Response surface‐based finite‐element model updating of a historic masonry minaret for operational modal analysis

This study aimed to use the response surface (RS) method for finite element (FE) model updating, using operational modal analysis (OMA). The RS method was utilized to achieve better agreement between the numerical and field‐measured structure response. The OMA technique for the field study was utilized to obtain modal parameters of the selected historic masonry minaret. The natural frequencies and mode shapes were experimentally determined by the enhanced frequency domain decomposition (EFDD) method. The optimum results between the experimental and numerical analyses were found by using the optimization method. The central composite design was used to construct the design of experiments, and the genetic aggregation approach was performed to generate the RS models. After obtaining the RS models, an attempt was made to converge the natural frequency values corresponding to the five‐mode shapes with the frequency values identified by the experimental analysis. ANSYS software was used to perform 3D finite element (FE) modeling of the historic masonry minaret and to numerically identify the natural frequencies and mode shapes of the minaret. The results of the experimental, initial, and updated FE model were compared with each other. Significant differences can be seen when comparing the experimental and analytical results with the initial conditions.     

Frequency domain identification of modal characteristics and loads from output-only measurements

This paper proposes a frequency domain framework for concurrently estimating the modal structural parameters and modal loads from the measured output response. A mathematical load model is theoretically developed and compared to the load determined by force identification. Unlike conventional modal identification schemes, the proposed approach can effectively accommodate the spectral shape of the external load in the frequency domain, enabling the determination of the modal parameters without explicit white noise assumption. The proposed approach is verified by applying it to a single-degree-of-freedom system system representing a modal response, an aeroelastic model in an atmospheric boundary layer wind tunnel, a multi-degree-of-freedom system, and the measured acceleration response of a 40-story building. The simulation results demonstrate that the proposed technique can reliably estimate the modal parameters and load model and is robust against the noise present in the response and the order of the load model. Additionally, the proposed technique can be applied to various loading conditions such as vortex-induced and buffeting effects since the modal parameters and the load model can be identified for any shape of the loading spectrum.     

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。     

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.     

Operational Modal Parameter Identification from Power Spectrum Density Transmissibility

Abstract: Operational modal analysis subjected to ambient or natural excitation under operational conditions has recently drawn great attention. In this article, the power spectrum density transmissibility (PSDT) is proposed to extract the operational modal parameters of a structure. It is proven that the PSDT is independent of the applied excitations and transferring outputs at the system poles. As a result, the modal frequencies and mode shapes can be extracted by combing the PSDTs with different transferring outputs instead of different load conditions where the outputs from only one load condition are needed. A five‐story shear building subjected to a set of uncorrelated forces at different floors is adopted to verify the property of PSDTs and illustrate the accuracy of the proposed method. Furthermore, a concrete‐filled steel tubular half‐through arch bridge tested in the field under operational conditions is used as a real case study. The identification results obtained from currently developed method have been compared with those extracted from peak‐picking method, stochastic subspace identification, and finite element analysis. It is demonstrated that the operational modal parameters identified by the current technique agree well with other independent methods. The real application to the field operational vibration measurements of a full‐sized bridge has shown that the proposed PSDTs are capable of identifying the operational modal parameters (natural frequencies and mode shapes) of a structure.     

Approximate modal analysis of multistory symmetrical buildings with restricted inelasticity

Simplified capacity curves are presented for modal decomposition of multistory inelastic cantilever bents. These structural systems are uniform over the height and plasticity is assumed to be restricted into the beams, since significant rotation ductility factors may be attained in these members without loss of strength. The approximate method of modal decomposition of multistory inelastic bents is based on the concept that the total response may be obtained from the contributions of equivalent nonlinear single‐degree‐of‐freedom (SDOF) modal systems, in combination with the technique of modal superposition. In particular, the contribution of the first mode equivalent inelastic SDOF system is examined, since its modal contribution is of higher importance. The response of such SDOF systems basically depends on their capacity curve, which may be formulated by using the dynamic properties (frequency, effective modal mass and mode shape) of the initially elastic bent, as well as the corresponding properties of the bent when the entire set of coupling beams is assumed to be yielded. The procedure is presented for plane cantilever bents, but it can be easily extended to symmetrical structural systems composed of different types of inelastic bents. Its application is illustrated by means of a 10‐story inelastic coupled‐wall bent subject to a strong earthquake motion, equal to 1·5× El Centro N–S ground excitation, and the results compare well with those obtained from a step‐by‐step nonlinear time history analysis of the discrete member model. Copyright © 2007 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.     

Prediction of nonlinear seismic demands of high‐rise rocking wall structures using a simplified modal pushover analysis procedure

This study presents a simplified analysis procedure for the convenient estimation of nonlinear seismic demands of high‐rise rocking wall structures. For this purpose, the displacement modification approach used in the nonlinear static procedure of ASCE/SEI 41‐13 is adopted. However, in the current study, this approach is extended to every significant vibration mode of the structure whereas the displacement modifying coefficients for different modes are calculated using the typical flag‐shaped hysteresis behavior of rocking walls. The parameters of this hysteresis behavior are selected to represent rocking walls with a practical range of energy dissipation capacity and postgap‐opening stiffness. The computed peak inelastic‐to‐elastic displacement ratios are presented as mean spectra, which can be used for the convenient estimation of pushover target displacement for every significant vibration mode. The accuracy of proposed procedure is examined using the seismic demands obtained from the nonlinear response history analysis of a 20‐story case study rocking wall structure. Furthermore, a modal decomposition technique is used to determine the individual modal seismic demands. The proposed procedure is found to predict both the combined and the individual modal demands with a reasonable accuracy and can serve as a convenient analysis option for the design and performance evaluation of high‐rise rocking wall systems.     

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.     

Modal identification with uncertainty quantification of large-scale civil structures via a hybrid operation modal analysis framework

In operational modal analysis (OMA), only structural responses are typically available. In this context, bias and variance (uncertainty) errors may exist in modal estimates (especially damping estimates), resulting in inaccurate determination of the modal properties of large-scale structures under harsh excitations. To this end, a hybrid OMA framework based on the modal decoupling, the natural excitation technique, the random decrement technique (RDT), and improved eigensystem realization algorithm (ERA) with the automated stabilization diagram is presented to perform high-accuracy modal estimates with uncertainty quantification for large-scale structures under normal and severe ambient excitations. The accuracy and effectiveness of the hybrid framework for identifying the modal parameters are validated by numerical simulation study of a framework structural model. Furthermore, the hybrid framework is applied to analyze recorded acceleration responses of a supertall building with 600-m height under normal excitations and typhoon condition to verify its applicability in field measurements. The numerical simulation and field measurement studies demonstrate that the hybrid framework can not only perform precise modal estimations with uncertainty quantification through a single ambient vibration measurement but also effectively reveal the variations of modal properties of supertall structures under harsh excitations from multiple perspectives. This paper aims to enhance the reliability and accuracy of modal estimation for engineering structures and further provide insight into the variations of dynamic properties of large-scale civil structures under severe excitations.     

Hybrid Time‐Frequency Blind Source Separation Towards Ambient System Identification of Structures

Abstract: Ambient system identification in noisy environments, in the presence of low‐energy modes or closely‐spaced modes, is a challenging task. Conventional blind source separation techniques such as second‐order blind identification (SOBI) and Independent Component Analysis (ICA) do not perform satisfactorily under these conditions. Furthermore, structural system identification for flexible structures require the extraction of more modes than the available number of independent sensor measurements. This results in the estimation of a non‐square modal matrix that is spatially sparse. To overcome these challenges, methods that integrate blind identification with time‐frequency decomposition of signals have been previously presented. The basic idea of these methods is to exploit the resolution and sparsity provided by time‐frequency decomposition of signals, while retaining the advantages of second‐order source separation methods. These hybrid methods integrate two powerful time‐frequency decompositions—wavelet transforms and empirical mode decomposition—into the framework of SOBI. In the first case, the measurements are transformed into the time‐frequency domain, followed by the identification using a SOBI‐based method in the transformed domain. In the second case, a subset of the operations are performed in the transformed domain, while the remaining procedure is conducted using the traditional SOBI method. A new method to address the under‐determined case arising from sparse measurements is proposed. Each of these methods serve to address a particular situation: closely‐spaced modes or low‐energy modes. The proposed methods are verified by applying them to extract the modal information of an airport control tower structure located near Toronto in Canada.     

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.     

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.     

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‐induced inter‐story drift analysis and equivalent static wind load for multiple targets of tall buildings

In super high‐rise buildings with varying story heights, the wind‐induced inter‐story drifts might violate the specified limit. However, these effects have seldom been concerned in wind‐induced response analysis. The theory and application of equivalent static wind load (ESWL) for wind‐induced inter‐story drifts of super high‐rise buildings were studied in this paper. A spectral decomposition method suitable for multi‐point excitation problems was firstly proposed. The formula of ESWL targeting for largest inter‐story drift was derived. For more reasonable structural design, the ESWL for multiple targets including displacement atop of building and inter‐story drifts at all story levels is put forward, in which the dominant modal inertial forces are adopted as the based load vectors. The presented methods were finally verified by its application for the wind‐induced response analysis for a tallest super tall building in Guangzhou. The researched results showed that the proposed spectral decomposition method not only has the same precision as the complete quadratic combination method but also possesses higher computation efficiency. The ESWL for multiple targets produces the same static responses for all the specified wind‐induced response, so it is much more rational for wind‐resistant structural design. Meanwhile, it is more reasonable to select the wind‐induced responses in the same direction simultaneously as the targeted values for obtaining the required ESWLs; however, the ESWL targeting for the wind‐induced responses in all degrees of freedom would generate more queer and unrealistic ESWLs distribution. Copyright © 2015 John Wiley & Sons, Ltd.     

HHT结合NExT法识别结构参数

信号处理方法在地震工程领域有着广泛的应用,尤其是在结构参数识别方面。Hilbert-Huang变换（HHT）是一种新的信号处理方法,它与NExT法相结合可以识别结构的模态频率、阻尼比和振型。对于剪切型结构,本文基于柔度法推导了层间刚度的计算公式,公式表明,只要已知任一完整模态,就能计算出所有层的层间刚度。在此基础上,本文根据堆聚质量法的原理将喜来登环球旅馆简化四层剪切结构,利用其在1994年北岭地震中所取得的强震记录,通过HHT与NExT法相结合,识别了结构的前三阶模态频率、阻尼比和振型,并计算出其层间刚度。最后,应用弹性时程分析法,利用已识别出的结构参数,计算结构的地震反应,计算结果与强震记录对比表明,识别出的结构参数是有效的。     

Dynamic characteristics and viscous dampers design for pile‐soil‐structure system

A series of large‐scale shaking table tests are conducted on tall buildings with and without energy dissipation devices on soft soils in pile group foundations, representing pile‐soil‐structure interaction (PSSI) system and the corresponding fixed‐base situations. The superstructure is a 12‐story reinforced concrete (RC) frame. The dynamic characteristics of the test models show that the frequencies decrease and the damping ratio increase in PSSI system by comparison with the fixed‐base structures. The mode shapes of PSSI system are different from that under fixed‐base condition, and the mode shapes of structure without dampers change greater than that with energy dissipation devices under various white noises. An improved method for structural dynamic characteristics, considering the impedance function of piles, is developed to address the issue of modal parameters with PSSI effect. In addition, the structural dynamic parameters of the large‐scale shaking table tests are identified using the modification method and other regulation methods, demonstrating that the improved approach is highly accurate and effective. Subsequently, a design procedure for viscous dampers of structures with PSSI effect is presented based on the dynamic characteristics of the system. Finally, the dynamic responses of the structure with viscous dampers in the practical engineering are decreased effectively, indicating the good performance of designed viscous dampers. The numerical results also show that the damping efficiency of interstory drift is larger than the acceleration and interstory shear force. Therefore, the improved modal parameters method, validated through a series large‐scale shaking table tests, is applicable for identifying dynamic characteristics of pile‐soil‐structure with energy dissipation devices system. The design procedure of viscous dampers, proved by a reinforced concrete frame structure located on a practical Shanghai soft site, can be employed to design the viscous dampers considering seismic PSSI effect.     

An alternative approach for assessing eccentricities in asymmetric multistory buildings. 2. Inelastic systems

The approximate method, presented in the companion paper, for assessing modal eccentricities of elastic multistory buildings with simple eccentricity is extended in systems composed by elastoplastic resisting bents. Following the technique of the aforementioned paper for computing modal properties of such buildings by means of an equivalent single‐story system composed of elastic elements, modal capacity curves of these systems may also be drawn when the resisting elements are defined by a bilinear force–displacement (characteristic) curve. The procedure for constructing element‐characteristic curves is based on the methodology presented by the author in an earlier paper, and modal capacity curves of the equivalent single‐story system may be drawn by performing a non‐linear pushover analysis using the inertia force eccentricity of each mode of this system. Therefore, base shears and their eccentricities for the first two modes of vibration of multistory inelastic buildings can be determined as in real one‐story non‐linear systems. The method is illustrated in a 10‐story partial symmetric building, having along the direction of the ground motion three identical, inelastic, coupled wall bents. The structure is analyzed for a strong ground motion, equal to 1·5 × El Centro earthquake excitation, and the results are compared with those obtained from a step‐by‐step non‐linear time history analysis of the discrete member model. Copyright © 2007 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.     

Noise reduction method of microseismic signal of water inrush in tunnel based on variational mode method

The extraction of effective signals of microseismic event caused by water inrush in tunnels is an important prerequisite for accurate location of event. In this paper, based on the characteristics of the main frequency components of the tunnel water burst signal, the variational modal method (VMD) with good frequency decomposition ability is adopted to effectively extract the high-frequency components of the water inrush signal. The effective modes are identified by the method of detrend analysis, and the modal decomposition number K is determined. At the same time, the boundary between noise and effective signal is determined. The method proposed in this paper solves the problem that noise in some modal components is mixed with effective signals, and further improves the ability of extracting weak high-frequency signals. Through the analysis of case data, the validity of the research results in this paper is verified, and an effective signal extraction method of tunnel water inrush microseismic event based on VMD-DFA principle is formed.