal parameter identification method was deduced and verified for the cylindrical shell—underwater acoustic field coupled subsystem. On this basis, the formulas were derived for transmitted power flow in the coupled system, and the nonlinear stiffness constitutive relation of the vibration isolation supports was expressed by softening and hardening characteristics. Finally, dynamic simulations were carried out by the Runge—Kutta method to analyze the effect of nonlinear stiffness characteristic parameters on the low-frequency vibration modes and vibro-acoustic transfer characteristics in the coupled system. The research shows that a superharmonic phenomenon is common in the steady vibration mode of the coupled system with a nonlinear softening (or hardening) stiffness characteristic under harmonic excitation. The stronger the softening (or hardening) stiffness characteristic is, the more complex the vibration form is, and the smaller (or larger) the low-frequency vibro-acoustic transfer level in resonance regions is.

Characterization of the iPhone LiDAR-Based Sensing System for Vibration Measurement and Modal Analysis.

Portable depth sensing using time-of-flight LiDAR principles is available on iPhone 13 Pro and similar Apple mobile devices. This study sought to characterize the LiDAR sensing system for measuring full-field vibrations to support modal analysis. A vibrating target was employed to identify the limits and quality of the sensor in terms of noise, frequency, and range, and the results were compared to a laser displacement transducer. In addition, properties such as phone-to-target distance and lighting conditions were investigated. It was determined that the optimal phone-to-target distance range is between 0.30 m and 2.00 m. Despite an indicated sampling frequency equal to the 60 Hz framerate of the RGB camera, the LiDAR depth map sampling rate is actually 15 Hz, limiting the utility of this sensor for vibration measurement and presenting challenges if the depth map time series is not downsampled to 15 Hz before further processing. Depth maps were processed with Stochastic Subspace Identification in a Monte Carlo manner for stochastic modal parameter identification of a flexible steel cantilever. Despite significant noise and distortion, the natural frequencies were identified with an average difference of 1.9% in comparison to the laser displacement transducer data, and high-resolution mode shapes including uncertainty ranges were obtained and compared to an analytical solution counterpart. Our findings indicate that mobile LiDAR measurements can be a powerful tool in modal identification if used in combination with prior knowledge of the structural system. The technology has significant potential for applications in structural health monitoring and diagnostics, particularly where non-contact vibration sensing is useful, such as in flexible scaled laboratory models or field scenarios where access to place physical sensors is challenging.

An Automated Procedure for Continuous Dynamic Monitoring of Structures: Theory and Validation

IntroductionStability diagrams are a helpful tool for operational modal analysis to obtain the physical modes of a structure. These modes can be defined by visualizing stable columns formed by consistently identified modes over a range of model orders. Extracting these modes manually becomes an obstacle if continuous identification of modal parameters is required.Materials and methodsIn this paper, a procedure is configured to automatically interpret the stability diagrams constructed with the identification results of the SSI-COV/ref algorithm. This procedure is based on some methodologies found in the literature, which follow three stages. First, a stability diagram cleaning stage is defined where modal validation criteria and partitioning clustering algorithms are used to detect spurious modes. Second, a mode grouping stage based on a hierarchical clustering algorithm is implemented to form sets of modes that share similar modal information. Finally, a selection stage is applied to define representative modal parameters from the set of physical modes.ResultsThe proposed procedure is validated by simulating a beam-type structural model with ten degrees of freedom affected by ambient temperature functions. Natural frequencies computed for the DT140 and DT220 datasets collection with the frequency-domain decomposition method agree with the computed ones with the proposed procedure, presenting MAC coefficients higher than 0.97. A total of 192 datasets are simulated, and the acceleration responses are polluted with two noise levels, SRN = 40 [dB] and SNR = 20 [dB].ConclusionsFor the analyzed beam, the modal tracking results showed that the procedure could perform continuous identification automatically. The variations in the natural frequencies are correlated to the variations in the ambient temperature functions.