Structural Modal Parameter Recognition and Related Damage Identification Methods under Environmental Excitations: A Review

Modal parameters can accurately characterize the structural dynamic properties and assess the physical state of the structure.Therefore,it is particularly significant to identify the structural modal parameters according to the monitoring data information in the structural health monitoring(SHM)system,so as to provide a scientific basis for structural damage identification and dynamic model modification.In view of this,this paper reviews methods for identifying structural modal parameters under environmental excitation and briefly describes how to identify structural damages based on the derived modal parameters.The paper primarily introduces data-driven modal parameter recognition methods(e.g.,time-domain,frequency-domain,and time-frequency-domain methods,etc.),briefly describes damage identification methods based on the variations of modal parameters(e.g.,natural frequency,modal shapes,and curvature modal shapes,etc.)and modal validation methods(e.g.,Stability Diagram and Modal Assurance Criterion,etc.).The current status of the application of artificial intelligence(AI)methods in the direction of modal parameter recognition and damage identification is further discussed.Based on the pre-vious analysis,the main development trends of structural modal parameter recognition and damage identification methods are given to provide scientific references for the optimized design and functional upgrading of SHM systems.

Modal Parameter Identification Method of Jacket Platform Structure Based on AFDD and Optimized FBFFT

Offshore platforms are susceptible to structural damage due to prolonged exposure to random loads,such as wind,waves,and currents.This is particularly true for platforms that have been in service for an extended period.Identifying the modal parameters of offshore platforms is crucial for damage diagno sis,as it serves as a prerequisite and foundation for the process.Therefore,it holds great significance to prioritize the identification of these parameters.Aiming at the shortcomings of the traditional Fast Bayesian Fast Fourier Transform(FBFFT) method,this paper proposes a modal parameter identification method based on Automatic Frequency Domain Decomposition(AFDD) and optimized FBFFT.By introducing the AFDD method and Powell optimization algorithm,this method can automatically identify the initial value of natural frequency and solve the objective function efficiently and simply.In order to verify the feasibility and effectiveness of the proposed method,it is used to identify the modal parameters of the IASC-ASCE benchmark model and the j acket platform structure model,and the Most Probable Value(MPV) of the modal parameters and their respective posterior uncertainties are successfully identified.The identification results of the IASC-ASCE benc hmark model are compared with the identification re sults of the MODE-ID method,which verifies the effectivene ss and accuracy of the proposed method for identifying modal parameters.It provides a simple and feasible method for quantifying the influence of uncertain factors such as environmental parameters on the identification results,and also provide s a reference for modal parameter identification of other large structures.

Flight Flutter Modal Parameters Identification with Atmospheric Turbulence Excitation Based on Wavelet Transformation

In view of the feature of flight flutter test data with atmospheric turbulence excitation, a method which combines wavelet transformation with random decrement technique for identifying flight flutter modal parameters is presented. This approach firstly uses random decrement technique to gain free decays corresponding to the acceleration response of the structure to some non-zero initial conditions. Then the continuous Morlet wavelet transformation of the free decays is performed; and the Parseval formula and residue theorem are used to simplify the transformation. The maximal wavelet transformation coefficients in different scales are searched out by means of band-filtering characteristic of Morlet wavelet, and then the modal parameters are identified according to the relationships with maximal modulus and angle of the wavelet transform. In addition, the condition of modal uncoupling is discussed according to variation trend of flight flutter modal parameters in the flight flutter state. The analysis results of simulation and flight flutter test data show that this approach is not only simple, effective and feasible, but also having good noise immunity.

Structural modal parameter identifi cation and damage diagnosis based on Hilbert-Huang transform

Traditional modal parameter identifi cation methods have many disadvantages,especially when used for processing nonlinear and non-stationary signals.In addition,they are usually not able to accurately identify the damping ratio and damage.In this study,methods based on the Hilbert-Huang transform(HHT) are investigated for structural modal parameter identifi cation and damage diagnosis.First,mirror extension and prediction via a radial basis function(RBF) neural network are used to restrain the troublesome end-effect issue in empirical mode decomposition(EMD),which is a crucial part of HHT.Then,the approaches based on HHT combined with other techniques,such as the random decrement technique(RDT),natural excitation technique(NExT) and stochastic subspace identifi cation(SSI),are proposed to identify modal parameters of structures.Furthermore,a damage diagnosis method based on the HHT is also proposed.Time-varying instantaneous frequency and instantaneous energy are used to identify the damage evolution of the structure.The relative amplitude of the Hilbert marginal spectrum is used to identify the damage location of the structure.Finally,acceleration records at gauge points from shaking table testing of a 12-story reinforced concrete frame model are taken to validate the proposed approaches.The results show that the proposed approaches based on HHT for modal parameter identifi cation and damage diagnosis are reliable and practical.

Modal parameter identification and damping ratio estimation from the full-scale measurements of a typical Tibetan wooden structure

Tibetan heritage buildings have a high historical and cultural value. They have endured adverse environmental loadings over hundreds of years without significant damage. However, there are few reports on their structural characteristics under normal environmental loadings and their behavior under dynamic loadings. In this research, a typical Tibetan wooden wall-frame building is selected to study its dynamic characteristics. Field measurements of the structure were conducted under environmental excitation to collect acceleration responses. The stochastic subspace identification （SSI） method was adopted to calculate the structural modal parameters and obtain the out-of-plane vibration characteristics of the slab and frames. The results indicated that the wall-frame structure had a lower out-of-plane stiffness and greater in-plane stiffness due to the presence of stone walls. Due to poor identified damping ratio estimates from the SSI method, a method based on the variance upper bound was proposed to complement the existing variance lower bound method for estimating the modal damping ratio to address the significant damping variability obtained from different points and measurements. The feasibility of the proposed method was illustrated with the measured data from the floor slab of the structure. The variance lower and upper bound methods both provided consistent results compared to those from the traditional SSI method.

Automatic modal parameter identification of high arch dams:feasibility verification

Modal parameters, including fundamental frequencies, damping ratios, and mode shapes, could be used to evaluate the health condition of structures. Automatic modal parameter identification, which plays an essential role in realtime structural health monitoring, has become a popular topic in recent years. In this study, an automatic modal parameter identification procedure for high arch dams is proposed. The proposed procedure is implemented by combining the densitybased spatial clustering of applications with noise(DBSCAN) algorithm and the stochastic subspace identification(SSI). The 210-m-high Dagangshan Dam is investigated as an example to verify the feasibility of the procedure. The results show that the DBSCAN algorithm is robust enough to interpret the stabilization diagram from SSI and may avoid outline modes. This leads to the proposed procedure obtaining a better performance than the partitioned clustering and hierarchical clustering algorithms. In addition, the errors of the identified frequencies of the arch dam are within 4%, and the identified mode shapes are in agreement with those obtained from the finite element model, which implies that the proposed procedure is accurate enough to use in modal parameter identification. The procedure is feasible for online modal parameter identification and modal tracking of arch dams.

IDENTIFICATION OF TIME-VARYING MODAL PARAMETERS USING LINEAR TIME-FREQUENCY REPRESENTATION

A new method of parameter identification based on linear time-frequencyrepresentation and Hubert transform is proposed to identity modal parameters of linear time-varyingsystems from measured vibration responses. Using Gabor expansion and synthesis theory, measuredresponses are represented in the time-frequency domain and modal components are reconstructed bytime-frequency filtering. The Hilbert transform is applied to obtain time histories of the amplitudeand phase angle of each modal component, from which time-varying frequencies and damping ratios areidentified. The proposed method has been demonstrated with a numerical example in which a lineartime-varying system of two degrees of freedom is used to validate the identification scheme based ontime-frequency representation. Simulation results have indicated that time-frequency representationpresents an effective tool for modal parameter identification of time-varying systems.

Identification of Modal Parameters with Linear Structure under Non-stationary Ambient Excitation

Empirical mode decomposition (EMD) is proposed to identify linear structure under non-stationary excitation,and non-white noise coefficient is introduced under the assumption of random signals consisting of white noise and non-white noise signals. The cross-correlation function of response signal is decomposed into mode functions and residue by EMD method. The identification technique of the modal parameters of single freedom degree is applied to each mode function to obtain natural frequencies, damping ratios and mode shapes. The results of identification of the five-degree freedom linear system demonstrate that the proposed method is effective in identifying the parameters of linear structures under non-stationary ambient excitation.

A Study on Crack Detection with Modal Parameters of A Jacket Platform

Crack detection procedures by different modal parameters are analyzed for identifying a crack and its location and magnitude in a jacket platform. The first ten natural frequencies and modal shapes of the jacket models are obtained by numerical experiments based on NASTRAN Code. A crack at different locations and of different magnitudes is imposed in the model at the underwater beams. Then, the modal evaluation parameters are calculated numerically, to illustrate the evaluation of modal parameter criteria used in jacket crack detection. The sensitivities of different modal parameters to different cracks are analyzed. A new technique is presented for predicting the approximate location of a breakage in the absence of the data of an intact model. This method can be used to detect a crack in underwater members by use of incomplete mode shapes of the top members of the jacket.

Estimation of structural modal parameters by fourier transform with an optimal window

An adaptive Fourier Transform （FT） with an optimal window has been proposed for the time-frequency analysis of nonstationary time series. The method allows for a good estimation of both frequency and amplitude of the spectrum and can be easily applied to the general case of time-varying signals. The evaluation of the proposed approach has been performed on measured time-varying signals from a suspension bridge model and a steel frame model whose data have the typical non-stationary characteristics. The numerical results show that the proposed approach can overcome some of the difficulties encountered in the classic Fourier transform technique and can achieve higher computation accuracy.

Application of Converted Displacement for Modal Parameter Identification of Offshore Wind Turbines with High-Pile Foundation

In the actual measurement of offshore wind turbines(OWTs),the measured accelerations usually contain a large amount of noise due to the complex and harsh marine environment,which is not conducive to the identification of structural modal parameters.For OWTs with remarkably low structural modal frequencies,displacements can effectively suppress the high-frequency vibration noise and amplify the low-frequency vibration of the structure.However,finding a reference point to measure structural displacements at sea is difficult.Therefore,only a few studies on the use of dynamic displacements to identify the modal parameters of OWTs with high-pile foundations are available.Hence,this paper develops a displacement conversion strategy to study the modal parameter identification of OWTs with high-pile foundations.The developed strategy can be divided into the following three parts:zero-order correction of measured acceleration,high-pass filtering by the Butterworth polynomial,and modal parameter identification using the calculated displacement.The superiority of the proposed strategy is verified by analyzing a numerical OWT with a high-pile foundation and the measured accelerations from an OWT with a high-pile foundation.The results show that for OWTs with high-pile foundations dominated by low frequencies,the developed strategy of converting accelerations into displacements and then performing modal parameter identification is advantageous to the identification of modal parameters,and the results have high accuracy.

Identification of Time-Varying Modal Parameters for Thermo-Elastic Structure Subject to Unsteady Heating

A time-varying modal parameter identification method combined with Bayesian information criterion(BIC)and grey correlation analysis(GCA)is presented for a kind of thermo-elastic structures with sparse natural frequencies and subject to an unsteady temperature field.To demonstrate the method,the thermo-elastic structure to be identified is taken as a simply-supported beam with an axially movable boundary and subject to both random excitation and an unsteady temperature field,and the dynamic outputs of the beam are first simulated as the measured data for the identification.Then,an improved time-varying autoregressive(TVAR)model is generated from the simulated input and output of the system.The time-varying coefficients of the TVAR model are expanded as a finite set of time basis functions that facilitate the time-varying coefficients to be time-invariant.According to the BIC for preliminarily determining the scope of the order number,the grey system theory is introduced to determine the order of TVAR and the dimension of the basis functions simultaneously via the absolute grey correlation degree(AGCD).Finally,the time-varying instantaneous frequencies of the system are estimated by using the recursive least squares method.The identified results are capable of tracking the slow time-varying natural frequencies with high accuracy no matter for noise-free or noisy estimation.

Sensitivity analysis and dynamic modification of modal parameter in mechanical transmission system

Sensitivity analysis is one of the effective methods in the dynamic modification. The sensitivity of the modal parameters such as the natural frequencies and mode shapes in undamped free vibration of mechanical transmission system is analyzed in this paper.In particular,the sensitivities of the modal parameters to physical parameters of shaft system such as the inertia and stiffness are given.A calculation formula for dynamic modification is presented based on the analysis of modal parameter.With a mechanical transmission system as an example, the sensitivities of natural frequencies and modes shape are calculated and analyzed. Furthermore, the dynamic modification is also carried out and a good result is obtained.

Aircraft Flutter Modal Parameter Identification Using a Numerically Robust Least-squares Estimator in Frequency Domain

Recently, frequency-based least-squares （LS） estimators have found wide application in identifying aircraft flutter parameters. However, the frequency methods are often known to suffer from numerical difficulties when identifying a continuous-time model, especially, of broader frequency or higher order. In this article, a numerically robust LS estimator based on vector orthogonal polynomial is proposed to solve the numerical problem of multivariable systems and applied to the flutter testing. The key idea of this method is to represent the frequency response function （FRF） matrix by a right matrix fraction description （RMFD） model, and expand the numerator and denominator polynomial matrices on a vector orthogonal basis. As a result, a perfect numerical condition （numerical condition equals 1） can be obtained for linear LS estimator. Finally, this method is verified by flutter test of a wing model in a wind tunnel and real flight flutter test of an aircraft. The results are compared to those with notably LMS PolyMAX, which is not troubled by the numerical problem as it is established in z domain （e.g. derived from a discrete-time model）. The verification has evidenced that this method, apart from overcoming the numerical problem, yields the results comparable to those acquired with LMS PolyMAX, or even considerably better at some frequency bands.

Operational modal parameter identification with colored noise excitation

Operational Modal Analysis(OMA) refers to the modal analysis of a structure in its operating state. The advantage of OMA is that only the output vibration signal of a system is used in the analysis process. Classic OMA is based on the white noise excitation assumption and many identification methods have been developed in both time domain and frequency domain. But in reality, many environmental excitations are not compliance with the white noise assumption. In this paper, a method of half power bandwidth analysis is applied to power spectrum analysis to deal with the colored noise and trapezoidal spectral excitation. The modal frequencies and modal damping ratios are derived and the error caused by trapezoidal spectral and colored noise excitation are analyzed. It is proved that the OMA algorithm based on the white noise assumption can be extended to the colored noise environments under certain conditions. Finally, a simulation example with a cantilever beam and a vibration test with four kinds of colored noise and trapezoidal spectrum base excitation are carried out and the results support the proposed method.

Effects of foundation damage and water-level change on vibration modal parameters of gravity-type caisson structure

In this paper,the effects of foundation damage and water-level change on vibration characteristics of gravity-type caisson structure are examined by analyzing modal parameters extracted from output-only information.To achieve the objective,the following approaches are implemented.Firstly,vibration response analysis methods are selected to estimate power spectral density and modal parameters such as natural frequency,damping ratio and mode shape of a lab-scale caisson structural system.Secondly,vibration tests on the lab-scale caisson system are performed under a series of test scenarios which include three water-level changes and three damage levels.Thirdly,experimental modal parameters corresponding to the damaging cases as well as the water level cases are extracted by frequency domain decomposition method and stochastic subspace identification method.Finally,the effects of the water-level variation and foundation damage on the extracted modal parameters are examined to assess the feasibility of the vibration-based damage detection in gravity-type caisson structures under water-level uncertainty.

Physical Parameter Identification Method Based on Modal Analysis for Two-axis On-road Vehicles:Theory and Simulation

Physical parameters are very important for vehicle dynamic modeling and analysis.However,most of physical parameter identification methods are assuming some physical parameters of vehicle are known,and the other unknown parameters can be identified.In order to identify physical parameters of vehicle in the case that all physical parameters are unknown,a methodology based on the State Variable Method（SVM） for physical parameter identification of two-axis on-road vehicle is presented.The modal parameters of the vehicle are identified by the SVM,furthermore,the physical parameters of the vehicle are estimated by least squares method.In numerical simulations,physical parameters of Ford Granada are chosen as parameters of vehicle model,and half-sine bump function is chosen to simulate tire stimulated by impulse excitation.The first numerical simulation shows that the present method can identify all of the physical parameters and the largest absolute value of percentage error of the identified physical parameter is 0.205%;and the effect of the errors of additional mass,structural parameter and measurement noise are discussed in the following simulations,the results shows that when signal contains 30 d B noise,the largest absolute value of percentage error of the identification is 3.78%.These simulations verify that the presented method is effective and accurate for physical parameter identification of two-axis on-road vehicles.The proposed methodology can identify all physical parameters of 7-DOF vehicle model by using free-decay responses of vehicle without need to assume some physical parameters are known.

Research on Breeze Vibration Law and Modal Identification Method of Conductor Considering Anti-Vibration Hammer Damage

In the harsh environment,the structural health of the anti-vibration hammer,which suffers from the coupled effects of corrosion and fatigue damage,is significantly reduced.As part of the conductor structure,the anti-vibration hammer is rigidly attached to the conductor,effectively suppressing conductor vibration.The conductor’s breeze vibration law and natural modal frequency are altered damage to the anti-vibration hammer structure.Through built a vibration experiment platform to simulate multiple faults such as anti-vibration hammer head drop off and position slippage,which to obtained the vibration acceleration signal of the conductor.The acceleration vibration signal is processed and analyzed in the time and frequency domains.The results are used to derive the breeze vibration law of the conductor under multiple faults and propose an anti-vibration hammer damage online monitoring technology.The results show that the vibration acceleration value and vibration intensity of the conductor are significantly increased after the anti-vibration hammer damage.The natural frequency increases for each order,with an absolute change ranging from 0.15 to 6.49 Hz.The anti-vibration hammer slipped due to a loose connection,the 1st natural frequency increases from 8.18 to 16.62 Hz.Therefore,in engineering applications,there can be no contact to determine the anti-vibration hammer damage situation by monitoring the modal natural frequency of the conductor.This is even a tiny damage that cannot be seen.This method will prevent the further expansion of the damage that can cause accidents.

Sequential Parameter Estimation Using Modal Dispersion Curves in Shallow Water

Existing sequential parameter estimation methods use the acoustic pressure of a line array as observations. The modal dispersion curves are employed to estimate the sound speed profile（SSP） and geoacoustic parameters based on the ensemble Kalman filter. The warping transform is implemented to the signals received by a single hydrophone to obtain the dispersion curves. The experimental data are collected at a range-independent shallow water site in the South China Sea. The results indicate that the SSPs are well estimated and the geoacoustic parameters are also well determined. Comparisons of the observed and estimated modal dispersion curves show good agreement.

An operational modal analysis method in frequency and spatial domain

A frequency and spatial domain decomposition method （FSDD） for operational modal analysis （OMA） is presented in this paper, which is an extension of the complex mode indicator function （CMIF） method for experimental modal analysis （EMA）. The theoretical background of the FSDD method is clarified, Singular value decomposition is adopted to separate the signal space from the noise space. Finally, an enhanced power spectrum density （PSD） is proposed to obtain more accurate modal parameters by curve fitting in the frequency domain. Moreover, a simulation case and an application case are used to validate this method.