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。     

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.     

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。     

Multi-point vibration measurement and mode magnification of civil structures using video-based motion processing

Image-based vibration measurement has gained increased attentions in civil and construction communities. A recent video-based motion magnification method was developed to measure and visualize small structure motions. This new approach presents a potential for low-cost vibration measurement and mode shape identification. Pilot studies using this approach on simple rigid body structures were reported. Its validity on complex outdoor structures has not been investigated. In this study, a non-contact video-based approach for multi-point vibration measurement and mode magnification is introduced. The proposed approach can output a full-field vibration map that increases the efficiency of the current structural health monitoring (SHM) practice. The multi-point approach is developed based on the local phases which also fill the gap of the existing intensity-based multi-point vibration measurement. As an extension of the phase-based motion magnification, the multi-point measurement result is then integrated with the maximum likelihood estimation (MLE) to estimate the magnified frequency bands at each identified structure mode for operational deflection shape (ODS) visualization. This proposed method was tested in both indoor and outdoor environments for validation. The results show that using the developed method, mode frequencies and mode shapes of multiple points in complex structures can be simultaneously measured. And vibrations in each mode can be visualized separately after magnification.     

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

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

Wavelet-Based Structural Health Monitoring of Earthquake Excited Structures

Abstract:   The article presents a wavelet-based structural health monitoring technique for structures subjected to an earthquake excitation utilizing the instantaneous modal information. The instantaneous mode shape information is first extracted from the vibration response data collected during an earthquake event by using a wavelet packet sifting process. A confidence index (CI) is proposed to validate the results obtained. The identified normalized instantaneous mode shapes in conjunction with the corresponding CIs can be effectively used to monitor damage development in the structure. The effectiveness of the proposed approach is illustrated for two damage scenarios, sudden stiffness loss and progressive stiffness degradation, and different base excitations including three real earthquake signals and a random signal. Consistently good results were obtained in all cases. Issues related to robustness of the method in the presence of a measurement noise and sensitivity to damage severity are discussed.     

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。     

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。     

Structural dynamic parameter identification of Saige building based on distributed synchronous acquisition method

在大型复杂工程结构上进行现场模态测试时，由于结构规模体量大并存在空间隔断，导致数据采集设备与传感器之间快速布设数据传输线困难。因此，有必要解决不同位置分布式同步采集设备时间精确同步问题，研发易于快速安装的分布式数据采集和无线传输设备。为此，提出基于“北斗”卫星授时的结构振动分布式同步采集算法，集成分布式同步采集硬件与研发数据在线采集和无线传输软件，获取大型复杂工程结构不同空间位置时间同步动态响应，基于随机子空间算法自[JP2]动识别工程结构服役状态下真实的模态参数。在赛格大厦振动事件溯源工作中，该系统成功捕捉到5月20日12:00—13:00[JP]结构共振时第69层与桅杆底部的加速度响应，发现四次共振均以频率2.12 Hz振动主导。基于该系统在环境激励条件下的现场模态测试，识别结构前19阶动力学参数，发现频率2.12 Hz是主体结构弯扭耦合和桅杆面内对称振动模态。基于现场激振测试识别频率2.12 Hz对应的阻尼比，发现阻尼比随着振幅的增加突然减小然后逐步增加，较低的阻尼比是导致赛格大厦发生共振的原因之一。     

基于分布式同步采集的赛格大厦结构动力学参数识别

在大型复杂工程结构上进行现场模态测试时,由于结构规模体量大并存在空间隔断,导致数据采集设备与传感器之间快速布设数据传输线困难。因此,有必要解决不同位置分布式同步采集设备时间精确同步问题,研发易于快速安装的分布式数据采集和无线传输设备。为此,提出基于“北斗”卫星授时的结构振动分布式同步采集算法,集成分布式同步采集硬件与研发数据在线采集和无线传输软件,获取大型复杂工程结构不同空间位置时间同步动态响应,基于随机子空间算法自[JP2]动识别工程结构服役状态下真实的模态参数。在赛格大厦振动事件溯源工作中,该系统成功捕捉到5月20日12:00—13:00[JP]结构共振时第69层与桅杆底部的加速度响应,发现四次共振均以频率2.12 Hz振动主导。基于该系统在环境激励条件下的现场模态测试,识别结构前19阶动力学参数,发现频率2.12 Hz是主体结构弯扭耦合和桅杆面内对称振动模态。基于现场激振测试识别频率2.12 Hz对应的阻尼比,发现阻尼比随着振幅的增加突然减小然后逐步增加,较低的阻尼比是导致赛格大厦发生共振的原因之一。     

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。     

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.     

钢结构环形天桥振动特性测试与分析

钢结构环形人行天桥是一种特殊的结构形式。本文以福州市某钢结构环形人行天桥为工程背景,进行了该桥的环境振动和强迫振动试验,利用基于频域法中基于传递率的参数识别方法进行识别与分析人行天桥的动力特性与振动响应。进一步,建立有限元模型对该桥的动力特性进行了理论模态分析,理论计算和实测结果吻合较好,并研究了梁高、墩壁厚参数变化对钢结构环形人行天桥动力特性的影响,为同类结构的振动研究提供参考。此外,建议人行桥舒适度指标允许值参考英国规范BSI,为目前人行天桥所存在的振动问题提出了有益的建议。     

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.     

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

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

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.     

Weighting ensemble least-square method for flutter derivatives of bridge decks

In this paper, a reliable but simple identification method, here called the weighting ensemble least-square method (WELS), has been developed to extract all eight flutter derivatives of bridge deck from free vibration records. For every wind speed, free vibration test of section model is generally repeated several times in order to obtain more reliable parameter estimates. In the WELS method, many free vibration records at the same wind speed are regarded as an ensemble. The common mode parameters are then identified simultaneously from the ensemble data. The parameter fit is obtained by a nonlinear least-square method. Weighting factors are proposed to make each experiment record with the same weight in total residual error analysis. The ensemble composed of many records can reduce the effect of the colored noise of few records on the convergence of least-square iteration process. The flutter derivatives of two section models are identified to indicate the reliability and effectiveness of the WELS method.     

环境激励下房屋建筑的阻尼比识别

阻尼比的准确取值一直是结构动力分析的难点,由于阻尼机理非常复杂,对阻尼比的取值一般通过实测得到。传统的模态参数识别方法需要同时利用激励和响应信号,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识别方法,利用环境激励(如施工机械振动、风、车辆、行人、地脉动等)下的结构振动响应数据,采用随机子空间(Stochastic Subspace Identification)法,有效地识别实际建筑结构的模态参数的方法。工程实例的模态参数识别结果表明,该方法不仅能准确识别出结构的模态频率,还能相对准确地得到结构的模态阻尼比。     

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.     

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.