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.     

Modal parameter identification of stay cables from output-only measurements

Stay cables are one of the most critical structural components in modern cable-stayed bridges and the cable tension plays an important role in the construction, control and monitoring of cable-stayed bridges. We propose a time domain and a time-frequency domain approaches for modal parameter identification of stay cables using output-only measurements. The time domain approach uses the subspace algorithm which is improved with a new modal coherence indicator. The time-frequency approach uses the wavelet transform of signals which is improved with a new analyzing wavelet. The wavelet transform is applied to the free response of ambient vibration which is obtained using the random decrement technique. Two experiments of stay cables are presented. The first experiment concerns a stay cable in laboratory where the external load is applied through an impact hammer and the vibratory signals are acquired through four accelerometers. The second experiment concerns the Jinma cable-stayed bridge that connects Guangzhou and Zhaoqing in China. It is a single tower, double row cable-stayed bridge supported by 112 stay cables. Ambient vibration of each stay cable is carried out using accelerometers. From output-only measurements, the modal parameters of stay cables are extracted. Once the eigenfrequencies and the damping coefficients are obtained, the cable forces and the Scruton number are derived. In a continuous monitoring and modal analysis process, the tension forces and Scruton numbers could be used to assess the health of stay cables in cable-stayed bridges.     

The inception of OMA in the development of modal testing technology for wind turbines

Wind turbines are immense, flexible structures with aerodynamic forces acting on the rotating blades at harmonics of the turbine rotational frequency. These harmonics are comparable to the modal frequencies of the structure. Predicting and experimentally measuring the modal frequencies of wind turbines have been important to their successful design and operation. Performing modal tests on wind turbine structures over 100 m tall is a substantial challenge, which has inspired innovative developments in modal test technology. For wind turbines, a further complication is that the modal frequencies are dependent on the turbine rotation speed. The history and development of a new technique for acquiring the modal parameters using output-only response data, called the Natural Excitation Technique (NExT), will be reviewed, showing historical tests and techniques. The initial attempts at output-only modal testing began in the late 1980s with the development of NExT in the 1990s. NExT was a predecessor to Operational Modal Analysis (OMA), developed to overcome these challenges of testing immense structures excited with natural environmental inputs. We will trace the difficulties and successes of wind turbine modal testing from 1982 to the present.     

Identification of modal parameters from nonstationary ambient vibration data using the channel-expansion technique

The identification of modal parameters from the response data only is studied for structural systems under nonstationary ambient vibration. In a previous paper by the authors, the modal parameters of a system were identified using the correlation method in conjunction with the curve-fitting technique. This was done by working within the assumption that the ambient excitation is a nonstationary white noise in the form of a product model. In the present paper, the Ibrahim time-domain method (ITD) is extended for modal-parameter identification from the nonstationary ambient response data without any additional treatment of converting the original data into the form of free vibration. The ambient responses corresponding to various nonstationary inputs can be approximately expressed as a sum of exponential functions. In effect, the ITD method can be used in conjunction with the channel-expansion technique to identify the major modes of a structural system. To distinguish the structural modes from the non-structural modes, the concept of mode -shape coherence and confidence factor is employed. Numerical simulations, including one example of using the practical excitation data, confirm the validity and robustness of the proposed method for identification of modal parameters from the nonstationary ambient response.     

基于有限元结构动力学模型的塔架振动分析

为深入了解风机塔架的动态特性,并解决运行过程中的塔架振动问题,研究了塔架有限元动力学方程的建模方法,建立了塔架动力学方程; 依据动力学方程,研究了塔架模态的求解方法,得到了塔架基础刚度、塔架质量及塔架刚度对塔架模态的影响趋势,为风机塔架制造、安装过程提供理论参考依据。并依据动力学方程,研究了塔架动力学相应的求解过程,进而设计了基于塔架激励减缓的多目标变桨控制方法,仿真和风场实验结果表明,此方法可有效减小塔架振动告警,减小风机停机次数,从而提高发电量。     

海上风力机塔架在风波联合作用下的动力响应数值分析

分析海上风力机塔架复杂的外界载荷工况,研究海上风力机圆筒形塔架在随机风载荷和波浪载荷作用下的动力响应数值分析方法。研究作用在圆筒形塔架上的气动力特别是非定常气动力与雷诺数的关系;应用线性波理论来仿真非规则的海浪,分析作用在圆筒形塔架上的波浪载荷,通过坐标变换,将二维线性波理论扩展为三维线性波理论,相应地,将平面的莫里森(MORISON)波浪力系发展成空间力系,建立波浪力的分析计算模型,以适应三维空间的分析和计算;编制非规则线性波浪力分析程序。用有限元数值分析方法,将圆筒形塔架用空间梁单元建模,求解塔架在风波联合作用下的位移、速度、加速度以及应力响应等。针对一台1.5 MW海上风力机塔架动力响应分析的算例表明：为整个海上风力机系统气动弹性分析、风力机塔架振动分析和疲劳寿命分析等提供实用的分析方法。     

USING CROSS—CORRELATION THEORY TO EXTRACT MODAL PARAMETERS IN FREQUENCY—DOMAIN

Conventional modal parameter identifications are usually based on frequency response functions, which require measurements of both the input force and the resulting response. However, in many cases, only response data are available while the actual excitations (such as wind/wave load) are not measurable. Modal parameters estimation must base itself on response-only data. Over the past years, many time-domain modal parameter identification techniques from output-only are proposed. A poly-reference frequency-domain modal identification scheme on response-only is presented. It is based on coupling the cross-correlation theory with conventional frequency-domain modal parameter extraction. An experiment using an airplane model is performed to verify the proposed method.     

Vibration modeling and modification of cutting platform in a harvest combine by means of operational modal analysis (OMA)

Vibration in combine cutting platform causes increase in grain loss, reduction of vehicle lifetime and driver’s comfort, and also affects the machine working precision. In order to determine vibration behavior of a mechanical structure, the model which relates acting forces on the structure with the resulting responses of it plays a significant role. For a great deal of mechanical structures, only response data are measurable while the actual loading conditions are unknown. Therefore, the system identification process will need to build on the output-only data. The use of such processes allows the identification of modal models of structures which are excited by unknown ambient vibration. In this contribution, controlled vibration experiments were conducted on cutting platform of a combine in order to recognize and reduce its vibration problem. A finite element model is constructed representing the vibration behavior of the cutting platform. Also, the frequency domain decomposition (FDD) technique is used to estimate the modal parameters of vibrating structures in operational conditions. Then, the finite element model is successfully updated by comparing the estimated results of the operational modal analysis. It is found that there is a resonance condition around 50 Hz. Then, the mass change strategy is used to estimate the scaling-factor and frequency response function (FRF) matrix. Finally, the resonance condition and subsequently vibration of cutting platform is reduced by the structural modification technique. As a result of this modification, natural frequency of fifth mode shape (50 Hz) of the combine cutting platform is shifted to 48 Hz.     

叶片振动响应的长度分形故障特征提取与诊断

为有效地从风力发电机组的振动响应中获得反映叶片响应的动态特征,将其作为叶片运行状态分析的特征量,依此达到对风力机叶片故障的检测与诊断识别.应用有限元分析方法,建立了300 W风力发电机组的动力学模型,通过计算与试验模态分析,分别获得整机组的固有频率和振型,并比较验证了试验模型的合理性.用锤击法测得叶片正常状态和偏心故障下的振动加速度响应信号,应用非线性动力系统的长度分形维数理论,计算其长度分形维数,并将其作为叶片偏心故障诊断识别的特征量.研究结果表明,该方法能有效识别风力机叶片正常状态和偏心故障状态,及其偏心位置和偏心量大小.     

Damping identification from non-linear random responses using a multi-triggering random decrement technique

The concept of multi-triggering random decrement technique is introduced. Like the single triggering technique, it reduces multi-mode multi-measurement stationary random responses to free decay responses but has the advantage of increasing the apparent number of the resulting free decay time response functions. The maximum number of these free decay responses is equal to the square of the number of random measurements. These free decay responses are then used in a linear time domain modal identification algorithm to extract frequencies, damping factors and mode shapes of a structure under test. The quasi-linear modal approach is used to deal with non-linearities by repeating the linear identification process at different levels of inputs/responses. The procedure is applied to rectangular panels subjected to acoustic random input ranging from 130 to 157 dB. The changes in frequencies and damping factors with input level are reported. This application is part of a sonic fatigue research program.     

内外压分别作用下冷却塔风振系数对比研究

现有冷却塔规范和文献中关于风振系数的研究和取值建议均针对外表面风荷载作用,并认为内压作用下风振系数与外压作用下的数值一致,这无法真实反映冷却塔内压引起的风振效应。为对比研究内、外压分别作用下超大型冷却塔结构的风振特性及风振系数,以国内某在建超规范限值高210m间接空冷塔为研究对象,首先,进行刚体同步测压风洞试验获取内、外表面平均和脉动风荷载;其次,建立塔筒-支柱-环基一体化有限元模型,采用完全瞬态法对超大型冷却塔在内、外压分别作用下的塔筒风振响应和风振系数进行了精细化计算分析,探讨了以塔筒径向位移、子午向轴力、Von Mises应力和环向弯矩4种典型目标响应下的风振系数取值标准,提炼出超大型冷却塔内、外压作用下的一维、二维和三维风振系数分布规律;最后,分别给出了此类超大型冷却塔内、外压作用下风振系数的取值建议和二维拟合公式。主要结论可为此类超大型冷却塔风振系数的精细化取值提供科学依据。     

叶片安装误差引起的不平衡质量对风力机塔架振动的影响

利用ANSYS建立了塔架的柔性体模型,并对其进行了模态分析,同时在考虑叶片安装误差引起的不平衡质量的基础上,利用ADAMS建立了把塔架作为柔性体的风力发电机系统的柔性体模型,研究了风速变化和变桨引起的风力发电机塔架上方各部件重心的变化对塔架振动的影响,得到了基于上述因素综合作用下的振动分析和动载荷分析结果,为塔架的优化设计提供了更准确的依据.     

基于控制方法的风机塔架减振研究

为利用控制方法减小兆瓦级风机运行过程中塔架的振动量,对塔架结构动态特性和塔架激励源动态特性进行了分析研究。以某2 MW机组为例,进行了塔架振动情况评估。基于评估结果,设计了增加气动阻尼的塔架振动控制方法,并进一步设计了直接加阻的主动控制结构,结合振动过大时主动降功率运行手段,实现了塔架振动的控制器干预。在许继WRTS-800和PRDS-600仿真实验平台上进行了仿真验证和等效疲劳载荷计算;在实验风场进行了现场实验,并对实验数据进行了统计分析。研究结果表明,采用该方法,塔架等效疲劳载荷明显减小,主动控制减振效果明显。     

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.     

基于Comsol Multiphysics的海上风力机塔架模态分析

塔架是风力机的主要支撑装置,鉴于海上特殊的工作环境,塔架振动在所难免。以海上3MW风力机塔架为对象,应用有限元分析软件Comsol Multiphysics对其进行模态分析,除了考虑叶轮激励频率的影响外,还要研究波浪频率对塔架的影响,通过求解有限元特征方程,得到前六阶固有频率及振型,确定引起塔架与外部激励共振主要取决于塔架的低阶频率;摆振是风力机塔架的主要振动,造成塔架顶端振幅较大。通过进行模态分析,为塔架设计、安全运行和结构动力学分析提供更可靠的理论依据。     

A framework for blind modal identification using joint approximate diagonalization

In this paper, a second-order statistical method employed in blind source separation (BSS) is adapted for use in modal parameter identification. Modal responses and mode shapes are estimated by the use of second-order blind identification (SOBI) on an expanded and pre-treated dataset. Frequency and damping can be obtained from the modal responses by simple single degree of freedom methods. Using this approach, a class of new non-parametric output-only modal identification algorithms is proposed and examples of its use are provided. It is demonstrated that the proposed methodology provides a novel and robust approach to modal identification. For the example shown, it is deduced that quality of the modal parameters produced by the method is competitive with the state of the art parametric methods.     

Frequency analysis of a tower-cable coupled system

This study considers the prediction of natural frequency to avoid resonance in a wind turbine tower-cable coupled system. An analytical model based on the Rayleigh-Ritz method is proposed to predict the resonance frequency of a wind turbine tower structure supported by four guy cables. To verify the validity of the analytical model, a small tower-cable model is manufactured and tested. The frequency and mode data of the tower model are obtained by modal testing and finite element analysis. The validity of the proposed method is verified through the comparison of the frequency analysis results. Finally, using a parametric study with the analytical model, we identified how the cable tension and cable angle affect the resonance frequency of the wind turbine tower structure. From the analysis results, the tension limit and optimal angle of the cable are identified.     

Damping estimation using free decays and ambient vibration tests

This paper studies the quality of modal damping ratios estimates based on ambient and free vibration tests using both numerical simulations and data collected on large Civil Engineering structures where both tests were performed. The simulated data allowed to study the influence of factors like non-proportional damping or proximity of natural frequencies on the quality of the estimates and also to illustrate the influence of the identification algorithms parameters on the accuracy of the results. The analysis of data collected on a cable-stayed bridge, on the suspended roof of a stadium and on a footbridge permitted to compare the results of both testing approaches in real applications where some factors that cannot be realistically included in the numerical simulations can play an important role. The processing of ambient vibration responses is performed with two output-only identification approaches: frequency domain decomposition and stochastic subspace identification methods. The numerically simulated and the measured free decays were analyzed with a simple method based on filters and fitting of exponential decays and also with the use of subspace models.     

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。