Modal identification of non-classically damped structures using generalized sparse component analysis

Modal identification method based on blind source separation (BSS) technique has gained extensive attentions for civil structures. Developing the complex modes estimation method is important in practical applications because the assumption of proportional damping is not always satisfied. Sparse component analysis (SCA) performs well in underdetermined BSS problems. However, SCA is confined to the situation of proportional damping. In this study, a generalized SCA method is proposed to extend the original SCA method to both real and complex modes identification. First, the general formulation of complex modes is extended by the analytic form to eliminate the complex conjugate part in the BSS model. A new single-source-point detection method that is available to handle real and complex modes is proposed. Local outlier factor method is adopted to remove the outliers in single source points. Subsequently, complex-valued modal matrix is calculated by the clustering technique. Then, modal responses are recovered using the complex version of smoothed zero norm method, where modal frequencies and damping ratios can be extracted. Finally, the effectiveness of the proposed method is demonstrated for identification of real and complex modes, close modes, and underdetermined problem. The application to a benchmark structure demonstrates the effectiveness for practical applications.     

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.     

钢板夹层阻尼高频TMD两阶段设计方法

随着工业化的发展,建筑结构逐渐轻量化,机械设备逐渐重型化、高效化,这使得机械设备高频扰力导致的结构振动问题越来越突出;为了减轻结构的高频受迫振动响应,可以在结构振动响应较大的位置安装高频高阻尼比的钢板夹层阻尼悬臂梁式调谐质量阻尼器(tuned mass damper,TMD).由于TMD的弹性元件与阻尼元件相互耦合,因...     

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.     

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。     

Iterative Method for Exponential Damping Identification

Exponential damping is a new potential damping model for dynamic analysis of systems. This article outlines a complex mode procedure for identifying the exponential damping model and discusses its applicability and limitations. A new iterative method for relaxation factor is proposed, without using the full set of modal data, which is simple, direct, and compatible with conventional modal testing procedures. Combined with the frequency response functions (FRFs)‐based model updating method, the finite element model with such nonviscous damping is updated. The proposed method and several related issues are illustrated by numerical examples. It is shown that the finite element model updated method for the systems with exponential damping can predict accurately not only the natural frequencies but also the FRFs of the systems.     

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.     

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.     

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.     

阻尼特性对组合结构地震反应的影响

首先根据组合结构的特点,通过输入简谐波分别计算了3种等效振型阻尼比模型时组合结构的地震反应,并与非比例阻尼模型时的真实地震反应相比较,讨论了不同等效振型阻尼比模型对组合结构地震反应的影响;然后根据共振条件下结构动力反应的相对误差,推导了组合结构等效振型阻尼比的估算公式;最后通过输入简谐波和实际El Centro地震波验算了这一等效振型比例阻尼比模型的计算精度。结果表明:任意假定组合结构的等效振型阻尼比是不合理的,有时会低估组合结构的地震反应;该估算方法具有很高的计算精度。     

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。     

网架模型结构模态分析的试验研究

实验模态分析是综合运用线性振动理论、动态测试技术、数字信号处理和参数识别等手段,进行系统识别的过程。模态分析是有效的结构检测和安全评估的方法之一,它是根据测量模态参数(固有频率、阻尼比、振型、模态刚度、模态质量)相对于正常值产生的变化,并通过相关分析与识别来判断结构安全程度的一种先进方法。本文通过对网架模型结构进行试验模态分析,研究了试验模态技术在实际运用中的试验方法,识别系统的模态参数并与有限元分析进行比较,有限元结果与实测频率有一定的不同,但前四阶模态频率的差值百分比均在9%以内,说明实测的结果与有限元分析是比较吻合的。     

环境激励下结构模态参数的识别方法

传统的模态参数识别方法同时需要已知激励和响应信号,但对实际建筑结构,激励施加存在困难。探讨了基于环境激励下的模态参数识别方法,提出采用随机减量法和ITD（Ibrahim Time Domain）法相结合来识别实际结构的模态参数。数值仿真算例识别结果表明,该方法不仅能准确的识别出结构的模态频率和阻尼比,也能准确的提取结构的模态振型,适合于环境激励下的结构工作模态参数识别。     

基于试验模态参数的索-拱铁路桥的改进有限元模型

介绍基于模态参数的索-拱铁路桥的校准数值模型。基于扩大的频域分解法,采用只输出技术,通过扰动测试来确定自振频率,桥梁振动的整体和局部模态对应的振型及阻尼系数。采用一种遗传算法对数值模型进行改进,该算法可以在数值模型的15个参数中得到最优解。为了与模态匹配,采用了一种基于模态应变能计算的新技术。考虑到不同的初始种群,大量参数的稳定性证明了数值模型在优化范围内所采用优化算法的鲁棒性。通过一个混凝土的变形模量的特征试验和铁路运输下的动力试验,对改进的数值模型进行了验证。结果显示数值模拟结果与试验结果吻合较好。     

Modal combination method for earthquake‐resistant design of tall structures to multidimensional excitations

This paper presents a modal combination method for earthquake‐resistant design of structures to multidimensional seismic excitations. With the assumption that an earthquake is a stationary random vibration, the correlation among the input components is considered in the proposed method. The relationship coefficients between the translational component and rotational component is then derived in the frequency domain. The combination method of response spectrum for structural response to multidimensional earthquakes is proposed based on the random vibration theory. With the help of the derived modal correlation coefficients, the formulation for structural response to the two‐dimensional earthquake excitations can be obtained. Numerical examples demonstrate the effectiveness and high precision of the proposed methods. Copyright © 2004 John Wiley & Sons, Ltd.     

Nonlinear Damping Identification in Precast Prestressed Reinforced Concrete Beams

Abstract:  This article presents a damage detection method for prestressed reinforced concrete (PRC) elements based on free vibration tests and nonlinear damping identification. Integrated static and dynamic experiments were carried out on three precast PRC beam specimens. The static loading induced different levels of damage to the beams. At each damage level, impulsive loading was applied to the beams and the free vibration response was measured. The dynamic response data were processed using different methods including the multi-input multi-output (MIMO) curve fitting and the Hilbert transform techniques. A strong correlation is observed between the level of concrete damage (cracks) and the amount of nonlinear energy dissipation that can be modeled by means of quadratic damping. The nonlinear damping can be extracted from the free vibration response for each vibration mode. The proposed method is suited for quality control when manufacturing precast PRC members, and can be further extended for in situ detection of damage in concrete structures under ambient vibration.     

粘滞阻尼减震结构振型分解法的研究

减震结构的分析方法之一是振型分解反应谱法。结构附加阻尼器之后，附加阻尼一般为非比例阻尼，并使振型复杂采用振型分解法求解会带来较大误差。通过计算结构的复数特征值和特征向量可以改善振型分解法。     

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%.     

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.     

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.