Operational modal identification of suspension bridge based on structural health monitoring system

An output-only modal identification method by a combination use of the peak-picking method and the cross spectrum methods are presented. Meanwhile, a novel mode shape optimum method of the deck is proposed. The methods are applied to the operational modal identification system of the Runyang Suspension Bridge, which can be used to obtain the modal parameters of the bridge from out-only data sets collected by its structural health monitoring system （SHMS）. As an example, the vibration response data of the deck, cable and tower recorded during typhoon Matsa excitation are used to illustrate the program application. Some of the modal frequencies observed from deck vibration responses are also found in the vibration responses of the cable and the tower. The results show that some modal shapes of the deck are strongly coupled with the cable and the tower. By comparing the identification results from the operational modal system with those from field measurements, a good agreement between them is achieved, but some modal frequencies identified from the operational modal identification system （OMIS）, such as L1 and L2, obviously decrease compared with those from the field measurements.

Modal identification to non-stationary random excitation based on wavelet transform and co-integration theory

A kind of method of modal identification subject to ambient excitation is presented. A new synthesis stationary signal based on structural response wavelet transform and wavelet coefficient processes co-integration is obtained. The new signal instead of structural response is used in identifying the modal parameters of a non- stationary system, combined with the method of modal identification under stationary random excitation-the NExT method and the adjusted continuous least square method. The numerical results show that the method can eliminate the non-stationarity of structural response subject to non-stationary random excitation to a great extent, and is highly precise and robust.

Output only modal identification and structural damage detection using time frequency & wavelet techniques

The primary objective of this paper is to develop output only modal identification and structural damage detection. Identification of multi-degree of freedom （MDOF） linear time invariant （LTI） and linear time variant （LTV--due to damage） systems based on Time-frequency （TF） techniques--such as short-time Fourier transform （STFT）, empirical mode decomposition （EMD）, and wavelets--is proposed. STFT, EMD, and wavelet methods developed to date are reviewed in detail. In addition a Hilbert transform （HT） approach to determine frequency and damping is also presented. In this paper, STFT, EMD, HT and wavelet techniques are developed for decomposition of free vibration response of MDOF systems into their modal components. Once the modal components are obtained, each one is processed using Hilbert transform to obtain the modal frequency and damping ratios. In addition, the ratio of modal components at different degrees of freedom facilitate determination of mode shape. In cases with output only modal identification using ambient/random response, the random decrement technique is used to obtain free vibration response. The advantage of TF techniques is that they arc signal based; hence, can be used for output only modal identification. A three degree of freedom 1：10 scale model test structure is used to validate the proposed output only modal identification techniques based on STFT, EMD, HT, wavelets. Both measured free vibration and forced vibration （white noise） response are considered. The secondary objective of this paper is to show the relative ease with which the TF techniques can be used for modal identification and their potential for real world applications where output only identification is essential. Recorded ambient vibration data processed using techniques such as the random decrement technique can be used to obtain the free vibration response, so that further processing using TF based modal identification can be performed.

Modal Identification of Offshore Platforms Using Statistical Method Based on ERA

Identification of modal parameters of a linear structure with output-only measurements has received much attention over the past decades. In the paper, the Natural Excitation Technique (NExT) is used for acquisition of the impulse signals from the structural responses. Then Eigensystem Realization Algorithm (ERA) is utilized for modal identification. For disregarding the fictitious ‘computational modes', a procedure, Statistically Averaging Modal Frequency Method (SAMFM), is developed to distinguish the true modes from noise modes, and to improve the precision of the identified modal frequencies of the structure. An offshore platform is modeled with the finite element method. The theoretical modal parameters are obtained for a comparison with the identified values. The dynamic responses of the platform under random wave loading are computed for providing the output signals used for identification with ERA. Results of simulation demonstrate that the proposed method can determine the system modal frequency with high precision.

Modal Analysis Using Operating Modal Identification Method

Sometimes it is very difficult for some large-scale operating structures tomeasure the input forces. Modal parameters must be estimated on response-only. A poly-referencetime-domain operating modal identification complex exponential method is presented sincecross-correlation functions have the same form as impulse response functions. Then a poly-referencefrequency-domain operating modal identification method is proposed in this paper. An experiment onan aircraft model is performed to verify the proposed schemes. The results show that both outlinedschemes can extract the parameters from output-only and the modal parameters extracted by proposedfrequency-domain method are more accurate than those by presented time-domain complex exponentialmethod.

Modal identification based on Hilbert-Huang Transform of structural response with S VD preprocessing

In recent years, Empirical mode decomposition and Hilbert spectral analysis have been combined to identify system parameters. Singular-Value Decomposition is pro- posed as a signal preprocessing technique of Hilbert-Huang Transform to extract modal parameters for closely spaced modes and low-energy components. The proposed method is applied to a simulated airplane model built in Automatic Dynamic Analysis of Mechanical Systems software. The results demonstrate that the identified modal parameters are in good agreement with the baseline model.

Dynamic Stability Analysis of Linear Time-varying Systems via an Extended Modal Identification Approach

The problem of linear time-varying（LTV） system modal analysis is considered based on time-dependent state space representations, as classical modal analysis of linear time-invariant systems and current LTV system modal analysis under the ＂frozen-time＂ assumption are not able to determine the dynamic stability of LTV systems. Time-dependent state space representations of LTV systems are first introduced, and the corresponding modal analysis theories are subsequently presented via a stabilitypreserving state transformation. The time-varying modes of LTV systems are extended in terms of uniqueness, and are further interpreted to determine the system＇s stability. An extended modal identification is proposed to estimate the time-varying modes, consisting of the estimation of the state transition matrix via a subspace-based method and the extraction of the time-varying modes by the QR decomposition. The proposed approach is numerically validated by three numerical cases, and is experimentally validated by a coupled moving-mass simply supported beam exper- imental case. The proposed approach is capable of accurately estimating the time-varying modes, and provides anew way to determine the dynamic stability of LTV systems by using the estimated time-varying modes.

New modal identification method under the non-stationary Gaussian ambient excitation

Based on the multivariate continuous time autoregressive （CAR） model, this paper presents a new time-domain modal identification method of linear time-invariant system driven by the uniformly modulated Gaussian random excitation. The method can identify the physical parameters of the system from the response data. First, the structural dynamic equation is transformed into a continuous time autoregressive model （CAR） of order 3. Second, based on the assumption that the uniformly modulated function is approximately equal to a constant matrix in a very short period of time and on the property of the strong solution of the stochastic differential equation, the uniformly modulated function is identified piecewise. Two special situations are discussed. Finally, by virtue of the Girsanov theorem, we introduce a likelihood function, which is just a con- ditional density function. Maximizing the likelihood function gives the exact maximum likelihood estimators of model parameters. Numerical results show that the method has high precision and the computation is efficient.

EXPERIMENTAL MODELING OF MIDDLE-RISE BUILDING VIA AMBIENT MODAL IDENTIFICATION

Experimental modeling of a middle-rise office building via ambient modal identification is presented. A 200-DOF (Dimension of freedom) test model is designed to correlate with finite element mode. A newly developed frequency-spatial domain decomposition ( FSDD ) technique is used to identify modal characteristics of the full-size building by using ambient response measurements. In the interested frequency ranges of 0～4.5 Hz and 0～ 6.5 Hz altogether 9 bending and torsion modes are identified. As one of the major focuses of the project, the accurate damping estimation is conducted based on FSDD. The identified modal frequencies and mode shapes are utilized for finite element model tuning. Excellent agreement has been achieved with respect to the final tuned finite element (FE) model up to 9 modes.

Review and comparison of methods and benchmarks for automatic modal identification based on stabilization diagram

Automatic modal identification via automatically interpreting the stabilization diagram provides key technique in bridge structural health monitoring.This paper reviews the progress in the area of automatic modal identification based on interpreting the stabilization diagram.The whole identification process is divided into four steps from establishing the stabilization diagram to removing the outliers in the identification results.The criteria and algorithms used in each step in the existing studies are carefully summarized and classified.Comparisons between typical methods in cleaning and interpreting the stabilization diagram are also conducted.Real structure benchmarks used in the existing studies to validate the proposed automatic modal identification methods are also summarized.Based on the review and comparison,the specific ratio method for cleaning the stabilization diagram,the hierarchical clustering method for interpreting the stabilization diagram and the adjusted boxplot for removing the outliers in the identification results are the most suitable methods for each step.The key point of automatic modal identification based on interpreting the stabilization diagram has also discussed,and it is recommended to pay more attention to cleaning the stabilization diagram.Future study about automatic modal identification under situation with very few sensors deployed should be more concerned.This review aims to help researchers and practitioners in implementing existing automatic modal identification algorithms effectively and developing more suitable and practical methods for civil engineering structures in the future.

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.

Improved polyreference time domain method for modal identification using local or global noise removal techniques

Modal identification involves estimating the modal parameters, such as modal frequencies, damping ratios, and mode shapes, of a structural system from measured data. Under the condition that noisy impulse response signals associated with multiple input and output locations have been measured, the primary objective of this study is to apply the local or global noise removal technique for improving the modal identification based on the polyreference time domain (PTD) method. While the traditional PTD method improves modal parameter estimation by over-specifying the computational model order to absorb noise, this paper proposes an approach using the actual system order as the computational model order and rejecting much noise prior to performing modal parameter estimation algorithms. Two noise removal approaches are investigated: a "local" approach which removes noise from one signal at a time, and a "global" approach which removes the noise of multiple measured signals simultaneously. The numerical investigation in this article is based on experimental measurements from two test setups: a cantilever beam with 3 inputs and 10 outputs, and a hanged plate with 4 inputs and 32 outputs. This paper demonstrates that the proposed noise-rejection method outperforms the traditional noise-absorption PTD method in several crucial aspects.

Development of a software platform for bridge modal and damage identification based on ambient excitation

Modal and damage identification based on ambient excitation can greatly improve the efficiency of high-speed railway bridge vibration detection.This paper first describes the basic principles of stochastic subspace identification,peak-picking,and frequency domain decomposition method in modal analysis based on ambient excitation,and the effectiveness of these three methods is verified through finite element calculation and numerical simulation,Then the damage element is added to the finite element model to simulate the crack,and the curvature mode difference and the curvature mode area difference square ratio are calculated by using the stochastic subspace identification results to verify their ability of damage identification and location.Finally,the above modal and damage identification techniques are integrated to develop a bridge modal and damage identification software platform.The final results show that all three modal identification methods can accurately identify the vibration frequency and mode shape,both damage identification methods can accurately identify and locate the damage,and the developed software platform is simple and efficient.

Modal Parameters Identification of A Real Offshore Platform From the Response Excited by Natural Ice Loading

This paper investigates the possibility of utilizing response from natural ice loading for modal parameter identification of real offshore platforms.The test platform is the JZ20-2 MUQ jacket platform located in the Liaodong Bay,China.A field experiment is carried out in winter season,as the platform is excited by floating ices.The feasibility is demonstrated by the acceleration response of two different segments.By the SSI-data method,the modal frequencies and damping ratios of four structural modes can be successfully identified from both segments.The estimated information from both segments is almost identical,which demonstrates that the modal identification is trustworthy.Furthermore,by taking the Jacket platform as a benchmark,the numerical performance of five popular time-domain EMA methods is systematically compared from different viewpoints.The comparisons are categorized as:(1)stochastic methods versus deterministic methods;(2)high-order methods versus low-order methods;(3)data-driven versus covariance-driven stochastic subspace identification methods.

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.

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.

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.

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.