Analytic wavelet transformation‐based modal parameter identification from ambient responses

Analytic wavelet transform (AWT) based on Gabor wavelet function overcomes the deficiency of the time‐domain localization of traditional Fourier transform and the limitation of the constant resolution in the time‐frequency domain of short‐time Fourier transform. The identification of modal parameters of structures may be carried out by both the amplitude and phase frequency information revealed by resorting to matching mechanism between the wavelet function and complex‐valued signal. By applying the AWT in conjunction with the well‐known random decrement technique, this paper analyses the time‐frequency resolution of Gabor wavelet and the process of identifying structural modal parameters. The method of selecting the parameters of Gabor wavelet function and the formula determining the usable lengths of signal are thus proposed. Eventually, the efficiency of the present method is confirmed by applying it to a numerical simulation data without and with noise contamination of a three degree‐of‐freedom (3DOF) structure with the closely spaced natural frequencies and to ambient vibration full‐scale measurements of a super high‐rise building—Shanghai Jin Mao Building excited by wind. Copyright © 2010 John Wiley & Sons, Ltd.     

Blind Modal Identification in Frequency Domain Using Independent Component Analysis for High Damping Structures with Classical Damping

Output‐only modal identification methods are practical for large‐scale engineering. Recently, independent component analysis (ICA) which is one of the most popular techniques of blind source separation (BSS) has been used for output‐only modal identification to directly separate the modal responses and mode shapes from vibration responses. However, this method is only accurate for undamped or lightly damped structures. To improve the performance of ICA for high damping structures, this article presents an extended ICA‐based method called ICA‐F, which establishes a BSS model in frequency domain. First, the basic idea of BSS and ICA applied in modal identification is introduced in detail. The free vibration responses and the correlation functions of ambient responses can be cast into the frequency‐domain BSS framework just by mapping the time history responses to frequency domain through fast Fourier transform (FFT). Then, an ICA‐based method in frequency domain called ICA‐F is proposed to accurately extract mode shapes and modal responses for both light and high damping structures. A simulated 3 degree of freedom mass‐spring system and a 4‐story simulated benchmark model developed by the IASC‐ASCE Task Group in Health Monitoring are employed to verify the effectiveness of the proposed method. The results show that the proposed method can perform accurate modal identification for both light and high damping structures. Finally, the IASC‐ASCE experimental benchmark structure is also utilized to illustrate the proposed method applied to practical structure.     

Identifying the Modal Parameters of a Structure from Ambient Vibration Data via the Stationary Wavelet Packet

Ambient vibration tests are conducted widely to estimate the modal parameters of a structure. The work proposes an efficient wavelet‐based approach to determine the modal parameters of a structure from its ambient vibration responses. The proposed approach integrates the time series autoregressive (AR) model with the stationary wavelet packet transform. In addition to providing a richer decomposition and allowing for an improved time–frequency localization of signals over that of the discrete wavelet transform, the stationary wavelet packet transform also has significantly higher computational efficiency than the wavelet packet transform in terms of decomposing time‐shifted signals because the former has a time‐invariance property. The correlation matrices needed in determining the coefficient matrices in an AR model are established in subspaces expanded by stationary wavelet packets. The formulation for estimating the correlation matrices is shown for the first time. Because different subspaces contain signals with different frequency subbands, the fine filtering property enhances the ability of the proposed approach to identify not only the modes with strong modal interference, but also many modes from the responses of very few measured degrees of freedom. The proposed approach is validated by processing the numerically simulated responses of a seven‐floor shear building, which has closely spaced modes, with considering the effects of noise and incomplete measurements. Furthermore, the present approach is employed to process the velocity responses of an eight‐storey steel frame subjected to white noise input in a shaking table test and ambient vibration responses of a cable‐stayed bridge.     

Enhanced Hilbert–Huang transform and its application to modal identification

The well‐known Hilbert–Huang transform (HHT) consists of empirical mode decomposition to extract intrinsic mode functions (IMFs) and Hilbert spectral analysis to obtain time–frequency characteristics of IMFs through the Hilbert transform. There are two mathematical requirements that limit application of the Hilbert transform. Moreover, noise effects caused by the empirical mode decomposition procedure add a scatter to derivative‐based instantaneous frequency determined by the Hilbert transform. In this paper, a new enhanced HHT is proposed in which by avoiding mathematical limitations of the Hilbert spectral analysis, an additional parameter is employed to reduce the noise effects on the instantaneous frequencies of IMFs. To demonstrate the efficacy of the proposed method, two case studies associated with structural modal identification are selected. In the first case, through identification of a typical 3‐DOF structural model subjected to a random excitation, accuracy of the enhanced method is verified. In the second case, ambient response data recorded from a real 15‐story building are analyzed, and nine modal frequencies of the building are identified. The case studies indicate that the enhanced HHT provides more accurate and physically meaningful results than HHT and is capable to be an efficient tool in structural engineering applications. Copyright © 2012 John Wiley & Sons, Ltd.     

Variational mode decomposition based modal parameter identification in civil engineering

An out-put only modal parameter identification method based on variational mode decomposition (VMD) is developed for civil structure identifications. The recently developed VMD technique is utilized to decompose the free decay response (FDR) of a structure into to modal responses. A novel procedure is developed to calculate the instantaneous modal frequencies and instantaneous modal damping ratios. The proposed identification method can straightforwardly extract the mode shape vectors using the modal responses extracted from the FDRs at all available sensors on the structure. A series of numerical and experimental case studies are conducted to demonstrate the efficiency and highlight the superiority of the proposed method in modal parameter identification using both free vibration and ambient vibration data. The results of the present method are compared with those of the empirical mode decomposition-based method, and the superiorities of the present method are verified. The proposed method is proved to be efficient and accurate in modal parameter identification for both linear and nonlinear civil structures, including structures with closely spaced modes, sudden modal parameter variation, and amplitude-dependent modal parameters, etc.     

On‐line system identification of structures using wavelet‐Hilbert transform and sparse component analysis

A new wavelet‐Hilbert transform based sparse component analysis (WHT‐SCA) method is presented for online system identification in indeterminate conditions. The instantaneous phase ratios of output signals are obtained by using a wavelet‐Hilbert transform based filter; and the out‐of‐phase data, that causes errors in identification accuracy, is detected and eliminated. Then, modal parameters of the structure are identified through existing relationships between the dispersion of filtered data in the frequency domain. Subsequently, to demonstrate the capability of the online identification, a new controller is introduced by combining the WHT‐SCA and a semi‐active tuned mass damper (STMD), resulting in creation of smart structures. The performance of the proposed method and controller is investigated through examples. The results demonstrate that, modal parameters of structures are identified accurately even with noise contamination and limited number of sensors. Also, the STMD is effectively robust against any variations in modal parameters of the structure.     

Modal parameter identification for closely spaced modes of civil structures based on an upgraded stochastic subspace methodology

Based on a recently developed stochastic subspace identification methodology equipped with an alternative stabilization diagram and a hierarchical sifting process, this research aims to improve this approach for more efficiently identifying the modal parameters of civil structures with closely spaced modes. The concept of a doubly folded stabilization diagram is proposed to combine the advantages of both the conventional and alternative stabilization diagrams for achieving better computational efficiency. In addition, the hierarchical sifting process is further refined to more properly handle closely spaced modes. The investigated cases for the occurrence of extremely close modes in civil engineering structures include axially symmetric stay cables, a symmetric cable-stayed bridge with respect to the pylon, and a uniformly arranged office building. Applying the upgraded SSI methodology established in this study, it is demonstrated that the modal parameter identification of civil engineering structures with extremely close modes can be elevated to an advanced level with a frequency space index at the order of 0.1%. Such an accurate identification and distinction is particularly important in the practical applications of structural health monitoring to prevent the false alarms resulting from the confusion of two extremely close modes. Furthermore, this approach also performs well in the determination of mode shape vectors for closely spaced modes to provide an excellent tool for observing their corresponding orthogonality property and high sensitivity.     

曲率模态法用于网壳结构损伤定位的有效性分析

曲率模态法是针对梁式结构提出的一种损伤识别方法,其用于网壳结构损伤定位的有效性需要进行研究和证实。以一个单层球面网壳为例,对曲率模态法用于该结构的损伤定位进行数值模拟,分析网壳结构模态局部化对损伤定位效果的影响。损伤定位的判断标准为绝对曲率差最大值所对应的节点为损伤位置,指示该节点上的杆件发生了损伤。数值分析的结果表明,对于单杆件损伤,使用损伤前后密集模态的绝对曲率差进行损伤定位,效果很差,而使用损伤前后稀疏模态的绝对曲率差进行损伤定位,效果很好。可见,模态局部化对曲率模态法应用于网壳结构损伤定位的影响很大,因此,只有选择稀疏模态才能较好地避开模态局部化现象,在一定程度上保证曲率模态法用于网壳结构损伤定位的有效性。     

基于环境激励下钢桁梁桥的模态识别

以一下承式钢桁梁桥模型为例进行数值模拟,研究了基于环境激励下的钢桁梁桥的模态参数识别,包括:对比分析了频域法和时域法识别的结果,利用频域法分析了钢桁梁桥在不同样本长度时的模态参数识别结果,得出一些重要结论。     

Modal Response‐Based Visual System Identification and Model Updating Methods for Building Structures

This article proposes a new system identification (SI) method using the modal responses obtained from the dynamic responses of a structure for estimating modal parameters. Since the proposed SI method visually extracts the mode shape of a structure through the plotting of modal responses based on measured data points, the complex calculation process for the correlation and the decomposition for vibration measurements required in SI methods can be avoided. Also, without dependence on configurations of SI methods inducing variations of modal parameters, mode shapes and modal damping ratios can be stably extracted through direct implementation of modal response. To verify the feasibility of the proposed method, the modal parameters of a shear frame were extracted from modal displacement data obtained from a vibration test, and the results were compared with those obtained from the existing frequency domain SI method. The proposed method introduces the maximum modal response ratio of each mode computed by modal displacement data, and from this, the contribution of each mode and each measured location to the overall structural response is indirectly evaluated. Moreover, this article proposes a model updating method establishing the error functions based on the differences between the analytical model and measurement for the natural frequencies and the modal responses reflecting both mode shape and modal contribution. The validity of the proposed method is verified through the response prediction and modal contributions of the models obtained from model updating based on dynamic displacement from a shaking table test for a shear‐type test frame.     

不同ICA算法在图像盲分离应用中的比较分析

对影响因素未知且没有先验信息的污染图像进行恢复和重构是图像处理的一项主要任务。ICA(Independent Component Analysis,独立分量分析)是20世纪90年代后期发展起来的一种盲信号处理方法,并成功应用于图像盲分离。近年来ICA技术得到了进一步发展,出现了多种算法。为了分析各种算法在图像盲分离中的优劣,对SOBI(二阶盲辨识)、JADE(联合近似特征矩阵对角化)、FastICA(快速独立分量分析)和KICA(基于非线性子空间的核独立分量分析)算法进行了比较实验。结果表明,KICA算法分离效果最好,FastICA算法次之;但是如果源图像或者混合图像中含有噪声,则以上四种方法分离效果都不佳。     

Modal Identification for High‐Rise Building Structures Using Orthogonality of Filtered Response Vectors

The modal parameters of civil structures (natural frequency, mode shape, and mode damping ratio) are used for structural health monitoring (SHM), damage detection, and updating the finite element model. Long‐term measurement has been necessary to conduct operational modal analysis (OMA) under various loading conditions, requiring hundreds of thousands of discrete data points for estimating the modal parameters. This article proposes an efficient output‐only OMA technique in the form of filtered response vector (frv)‐based modal identification, which does not need complex signal processing and matrix operations such as singular value decomposition (SVD) and lower upper (LU) factorization, thus overcoming the main drawback of the existing OMA technique. The developed OMA technique also simplifies parameters such as window or averaging, which should be designed for signal processing by the OMA operator, under well‐separated frequencies and loading conditions excited by white noise. Using a simulation model and a 4‐story steel frame specimen, the accuracy and applicability were verified by comparing the dynamic properties obtained by the proposed technique and traditional frequency‐domain decomposition (FDD). In addition, the applicability and efficiency of the method were verified by applying the developed OMA to measured data, obtained through a field test on a 55‐story, 214‐m‐tall high‐rise building.     

Environmental effects on the dynamic characteristics of the Gülburnu Highway Bridge

This paper investigates environmental effects on dynamic characteristics of isolated highway bridges constructed with the balanced cantilever method using ambient vibration test. The Gülburnu Highway Bridge located on the Giresun-Espiye state highway is selected as an application. Measurement time, frequency span and effective mode number are selected by considering similar studies found in the literature. The first measurement tests are conducted in June 2009 and traffic over the bridge is used as a source of ambient vibrations to obtain the dynamic characteristics such as natural frequencies, mode shapes and damping ratios. The second measurement tests are conducted in November 2011 using ambient vibrations and the dynamic characteristics are obtained, experimentally. The output-only modal identification of the bridge is effectively carried out using the enhanced frequency domain decomposition method in the frequency domain and stochastic subspace identification method in the time domain. At the end of the study, experimentally identified dynamic characteristics are compared with each other and environmental effects are investigated in detail. The analysis results reveal that the identified natural frequencies provide an effective indication for changes of dynamic characteristics of the bridge due to environmental effects. Significant variability in the identified natural frequencies is changing by up to maximum 14%.     

Impact of basis,orthogonalization, and normalization on the constrained Finite Strip Method for stability solutions of open thin-walled members

The objective of this paper is to explain and establish the sensitivity of the modal decomposition and modal identification capabilities of the constrained Finite Strip Method to choice of basis, orthogonalization, and normalization. The constrained Finite Strip Method provides a mechanical means to separate the deformations of a thin-walled member into those consistent with global, distortional, local, and other (e.g., shear and transverse extension) modes. For eigen-buckling analysis of thin-walled members this enables isolation of any given mode (modal decomposition) or quantitative measures of the interactions within a given general eigenmode (modal identification). Automated strength prediction of thin-walled members, as well as deeper studies of modal interactions are greatly enabled by establishing agreed upon methods for modal identification and decomposition, as such, the sensitivity of the solution to choice of basis, orthogonalization, and normalization is important for advancing understanding of thin-walled members. As shown herein, the mechanical definitions used to separate the deformations lead to unique vector spaces for global, distortional, and local deformations – but not for other (shear and transverse extension) deformations. Further, although the vector spaces are generally unique the choice of basis and its normalization within the space are not, and have an impact on modal decomposition and identification solutions. A series of illustrative examples are provided to demonstrate the impact of basis, orthogonalization, and normalization. Based on these studies recommendations are made for choice of basis, orthogonalization, and normalization when employing the constrained Finite Strip Method.     

A Comparative Study of Modal Parameter Identification Based on Wavelet and Hilbert–Huang Transforms

Abstract:   This article presents a comparative study of the modal parameter identification of structures based on the continuous wavelet transform (WT) using the modified complex Morlet wavelet function and the improved Hilbert–Huang transform (HHT). Special attention is given to some implementation issues, such as the modal separation and end effect in the WT, the optimal parameter selection of the wavelet function, the new stopping criterion for the empirical mode decomposition (EMD) and the end effect in the HHT. The capabilities of these two techniques are compared and assessed by using three examples, namely a numerical simulation for a damped system with two very close modes, an impact test on an experimental model with three well-separated modes, and an ambient vibration test on the Z24-bridge benchmark problem. The results demonstrate that for the system with well-separated modes both methods are applicable when the time–frequency resolutions are sufficiently taken into account, whereas for the system with very close modes, the WT method seems to be more theoretical and effective than HHT from the viewpoint of parameter design.     

Damage Identification for Hysteretic Structures Using a Mode Decomposition Method

This article investigates structural health monitoring (SHM) of multidegree of freedom (MDOF) structures after major seismic or environmental events. A recently developed hysteresis loop analysis (HLA) SHM technique has performed robustly for single degree of freedom (SDOF) and single mode dominant MDOF structures. However, strong ground motions can trigger higher vibration modes, resulting in irregular hysteresis loops and making this otherwise robust identification difficult. This study presents a new filtering tool, enabling reconstruction of single mode dominant restoring force‐displacement loops which can be readily used for HLA. The proposed filtering tool is based on a classic modal decomposition using optimized mode shape coefficients. The optimization process is carried out in a modal space and is based on decoupling frequency response spectra of interfering modes. Application of modal decomposition using the optimized mode shape coefficients allows for reconstruction of single‐mode dominant hysteresis loops, which can be effectively identified using HLA. The proposed filtering tool is validated on the reconstruction of hysteresis loops on an experimental bridge pier test structure with notable contributions from at least two modes. The results show the method eliminates the influence of all higher modes that contain significant energy content and yields the reconstruction of “smooth” single mode dominant hysteresis loops. The resulting SHM analysis on the reconstructed experimental hysteresis loops identified degradation in the elastic stiffness profiles, indicating damage within the structure and matching prior published results based on physical inspection of damage. The overall method presented increases the breadth of potential application of the HLA method and can be readily generalized to a range of MDOF structures.     

Damping estimation using enhanced virtual dynamic shaker: A web‐enabled framework

Damping estimation from laboratory, full‐scale, or computational simulation is critical in response prediction of structures under wind, waves, or earthquake effects. A virtual dynamic shaker (VDS)‐based scheme was recently developed for system identification (SI) of structures for processing (weakly) stationary responses, that is, frequency and damping features that offers, especially the added advantage of its basic simplicity over other schemes. While the VDS has shown performance, equivalent to other popular SI schemes, it is based on the assumption of the global flatness of the load spectrum (i.e., white noise assumption) like used in most other SI schemes, which may not always be appropriate in practical applications. In addition, it is restricted to data from a single‐degree‐of‐freedom (SDOF) response (or unimodal response) to obtain accurate modal characteristics. To address these potential shortcomings, this study revisits the VDS scheme and offers an enhancement by invoking local flatness assumption (EVDS) to possibly improve the damping estimation with the assumption that the load spectrum is flat only around the natural frequencies of the desired modes. A new formulation involving the effect of the ground motion induced vertical vibrations of a building is also introduced for both the VDS and the EVDS. Extensive examples through numerical simulation and full‐scale data, including a comparison with other popular SI schemes, demonstrate the efficacy of the proposed EVDS scheme. To facilitate expeditious and convenient utilization of the proposed EVDS as well as the VDS, this study has implemented a web‐enabled framework, named VDS‐Damping, for on‐demand and on‐the‐fly applications through user‐friendly input and result interfaces. A recently developed mode decomposition scheme, state space‐based mode decomposition (SSBMD), is implemented in the framework to assist in analyzing output from multiple modes and eliminates restriction of SDOF system. Accordingly, the SSBMD can also serve as a stand‐alone mode decomposition tool to separate response in each mode. This framework enables users to estimate damping on‐the‐fly by uploading with ease their data.     

Probabilistic assessment of vibration exceedance for a full‐scale tall building under typhoon conditions

Full‐scale wind and vibration measurements were conducted on a 270‐m tall building in Hong Kong. For the modal identification, a refined fast Bayesian fast Fourier transform method was newly developed by considering the exponential form of the modal wind force spectrum. Then, the modal parameters of the monitored building and their uncertainties were identified from the full‐scale vibration data under typhoon conditions by the proposed refined fast Bayesian fast Fourier transform method. For assessing the vibration exceedance of the monitored building under typhoon, a stochastic wind force field generation technique was developed by combining the spectral representation method and the computational fluid dynamics method. Wind‐induced vibration of the tall building under Typhoon Kammuri was reanalyzed with generated wind force time history data. Finally, a time‐domain Monte Carlo simulation framework was proposed by integrating the modal identification and the stochastic wind force field generation technique. In this framework, the Metropolis–Hastings sampling algorithm was adopted to estimate the vibration exceedance probability, which was defined through a limit state performance function associated with the ISO vibration assessment criteria.     

Monitoring of structural modal parameters and dynamic responses of a 600m‐high skyscraper during a typhoon

This paper presents field measurement results of structural dynamic properties and wind‐induced responses of 600m‐high Ping‐An Finance Center in Shenzhen during the passage of Typhoon Haima. The field measurements included wind speed, wind direction, and structural acceleration responses during the typhoon. Analysis of the field measurements is carried out to investigate the wind‐induced structural vibrations and dynamic properties of the skyscraper under typhoon condition. In the analysis, natural frequencies and damping ratios of Ping‐An Finance Center are estimated using Peak‐Picking method, half‐power bandwidth method in frequency domain, and random decrement technique in time domain, respectively. Two band‐pass filtering methods, namely, elliptical filtering method and Kaiser‐window FIR filter, are adopted to deal with the measured acceleration signals. Consequently, the modal parameters identified with the Peak‐Picking, half‐power bandwidth, and random decrement technique methods are presented and discussed in detail. In addition, the probabilistic characteristics of the recorded acceleration responses are analyzed using the generalized extreme value distribution, and then the serviceability of the skyscraper during the typhoon is evaluated.     

随机子空间法参数识别与有限元分析

随机子空间法是近些年来发展起来的一种线性系统识别方法,可以有效地从环境激励的结构反应中获取模态参数。属于时域的方法,这种时域识别方法基于状态空间模型,仅利用结构输出反应,避免了传统的人工识别和迭代过程。它不仅可以识别结构的频率,而且可以识别结构的阻尼和振型。介绍了随机子空间的理论,用该方法对一框架模型进行参数识别,通过与有限元识别结果的比较证明了随机子空间方法不失为一种有效的模态参数识别方法。