基于近似似然的频响函数不确定性模型修正

贝叶斯模型修正框架下,以频响函数作为目标,提出了一种使用近似似然函数的不确定性模型修正方法。相比于模态参数,频响函数包含了结构更加充分的信息,用于结构动力学模型修正时有诸多优点,但现有的不确定性模型修正方法并不能很好地实现将频响函数作为目标进行修正。针对此问题,介绍了频响函数和贝叶斯框架下的不确定性模型修正理论,基于近似贝叶斯计算提出了一种近似似然函数,可适用于频响函数作为目标进行不确定性修正。将提出的似然函数应用到三自由度数值和H型非对称梁的有限元模型修正算例中,并结合DREAM算法对不确定性参数进行识别。研究结果表明:修正后参数的上、下限与目标值相差无几,修正后模型的频响函数与目标值几乎重合,在一定噪声水平下仍具有较好的修正效果,验证了所提方法的有效性。     

基于近似似然的频响函数不确定性模型修正

贝叶斯模型修正框架下，以频响函数作为目标，提出了一种使用近似似然函数的不确定性模型修正方法。相比于模态参数，频响函数包含了结构更加充分的信息，用于结构动力学模型修正时有诸多优点，但现有的不确定性模型修正方法并不能很好地实现将频响函数作为目标进行修正。针对此问题，介绍了频响函数和贝叶斯框架下的不确定性模型修正理论，基于近似贝叶斯计算提出了一种近似似然函数，可适用于频响函数作为目标进行不确定性修正。将提出的似然函数应用到三自由度数值和H型非对称梁的有限元模型修正算例中，并结合DREAM算法对不确定性参数进行识别。研究结果表明：修正后参数的上、下限与目标值相差无几，修正后模型的频响函数与目标值几乎重合，在一定噪声水平下仍具有较好的修正效果，验证了所提方法的有效性。     

基于频响函数相关性的灵敏度分析的有限元模型修正

有限元模型的修正对机械结构的动态特性进行准确而可靠的预测是很重要的。利用试验测试和预测的有限元模型计算得到的频响函数（FRF），引入两种频响函数相关性的判定标准，提出基于频响相关函数的灵敏度分析的修正方程。数值实例研究结果表明，该方法利用少量的测量数据，即使测试数据含附加噪声，也可在很宽的频率范围内得到接近真实结构的有限元模型修正解。本文的方法可适用于大型复杂结构的模型修正。     

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.     

螺栓松动应变频响模型修正识别方法

为了有效识别工程结构中的螺栓连接松动，防范结构连接失效风险，以应变频响函数（SFRF）作为响应特征指标，提出了一种基于模型修正思想的螺栓连接结构松动识别方法。对含4个螺栓连接的搭接板结构，采用薄层单元描述螺栓连接，分别提取仿真模型和松动损伤结构模型螺栓连接位置的应变频响曲线，拾取频响曲线的特征点并构造目标函数。采用拉丁超立方抽样和径向基函数近似方法，构造了连接参数和目标函数之间的代理模型关系。基于模型修正思想，采用遗传算法对目标函数进行优化，识别模型中连接参数值。通过比较模型的初始连接参数和识别出的参数值，可定量描述结构松动损伤。数值算例结果表明，薄层单元有限元建模方式能较准确地模拟螺栓连接特性，使用代理模型可提高搜索效率，能有效识别螺栓连接结构的松动程度。     

基于加速度频响函数的改进响应面模型修正

为提高模型修正精度,将加速度频响函数引入到改进的响应面模型修正当中.首先分别采用模态参与度准则和有效独立法确定试验最佳激励点和测量点,然后根据待修正参数选取样本点,计算其对应的加速度频响函数,构造初始响应面模型;其次利用三倍方差准则,对预测值进行检验,剔除远离响应面的离群点;再优化初始响应面模型得到最优解作为新的样本点,利用比值型加权方法进行加权,构造加权响应面模型;之后使用改进的响应面模型代替有限元模型,再以频率响应差最小构造目标函数,利用布谷鸟算法求解参数修正值.使用典型的桁架结构模型进行验证,结果表明,改进后的响应面模型计算精度和计算效率都有所提高.     

基于Kriging模型和小波包能量谱的随机模型修正

针对随机模型修正精度和效率低的问题,提出一种基于Kriging模型和小波包能量谱的随机有限元模型修正方法。首先,假设模型待修正参数和响应特征均服从正态分布,将不确定性的模型修正转化为均值和标准差的修正;其次,将待修正参数作为Kriging模型输入,加速度频响函数经过小波包分解后提取的结点能量作为输出,引入政治优化算法优化相关系数以构造Kriging模型;然后,将最小化试验响应与预测响应之差的绝对值作为修正均值的目标函数,最小化交叉熵作为修正标准差的目标函数,通过政治优化算法先后修正参数均值和标准差;最后,以空间桁架结构为例,选取弹性模量和密度为待修正参数验证该方法的可行性。结果表明,所提方法能够有效地修正结构参数均值和标准差,修正后的参数均值、标准差的误差分别低于0.1%、3.5%。     

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...     

利用频响函数对振动系统进行优化设计

在估算系统参数,建立力学教学模型的基础之上,利用频响函数的相对灵敏度和模态参数之间的关系,通过实测的频响函数对振动系统的物理参数进行修正。     

Model updating of damped structures using FRF data

Due to the important contribution of damping on structural vibration, model updating of damped structures becomes significant and remains an issue in most model updating methods developed to date. In this paper, the frequency response function(FRF) method, which is one of the most frequently referenced model updating methods, has been further developed to identify damping matrices of structural systems, as well as mass and stiffness matrices. In order to overcome the problem of complexity of measured FRF and modal data, complex updating formulations using FRF data to identify damping coefficients have been established for the cases of proportional damping and general non-proportional damping. To demonstrate the effectiveness of the proposed complex FRF updating method, numerical simulations based on the GARTEUR structure with structural damping have been presented. The updated results have shown that the complex FRF updating method can be used to derive accurate updated mass and stiffness modelling errors and system damping matrices.     

On the use of damped updated FE model for dynamic design

Model updating techniques are used to update the finite element model of a structure, so that updated model predicts the dynamics of a structure more accurately. The application of such an updated model in dynamic design demands that it also predicts the effects of structural modifications with a reasonable accuracy. Most of the model updating techniques neglect damping and so these updated models cannot be used for predicting amplitudes of vibration at resonance and antiresonance frequencies. This paper deals with updating of the finite element model using the FRF data with damping identification using complex modal data and its subsequent use for predicting the effects of structure modifications. The updated model is obtained in two steps. In the first step, mass and stiffness matrices are updated using FRF-based model updating method. In the second step, damping is identified using updated mass and stiffness matrices, which are obtained in first step. Structural modifications in terms of mass and beam modifications are then introduced to evaluate the updated model for its usefulness in dynamic design.     

考虑模型偏差的结构动力学模型修正

针对结构有限元模型修正后仍可能存在模型偏差的问题,提出用待修正参数的不确定性来表征模型偏差的有限元模型修正方法。首先,基于响应面方法识别得到待修正参数的最优值,并通过计算结果与试验结果比较获得模型偏差;然后,基于响应面模型并结合灵敏度分析计算得到模型偏差对待修正参数的影响,从而得到考虑模型偏差后待修正参数的区间;最后,通过一个悬臂梁工程实例的模型修正,验证了笔者所提出方法的可行性。结果表明,考虑模型偏差的修正可以提高模型可靠性。     

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     

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。     

使用应变模态和遗传算法的有限元模型修正方法

提出了采用应变模态置信度为待修正响应特征的有限元模型修正方法。应变模态置信度是评价有限元仿真与试验测试结果相关性的方法,可以为模型修正提供全局的频率误差信息和局部的应变相关性信息。首先,介绍了应变模态和有限元模型修正的相关理论方法;然后,以某航空加筋壁板结构为对象,通过仿真分析和"仿真试验"获得结构的应变模态频率以及对应的应变振型,进一步计算频率误差和应变模态置信度误差;最后,基于两种误差构造模型修正的目标函数,采用遗传算法对目标函数进行优化,修正结构中的待修正参数,并将修正后参数代入模型,验证所提方法的正确性和有效性。结果表明:所采用的方法获得的修正后有限元模型具有复现修正响应特征的能力,并且对于未修正频段内的响应也具有较好的预测能力。     

Optimal selection of artificial boundary conditions for model update and damage detection

Sensitivity-based model error localization and damage detection is hindered by the relative differences in modal sensitivity magnitude among updating parameters. The method of artificial boundary conditions is shown to directly address this limitation, resulting in the increase of the number of updating parameters at which errors can be accurately localized. Using a single set of FRF data collected from a modal test, the artificial boundary conditions (ABC) method identifies experimentally the natural frequencies of a structure under test for a variety of different boundary conditions, without having to physically apply the boundary conditions, hence the term “artificial”. The parameter-specific optimal ABC sets applied to the finite element model will produce increased sensitivities in the updating parameter, yielding accurate error localization and damage detection solutions. A method is developed for identifying the parameter-specific optimal ABC sets for updating or damage detection, and is based on the QR decomposition with column pivoting. Updating solution residuals, such as magnitude error and false error location, are shown to be minimized when the updating parameter set is limited to those corresponding to the QR pivot columns. The existence of an optimal ABC set for a given updating parameter is shown to be dependent on the number of modes used, and hence the method developed provides a systematic determination of the minimum number of modes required for localization in a given updating parameter. These various concepts are demonstrated on a simple model with simulated test data.     

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.