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.     

基于灵敏度分析的机械系统损伤识别方法

提出了一种基于振动灵敏度分析的机械系统损伤识别方法。该方法同时考虑了固有频率灵敏度和固有模态灵敏度 ,既可用于损伤定位 ,也能用于确定损伤大小 ,且对单个损伤和多个损伤情况都适用。为了提高识别的精度 ,考虑了二阶灵敏度。针对工程实际的需要 ,分析了不完备模态和模态测量误差对该方法识别精度的影响。算例表明 :本方法合理可靠 ,具有足够的精度。     

利用电场与磁场耦合制备微型化频率选择表面

利用感性表面(金属栅格)与容性表面(间隔的金属环形贴片)之间的耦合机制制备了微型频率选择表面(MEF-SS).依据传输线理论给出电感、电容近似公式,定性分析了MEFSS结构参数,采用全波分析矢量模匹配法计算了不同几何结构参数与耦合层电参数MEFSS的传输特性.通过镀膜与光刻法在500 μm厚聚酰亚胺膜两侧以矩形排列方式...     

Operational modal analysis in the presence of harmonic excitations by the use of transmissibility measurements

Operational modal analysis (OMA) is based on the assumption that the forces on the structure are the result of a stochastic process, so being white noise. In practice, however, structural vibrations observed in operation cannot always be considered as pure white-noise excitation. In many mechanical structures the loading forces are often more complex and even harmonic components can be present in the response. This is especially true, when measuring on mechanical structures containing rotating parts (e.g. cars, turbines, windmills), but also civil engineering structures may have responses superimposed by harmonic components. OMA procedures are, strictly speaking, not applicable in these situations. Current techniques may encounter difficulties to correctly identify the modal parameters, especially for modes with eigenfrequencies close to the harmonic frequencies. In this paper a recently proposed OMA technique based on transmissibility measurements will be applied. This method reduces the risk to wrongly identify the modal parameters due to the presence of harmonics. The unknown operational forces can be arbitrary (coloured noise, swept sine, impact, etc.) as long as they are persistently exciting in the frequency band of interest.     

基于模态参数计算边界条件的方法

提出了一种计算结构边界支撑刚度的新方法。该方法以结构的实测模态参数为基础,利用结构在无支撑条件下低阶固有频率为零这一特点,通过逆推计算来确定结构的边界支撑刚度。该方法也可用来预测边界条件改变时固有频率和固有振型的变化规律。通过两个理论实例对该方法进行了解释和验证,计算结果表明,该方法是正确的和有效的。该方法已成功地应用于印刷机边界支撑刚度的识别,并发现了印刷机安装过程中的支撑不对称性。     

一种结构损伤评估的两阶段法研究

结构损伤会引起结构动力特性的改变,这种改变可以用模态参数和结构参数表示。文中将柔度投影法和遗传算法相结合,提出一种基于不完整模态数据的结构损伤定位和定量评估的两阶段法。第一阶段,用柔度投影法进行损伤定位,并进行深入分析。第二阶段,用遗传算法确定损伤程度。文中提出一种用于遗传搜索的新的目标函数形式。最后,用一六跨平面桁架桥模型进行数值模拟,验证文中所提方法的有效性。     

On the modal curve of nonlinear normal modes

In a nonlinear holonomic conservative system having two-degree-of-freedom, the modal curves of normal mode vibrations are investigated investimgated by the harmonic balance method. The general procedure to compute the modal curve is suggested. Even if the linearized frequencies of the system are satisfied with the commensurability condition under which the approaches using the perturbation method have the problem of small divisor, the modal curve can be obtained by this method, provided that the fundamental harmonics are dominant when the normal modes are expanded in Fourier series in time domain. As an example, in a system with cubic nonlinearity the modal curves are computed analytically and numerically to compare both results.     

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.     

DYNAMIC FINITE ELEMENT MODEL UPDATING BASED ON GLOBAL INFORMATION OF STRUCTURES

Finite element model updating method based on global information is proposed. Prior investigation upon design space of structural parameters is performed before updating using statistic analysis, including parameter screening using variance analysis and response surface fitting using regression analysis. The parameter screening method selects the design parameters considering the result of hypothesis testing, which is a kind of global information. Meanwhile, the traditional updating method considers local sensitivity which only gives the information at sole point in the design space. Response surface fitting constructs a close-form multinomial which describes the relationship between concerned structural feature and selected updating parameters. It is an approximation to finite element models(FEM) and used as a substitution in the updating iterations. The presented updating method can be applied without the restriction of linear assumption. In addition, there is no data exchange between the updating prog     

TUNING OF NORMAL MODES BY MULTI-AXIAL BASE EXCITATION

Normal mode testing is commonly performed on large aerospace structures in order to identify their eigenfrequencies, mode shapes, modal damping values, and generalized masses. Normally, multiple-point sinusoidal excitation is applied. For each normal mode, the exciter configuration is adapted in location and magnitude in order to compensate for the internal damping forces of the test structure. An alternative to multiple-point excitation is a driven-base test using a multi-axial shaker table. Multi-axis shaker facilities have been developed for structural dynamic qualification. However, they can be used for normal mode testing as well, whereby the overall structure is accelerated in space in order to compensate for the internal damping forces. This requires a suitable combination of all six spatial dof of the base excitation. In the case of resonance, the structure responds in quadrature related to the base excitation. If this criterion is fulfilled, the structure vibrates in an eigenmode of vibration in the sense of a sdof system. This article gives the theoretical background of the test method with particular emphasis on the damping estimation, on the determination of the generalized mass, and on finding a suitable base axis combination. A suitable test rig for the normal mode testing by base excitation, DLR's Multi-Axis Vibration Simulator (MAVIS) in Göttingen (FRG), is presented. The test procedure and test data evaluation as applied to a test structure characterized by closely spaced eigenfrequencies is presented. The advantages and disadvantages of normal mode testing by means of base excitation are pointed out.     

DAMAGE IDENTIFICATION USING CHANGES OF EIGENFREQUENCIES AND MODE SHAPES

In the present paper, we describe an approach to identify the location and the extent of the damage introduced into the steel frame, using a two-step procedure. In the first step, the measured dynamic response of the original undamaged structure was used to generate a reference finite element (FE) model of the structure. The selected parameters were identified by means of a mathematical optimisation algorithm (‘updating procedure'), minimising an objective function containing the test/analyses differences of eigenfrequencies and mode shapes. The uncertain model parameters had to be chosen with care in order to retain the physical significance of the updated model. In the next step, the experimental modal data of the damaged structure were used to identify the extent of the damages. This was based on comparing the changes of stiffness parameters identified from the undamaged and the damaged structure. With the identified parameters, the FE model was able to reproduce the experimental data as close as possible and allowed the identification of the extent of the damage.     

DAMAGE ASSESSMENT USING VIBRATION ANALYSIS ON THE Z24-BRIDGE

Vibration monitoring is a useful evaluation tool in the development of a non-destructive damage-identification technique, and relies on the fact that occurrence of damage in a structural system leads to changes in its dynamic properties. It can give global information of a structure, and the location of the damage has not to be known in advance. The damage-identification technique is based on the observed shifts in eigenfrequencies and modeshapes and relate the dynamic characteristics to a damage pattern of the structure. The presented technique makes use of the calculation of modal bending moments and curvatures to derive the bending stiffness at each location. The basic assumption is that damage can be directly related to a decrease of stiffness in the structure. Damage-assessment techniques are validated on the progressively damaged prestressed concrete bridge Z24 in Switzerland, tested in the framework of the Brite Euram project SIMCES. A series of full modal surveys are carried out on the bridge before and after applying a number of damage scenarios.     

GLOBAL DAMAGE IDENTIFICATION OF THE ‘STEELQUAKE’ STRUCTURE USING MODAL DATA

This paper deals with the important question of structural safety after extreme loadings like an earthquake. The structure investigated here is the so-called ‘Steelquake’ benchmark structure, a two-storey building which was subjected by an artificial seismic loading causing cracks at three locations. The aim of the method is the identification of multiple damage. It is based on the changes of the measured eigenfrequencies and normal modes before and after the pseudo-seismic event. The measured changes of the modal quantities and the physical structural changes are linked together by means of a computational model. This leads to an inverse problem. Four different model-based approaches are discussed and applied to the benchmark structure. The ability of these approaches to find the damage is investigated and it is shown that all three cracks could be identified.     

不确定性参数识别的模态区间逆响应面法

结合模态区间分析及响应面的相关理论,提出一种新的不确定性参数识别方法,即模态区间逆响应面法。首先,以有界区间数来量化结构参数的不确定性,通过合理的实验设计确定样本数据;然后,以响应为输入,设计参数为输出,采用逐步回归分析构造设计参数与结构响应的模态区间逆响应面模型,进而直接在模态区间逆响应面模型上进行模态区间运算,即可识别材料参数的变异性区间;最后,采用一组钢板模态实验来验证所提方法的可行性及可靠性。结果表明:所提方法可准确识别钢板材料参数的取值区间,有效地解决多重变量区间运算存在的区间过估计问题,识别过程避免区间迭代优化,具有较高的计算效率。     

基于响应曲面法的液力透平叶轮多目标优化设计

建立了基于试验设计理论和响应面近似的液力透平叶轮的优化设计方法。以最高效率、高效区范围及转轮所得扭矩-流量曲线在小流量区的稳定性为目标函数。在使用CFturbo软件建立液力透平叶轮的参数化模型后,先用Plackett-Burman试验设计筛选结构参数,并根据结构参数对目标函数的影响将其划分为三个等级:显著因素、次显著因素和不显著因素;再用正交试验法确定次显著因素的设计中心点;最后由中心复合和Box-Behnken设计及响应面分析确定各级结构参数的最优设计点。该方法以计算流体力学(CFD)的计算结果为基础,共进行40次试验,构造了液力透平叶轮的结构参数与多目标函数的响应面近似模型,分析了结构参数间的交互效应。对最优设计点的液力透平进行了实验研究,试验结果及CFD计算值与响应面近似值吻合,且较优化前的模型在性能上有明显改善,表明基于试验设计和响应面的优化设计方法可用于液力透平叶轮的优化设计。     

固支梁振型与损伤关系的试验模态分析

结构的动力特性和结构参数直接相关,结构的损伤将引起相应动力特性的改变。因此,如果能建立结构动力特性变化与结构损伤之间的映射关系,则可以利用结构振动测试信息实现结构损伤识别。按照采用数据和识别原理的不同,大致可以分为基于频率的方法、基于振型的方法、基于模态柔度的方法以及基于神经网络的方法等,但是在大型土木工程结构的测试中,一般只能获得低阶模态及不完备的自由度测试信息。     

加工中心关键部件的动态特性分析

可分度车削头是加工中心的关键部件,它的动态特性好坏直接影响到机床的加工精度和表面粗糙度.以车削头为研究对象,利用Solidworks实体建模,借助有限元分析软件ANSYS进行模态分析,并采用现有的高精度信号采集仪和测试分析软件进行模态试验.对比这两种不同的模态分析结果,找出了该关键部件的薄弱环节.结合对车削主轴动刚度的测试,为提高机床的动态性能和结构优化提供了有效依据.     

基于曲率模态与柔度曲率的损伤识别

以含两条裂纹的两端固定梁为例,采用曲率模态差和模态柔度曲率差来检测结构的损伤。首先将梁的裂纹模拟为无质量的等效扭转弹簧,推导了裂纹梁的特征微分方程,利用边界条件和裂纹位置的连续性条件推导得到该裂纹梁的振形函数解析表达式。然后用中心差分法分别求解裂纹梁损伤前后的曲率模态值和模态柔度曲率值,利用其差值确定梁的损伤位置,进而确定损伤程度。最后讨论了曲率模态和柔度曲率对结构损伤识别的敏感性。     

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.     

短样本密集模态数据高精度识别方法的研究

运用现代控制理论识别结构的动力学参数有频域法和时域法两类。本文综合两类方法的特点,提出“时域—频域”综合识别模式以提高具宽频宽、密集模态特征结构的参数识别精度和置信度。文中论述了“时域—频域”识别模式的基本思想和数学原理,并给出了工程应用实例。