Spurious mode distinguish by modal response contribution index in eigensystem realization algorithm

Modal identification process has played an important role for civil engineering structures. Among the identification methods, eigensystem realization algorithm is one of the most popular one. However, the noises in practical environment can influent the effectiveness of eigensystem realization algorithm, which can introduce spurious modes due to the overestimated physical order for the structure. This paper proposes a new index named the modal response contribution index (MRCI) for the eigensystem realization algorithm, which can determine the structural physical order and then distinguish spurious mode more precisely. First, the structural responses are divided into different modal response by the well‐known modal superposition theory. Then the square root summation of each modal response is obtained and named as MRCI. A modified stabilization diagram is also presented, which increases the row number of Hankel matrix with the determined order by MRCI. The straight lines formed by the stable points in the modified stabilization diagram designate the structural modal parameters. Finally, one numerical example and the monitoring data of a practical cable‐stayed bridge are employed. The results show that the proposed MRCI and modified stabilization diagram can identify the structural physical mode more precisely.     

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.     

基于随机子空间结合稳定图的拱桥模态参数识别方法

为了避免目前常用的结构模态参数识别方法容易出现虚假模态等缺陷,提出了一种将随机子空间法与稳定图法相结合的模态参数识别方法。通过随机子空间法有效地从环境激励的结构响应中获取模态参数,通过稳定图方法确定系统阶次。通过对稳定图方法的改进,避免了虚假模态的出现,进而提高了随机子空间方法的识别精度,并在一钢管混凝土拱桥上对这种新方法进行了验证。结果表明,该方法具有良好的识别效果。     

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.     

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.     

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。     

基于多维ARX模型理论识别脉动风激励下穹顶结构模态的研究

环境激励下大型土木工程结构的实测工作对于新型结构的理论研究和设计分析具有重要意义.从状态空间理论出发,建立多维ARX模型,推得了结构的模态参数.在脉动风的作用下,对穹顶结构进行脉动法实测,将实测值与有限元分析结果进行比较.结果表明,多维ARX模型用于大型土木工程结构的模态参数在线识别是可行的.     

WPT模态控制算法在空间结构振动控制上的应用

针对复杂结构自由度庞大、频率密集的特点,引入了小波包分解对传统的模态半主动控制算法进行改进,提出了WPT模态半主动控制算法。通过在一体育场挑篷结构上进行的数值仿真结果表明:WPT控制算法在竖向地震激励下可以有效减小结构的地震响应,其对峰值反应的控制效果比传统模态控制算法有所改进。由于WPT模态控制算法中控制方程的维数较少,因而具有更好的实用性和工程应用前景。     

Additional viscous dampers for civil structures: Analysis of design methods based on effective evaluation of modal damping ratios

Design methods for supplemental dampers aimed at reducing vibrations of civil structures often leave unanswered the following question: starting from the structural inherent damping, the adoption of supplemental dampers which level of damping can achieve? From this perspective, the paper shows a methodology based on the well known state-space representation of dynamical systems to calculate the modal damping ratios of non classical/non proportional damping schemes. The methodology is then adopted to analyse a number of design methods for supplemental damping systems found in the scientific literature. The analysis shows that many design methods yield a similar result of implicitly suggesting a 1st modal damping ratio of about 20%. The same methodology is also adopted to show that the contribution of higher modes is generally negligible in designing a supplemental damping system and that the required damping level can be typically obtained with a limited number of supplemental devices.     

桥梁风洞试验模态参数识别的随机子空间方法

模态参数识别是桥梁风洞试验中的一项重要内容,发展了基于参考点、无需输出协方差估计的识别振动系统模态参数的随机子空间方法,其识别精度和可靠性通过数值算例验证。对状态空间理论中的稳定图作了全面的阐释。根据苏通大桥和苏拉马都大桥主梁三自由度节段模型风洞试验采集到的位移信号,采用随机子空间方法识别了侧弯、竖弯和扭转模态频率和阻尼比,并且与随机搜索方法识别结果进行对比。分析结果表明,随机子空间方法和随机搜索方法识别结果非常吻合,本文发展的随机子空间方法是识别风洞试验桥梁模态参数的一种有效和实用方法。     

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.     

双协调自由界面模态综合方法在框架结构上的应用研究

本文研究双协调自由界面模态综合方法,并将其运用于土木工程结构中。首先介绍了双协调自由界面模态综合方法的基本思路和公式推导,进而提出了相应的模态截取准则。最后,通过一个11层的框架结构进行数值模拟。数值模拟分析结果验证了双协调自由界面模态综合方法在土木工程结构上应用的可行性,进一步通过算例对比,证明了本文提出的双协调自由界面模态综合方法的模态截取准则的正确性,为今后大型结构子结构研究方法提供了必要的理论基础。     

Modal interactions in resonant metamaterial slabs with losses

Modal phenomena in planar metamaterial structures modeled by simple scalar frequency-dependent constitutive parameters are investigated. Modal interactions and modal transformations are found in frequency ranges close to the medium resonances when material losses are introduced and their level is continuously varied through certain critical values. Numerical results for TE and TM modes of a grounded metamaterial slab are reported in the form of dispersion curves and pole loci in the complex wavenumber plane for both surface- and leaky-wave propagation regimes. Useful insights into the reported results are provided through the identification of the branch-point singularities in the complex frequency plane that govern the modal interactions.     

土木结构中的附加黏滞阻尼器:基于阻尼比模式评估的设计方法分析

为减少土木工程结构中的振动,设置附加黏滞阻尼器。阻尼器的设计方法经常留下悬而未解的问题:结构的固有阻尼,附加黏滞阻尼器所能达到的阻尼程度。从这些问题出发,基于动力系统状态矢量空间的表示方法,提出计算非经典及非比例阻尼方案阻尼比的方法论。根据所提出的方法论,对文献中一系列附加黏滞阻尼器系统设计方法进行分析。分析显示,很多设计方法给出了第一模式阻尼比大约为20%的类似结果。采用该方法论同时显示,在设计黏滞阻尼器系统时,较高模式的贡献一般可忽略不计;随着对附加装置个数的限定,能够获得所需的阻尼程度。     

结构运营模态测-辨相和理论

运营模态是表征实际工程结构动力特性的重要参数。从结构动力学基本理论出发,阐释了振动测试与模态识别的动力学互馈本质,指出传统模态测试精度不高的根本原因在于两者的割裂操作,提出“振动测试正向服务模态辨识、模态辨识逆向指导振动测试”的动力学统一范畴,建立了结构运营模态测 辨相和理论,给出由响应强度、识别误差和重构精度三大系列评价准则构成的理论体系框架,以健康监测基准模型模拟数据和某大跨径桥梁实测数据为例,共同印证该理论可有效解决以往振动测试的盲目性和模态识别的被动性。文末,总结并展望了结构运营模态测 辨相和理论的发展趋势。     

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.     

高灵敏度温度自补偿型光纤光栅加速度传感器设计

光纤光栅传感技术近年来越来越多地被应用于土木工程领域,并逐渐显现出了其优势,但对结构振动的测试,尚缺少较为成熟可靠的光纤光栅加速度传感器.提出一种新型的光纤光栅加速度传感器设计方案,其具有高灵敏度和温度自补偿的特性,能够满足结构测试中低频、微幅振动,并克服温度的影响.介绍了传感器的原理,及进行的参数优化,在保证量程和量测频率范围的前提下使灵敏度达到了最大;还对所设计的传感器进行了有限元分析,得到了其幅频、相频、灵敏度、线性度等特性,有限元计算结果和理论优化值相符合.     

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.     

A modal-based Kalman filtering framework for mode extraction and decomposition of damped structures

The mode shape is one of the important modal parameters that enables to visualize the intrinsic behavior of a structure as well as the quantity of interest by extracting or separating modal response from measurements. In this study, a new output-only framework is proposed to extract modes using a modal-based Kalman filter defined in the modal space and identify the mode shape by manipulating the correlation between the separated modes and the measured responses. It is also shown that the proposed framework can be extended to estimate the mode shapes of a non-classically damped structure in state space when the state variable is constructed from the measured responses and applied to the modal-based Kalman filter. The mode shape estimation framework proposed in this study was verified by numerical simulations and full-scale measurements. From the verification examples and their results, it was noted that the proposed modal identification framework is not influenced by the presence of noise, and it can be applied to identify the state-space mode shapes of non-classically damped systems as well as systems with very closely distributed modes such as buildings equipped with tuned mass dampers.