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.     

Field measurements of amplitude‐dependent damping in a 79‐storey tall building and its efects on the structural dynamic responses

This paper describes some results obtained from full‐scale measurements of wind effects on a super‐tall building, Di‐Wang Tower, located in Shenzhen, China. This tall building has 79‐storeys with a height of approximately 324 m. Field measurements including wind speed, wind direction and wind‐induced acceleration responses have been made. The amplitude‐dependent characteristics of damping are obtained by using the random decrement technique from the detailed analysis of the field acceleration measurements. The main objective of this paper is to present detailed investigations into the effects of nonlinear damping on the dynamic responses of the tall building subjected to various types of applied loads based on the measured amplitude‐dependent damping characteristics. The predicted dynamic responses of the building obtained by using the measured damping characteristics were compared with those computed by using constant damping parameters assumed by the structural designers. It is concluded from the investigations that knowledge of actual damping characteristics are very important in the accurate prediction of the dynamic responses of a tall building when the major harmonic components of the applied loads overlap with the lowest natural frequencies of the building. The design damping level for tall building structures currently used by structural engineering practitioners appears to be high and not conservative. Copyright © 2002 John Wiley & Sons, Ltd.     

Wavelet_Huang和Hilbert_Huang方法用于非高斯风压信号分析的比较研究

非高斯风压时程具有间歇性的大脉冲信号和不对称性,传统的傅里叶变换无法得到信号的频谱特性随时间的变化过程,也不能识别出不同频段处信号的变异性。采用一种结合经验模式分解(EMD)和小波变换(WaveletTransform)的方法(简称WHT)对非高斯风压信号进行时-频-谱联合特性分析,随后讨论了不同频段处信号的奇异性、冲击性和分辨率;并和Hilbert_Huang变换(简称HHT)分析的结果进行对比。两种方法处理非高斯信号都能很好地提取信号的主要特征和分解、重构;由于小波基尺度有限并受到测不准原理的限制,WHT方法得到的小波谱的能量在频率范围内分布较宽,而HHT方法得到的Hilbert能量谱大多都集中在有限的能量谱线上;WHT方法进行不同频段处信号的变异性检测是对EMD分解得到的IMF分量进行小波分解,其更能反映原始数据的固有特性,在任意感兴趣的频段捕捉到信号的局部特征。研究结果表明,HHT方法可以更好地进行非高斯信号的谱特性分析,而WHT方法在信号的分解、重构和变异性检测时效果更好。     

Real-time structural health monitoring of a supertall building under construction based on visual modal identification strategy

This paper presents a real-time structural health monitoring technique for a supertall building under construction, Lotte World Tower (LWT), the tallest building in Korea. To evaluate the state and safety of the supertall building under construction, this study presents a visual modal identification method to identify mode shape and damping ratio based on modal responses from the monitoring system. In the method, mode shape and damping are visually identified from the time history plotting of well-filtered modal responses in real time. Since the presented method does not include a kind of complex calculation for measured data required in the previous SI methods, it can avoid time consuming in system identification (SI) as well as variation in value of modal parameter extracted from measurement. An ambient vibration test on the LWT under construction was performed in 2015. Using the test data, the presented method identified the mode shapes and damping of the LWT visually with small variations without any complicated computations. Further, this study presents a model updating method with a simplified pseudo frame model to construct a baseline model for the LWT under construction using measured modal responses. The validity of the updated model for the LWT was verified through estimations of mode shape and structural responses.     

Evaluation of wind loads on super‐tall buildings from field‐measured wind‐induced acceleration response

With the nonstationary wind‐induced acceleration data from full‐scale measurements, an approach for estimation of the wind‐induced overturning bending moments for super‐tall buildings was proposed in this paper. The empirical mode decomposition was employed to decompose the measured acceleration data into a set of intrinsic mode functions and a residual component. To remove the baseline offset, the residual component and the intrinsic mode function components with long‐period were eliminated before their integrations into velocity and displacement components. Then, the intrinsic mode function components, which have the same dominant periods as the natural periods of the studied tall buildings, were extracted from the original signals, and the natural frequency and damping ratio for the first vibration mode of the building were identified. Finally, the wind‐induced overturning bending moments of the building were obtained from the generalized wind loads for the first vibration mode, which could be obtained from the time history analysis of dynamic equation. The Hilbert spectrum of wind‐induced overturning bending moments was utilized to observe its characteristics in both time and frequency domains, and the Strouhal number was thus identified. The proposed scheme and some selected results may be helpful for further understanding of wind effects on super‐tall buildings. Copyright © 2012 John Wiley & Sons, Ltd.     

Experimental study of across‐wind aerodynamic damping of super high‐rise buildings with aerodynamically modified square cross‐sections

Across‐wind aerodynamic damping ratios are determined from the wind‐induced acceleration responses of 10 aeroelastic models of square super high‐rise buildings in an urban flow condition (exposure category C in the Chinese code) using the random decrement technique. Moreover, the influences of amplitude‐dependent structural damping ratio on the estimation of aerodynamic damping ratio are discussed. The validity of estimated damping is examined through a comparison with previous research achievements. On the basis of the estimated results, the characteristics of the across‐wind aerodynamic damping ratios of modified square high‐rise buildings are studied. The effects of aerodynamically modified cross‐sections, such as chamfered, slotted and tapered cross‐section, on the across‐wind aerodynamic damping ratio are investigated. The results indicate that modifications of cross‐sections are not always effective in suppressing the aeroelastic effects of super high‐rise buildings. Low corner‐cut ratios (chamfer ratios from 5% to 20% and slot ratios from 5% to 10%) and low taper ratio (1%) significantly decrease the magnitudes of absolute aerodynamic damping ratios. However, large modifications of cross‐sections (slot ratio of 20% and taper ratios from 3% to 5%) increase wind‐induced responses by changing the aerodynamic damping ratios. According to the database, empirical aerodynamic damping function parameters are fitted for high‐rise buildings with aerodynamically modified square cross‐sections. Copyright © 2013 John Wiley & Sons, Ltd.     

Modal parameter identification of Tsing Ma suspension bridge under Typhoon Victor: EMD-HT method

This paper aims to identify the natural frequencies and modal damping ratios of the Tsing Ma suspension bridge during Typhoon Victor using the newly emerged empirical mode decomposition (EMD) method in conjunction with the Hilbert-transform (HT) technique. Stationary tests on the acceleration responses of the bridge recorded at different locations and in different directions during Typhoon Victor are first carried out to classify the recorded response data. Natural frequencies and modal damping ratios identified by the EMD-HT method are then compared with those obtained by the traditional fast Fourier transform (FFT)-based method. The modal parameters identified by the EMD-HT method from the bridge responses recorded at different locations are compared with each other to check their consistency. Furthermore, the variations of natural frequency and total modal damping ratio with vibration amplitude and mean wind speed are examined. The results demonstrated that the EMD-HT method is applicable to modal parameter identification of large civil structures under typhoons. The EMD-HT method and the FFT-based method produced almost the same natural frequencies but the FFT-based method gave higher modal damping ratios than the EMD-HT method in general.     

基于AEEMD和改进DATA-SSI算法的桥梁结构模态参数自动化识别

模态参数作为桥梁结构最重要的动力参数之一,在实际运用中,可通过监测其变化情况来辨识结构的使用性能,精确地参数识别对保障桥梁健康运营具有十分重要的意义。鉴于此,该文对现阶段常用的振动信号降噪处理算法和模态参数识别算法进行了相应的改进。一方面,提出一种新的信号自适应分解与重构算法,即自适应总体平均经验模态分解算法（AEEMD）,该算法相比总体平均经验模态分解算法（EEMD）而言,能够根据信号的自身特征自动化确定添加白噪声的幅值标准差和集成平均次数|能更好地处理端点效应|同时还能够保证所得本征模态函数之间不存在模态混叠现象|最终实现有效IMF分量的自动化筛选和信号重构。另一方面,将多维数据聚类分析算法引入随机子空间算法中,并以频率值、阻尼比以及振型系数为因子建立判别矩阵,以智能化区分虚假模态和真实模态,最终实现模态参数自动化识别。文章最后分别用模拟信号和实际桥梁测试信号对所提算法的有效性进行验证,结果表明,该文所提算法能运用于实际桥梁结构的模态参数自动化识别。     

Time-frequency analysis of typhoon effects on a 79-storey tall building

Di Wang Tower located in Shenzhen, PR China, has a height of approximately 325 m and is a 79-storey tall building. This paper presents selected results of full-scale measurements of typhoon effects on Di Wang Tower. Wind speed, wind direction, wind-induced acceleration and displacement responses were simultaneously and continuously measured from the super tall building with anemometers, accelerometers and global position system (GPS) during a typhoon. The advanced data analysis method called Hilbert-Huang transform (HHT) was adopted in this study to analyze the non-stationary characteristics of wind speed and wind-induced responses of this building under typhoon condition. By using the empirical mode decomposition (EMD) method, the measured data were decomposed into several inherent intrinsic mode functions (IMFs). The probability density and power spectral density of fluctuating wind speed were obtained by traditional methods and were further analyzed by considering time-varying mean values of the measured data via the EMD method. The wind-induced responses with non-stationary features were studied by applying the HHT to each IMF for obtaining their instantaneous frequency and Hilbert-Huang composite spectrum. Meanwhile, the transient energy distributions of the wind-induced responses were analyzed in time-frequency domain, which were compared with the traditional power spectral densities obtained from the fast Fourier transform (FFT) method and those from the wavelet transform. Furthermore, the amplitude-dependent damping ratios were determined by combining the EMD and the random decrement technique (RDT) method. Through comprehensive analysis of the measured data, it was testified that the HHT method is a promising tool for the time-frequency analysis of random signal and can serve as a flexible and effective tool for analyzing field data of wind speed and wind-induced response with non-stationary features.     

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.     

Wind effects on Shenzhen Zhuoyue Century Center: Field measurement and wind tunnel test

Field measurements of wind effects on Zhuoyue Century Center were conducted during 4 typhoon events in the recent 5 years, during which the field data such as wind speeds, wind directions, and acceleration responses were simultaneously and continuously measured. On the basis of field measured data, dynamic characteristics of this super‐tall building were determined by recently developed fast Bayesian fast Fourier transform method. Using full‐scale measurement data under 4 typhoons and breezy conditions for modal identification, one could observe a relatively wide scatter in the identified modal damping ratios, and the damping ratios do not appear to have an obvious nonlinear relationship with vibration amplitude. The average damping ratios of the first 2 modes were 0.70% and 0.73%, respectively. Serviceability of the super‐tall building under wind action was analyzed on the basis of the field measured response. Finally, the measured wind‐induced acceleration responses were further compared with those obtained from the wind tunnel test to evaluate the accuracy of the model test results.     

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.     

Modal identification of Di Wang Building under Typhoon York using the Hilbert–Huang transform method

The Di Wang Building is one of the tallest composite buildings in the world, located in downtown Shenzhen City of China about 2 km from the Hong Kong border. On 16 September 1999, Typhoon York – that is the strongest typhoon since 1983 and the typhoon of longest duration on record – attacked Hong Kong and Shenzhen. The wind and structural monitoring system installed in the Di Wang Building timely recorded wind and structural response data. The newly emerged Hilbert–Huang transform (HHT) method in conjunction with the random decrement technique (RDT) is applied to the measured data in this paper to identify dynamic characteristics of the building. A series of natural frequencies and modal damping ratios of the building under different wind speeds in different directions are identified and compared with those from the fast Fourier transform (FFT)‐based method. The variations of natural frequency, total modal damping ratio and net structural modal damping ratio with wind speed and vibration amplitude are also investigated. The results show that the natural frequencies identified by the HHT method are almost the same as those obtained by the FFT‐based method. The first two modal damping ratios given by the HHT method are, however, lower than those by the FFT‐based method, which may indicate that the FFT‐based method overestimates the modal damping ratios. Both the total and the net structural modal damping ratios increase with increasing wind speed and vibration amplitude but the situation is reversed for the natural frequency. Copyright © 2003 John Wiley & Sons, Ltd.     

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.     

Three‐dimensional coupled wind‐induced vibration calculation method for super high‐rise buildings based on high‐frequency force balance technology

High‐frequency force balance test is a major technical means to evaluate the wind effect of super high‐rise buildings. Most super high‐rise buildings have the characteristic that the first two‐order modal frequencies are close, and thus, considerable modal coupling effects (MCEs) may occur under wind load. For a balance model system (BMS), MCEs increase the difficulty of correcting aerodynamic distortion signals. For the wind‐induced vibration analysis of a structural system (PSS), the calculation results of the wind‐induced response and the equivalent static wind load (ESWL) may be significantly affected without considering MCE. Based on the above‐mentioned signal distortion of BMS and the modal coupling problem of PSS, this study proposes a wind‐induced vibration calculation method for the two coupled systems (BMS and PSS). The method uses the second‐order blind identification technique based on complex modal theory and the Bayesian spectral density method considering full aerodynamic characteristics to achieve effective correction of the distortion signal in BMS. In addition, it deduces the calculation method of the wind‐induced response and ESWL considering the three‐dimensional coupled vibration of a super high‐rise building. The wind effect calculation results of a 528‐m super high‐rise building confirm the necessity and effectiveness of the proposed method.     

Application of stress wave propagation technique for condition assessment of timber poles

Abstract

The stress wave propagation technique can be effectively used to assess the condition of timber utility poles. However, reliable detection of damage based on the reflected wave within the time domain is not always possible. Therefore, various signal processing methods such as frequency-domain analysis and time-frequency analysis can be adopted to overcome this problem depending on the application. In this paper, Hilbert–Huang and continuous wavelet transforms are selected as signal processing methods to analyse the reflected wave. The signal is initially subjected to an empirical mode decomposition process prior to the computation of instantaneous frequencies of the decomposed signals using the Hilbert–Huang transformation. The anomalies in the instantaneous frequency plots can be used to identify any damage and its location along the pole. Additionally, the decomposed signals are subjected to a wavelet transformation to further confirm the existence of damage. The combined Hilbert–Huang and continuous wavelet transform technique is applied to the stress wave signal recorded from the in-service poles to assess the accuracy of the proposed method. This method increases the confidence level of defect identification of timber utility poles.     

环境风激励下的深圳平安金融中心模态参数识别

对高度600 m的超高层建筑——深圳平安金融中心在外界环境风激励下的风振响应进行了现场实测。通过安装在塔楼118层的2组加速度传感器测得结构的风致加速度响应,采用经验模态分解法（EMD）与随机减量技术（RDT）相结合的方法计算了结构的自振频率和阻尼比。建立了深圳平安金融中心三维有限元模型,通过有限元分析得出结构的自振频率,并与实测结果进行对比。结果表明:由EMD和RDT相结合的方法计算得出结构1阶横弯自振频率约为0.12 Hz,阻尼比为0.3%~0.6%;结构1阶扭转自振频率约为0.28 Hz,阻尼比为0.8%~1.0%;深圳平安金融中心实测结构自振频率和阻尼比与其他结构高度相似的超高层建筑实测结果相近,且实测结果和有限元分析结果吻合较好,验证了EMD和RDT结合方法分析超高层建筑模态参数的有效性;测试结果可以为超高层建筑设计和相关研究提供依据。     

Robustness of base‐isolated high‐rise buildings under code‐specified ground motions

The robustness of base‐isolated high‐rise buildings is investigated under code‐specified ground motions. Friction‐type bearings are often used in base‐isolated high‐rise buildings to make the natural period of those buildings much longer. While additional damping can be incorporated into every story in passive controlled structures with inter‐story type passive members, that can be incorporated into the base‐isolation story only in the base‐isolated building. This fact leads to the property that, as the number of stories of the building becomes larger, the damping ratio reduces. This characteristic may cause some issues in the evaluation of robustness of base‐isolated high‐rise buildings. The purpose of this paper is to reveal the robustness of base‐isolated high‐rise buildings. A kind of inverse problem for the target drift in the base‐isolation story is formulated in order to determine the required quantity of additional viscous damping. It is demonstrated numerically that, as the base‐isolated building becomes taller, the damping ratio becomes smaller and the ratio of the friction‐type bearings in the total damping becomes larger. This may lead to the conclusion that base‐isolated high‐rise buildings have smaller robustness than base‐isolated low‐rise buildings. Copyright © 2007 John Wiley & Sons, Ltd.     

Seismic performance analysis of viscous damping outrigger in super high‐rise buildings

This paper introduces a seismic energy dissipation technology—viscous damping outrigger (VDO)—which is composed of outrigger truss and viscous damper. The viscous damper is set up vertically at the end of outrigger truss, which is an innovative and high‐efficiency arrangement. VDO can fully utilize the characteristic of structural lateral deformation of super high‐rise buildings to increase the efficiency of viscous dampers for enhancing structural security, improving seismic performance, and reducing construction expenditure. In this paper, working principle and seismic energy dissipating mechanism of VDO are explained firstly. Then, the influence of viscous damper parameters on energy dissipation efficiency is studied. Next, the optimal position of VDO in a super high‐rise building is analyzed in detail. Lastly, the application of VDO in structural seismic design of a super high‐rise building in China will be clearly verified based on their feasibility, economy, and safety.     

A frequency‐domain noniterative algorithm for structural parameter identification of shear buildings subjected to frequent earthquakes

System identification is the key technique for damage detection in application of structural health monitoring. In contrast to modal parameters, changes in structural parameters (stiffness and damping) are more sensitive and straightforward for damage detection of a building under severe environments such as earthquakes. In this study, we first present the fundamental theory for direct identification of structural parameters by using the frequency‐domain responses of a shear building in frequent earthquakes. Shear buildings are widely adopted for structural analysis of low‐ and middle‐rise buildings in practice. Modal information, in terms of spectrum ratios, is implicitly used in the proposed noniterative algorithm to greatly improve the estimation accuracy as well as to avoid any human intervention. The fundamental theory is validated by the numerical and physical examples. The numerical examples are further used to verify the high efficiency, accuracy, and robustness of the proposed algorithm against noised responses. The proposed algorithm is highly efficient because no iterative computation is necessary, while the necessary Fourier transform of the dynamic responses is not very time consuming. Furthermore, the proposed algorithm is highly accurate and robust because (a) the fundamental theory behind the algorithm is straightforward: the identification values should have the same value irrespective of circular frequencies, according to the theory; (b) error in modal parameter identification is completely avoided because it is unnecessary to identify the exact values of the frequencies as in many existing methods.