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     

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.     

Identification of modal parameters of a time invariant linear system by continuous wavelet transformation

The applications of wavelet transforms have received significant attentions in many fields. This work proposes a procedure for identifying modal parameters of a linear system using the continuous wavelet transform. The merits of the proposed procedure over the exiting schemes of applying the wavelet transform to system identification for a linear system are in use of the time invariance property and filtering ability of the transform to enhance the efficiency of identifying the modal parameters of a structure from its earthquake responses or free vibration responses. The effectiveness and accuracy of the proposed procedure are validated via numerical simulations. The effects of noise and wavelet function on identifying the modal parameters of the structure are also explored in processing the numerically simulated acceleration responses of a six-story shear building subjected to base excitation. The dynamic characteristics of close modes are accurately determined. Finally, the proposed procedure is adopted to obtain the modal parameters of a three-story non-symmetric steel frame from its measured acceleration responses in a shaking table test. A total of nine modes are identified, including modes with high frequencies and very small amplitude.     

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VMD和LSTM模型的航空液压管路卡箍故障诊断

航空发动机液压管路-卡箍系统中卡箍振动信号具有非线性和非平稳性的特点,难以从卡箍故障信号中准确识别出其故障类型。针对该问题,提出了一种基于变分模态分解(Variational Mode Decomposition,VMD)-长短时记忆(Long Short-Term Memory,LSTM)神经网络模型的智能故障诊断方法。首先,利用遗传算法对VMD的模态分量k值和惩罚因子α进行参数优化;然后,将优化后的VMD对卡箍故障振动信号进行分解处理;最后,将分解后的模态分量输入LSTM网络中进行特征学习,从而实现卡箍故障的识别。实验表明:该方法实现了对卡箍螺栓松动状态、根部断裂状态、衬垫磨损等3种典型故障的精准识别,故障总体识别准确率能够达到98.5%以上,有效地提高了航空液压管路卡箍故障识别的准确率。     

汽车动力总成悬置系统多工况运行模态试验研究

由试验测得发动机启动、怠速和急加速三种典型工况下的振动响应,进行了动力总成悬置系统的运行模态参数识别。采用多参考点最小二乘复频域法,通过试验测得的振动响应获得系统工作振型。由于发动机激励不具备零均值白噪声的特点,运用了多种模态置信度指标进行模态验证,获得了较可信的模态参数。试验结果表明,动力总成悬置系统的运行模态参数与发动机工况有关,对于大阻尼和密集模态的动力总成悬置系统,多工况的运行模态试验可以更准确地识别悬置系统的模态参数。研究结果对悬置元件参数设计具有重要的参考价值。     

基于随机减量技术的模态参数识别方法探讨

大型基础工程结构的特征参数识别通常是通过对环境载荷激励的结构响应进行分析来实现,随机减量(Random Decrement,RD)技术是环境激励下的模态参数识别方法中应用较广的方法。在实际应用中受环境、测量等条件的限制,信号常为含有某些优势频率的非平稳信号,常常导致随机减量技术在识别结构参数尤其是系统阻尼时带来较大误差。为提高随机减量技术在环境激励作用下识别结构参数的准确性,文中从分析随机减量信号频谱中的频率分布特性入手,结合随机减量函数产生的触发条件,给出了一种利用信号频谱的统计特征进行模态参数识别的方法。数值仿真结果表明该函数能准确识别在含有优势频率环境载荷作用下的结构参数。     

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.     

Identification of the beat characteristics and damping ratios of the Hwacheon World Peace Bell using wavelet transform

In this paper, a new measurement technique is proposed to identify the beat characteristics and modal damping ratios of a Korean bell in the casting field. The beat response caused by the mutual interference of mode pair with very close doublet frequency is unique feature of the Korean bell and should be accurately measured in order to quantitatively estimate the bell sound. However, the conventional method based on a filtering concept such as the Fourier transform has difficulty in extracting the beat frequencies and modal damping ratios because the method should individually decompose the measured signal into each mode. The aim of this paper is to propose an effective measurement method to identify the beat frequencies, mode pairs and modal damping ratios using the continuous wavelet transform in a real striking condition. The proposed method is verified with the Hwacheon World Peace Bell cast in the year 2008, which is the largest bell in Korea. In the future, the proposed method can be applicable to the casting field of the Korean bell to effectively estimate its beat characteristics and damping characteristics.     

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.     

基于Hilbert-Huang变换与理想带通滤波器的系统识别

针对经验模态分解存在模态混叠现象,提出基于Hilbert-Huang变换与理想带通滤波器的系统识别方法。该方法利用傅里叶变换得到结构加速度响应频响函数,粗略估计固有频率范围,通过半功率带宽法设计理想带通滤波器,定量化确定通带带宽,使信号在经过滤波器后频域内零相移,同时不改变其幅值谱。结构响应通过指定频带的理想带通滤波器产生若干窄带信号,利用经验模态分解获取结构模态响应,经Hilbert变换构造模态响应解析信号,并通过线性最小二乘拟合提取结构模态参数与物理参数。结果表明:半功率带宽法可实现带通滤波器频带的定量化设计,理想带通滤波器的零相移特点较好契合Hilbert-Huang变换用于系统识别的要求,两者结合可有效地解决模态混叠现象,减少虚假模态,大大提高结构系统识别精度。     

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.     

Identifying joints from measured reflection coefficients in beam-like structures with application to a pipe support

The properties of joints in mechanical systems are notoriously uncertain causing corresponding uncertainty in the systems’ dynamic responses. A piping system is one such example where an accurate knowledge of joint properties is useful for the purposes of structure-borne sound transmission, fatigue considerations and structural health monitoring. This paper presents an inverse technique that is applicable to joint estimation in one-dimensional structures such as a pipe. Measured wave reflection coefficients are used which have several advantages over modal information. First, they characterise just the joint and adjacent pipes and are independent of the rest of the built-up system. Second, they are potentially more sensitive to the joint parameters in question than are modal parameters.The method is illustrated by means of an experimental case study featuring a straight pipe suspended by a cantilevered hanger. The stiffness and inertia of the hanger are accurately identified from measured data at frequencies significantly higher than the fundamental modes of the structure.     

一种模态弱响应且模态密集的参数识别方法

针对运行模态分析中响应信号数据样本较短、模态密集,以及弱响应信号淹没在大噪声中,系统模态难以全部辨识的问题,提出了联合相关函数与传递率识别系统模态参数的方法(联合方法),该方法先应用传递率近似频响函数获取系统弱响应频率特征函数,然后再通过小波变换进行模态识别。运用随机激励下的GARTEUR飞机模型仿真运行状态的输出进行了数值仿真实验。结果表明:相比于多参考最小二乘复频域法,联合方法不仅能提高模态频率的识别精度,而且还能极大地提高阻尼比的识别精度,尤其是传递率对模态密集的弱响应模态识别结果良好。     

振动模态固有频率和阻尼比的EMD识别方法

针对机械系统固有频率和阻尼比的识别问题,提出了基于经验模式分解(EMD)的模态参数识别方法.该方法首先对脉冲激励下机械系统的位移响应进行了EMD分解,确定与该系统的各阶模态对应的固有模式函数(IMF),分别对各阶IMF进行希尔伯特变换以得到各自的瞬时幅值和瞬时相位曲线,并对所得曲线进行线性拟合,最后根据拟合曲线的参数来...     

Modified ERA method for operational modal analysis in the presence of harmonic excitations

Operational modal analysis (OMA) is a procedure which allows to extract modal parameters of structures from measured responses to unknown excitation arising in operation. It is based on the assumption that the input to the structure is stationary white noise. In practice, however, structural vibration observed in operation cannot always be considered as pure white-noise excitation. In many practical cases, vibrations are induced by a combination of white-noise and harmonic excitations. Harmonic excitations in addition to random inputs can occur due to rotating components or fluctuating forces in electric actuators for instance. The usual way to compute modal parameters in the presence of harmonic excitations is to consider harmonically excited frequencies as being virtual eigenfrequencies of the structure. However, if the frequencies of the harmonic inputs are close to an eigenfrequency of the system, OMA procedures fail to identify the modal parameters properly. In this paper a modified ERA method is proposed, which can be applied as an identification procedure to include the effect of purely harmonic vibrations, assuming the harmonic frequencies are known a priori. The efficiency of the proposed approach is evaluated for an experimental example of a pinned–pinned beam structure excited by multi-harmonic loads superposed on random excitation.     

基于ICA和小波变换的滚动轴承故障诊断方法研究

提出了结合独立分量分析(ICA)和小波变换进行滚动轴承故障诊断的方法。在设计的系统平台上,首先对冲击脉冲信号进行预处理,使信号较好地满足独立分量分析的前提条件。然后,应用独立分量快速算法分离故障轴承的冲击脉冲信号,通过小波快速算法完成信号重构,实现滚动轴承故障的识别。实验结果表明,利用独立分量分析方法提取的故障状态特征向量与小波快速算法相结合可以有效、准确地识别滚动轴承的故障信号。     

Rotor crack detection based on high-precision modal parameter identification method and wavelet finite element model

In this paper, a new method based on high-precision modal parameter identification method and wavelet finite element (WFE) model is presented to determine the depth and location of a transverse surface crack in a rotor system. The rotor system is modeled using finite element method of B-spline wavelet on the interval (FEM BSWI), while the crack is equivalent as a weightless rotational spring. Additionally, a novel method based on empirical mode decomposition (EMD) and Laplace wavelet is proposed to acquire modal parameters with high precision, which is implemented to improve the precision of crack identification. By providing the first three natural frequencies, contours for the specified natural frequency are plotted in the same coordinate, and the intersection of the three curves predicts the crack location and size. The experimental results indicate that the proposed method can accurately identify the position and depth of different cracks. The effectiveness and reliability of the proposed method is verified.     

Modal testing of nanocomposite materials through an optimization algorithm

An efficient identification method for modal testing of viscoelastic composite materials is demonstrated in this paper, through the analytical–experimental transfer function method. The procedure for the identification of analytical–experimental transfer functions is carried out using a genetic algorithm (GA) by minimizing the difference between the measured response from tests and the calculated response, which is a function of the modal parameters. The analytical transfer functions provide a sub-structuring process to identify modes, as a function of damped natural frequencies and loss factors of a complex structure and it is insensitive to experimental noise as well as the modal coupling effect. The proposed method is verified with the calculation of the elastic modulus and modal properties of a cantilever steel beam with the FEM and compared with the identification results of the proposed algorithm. The effectiveness of the proposed method is demonstrated by investigating the static and dynamic behavior of epoxy cantilever beam specimens reinforced with silica nanoparticles. Analytical–experimental transfer functions accurately identified the viscoelastic and dynamic response of the studied specimens, while the results indicated that the inclusion of nanosilica particles increased the stiffness of the epoxy network and the damping response of the reinforced specimens is improved.