Unsupervised identification of arbitrarily-damped structures using time-scale independent component analysis: Part I

In this study, a new method is proposed to identify the dynamic parameters of structures with higher accuracy compared to current methods. First, the wavelet-transformed representation of system responses is extracted from measured responses, and then the independent component analysis is used to achieve the modal characteristics. The simulation results of a multi-degree-of-freedom system illustrate that this method is capable of accurately identifying the modal information of lightly- and highly-damped structures. It is represented that continuous wavelet transform, due to its adaptive time-frequency resolution, is more efficient to be incorporated into independent component analysis compared to Short time Fourier transform (STFT). The latter is unable to accurately determine the modal response, especially at higher frequencies, while the proposed method can identify the system with marked accuracy. The efficiency of proposed method is also investigated under additive noise. Results shown that for highly- and lightly- damped system, the proposed method is able to capture the modal parameters especially in higher frequencies of vibration, along with the modal assurance criterion values with satisfactory accuracy, which indicates the robustness of the procedure compared to other available methodologies.     

IDENTIFICATION OF TIME-VARYING MODAL PARAMETERS USING LINEAR TIME-FREQUENCY REPRESENTATION

A new method of parameter identification based on linear time-frequency representation andHilbert transform is proposed to identify modal parameters of linear time-varying systems frommeasured vibration responses. Using Gabor expansion and synthesis theory measured responses arerepresented in the time-frequency domain and modal components are reconstructed by time-frequencyfiltering. The Hilbert transform is applied to obtain time histories of the amplitude and phase angle ofeach modal component, from which time-varying frequencies and damping ratios are identified. The     

基于递归理论的泵站压力管道运行状态监测

为了准确地识别建筑结构的模态参数,提出了一种基于多重信号分类算法（multiple signal classification,简称MUSIC）、经验小波变换（empirical wavelet transform,简称EWT）和同步提取小波变换（synchroextracting transform ,简称SET）的结构模态参数识别方法。首先,通过MUSIC-EWT对实测振动信号进行分解;其次,使用SET对单模态信号进行去噪处理;然后,采用自然环境激励技术（natural excitation technique,简称NExT）得到单模态信号的自由衰减响应;最后,利用Hilbert变换（hilbert transform,简称HT）和曲线拟合获得结构的自振频率和阻尼比。通过三层框架结构的数值模拟验证了该方法的准确性和鲁棒性。利用该方法对台风“达维”作用下广州中信广场的实测加速度数据进行分析,并将估计的结构模态参数和其他识别方法的分析结果进行对比,进一步证明了该方法的准确性和鲁棒性。     

基于递归理论的泵站压力管道运行状态监测

针对不利因素导致的管道运行异常问题,提出一种基于递归理论的泵站管道运行状态监测方法。首先,通过振动传感器提取压力管道关键部位的实测信息,并将同一位置不同方向的数据信息进行融合,得到一组反映结构整体动力特性的综合数据;其次,利用伪近临法与互信息法分别选取相空间重构参数m和τ;最后,绘制并计算代表管道动力特性的递归图及递归量化指标。将该方法应用于景泰川工程二期七泵站管道运行监测,通过设置不同的运行工况进行验证,结果表明：机组开关瞬间与稳定运行工况下,管道结构振动信号的递归图呈现不同模式,递归量化指标-确定性、对角线平均长度L、递归率及递归熵也呈现明显差异,能有效区分管道振动状态。该方法为压力管道的无损动态监测提供了新思路。     

基于小波变换方法的材料小阻尼识别

基于连续小波变换实现了对振动系统的小阻尼识别。该方法基本原理为通过对系统自由衰减响应的小波系数取极大获取小波脊,借助小波脊理论确定系统的各阶模态频率与指数衰减系数iζωni,采取求中值的方法获取衰减稳定段的参数,进而识别出各阶模态阻尼比。与HT法相比,该方法具有较高的稳定性和识别精度,仿真结果表明,无噪声时识别误差为0.023%,30%噪声时识别的最大误差为3.49%,而且研究中发现阻尼识别的误差与信号采样频率相关。进行了LY12材料的阻尼测试试验,根据试验测试数据对阻尼识别的结果,证明了本文方法的有效性。     

Measurements of dynamic properties of a medium span suspension bridge by using the wavelet transforms

The aim of this paper is to show the capabilities of the real-time kinematic (RTK) global positioning network system (GPS) to measure the low-frequency vibration of a medium span suspension bridge. In particular, this paper presents the results of studies conducted on the identification of modal parameters including natural frequencies, damping coefficients and mode shapes of a suspension bridge using ambient excitation loads. A real-time kinematic (RTK) global positioning system (GPS) was designed and installed on the Nottingham Wilford Bridge to provide long-term and real-time measurement of bridge deck movement. An approach to estimate modal parameters, from only output data in the time domain using the wavelet transform, is presented. Displacements responses of the bridge are used in the wavelet transform to identify its dynamic characteristics. The modal properties were extracted using a two-step methodology. In the first step, the random decrement method was used to transform random signals in free vibration responses. Secondly, a wavelets-based technique was used to extract natural frequencies and to determine the mode shapes of the structure. This method was compared with the well-established techniques eigensystem realisation algorithm showing a difference of 1% in the estimated first natural frequency.The efficiency of RTK–GPS was demonstrated in the full-scale measurement. In particular, the results showed that the RTK–GPS data can be used for extracting modal properties from in-service-loads induced low-frequency vibration (<5 Hz) by processing the signal with the wavelets transform.     

Time-frequency characterization of nonlinear normal modes and challenges in nonlinearity identification of dynamical systems

Presented here is a new time-frequency signal processing methodology based on Hilbert-Huang transform (HHT) and a new conjugate-pair decomposition (CPD) method for characterization of nonlinear normal modes and parametric identification of nonlinear multiple-degree-of-freedom dynamical systems. Different from short-time Fourier transform and wavelet transform, HHT uses the apparent time scales revealed by the signal's local maxima and minima to sequentially sift components of different time scales. Because HHT does not use pre-determined basis functions and function orthogonality for component extraction, it provides more accurate time-varying amplitudes and frequencies of extracted components for accurate estimation of system characteristics and nonlinearities. CPD uses adaptive local harmonics and function orthogonality to extract and track time-localized nonlinearity-distorted harmonics without the end effect that destroys the accuracy of HHT at the two data ends. For parametric identification, the method only needs to process one steady-state response (a free undamped modal vibration or a steady-state response to a harmonic excitation) and uses amplitude-dependent dynamic characteristics derived from perturbation analysis to determine the type and order of nonlinearity and system parameters. A nonlinear two-degree-of-freedom system is used to illustrate the concepts and characterization of nonlinear normal modes, vibration localization, and nonlinear modal coupling. Numerical simulations show that the proposed method can provide accurate time-frequency characterization of nonlinear normal modes and parametric identification of nonlinear dynamical systems. Moreover, results show that nonlinear modal coupling makes it impossible to decompose a general nonlinear response of a highly nonlinear system into nonlinear normal modes even if nonlinear normal modes exist in the system.     

MODELLING AND IDENTIFICATION OF THE DYNAMIC RESPONSE OF A SUPPORTED BRIDGE

This paper describes the dynamic tests performed on a simply supported bridge in Northern Italy under traffic excitation. The acceleration data have been used for the identification of the natural frequencies, viscous damping ratios and mode shapes of the bridge. Modal parameters have been extracted using the wavelet estimation technique, previously implemented by the authors of this paper. This work represents the first attempt in using the wavelet estimation technique directly on transient data and not on the impulse response estimates obtained via the random decrement technique. The capability of the wavelet estimation technique for extracting modal parameters from transient time responses has first been inspected by analysing a simulated set of data. The data have been obtained from the analytical continuous model of a three-span supported bridge. The bridge, excited by moving vehicles, has been modelled as a supported orthotropic plate and its response has been evaluated using the convolution technique. The vehicles have been modelled as multi-body systems, with linear suspensions and tyres flexibility, having globally seven degrees of freedom. An iterative procedure to include the dynamic interaction between the bridge and the vehicles has been implemented. The real bridge, 20 m long approximately, has been monitored using six capacitive accelerometers, measuring the accelerations in seven points of its north edge in two points of its south edge. In particular, the accelerometers on the south edge have been kept in fixed positions, acting as reference points. On the north edge, one accelerometer has been kept fixed at the mid-span location, while the remaining three have been positioned in two different set-ups. Each test has been repeated four times. The estimation of the modal parameters has been performed three times, using as reference point each of the fixed accelerometers. The results obtained from each estimation have been evaluated by means of a modal estimation ‘quality index’ introduced within the wavelet estimation technique.     

Identification of modal parameters of unmeasured modes using multiple FRF modal analysis method

Current modal analysis methods seek to identify the modal parameters of some or all of the modes in the measured frequency range of interest. In many applications however, it will be very useful if modal parameters of some of the out-of-range modes can be identified during modal analysis. Such a goal is obviously theoretically possible since the raw measured frequency response functions (FRFs), upon which modal analysis is performed, do contain adequate information about the out-of-range modes in the form of residue contributions. In this paper, a new method for the estimation of modal parameters using multiple FRFs analysis is presented. In the process of modal identification, the proposed method not only presents accurate modal parameters of the modes which are present in the measurement frequency range, but also quite accurately identifies some of the modes which are not measured. The method calculates the required modal parameters by solving eigenvalue problem of an equivalent eigensystem derived from those measured FRF data. All measured FRFs are used simultaneously to construct the equivalent eigensystem matrices from which natural frequencies, damping loss factors and modeshape vectors of interest are solved. Since the identification problem is reduced to an eigenvalue problem of an equivalent system, natural frequencies and damping loss factors identified are consistent. Applications of the method to both numerically simulated and practically measured FRF data are given to demonstrate the practicality of the proposed method and the results have shown the method is capable of accurately identifying modal parameters of out-of-range modes.     

Output-only modal analysis of wind turbine tower based on vibration response under emergency stop

The identification technique of output-only modal parameters is proposed for the large wind turbine tower under emergency stop. Compared with the response of regular operating conditions, the immediate tower structural response under emergency stop much more resembles a state of free vibration, which is more appropriate for the modal identification of the wind turbine tower. The vibration response is measured in the nacelle, which is easy to perform in the field modal test. The variational mode decomposition (VMD) is applied to decompose the vibration response into several band-limited intrinsic mode functions. The free responses of decomposed functions are extracted by applying the random decrement technique (RDT). Finally, the modal damping ratio and natural frequency are identified from each free modal response by using the Hilbert transform method. Simulations and a 1.5 MW wind turbine field modal test results verify the effectiveness of the proposed identification method. The main modal parameters of wind turbine, including weak modes, are effectively extracted by using output-only vibration responses under emergency stop. The modal parameter identification method is provided for the large wind turbine structure under the engineering condition.     

Modal identification of linear non-proportionally damped systems by wavelet transform

A time-frequency identification technique based on wavelet transform is formulated and applied to free-decay responses of linear systems with non-proportional viscous damping. The Cauchy mother wavelet is used. Frequencies, modal damping ratios and complex mode shapes are identified from output-only free vibration signals. This identification technique has also shown to be effective when the (non-proportional) damping is significant.     

基于小波分析的简支梁桥损伤识别

提出了基于小波子带信号能量曲率变化的损伤识别方法。分别对完好和损伤状态下结构的振动响应进行二进离散小波变换,通过信号子带分解与重构将响应分解到不同频带,使叠加的模态响应分离。定义了信号相对能量曲率差损伤指标,利用该指标对结构的损伤进行识别定位。应用此方法对一简支梁桥进行损伤数值分析,结果表明:二进离散小波变换可以对结构振动响应中叠加的多阶模态信息进行有效分离;信号相对能量曲率差指标可以对损伤进行有效识别,且不受激励位置及荷载大小影响。最后通过模型实验验证了该方法的正确性及可行性。     

Online automatic identification of the modal parameters of a long span arch bridge

The “Infante D. Henrique” bridge is a concrete arch bridge, with a span of 280 m that crosses the Douro River, linking the cities of Porto and Gaia located in the North of Portugal. This structure is being monitored by a recently installed dynamic monitoring system that comprises 12 acceleration channels. This paper describes the bridge structure, its dynamic parameters identified with a previously developed ambient vibration test, the installed monitoring equipment and the software that continuously processes the data received from the bridge through an Internet connection. Special emphasis is given to the algorithms that have been developed and implemented to perform the online automatic identification of the structure modal parameters from its measured responses during normal operation. The proposed methodology uses the covariance driven stochastic subspace identification method (SSI-COV), which is then complemented by a new algorithm developed for the automatic analysis of stabilization diagrams. This new tool, based on a hierarchical clustering algorithm, proved to be very efficient on the identification of the bridge first 12 modes. The results achieved during 2 months of observation, which involved the analysis of more than 2500 datasets, are presented in detail. It is demonstrated that with the combination of high-quality equipment and powerful identification algorithms, it is possible to estimate, in an automatic manner, accurate modal parameters for several modes. These can then be used as inputs for damage detection algorithms.     

基于连续小波变换的三自由度链模型模态参数辨识

采用连续小波变换的方法,在大型结构模态参数辨识方面提出了系统化的辨识流程,并对相近的频率所造成的辨识难点提出了解决的办法。通过三自由度模型模态参数的辨识,表明连续小波变换对于大型结构的模态参数辨识准确度高,具有现实意义。     

Structural damage detection with statistical analysis from support excitation

The unit impulse response (UIR) functions obtained from a structure under support excitation are used to identify local structural damages. The extraction of the UIR with the aid of discrete wavelet transform from the measured acceleration is described. The sensitivity matrix of these UIRs is then obtained based on the finite element model and the time-stepping integration method. Based on the computed sensitivity matrix of the UIRs from several accelerometers, a two-step model updating method is adopted for identifying the local damages. Statistical analysis is included into the damage identification procedure with the measurement noise taken as an independent random variable in the measured UIRs. A new damage localization index is proposed and the mean values of the identified parameters are taken as the damage severity. Finally, a nine-bay three-dimensional frame structure is analyzed numerically and experimentally using the proposed technique. The damage scenarios of multiple damages with different levels of noise are considered. The identified results are shown satisfactory, indicating the feasibility and effectiveness of the proposed technique.     

Matrix of the covariance of covariance of acceleration responses for damage detection from ambient vibration measurements

A new matrix on the covariance of covariance is formed from the auto/cross-correlation function of acceleration responses of a structure under white noise ambient excitation. The components of the covariance matrix are proved to be function of the modal parameters (modal frequency, mode shape, and damping parameter) of the structure. Information from all the vibration modes of the structure limited by the sampling frequency contributes to these components. The formulated covariance matrix contains more information on the vibration modes of the structure that cannot be obtained by the general methods for extracting modal parameters. When the component of the covariance matrix is used for damage detection, it is found more sensitive to local stiffness reduction than the first few modal frequencies and mode shapes obtained from ambient excitation. A simply supported 31 bar plane truss structure is studied numerically where a multiple damage scenario with different noise levels is identified with satisfactory results.     

Output-only modal identification based on hierarchical Hough transform

Sparse component analysis (SCA) has been introduced to the output-only modal identification for several years. This paper proposes a new method based on hierarchical Hough transform to extract the modal parameters of mechanical structures. First, the measured system responses are transformed to Time-frequency (TF) domain using Short time Fourier transform (STFT) to get a sparse representation. Then, Hough transform is applied to the TF coefficients hierarchically to identify the hyperplanes and the mixing matrix is calculated. Finally, the modal responses are recovered by using l ₁ -optimization and inverse STFT. From the recovered modal responses, natural frequencies and damping ratios are extracted. Numerical simulation of a 4 Degree-of-freedom (DOF) spring-mass system verifies the validity of the method. Free vibration of a steel cantilever beam is captured by a high-speed camera and then analyzed by the proposed method. The comparison of the estimated natural frequencies and damping ratios illustrates the good performance of the proposed algorithm.     

桥梁颤振导数识别的一种方法

运用系统识别理论识别桥梁颤振气动导数的过程，可分为复模态识别与模成坐标转换为物理坐标两个阶段。文中着重研究坐标转换算法，该算法建立一个带约束的二次泛函，利用惩罚函数法以一定的搜索方向使二次泛函数取得极小值，并同时求得8个气动导数。数字仿真与实验试验结果表明文中方法有效、可行。     

Identification of modal parameters from ambient vibration data using eigensystem realization algorithm with correlation technique

An effective identification method is developed for the determination of modal parameters of a structure based on the measured ambient response data. In this study, modification to Eigensystem Realization Algorithm with Data Correlation is proposed for modalparameter identification of structural systems subjected to stationary white-noise ambient vibration. By setting up a correlation -function matrix of stationary responses, as well as by introducing an appropriate matrix factorization, modal parameters of a system can be identified effectively through singular -value decomposition and eigenvalue analysis. Numerical simulations using practical excitation data confirm the validity and robustness of the proposed method in identifying modal parameters from stationary ambient vibration data under noisy conditions.     

基于小波包样本熵的连续梁桥损伤识别

为了减少现行桥梁检测中所需布置传感器数量,将小波包分解和样本熵有机结合起来,对利用单点动力响应数据检测识别连续梁桥结构损伤的新方法进行了研究,笔者提出了连续梁桥结构的损伤识别指标和方法。利用小波包变换对移动荷载作用下桥梁的加速度响应进行分解和重构,计算重构信号的样本熵值,建立了对数加速度能量差小波包样本熵损伤识别指标;并通过三跨变截面连续梁桥的动力仿真分析,验证了指标和方法的适用性与噪声鲁棒性。研究结果表明,笔者所提出指标和方法仅利用桥上一个测点的加速度响应就能够很好地识别连续梁桥的损伤位置和损伤程度,且对噪声不敏感。