Modal Parameter Identification Method Research Articles

Silicone Rubber-Packaged FBG Sensing Information and SSI-COV-Recognized Modal Parameters Motivated Damage Identification in Pipe Structures

Pipes are the main structures serving as the lifeline for oil and gas transportation. However, they are prone to cracks, holes and other damages due to harsh working environments, which can lead to leakage incidents and result in significant economic losses. Therefore, the development of structural health monitoring systems with advanced online diagnostic methods is of great importance for identifying local damages and assessing the safety state of pipe structures. These efforts can guide rapid repairs and ensure the continuous, efficient and cost-effective transportation of oil and gas resources. To address this problem, this paper proposes the development of a pipe monitoring system based on quasi-distributed fiber Bragg grating (FBG) sensing technology. The SSI-COV method is employed to process the sensor responses and extract the modal parameters of the structure. Based on this foundation, an enhanced damage identification index is proposed, which mitigates the effects of support and excitation positions on damage identification. The pipe structure can be regarded as a continuous super-statical beam, and based on its structural symmetry, a unit structure, specifically a stainless-steel pipe with fixed ends, is regarded as the experimental subject. Impact experiments have been conducted to analyze its behavior in both undamaged and damaged states. The research indicates that by using the proposed modal parameter identification method and the ASMDI damage index, ASMDI exhibits peak values at damage locations of the pipe structure. This allows for the identification of structural damage with high accuracy, fast processing efficiency and strong robustness. The study provides an effective and reliable damage diagnosis method, which can contribute to the refinement and visualization of pipe structural health monitoring systems.

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

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

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.

Research on railway vehicle modal parameter identification method based on drop impact load

This paper investigates the modal parameter identification technique utilizing a drop impact load. A 12-DOF mathematical model of a Railway Vehicle System (RWVS) was constructed, followed by theoretical calculations, simulation analysis, and tests with four different drop impact loads. The responses to these loads were inspected through FFT, and the modal frequencies of the RWVS were determined by the Peak Picking (P-P) method. The simulation demonstrated that four types of drop impact loads can activate the bounce, pitch, and roll modes of the RWVS. The theoretical calculation and simulation analysis revealed that the maximum error of modal frequency identification is no greater than 6.5%. The experimental results verified that the drop impact excitation method can be used to identify the modal parameters of a complex railway vehicle system, which is highly beneficial for the design and verification of the vehicle structure.

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.

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.

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.

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.

Adaptive modal identification of honeycomb thin-walled composite structures with pit defects under thermal modal testing using variational mode decomposition technique based on digital image correlation

The active imaging blue light high-speed three-dimensional digital image correlation (3D-DIC) system was combined with a transient aerodynamic heating system and random pulse excitation technology to establish a high-frequency thermal vibration optical test system capable of multi-temperature zone testing at 900 °C to accurately obtain the thermal modal parameters of thin-walled structures. The full-field temperature distribution of a novel honeycomb thin-walled composite structure (HTWCS) with pit defects under non-uniform temperature was accurately simulated through reinforcement learning. The first six modal frequencies of honeycomb thin-walled composite structure with pit defects at room temperature increased compared with the non-destructive honeycomb thin-walled composite structure, and the third and fourth modal shapes interchanged. An adaptive modal parameter identification method for full-field three-dimensional vibration measurements under high-temperature environments was developed by combining the successive multivariate variational mode decomposition (VMD) with the modal superposition method. This method can effectively identify close modes. The area ratio-based approach was used to evaluate the damping of the measured response. The finite element model (FEM) of the HTWCS with pit defects at different temperatures was updated using a multi-state step-by-step model updating method and the temperature-dependent material properties were established. The results showed that the introduction of a damping ratio improved the accuracy of the updated FEM of HTWCS with pit defects. The proposed technique is anticipated to provide an effective method for high-frequency thermal vibration optical measurement and modal identification of thin-walled structures under multi-temperature regions.

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.

Modal Parameter Identification of Civil Engineering Structure Based on XGBoost Algorithm

In order to prevent the structural problems of buildings and related civil engineering from becoming potential risks, the modal parameter identification method of civil engineering structures is studied based on XGBoost algorithm. First of all, it is necessary to design and extract the modal parameters of civil engineering structures, and then detect civil engineering structures according to the modal parameter identification model, identify the existing problems of the structures, discuss and analyze them, verify the effect of the detection method of civil engineering structures based on modal parameter identification, and make a comparative analysis with the traditional modal parameter identification methods such as SSI. By analyzing the basic principle and algorithm of XGBoost algorithm, this study analyzes the research characteristics and present situation of the method, identifies the implementation and feasibility of modal parameters of civil engineering structures, and provides theoretical basis and data reference for the development of related professions and related industries.

The effect of constituent units on the vibration reduction of bamboo engineering materials: The synergistic vibration reduction mechanism of bamboo stiffness and wood damping

Determination of the influence and mechanism of constituent units on the vibration reduction performance of bamboo engineering materials is required to optimize application of these materials in the fields of construction and transportation. Testing was performed of typical bamboo engineering materials of Bamboo scrimber (BS), bamboo-wood composites (BWC), and Bamboo Glued laminated timber (GLT), all with different constituent units. Vibration reduction performance and parameters of vibration models were determined and compared using point-by-point multi-point tests and modal parameter identification methods. On this basis, equivalent stiffness was approximated based on inherent frequency. The results show that, BWC had the best vibration reduction performance, followed by BS, and GLT. The first three-order damping ratios of BWC were the largest, 2.14 %, 2.52 %, and 2.43 %, and those of GLT were the smallest, 1.40 %, 1.58 % and 1.60 %. Overall, the equivalent stiffness of the tested materials was in the order of: BS>BWC>GLT. The first three-order modal shape resembled the typical first-order quadrilateral torsional bump, the second-order middle-position bending bump, and the third-order bending-torsional bump. The resonance bands were mostly distributed at the middle position for GLT and BS, and at both ends of BWC. Vibration reduction of GLT was mainly attributed to the vibration reduction of solid bamboo, that of BS was mainly due to the high stiffness vibration reduction of bamboo fibers after recombination, and that of BWC resulted from the synergistic effect of the rigid surface layers and the even lamination of the low density and high porosity damping core layer after bamboo veneers. These results provide scientific reference for the vibration reduction design and optimization of bamboo engineering materials for applications in the fields of construction and transportation.

Output-Only Time-Varying Modal Parameter Identification Method Based on the TARMAX Model for the Milling of a Thin-Walled Workpiece.

The process parameters chosen for high-performance machining in the milling of a thin-walled workpiece are determined by a stability prediction model, which needs accurate modal parameters of the machining system. However, the in-process modal parameters are different from the offline modal parameters and are difficult to precisely obtain due to material removal. To address this problem, an accurate time-dependent autoregressive moving average with an exogenous input (TARMAX) method is proposed for the identification of the modal parameters in the milling of a thin-walled workpiece. In this process, a TARMAX model considering external force excitation is constructed to characterize the actual condition in the milling of a thin-walled workpiece. Then, recursive method and sliding window recursive method are used to identify TARMAX model parameters under time-varying cutting conditions. Subsequently, a three-degree of freedom (3-DOF) time-varying structure numerical model under theoretical milling forces and white-noise excitation is established, and the computational results show that the predicted natural frequencies using the proposed method are in close agreement with the simulated values. Finally, several experiments are designed and carried out to validate the effectiveness of the proposed method. The experimental results show that the predicted accuracy of the proposed method using actual cutting forces is 95.68%. Good agreement has been drawn in the numerical simulation and machining experiments. Our further research objectives will focus on the prediction of the damping ratios, modal stiffness, and modal mass.

Synthetical Modal Parameters Identification Method of Damped Oscillation Signals in Power System

It is vital to improve the stability of the power system by accurately identifying the modal parameters of damped low-frequency oscillations (DLFO) and controlling the oscillation in time. A new method based on empirical mode decomposition (EMD), stochastic subspace identification (SSI), and Prony algorithms, called synthetical modal parameters identification (SMPI) method, is developed by efficiently matching the modal parameters of DLFO which are acquired from the SSI and Prony algorithm. In this approach, EMD is used for denoising the raw oscillation signals thereby enhancing the noise resistance, and then using the SSI and Prony algorithms to identify the precise modal parameters assisted by parameter matching. It is demonstrated that the proposed SMPI method holds great accuracy in identifying full modal parameters including natural frequencies, damping ratios, amplitudes, and phase angles with simulated signals with known modal parameters and real-time signals from some power system case studies. The strategy of SMPI has effectively overcome the weakness of a single approach, and the identification results are promising to heighten the stabilization of power systems. Besides, SMPI shows the potential to troubleshoot in different fields, such as construction, aeronautics, and marine, for its satisfactory robustness and generalization ability.

Iterative reference-driven S-transform time-varying parameter identification for bridges under moving vehicle

Traditional bridge health monitoring is both expensive and time-consuming because of the need for installing a large quantity of sensors on the bridge. The indirect monitoring method as a feasible alternative has become popular over the last decade, as useful information can be gathered from moving vehicles installed with sensors by considering vehicle-bridge interaction. This paper describes an indirect time-varying modal parameter identification method for bridges under a moving test vehicle. A novel reference-driven S-transform is proposed for the parametric modal identification of time-varying structural systems with non-stationary characteristics based on a multisensory arrangement, comprising a fixed reference sensor installed on the bridge and another movable sensor installed on a moving test vehicle. By the phase-preservation property of S-transform and the multisensory time-frequency analysis, the proposed iterative reference-driven S-transform can be used to extract the time-varying modal parameters of the vehicle-bridge system when the vehicle moves on the bridge. Based on the coherence between measurements from the sensors mounted on the bridge and vehicle, one can track the time-varying characteristics by combining the spatial and time-frequency information obtained by the multisensory array. The efficiency of the proposed reference-driven S-transform method is validated by numerical simulations and laboratory experiments using a simply supported beam with a moving vehicle. The effects of the vehicle property, driving speed, road roughness and measurement noise are discussed. The numerical and experimental results have demonstrated that the proposed method is useful for time-varying parameter extraction with a multisensory system. This will be useful to structural condition monitoring of bridges.

Vision-based modal parameter identification for bridges using a novel holographic visual sensor

Noncontact monitoring using holography can be quite useful in vision-based structural health monitoring owing to its advantages in terms of data visualization and real-time applications. Aimed at exploring the potential of vision-based sensors for structural health monitoring in more general applications, this paper has developed the holographic visual sensor (HVS) with a vision-based modal parameter identification method. This strategy is an extension of the current vision-based techniques and holography. Based on the newly introduced spatial and temporal sequence data measured by HVS, the vision-based modal parameter identification method was proposed and applied to structural health monitoring for the first time. Accordingly, the feature point set describing the geometric morphology of the structural holography and the time-state-space mathematical model of the structural dynamics system was constructed. In this way, the mechanical behavior characteristics could be extracted from serial transient holographic responses following excitation, and the structural modal parameters were then calculated and quantitatively analyzed. Laboratory experiments and field tests were employed for validation based on the comparison between the results determined by the proposed HVS and those determined by conventional, high-precision contact sensors. The developed HVS and identification algorithms were able to visually collect and identify modal parameters at a higher data resolution and provide smoother modal shapes. The proposed method can thus be used to complement and improve existing computer-vision-based measurement techniques and damage detection.

Damping characteristics of single-layer aluminum alloy reticulated spatial structures based on improved modal parameter identification method

An improved identification method is proposed for the modal parameter identification of multi-modal vibration attenuation signals based on the analytical mode decomposition and the particle swarm optimization. Through examples of analog signals, it is proved that the proposed method can identify modal parameters under a strong colored noise environment. Field tests were carried out on four in-service aluminum alloy reticulated structures to obtain the acceleration response of the structures. The improved identification method proposed in this paper is used to identify the modal parameters of each acceleration response curve, based on which the damping characteristics of the aluminum alloy reticulated structures are analyzed. The results show that the damping characteristics of such structures obey a three-stage change rule, with the increase of the acceleration amplitude. In addition, a practical calculation method of the damping ratios of aluminum alloy reticulated structures is proposed on the basis of the experimental results.

Research on Modal Parameter Identification Method of Railway Carbody Based on 6-DOF Vibration Test Bench

In order to avoid the additional influence on the test results caused by the inconsistency between the boundary conditions of the carbody and the reality when using the vibration exciter or hammer to test the free mode of the carbody, a 6-DOF vibration test bench is tried to simulate the actual motion posture of the carbody to test its modal parameters. For in-depth discussion, a full-scale virtual prototype of the 6-DOF vibration test bench was built, and on this basis, the test bench-carbody rigidflexible coupling virtual test system was established. According to the modal frequency range of the carbody to be tested and the actual load capacity of the test bench, the excitation frequency and amplitude of the test bench are determined. Through the virtual modal test, it is determined that the carbody should be elastically supported when testing the modal parameters of the carbody by using the vibration test bench, so as to accurately obtain the modal parameters of the carbody.

Output-Only Modal Parameter Identification of Systems Subjected to Various Types of Excitation

This study presents a novel modal parameter identification method enabling approximation of the mode shapes of linear systems using white-noise or earthquake inputs. The majority of well-established existing system identification methods perform successfully when the system is excited by broadband white-noise excitation. However, they encounter serious limitations when analyzing the vibrations triggered by nonstationary earthquake inputs. Thus, the presented technique extends the applicability of system identification and modal-based structural health monitoring methods. The method operates in modal space and is based on mode superposition in short windows. The mode shapes are identified using an optimization algorithm minimizing the weighted sum of cross-correlation of frequency response spectra. The technique is validated analytically using simulation results of a simple three-dimensional (3D) structure representing a simplified model of a real bridge pier structure, which enables exact comparison with known properties. The results show the method provides relatively good identification accuracy of modal parameters of systems excited by white-noise and earthquake inputs. The identified modal frequencies showed <1% error, where the mode-shape coefficients were identified within 5% error. The method performs robustly even for high levels of simulated sensor noise and can be readily applied to more complex multiple degree of freedom (MDOF) systems.