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.

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.

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.

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.

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.

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.

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.

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.

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.

A new damping ratio identification method based on pattern search

In order to improve the effectiveness of traditional time domain identification methods in identifying damping ratios, a new damping ratio identification method based on pattern search is proposed by fluctuating the reliable natural frequency obtained through traditional time domain identification methods by about 10% to build the boundary conditions, using all the initial identification results to establish the free decay response of the system, and using the pattern search method to correct the initial identification results with the residual sum of squares between the free decay response and the actually measured free-decay signal as the objective function. The proposed method deals with the actually measured free-decay signal with curve fitting and avoids enlarging the identified error caused by intermediate conversion, so it can effectively improve the identified accuracy of damping ratios. Simulations for a room-sized vibration isolation foundation show that the relative errors of analyzed three damping ratios are down to 1.05%, 1.51% and 3.7% by the proposed method from 8.42%, 5.85% and 8.5% by STD method when the noise level is 10%.

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.

Operational Modal Analysis of a Ship Model in the Presence of Harmonic Excitation

A ship is operated under an extremely complex environment, and waves and winds are assumed to be the stochastic excitations. Moreover, the propeller, host and mechanical equipment can also induce the harmonic responses. In order to reduce structural vibration, it is important to obtain the modal parameters information of a ship. However, the traditional modal parameter identification methods are not suitable since the excitation information is difficult to obtain. Natural excitation technique-eigensystem realization algorithm （NExT-ERA） is an operational modal identification method which abstracts modal parameters only from the response signals, and it is based on the assumption that the input to the structure is pure white noise. Hence, it is necessary to study the influence of harmonic excitations while applying the NExT-ERA method to a ship structure. The results of this research paper indicate the practical experiences under ambient excitation, ship model experiments were successfully done in the modal parameters identification only when the harmonic frequencies were not too close to the modal frequencies.

Damage Localization of Offshore Platforms Under Ambient Excitation

In this paper Nondestructive Damage Detection (NDD) for offshore platforms is investigated under operational conditions. As is known, there is no easy way to measure ambient excitation, so damage detection methods based on ambient excitation have become very vital for the Structural Health Monitoring (SHM) of offshore platforms. The modal parameters (natural frequencies, damping ratios and mode shapes) are identified from structural response data with the Natural Excitation Technique (NExT) in conjunction with the Eigensystem Realization Algorithm (ERA) . A new method of damage detection is presented, which utilizes the invariance property of element modal strain energy. This method is to assign element modal strain energy to two parts, and defines two damage detection indicators. One is compression modal strain energy change ratio (CMSECR); the other is flexural modal strain energy change ratio (FMSECR). The present modal strain energy is obtained by incomplete modal shape and structural stiffness matr

Self-contained eigenvector algorithm applied to the identification of aerodynamic derivatives of bridge model

On one hand, when the bridge stays in a windy environment, the aerodynamic power would reduce it to act as a non-classic system. Consequently, the transposition of the system’s right eigenmatrix will not equal its left eigenmatrix any longer. On the other hand, eigenmatrix plays an important role in model identification, which is the basis of the identification of aerodynamic derivatives. In this study, we follow Scanlan’s simple bridge model and utilize the information provided by the left and right eigenmatrixes to structure a self-contained eigenvector algorithm in the frequency domain. For the purpose of fitting more accurate transfer function, the study adopts the combined sine-wave stimulation method in the numerical simulation. And from the simulation results, we can conclude that the derivatives identified by the self-contained eigenvector algorithm are more dependable.