基于参数模型的频响函数估计方法

针对传统的非参数频响函数估计方法不适用于短记录数据的情况,提出了一种基于公分母模型的参数化频响函数估计方法.该方法使用输入输出信号的快速傅里叶变换(输入输出谱)作为主要数据,通过最小二乘法求解参数,利用奇异熵技术对系统进行定阶.最后采用一个二层框架的仿真算例对所提出的算法进行了验证.仿真算例结果表明,通过响应信号的奇异...     

最佳无偏整体估计方法

提出一种最佳无偏整体估计方法,给出整体参数的估计量及其协方差公式,建立正态分布、Weibull分布和极值分布等位置-尺度分布族的点估计与区间估计。传统的回归分析只适用于正态分布和完全数据,最佳无偏整体估计方法则将回归分析推广到工程中常见的位置-尺度分布族和截尾数据的情况。该方法可以将不同条件(状态)下的试验数据作为一个整体进行统计推断,能够全面开发利用不同条件下试验数据之间的横向信息,使其可利用的信息量远远大于只能分别在各自条件下对试验数据进行处理的传统最佳线性无偏估计方法。最佳无偏整体估计方法对一种条件下只有一个失效数据的情况也能进行分析,传统最佳线性无偏估计方法则要求在一种条件下有较多的失效数据,因此前者具有小样本性质;并且前者的参数估计量是所有条件下顺序统计量的线性函数,后者的参数估计量只是一种条件下顺序统计量的线性函数,所以前者的参数估计量具有更好的正态分布特性。大量Monte Carlo模拟和工程应用表明,在试样数相同的情况下,文中方法比传统方法具有更高的精度,而在精度相同的情况下,则可节省大量试样。     

基于频响函数的稳健有限元模型修正

传统的基于频响函数(frequency response function,简称FRF)的模型修正方法在测试噪声较大、初始分析频响与测试频响残差较大、待修正参数较多等情况下不易收敛,为此提出了一种采用移频技术的极大似然估计有限元模型修正方法。首先,利用"先验"的频响函数方差信息,构造极大似然估计器,迭代求得最优的待修正参数估计;其次,在迭代方程中引入移频方法,采用总体最小二乘平差方法计算方程的解,以提高参数识别的收敛性和稳定性;最后,根据频率点的筛选准则剔除数据,采用一种高精度的频响扩充方法以减小扩充所带来的额外误差。列车转向架构架仿真算例和三角机翼飞机测试模型的修正结果表明,该方法抗噪性较强,在复杂情况下仍可以得到较好的修正结果。     

大型六自由度振动平台的运动控制研究

提出了一种应用于工程机械测试的大型六自由度振动平台.在分析平台姿态解算函数的同时,给出了一种基于EV模型频响函数估计的波形复现算法,该算法实质是频响函数的实时在线修正方法,有利于提高波形复现精度.仿真结果表明:平台姿态解算函数正确,基于EV模型频响函数估计的波形复现算法能够实现平台对输入波形的准确复现,具有较高的控制精度.     

基于频响函数 Neumann 级数展开的有限元模型修正

针对有限元模型修正中测试自由度不完备、求解不适定的问题,提出了一种基于频响函数Neumann级数展开的模型修正方法。首先,利用测试和有限元分析模态数据构造完整的实测频响函数。然后,根据Neumann级数展开式建立实测频响函数与有限元模型频响函数之间的关系式,以此构建模型修正目标函数。最后,采用改进鲸鱼优化算法求解目标函数获取修正结果。通过平面桁架数值算例表明,该方法具有较强的噪声鲁棒性,模型修正精度较好,15%噪声时修正后的平均相对误差不超过1%。利用4层剪力框架结构测试算例进一步验证所提方法,结果表明,修正后的模型能反映结构真实状况。     

线性系统传递函数的无偏估计方法

无论从理论上还是实际应用中， 从被噪声污染的输入输出量测数据中精确地辩识系统的传递函数都是十分重要的。现有的传统辩识对象的传递函数方法， 当输入输出信号存在量测噪声时只能得到真实传递函数的有偏估计。基于有关信号的频谱分析， 提出了两种基于谱函数的传递函数的无偏估计方法，为实际应用提供了理论依据。由于这种无偏估计不依赖于任何噪声的先验知识， 测试方法更具有鲁棒性     

相关小波法在结构系统识别中的应用

对于一个线性结构系统，从输入输出数据中提取精确的脉冲响应函数和频响函数是对系统进行动力学建模和参数识别的关键步骤。在循环小波变换的基础上，研究了提取脉冲响应函数的相关小波法及其相应的平均算法。数值仿真结果表明，对于不同的激励信号，相关小波法都能够获得比FFT方法精度更高的脉冲响应函数和频响函数，具有更大的优越性。利用悬臂梁实验验证了相关小波法在实际结构中的正确性和有效性。     

基于RCSA的深孔内圆磨床主轴端点频响函数预测

基于响应耦合子结构分析法预测了深孔内圆磨床主轴端点的频响函数。首先对磨床主轴进行子结构划分,计算各子结构自由状态下的频响函数矩阵,然后顺序刚性耦合各子结构的频响函数矩阵,对轴承支撑点使用结构修改法修改轴承约束下的已耦合子结构频响函数矩阵,直至耦合到最后一个子结构,得到主轴端点的频响函数。以某深孔内圆磨床为研究对象,分别基于该方法和有限元法,对其主轴端点的频响函数进行预测,并对其进行实验测试。实验及分析结果表明：该方法预测精度高于有限元分析方法预测精度、计算速度快,便于深孔内圆磨床主轴系统的结构优化。     

非整周期采样信号频率估计的相频匹配方法

为提高非整周期采样信号的频率估计精度,提出一种非整周期采样信号频率估计的相频匹配方法。首先,为抑制信号非整周期采样对自相关的影响,对采样信号进行加窗自相关;其次,根据加窗自相关信号初相位为零的特点生成参考信号,实现参考信号与加窗自相关信号的相位匹配;最后,根据柯西不等式,利用参考信号和加窗自相关信号构造反映参考信号和加窗自相关信号频率匹配程度的误差函数,误差函数最小值对应的频率即为信号频率估计值。计算验证和LFMCW雷达测距实验表明该方法不受信号非整周期采样的影响,有效地提高了非整周期采样信号的频率估计精度,改善了LFMCW雷达的测距精度。     

基于RCSA与GA的铣刀刀尖点频响函数预测

基于响应耦合子结构分析法建立了铣刀刀尖点的频响函数预测模型,针对其中主轴—刀柄基座系统频响函数矩阵难以理论计算和实验测试的问题,提出了基于实验模态测试与遗传算法寻优相结合的主轴—刀柄基座系统频响函数矩阵的优化拟合方法。以VMC850E型立式加工中心主轴系统为研究对象,基于上述方法对铣刀刀尖点频响函数进行了预测,并与其实测频响函数进行对比。结果表明:刀尖点的预测频响函数曲线与实测频响函数曲线符合较好,预测频响函数的固有频率与实测固有频率在0~4 000Hz范围内的相对误差小于4.37%。     

A non-parametric approach for linear system identification using principal component analysis

This paper considers the applications of principal component analysis (PCA) for signal-based linear system identification. Linear time-invariant (LTI) single-input-single-output (SISO) and multi-input-multi-output (MIMO) system frequency response function (FRF) estimation problems are formulated on the basis of the eigen-value decomposition (EVD) of the input–output measurement spectral correlation matrix. It is demonstrated that resulting algorithms for the SISO and MIMO cases are equivalent to that of the maximum likelihood (ML) and the total least squares (TLS) approaches respectively. Originating from the proposed FRF estimation scheme, a moving-segment EVD procedure is developed for SISO time-varying transfer function estimation. Based on the sensitivity of the time-domain PCA to delays/shifts between signals, an extended lagged-covariance-matrix approach is introduced for delay detection from time series.     

An experimental investigation on the effects of exponential window and impact force level on harmonic reduction in impact-synchronous modal analysis

A novel method called Impact-synchronous modal analysis (ISMA) was proposed previously which allows modal testing to be performed during operation. This technique focuses on signal processing of the upstream data to provide cleaner Frequency response function (FRF) estimation prior to modal extraction. Two important parameters, i.e., windowing function and impact force level were identified and their effect on the effectiveness of this technique were experimentally investigated. When performing modal testing during running condition, the cyclic loads signals are dominant in the measured response for the entire time history. Exponential window is effectively in minimizing leakage and attenuating signals of non-synchronous running speed, its harmonics and noises to zero at the end of each time record window block. Besides, with the information of the calculated cyclic force, suitable amount of impact force to be applied on the system could be decided prior to performing ISMA. Maximum allowable impact force could be determined from nonlinearity test using coherence function. By applying higher impact forces than the cyclic loads along with an ideal decay rate in ISMA, harmonic reduction is significantly achieved in FRF estimation. Subsequently, the dynamic characteristics of the system are successfully extracted from a cleaner FRF and the results obtained are comparable with Experimental modal analysis (EMA).     

Frequency response function shape-based methods for structural damage localisation

The ultilisation of structural shape signals for damage localisation has shown some promise, especially in the applications where an accurate finite element model of the structure is not available. For this purpose, traditional shape signals, like mode shapes, flexibility matrices, uniform load surface (ULS) and operational deflection shapes (ODS) have been widely used. Using frequency response function (FRF) shapes for structural damage localisation is however, a relatively new but promising technique. Unlike mode shapes, ULS and ODS, FRF shapes are defined on broadband data and so have potential to reveal damage location more clearly. Another advantage of using FRF shapes is that the test data can be directly used without the necessity of conducting modal identification. Nevertheless, some problems associated with this approach still remain to be solved. No solid foundation or deduction about the use of FRF shapes for damage localisation has been given in any literature so far. In addition, it has been observed that this method only works for a low-frequency range. This limitation of FRF shapes has not been explained or well treated so far. In this study, a scheme of using FRF shapes for structural damage localisation is proposed. Methods within this scheme include some important modifications like using the imaginary parts of FRF shapes and normalising FRF shapes before comparison. The theoretical explanation of using FRF shapes for damage localisation is presented and the limitations of the previous FRF shape methods have been overcome. The proposed methods have shown great potential in structural damage localisation.     

Improved (non-)parametric identification of dynamic systems excited by periodic signals

The steady state response of a system to a periodic input is still subject to noise transients. For lightly damped systems these noise transients can significantly increase the variance of the estimated frequency response function (FRF). This paper presents a method that suppresses the influence of the noise transients (leakage errors) in nonparametric FRF and noise (co-)variance estimates of dynamic systems excited by periodic signals. The method is based on a local polynomial approximation of the noise leakage errors on the FRF. Compared with the classical approaches, the proposed procedure is more robust and needs less measurement time (two signal periods are sufficient). The theory is supported by simulation and real measurement examples.     

An average inverse power ratio method for the damping estimation from a frequency response function

The well-known bandwidth method, especially the half-power bandwidth method [1], [3], [4] (Bishop and Gladwell, 1963; Nashif et al., 1985; Yin, 2008) is probably the simplest method for the damping estimation from a frequency response function (FRF). This method is quite efficient for simple model test cases when modes are well separated. However, the determination of the two frequencies corresponding to a given power ratio value requires numerical interpolations of experimental discrete data of frequency response functions. In this paper, an average inverse power ratio method is proposed. The average value is computed at two frequencies symmetrically located from a peak amplitude frequency. Then the damping ratio can be estimated by using a formula similar to that of the bandwidth method. In this way, the damping estimation becomes straightforward from the FRF data. This new method could be useful for engineers in practice due to its extreme simplicity.     

Analysis of swept-sine runs during modal identification

Experimental modal analysis of large aerospace structures in Europe combine nowadays the benefits of the very reliable but time-consuming phase resonance method and the application of phase separation techniques evaluating frequency response functions (FRF). FRFs of a test structure can be determined by a variety of means. Applied excitation signal waveforms include harmonic signals like stepped-sine excitation, periodic signals like multi-sine excitation, transient signals like impulse and swept-sine excitation, and stochastic signals like random. The current article focuses on slow swept-sine excitation which is a good trade-off between magnitude of excitation level needed for large aircraft and testing time. However, recent ground vibration tests (GVTs) brought up that reliable modal data from swept-sine test runs depend on a proper data processing. The article elucidates the strategy of modal analysis based on swept-sine excitation. The standards for the application of slowly swept sinusoids defined by the international organisation for standardisation in ISO 7626 part 2 are critically reviewed. The theoretical background of swept-sine testing is expounded with particular emphasis to the transition through structural resonances. The effect of different standard procedures of data processing like tracking filter, fast Fourier transform (FFT), and data reduction via averaging are investigated with respect to their influence on the FRFs and modal parameters. Particular emphasis is given to FRF distortions evoked by unsuitable data processing. All data processing methods are investigated on a numerical example. Their practical usefulness is demonstrated on test data taken from a recent GVT on a large aircraft. The revision of ISO 7626 part 2 is suggested regarding the application of slow swept-sine excitation. Recommendations about the proper FRF estimation from slow swept-sine excitation are given in order to enable the optimisation on these applications for future modal survey tests of large aerospace structures.     

一种逐点连续计算相关函数的方法

本文提出了一种逐点连续计算相关函数的方法，讨论了这种方法在检测中应用的若干问题。它算法简单，运算连续，特别适用于延迟时间较长的对象或低频信号的在线连续检测分析。这种方法还克服了ＦＦＴ方法存在的有偏估计的缺点，提高了相关函数计算的准确度。     

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.     

Phase correction for frequency response function measurements

In modal testing, an impulse is often used to excite the structure and a linear transducer is used to measure the response. For these impact tests, two signals are measured: the impulsive force and the vibration response. Any lack of synchronization in the time domain acquisition of the two signals results in a frequency-dependent phase error in the frequency response function, or FRF. However, knowledge of the time delay may be used to correct the corresponding phase error. In this research, tests were conducted to measure the frequency-dependent phase error for a capacitive sensor and a frequency domain technique is proposed to correct the FRF. The method was validated using an FRF measurement of a cylindrical artifact mounted in a milling machine spindle.