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.     

Harmonics elimination algorithm for operational modal analysis using random decrement technique

Operational modal analysis (OMA) extracts modal parameters of a structure using their output response, during operation in general. OMA, when applied to mechanical engineering structures is often faced with the problem of harmonics present in the output response, and can cause erroneous modal extraction. This paper demonstrates for the first time that the random decrement (RD) method can be efficiently employed to eliminate the harmonics from the randomdec signatures. Further, the research work shows effective elimination of large amplitude harmonics also by proposing inclusion of additional random excitation. This obviously need not be recorded for analysis, as is the case with any other OMA method. The free decays obtained from RD have been used for system modal identification using eigen-system realization algorithm (ERA). The proposed harmonic elimination method has an advantage over previous methods in that it does not require the harmonic frequencies to be known and can be used for multiple harmonics, including periodic signals. The theory behind harmonic elimination is first developed and validated. The effectiveness of the method is demonstrated through a simulated study and then by experimental studies on a beam and a more complex F-shape structure, which resembles in shape to the skeleton of a drilling or milling machine tool. Cases with presence of single and multiple harmonics in the response are considered.     

Influence of a harmonic in the response on randomdec signature

Operational Modal Analysis (OMA) extracts modal parameters of a structure using their output response, during operation in general. OMA, when applied to mechanical engineering structures is often faced with the problem of harmonics present in the output response, and can cause erroneous modal extraction. The random decrement (RD) method of OMA helps extract randomdec signature data that can be further processed to obtain modal parameters of a structure. This paper for the first time analyses influence of a harmonic in the response on randomdec signature. Fundamental equations based on probability are derived for analyzing the influence of a harmonic on randomdec signature. These probabilistic equations are then used to predict the amplitude of the harmonic in randomdec signature. Randomdec signature of a pure harmonic signal is also derived and it is shown that it is of the same frequency as that of the harmonic signal, but has an amplitude equal to the trigger level used to find the randomdec.Based on the developed theory, new insights into the influence of harmonic on randomdec are presented based on an example. It is shown that the influence of the harmonic on randomdec is characterized by the conditional probability density function of the harmonic. It is found that more unsymmetrical is this PDF, more is the amplitude of the harmonic that is present in the randomdec signature. The amplitude of the harmonic in the randomdec is shown to be the conditional expected value of the harmonic. It is also shown that as the random component of the response increases then the amplitude of the harmonic in the randomdec decreases and in the limit can be completely eliminated.     

ARMAX modal parameter identification in the presence of unmeasured excitation—II: Numerical and experimental verification

The performance of an autoregressive moving average with exogenous excitation (ARMAX) time-domain parameter estimation algorithm is assessed using data simulating the response of a two degree-of-freedom system and also experimental data obtained from a cantilever aluminium beam. The algorithm is aimed at identifying modal parameters in the presence of significant measurement noise and unmeasured sources of periodic and random excitation. The simulated system exhibits lightly damped modes and is excited with measured random excitation as well as unmeasured random and periodic excitation. A second case is considered where the modal frequencies of the simulated system are separated by 0.345 Hz and the frequency of an unmeasured periodic excitation is 0.257 Hz below the first modal frequency. Electrodynamic shakers as well as piezoceramic plates are used to apply multiple independent excitation forces, including measured random noise and also unmeasured random and periodic signals. Successful identification of modal parameters is achieved in the presence of up to 10% random measurement noise, as well as over 200% unmeasured periodic and random excitations. Results showed that the ARMAX algorithm achieved better results than ARX models estimated from experimental data corrupted by the effects of unmeasured excitations. The use of piezoceramic plates for structural excitation was demonstrated in experiments and the ability to excite modes was observed to be dependent on the deflection of a particular mode in the contact area of the piezoceramic plates.     

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.     

基于贝叶斯运行模态分析法的砂轮架动态特性分析

为了研究砂轮架的固有模态和在工作环境中的谐波模态,运用贝叶斯理论和运行模态分析相结合的模态参数识别技术--分步测试的贝叶斯运行模态分析法对环境状态下的砂轮架进行模态识别,获得了结构的动态特性,包括固有频率、振型以及阻尼特性等,并对外激励和预测误差水平以及信噪比进行了评估;将该模态识别结果与传统试验模态分析结果进行对比,验证了贝叶斯运行模态分析法的应用可行性;进一步在工作环境下对砂轮架进行了振动测试,对比开机前的模态识别结果和开机后砂轮架的功率谱密度图,成功地区分出砂轮架的固有模态和实际工作环境中由结构周期激励引起的谐波模态。     

影响汽车振动特性的几个参数研究

建立汽车制动时的4自由度动力学模型,并利用仿真方法研究汽车动态特性.研究表明,即使当路面为简谐的情形,车身与轮子的振动均为非简谐的,甚至不是周期的.汽车的结构参数对其整车的振动影响是剧烈、不同和复杂的,合理选择有关结构参数,如距离l1、悬架弹簧刚度等,可以使车身的振动很小.道路表面的波长也会影响汽车的振动且扮演着变频激励的作用.     

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。     

基于伪频响函数矩阵法的运行模态分析方法

基于传递率测量的伪频响函数法运行模态分析技术无需白噪声激励假设,具有强"谐波模态抑制"能力,但其模态识别结果依赖待分析伪频响函数的选取、稳定性欠佳。为解决该问题,建立了基于伪频响函数矩阵法的运行模态分析方法。该方法首先构造多参考测点、多参考工况的伪频响函数矩阵,然后基于伪频响函数矩阵采用最小二乘复频域法求解模态频率和阻尼比、基于传递率函数矩阵求解模态振型,最后通过建立相应的稳态图并结合以多参考测点平均的传递率函数矩阵第2阶奇异值的倒数为基础的模态指示函数来确定模态阶数与最终的模态结果。5自由度质量-弹簧-阻尼系统仿真结果及自由梁的运行模态试验结果均表明,提出方法既继承了基于伪频响函数法的运行模态分析方法的强"谐波模态抑制"能力,亦能有效解决伪频响函数法识别结果稳定性欠佳的问题、一定程度上提高模态识别精度,且更利于自动化。     

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.     

ARMAX modal parameter identification in the presence of unmeasured excitation—I: Theoretical background

This study investigates the performance of a time-domain parameter estimation algorithm aimed at identifying modal parameters from excitation and response data corrupted with significant measurement noise and unmeasured sources of periodic and random excitation. The parameters of an autoregressive moving average with exogenous excitation (ARMAX) model are estimated using an iterative multistage estimation algorithm. The use of backwards autoregressive with exogenous excitation (ARX) models in the multistage algorithm allows vibrational modes to be distinguished from spurious numerical poles and is also the basis of a model selection criterion. A diagonal parameterisation of the autoregressive (AR) polynomial matrices allows the MIMO ARMAX model to be separated into a number of MISO systems, and permits simple manipulation and stabilisation of the estimated model. Measurement noise and sources of unmeasured random and periodic excitations are accounted for by the ARMAX model structure. In this paper, the theory and algorithm of the ARMAX model is given.     

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.     

THE EXTENDED KALMAN FILTER IN THE FREQUENCY DOMAIN FOR THE IDENTIFICATION OF MECHANICAL STRUCTURES EXCITED BY SINUSOIDAL MULTIPLE INPUTS

A modal parameter identification method applied to mechanical structures excited by correlated sinusoidal multiple inputs was developed. The algorithm is based on the same formulation of the extended Kalman filter, applied as a system parameter identifier in the frequency domain to mechanical structures subject to excitations characterised by an inherently high degree of correlation. The algorithm was validated by using simulated data on a multi-degree-of-freedom system. The tests demonstrate that the proposed technique is of practical application value. The method is devoted to the identification of the modal parameters of supporting structures of rotating machinery, using data obtained during the normal operation of the machines. Nonetheless, it can have an interest for more general applications in the field of the experimental modal analysis. This study was undertaken in the framework of the BRITE EURAM III project MODIAROT (MOdel based DIAgnosis of ROTors in power plants).     

大型空间柔性桁架结构模态实验研究

提出杆系结构的内力脉冲激振法,克服了宽带随机激振法能量分散不易激起各阶模态以及正弦激励慢的缺点,并用半正弦冲击波形完成了大型空间柔性桁架结构的模态实验,得到了系统的固有频率和模态振型。实验结果与理论计算结果非常吻合,验证了理论计算方法的正确性。实验结果表明采用内力脉冲激振的方法能够有效地激起结构的固有频率。实验所得振动参数可为下一步空间柔性桁架结构振动主动控制提供直接依据。     

Environmental effects on the identified natural frequencies of the Dowling Hall Footbridge

Continuous monitoring of structural vibrations is becoming increasingly common as sensors and data acquisition systems become more affordable, and as system and damage identification methods develop. In vibration-based structural health monitoring, the dynamic modal parameters of a structure are usually used as damage-sensitive features. The modal parameters are often sensitive to changing environmental conditions such as temperature, humidity, or excitation amplitude. Environmental conditions can have as large an effect on the modal parameters as significant structural damage, so these effects should be accounted for before applying damage identification methods. This paper presents results from a continuous monitoring system installed on the Dowling Hall Footbridge on the campus of Tufts University. Significant variability in the identified natural frequencies is observed; these changes in natural frequency are strongly correlated with temperature. Several nonlinear models are proposed to represent the relationship between the identified natural frequencies and measured temperatures. The final model is then validated using independent sets of measured data. Finally, confidence intervals are estimated for the identified natural frequencies as a function of temperature. The ratio of observed outliers to the expected rate of outliers based on the confidence level can be used as a damage detection index.     

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.     

短时脉冲激励下隧道振动响应与模态参数识别

为了研究短时脉冲激振力下隧道结构振动响应及有效地提取隧道结构的模态特征。首先分析了锤击作用下的不同短时脉冲激振力精度及其频域特性,其次将短时脉冲激振力应用于上海地铁12号某盾构隧道进行了现场动力测试,最后分析了脉冲激振与隧道结构响应之间的传递函数,并结合随机减量、正交多项式法及自回归滑动平均模型法有效地提取隧道结构的模态参数。结果表明:短时脉冲激振力的中低频振动信号在隧道结构中传递特性较好,传递距离较远。隧道结构的模态频率呈现明显低频特征,前10阶模态频率在100 Hz以下。因此,短时脉冲激振力能够很好地应用于隧道动力测试及模态识别,可为基于模态特征的隧道结构损伤识别及健康监测多个研究领域提供有效的支撑和参考依据。     

Modal parameter identification in atmospheric turbulence excitation flutter test based on Hilbert-Huang transform

In flutter tests, particularly in wind tunnel experiments, the aircraft model is generally excited by atmospheric turbulence, which increases the difficulty in precisely identifying the modal parameters. To estimate the modal parameters under turbulence excitation for flutter boundary prediction, a technique was developed and evaluated depending on the Hilbert-Huang transform in this paper. The results of simulated flutter cases show that the developed technique can identify modal frequencies more precisely than the modal damping ratio, while the estimation of the modal damping ratio is quite good. Finally, in a wind tunnel flutter test, good flutter boundaries were predicted in advance by using the modal parameters identified from the turbulence response at low airspeeds.

     

发电机定子线棒振动故障诊断

利用锤击激振法进行了线棒结构动特性测试,进行了线棒二倍频的振动故障诊断。线棒重新绑扎后,其结构特性得到了很好的改善。实验表明,对大修过程中处理的线棒进行二倍频的振动故障诊断具有非常重要的意义。