Model error correction from truncated modal flexibility sensitivity and generic parameters. II: experimental verification

This paper reports on the experimental verification of the truncated modal flexibility sensitivity based model updating method proposed in the companion paper (Wu and Law, Mechanical System and Signal Processing, doi: 10.1016/S0888-3270 (03) 00094-3) with real measurements on a three-dimensional cantilever frame structure in the laboratory. Two schemes of model error correction are presented to improve the initial inaccurate finite-element model of the structure. The first procedure updates the initial model in two stages. The systematic model errors are firstly updated using macrogeneric parameters. The local errors are then improved using elemental eigenparameters. The second procedure improves both the systematic and local errors without a measured baseline reference simultaneously. The first procedure can differentiate the types of errors in the structure while the latter procedure removes the usual requirement in most existing model based updating methods that an accurate finite -element model should be used as reference.     

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.     

Finite element model updating of concrete-filled steel tubular arch bridge under operational condition using modal flexibility

This paper presents finite element (FE) model updating method for real bridge structure under operational condition using modal flexibility. The theoretical background of the updating procedure is presented. The case study of a simulated simply supported beam demonstrates an effectiveness of modal flexibility in objective function. This objective function is then implemented in case study of a real concrete-filled tubular arch bridge. The bridge was tested under operational condition. Followed by the three-dimensional FE modeling of the bridge, an eigenvalue sensitivity study is carried out to select the most sensitive parameters to the concerned modes. Guyan technique is used to the mass normalization of the mode shapes extracted from ambient modal test to calculate the modal flexibility. The updated FE model of the bridge is able to produce a sufficient improvement on modal parameters of the concerned modes, which is in close agreement with the experiment results and updated parameters still preserve the physical meaning in practice.     

大型复杂结构损伤识别两步法研究

基于模型修正技术及模态柔度曲率差方法提出了一种解决大型复杂结构损伤识别问题的两步法。首先运用基于模型修正的损伤识别方法进行模糊识别,通过建立带约束边界非线性最小二乘目标函数,极小化结构实测模态与解析模态之间的误差,将损伤识别问题转化为优化问题,并采用信赖域方法求解该优化问题,识别出损伤所属单元组。然后运用模态柔度曲率差方法,对损伤进行精确定位。对某导弹发射台骨架的数值仿真及试验研究结果表明,该损伤识别两步法识别效果较为理想,为解决大型复杂结构的损伤识别问题提供了新思路。     

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。     

一种计及滑块裙部变形的滚珠直线导轨副模态分析方法

基于计及滚珠直线导轨副滑块裙部变形的刚度模型,提出了一种滚珠直线导轨副的有限元模态分析方法,建立了一种滚珠直线导轨副的三维有限元模型并进行了有限元模态分析,求得了滚珠直线导轨副的模态频率及模态振型。利用实验模态分析技术,对滚珠直线导轨副进行了模态测试,测得了滚珠直线导轨副的模态。测试结果验证了有限元建模与分析方法的有效性。     

火箭仪器舱试验与计算模态相关性分析

针对火箭仪器舱,研究了计算模态和试验模态的相关性分析问题。首先介绍模态相关性分析的一般方法。针对仪器舱结构复杂和模态密集的特点,引入整体模态和局部模态的概念,并提出一种用模态应变能比值区分整体模态和局部模态的定量的方法。进而研究了模态向量减缩、误差定位和模型修改等问题。在此基础上,得到了较高的试验和计算模态相关性结果,验证了计算模型,并为进一步的仪器舱减振设计提供了依据。     

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.     

Perturbation methods for the estimation of parameter variability in stochastic model updating

The problem of model updating in the presence of test-structure variability is addressed. Model updating equations are developed using the sensitivity method and presented in a stochastic form with terms that each consist of a deterministic part and a random variable. Two perturbation methods are then developed for the estimation of the first and second statistical moments of randomised updating parameters from measured variability in modal responses (e.g. natural frequencies and mode shapes). A particular aspect of the stochastic model updating problem is the requirement for large amounts of computing time, which may be reduced by making various assumptions and simplifications. It is shown that when the correlation between the updating parameters and the measurements is omitted, then the requirement to calculate the second-order sensitivities is no longer necessary, yet there is no significant deterioration in the estimated parameter distributions. Numerical simulations and a physical experiment are used to illustrate the stochastic model updating procedure.     

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     

New iterative method for model updating based on model reduction

Model reduction technique is usually employed in model updating process. Here, a new iterative method associating the model updating method with the model reduction technique is investigated. Using the traditional iterative method, the errors resulted from replacing the reduction matrix of the experimental model with that of the finite element (FE) model are not fully considered, which needs more iterations and computing time. In order to reduce the errors produced in the replacement, a new iterative method is proposed based on the traditional method, in which the correction term related to the errors is added. The comparisons between the traditional iterative method and the proposed iterative method are shown by model updating examples of solar panels and both of these two iterative methods combine the cross-model cross-mode (CMCM) method and the succession-level approximate reduction (SAR) technique. The results indicate that the convergence rate and the computing time of the new method are significantly superior to those of the traditional iterative method with or without noise.     

基于逆有限元的应变模态损伤检测方法

基于光纤光栅传感器(fiber Bragg grating,简称FBG)逆有限元方法(inverse finite element method,简称iFEM),仅利用有限测点的应变数据进行全域应变场重构,得到近似完全测量应变模态,提高了直接采用实测应变数据来构建应变模态损伤指标的实用性。利用基于损伤应变模态差分原理的损伤指标法,只需用损伤后应变模态数据即能定位损伤,并给出了损伤指标数学模型。计算结果表明,基于光纤光栅传感器和逆有限元方法可以快速进行全域应变场重构,为基于应变模态的损伤检测提供数据保障,而应变模态差分曲线只在损伤处发生剧烈变化,损伤程度不同,曲线突变程度略有不同但规律一致。最后以某板的实验结果证明了该方法的有效性。     

基于灵敏度分析的刀形天线有限元模型修正

准确可靠的有限元模型是结构动态特性分析、设计改进的基础,文中利用模态试验得到的模态参数对某刀形天线进行有限元模型修正.首先建立天线结构的参数化模型,然后通过灵敏度分析选择合适的设计参数作为后续优化对象,利用计算与试验的模态频率之间的相对误差构造加权的优化目标函数,最后应用1阶优化方法修正结构的有限元模型.修正后有限元模型的模态频率最大相对误差降低至10%以内,模态置信度(MAC)均大于0.8.该修正模型可用于后续的动力学分析.     

一种基于模型修改的结构多点损伤识别方法

可用于结构损伤识别的方法很多。一般来讲正向方法直接利用结构模态参数的变化，逆向方法则利用模态参数变化反演结构物理参数变化，还有些方法利用了神经网络和模式识别技术。文中利用模型修改的思想，通过逆向方法计算结构单元刚度变化系数来对结构的多点损伤进行识别。以一个七自由度弹簧阻尼质量系统作为研究对象，用数值模拟方法及特征系统实现算法计算系统的模态参数，并用这些模态参数验证所提出方法的可行性，结果表明该方法对多点损伤的识别是简单而可行的。     

步兵战车车体结构有限元模型修正

针对某型步兵战车整车刚柔耦合发射动力学中柔性车体有限元模型精度低的问题,基于模态试验数据,应用支持向量机响应面模型修正理论对车体结构有限元模型进行了修正。应用ANSYS有限元分析软件对车体结构进行模态分析,提取前6阶模态的固有频率和振型。为验证模型,设计了模态试验方案,实测了车体结构的模态信息。基于有限元模型数据与实测数据的相对误差,采用支持向量机响应面模型修正方法对车体结构弹性模量和密度进行修正。模型确认结果和动力学模型应用结果表明,修正后的车体有限元模型精度有了大幅度提高,能更加真实地反映车体的结构特征,为射击精度分析提供了准确的模型基础。     

Vibration analysis of HDD actuator with equivalent finite element model of VCM coil

As the rate of increase in areal density of the HDD has accelerated, dynamic characteristics of the HDD actuator need to be improved with respect to the performance of the tracking servo and shock transmission. Therefore, it is important to analyze the vibration characteristic of the HDD actuator that consists of the VCM part, E-block and pivot bearing. In this paper, vibration modes of the HDD actuator are investigated the using finite element and experimental modal analyses methods. To develop a detailed finite element model, finite element models of each components of the actuator assembly are constructed and tuned to the results of the EMA. The VCM coil is modeled as an equivalent finite element model that has an orthotropic material property using auto-model updating program. Auto-model updating program with improved sensitivity based iterative method is applied to build a detailed finite element model using the result of the EMA. A detailed finite element model of the HDD actuator is then constructed and analyzed.     

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。     

信息融合与响应面联合的渡槽结构模型修正

针对大型渡槽损伤诊断研究中有限元模型精度问题,提出一种基于信息融合与响应面法(response surface method,简称RSM)的有限元模型修正方法,能够兼顾优化目标和参数优化两个环节。以某灌区渡槽为研究对象,建立初始有限元模型,采用试验设计方法构建待修正参数与特征频率的设计空间,经过参数筛选后建立设计样本的响应面模型;引入自适应噪声的完整集成经验模态分解和奇异值分解(complete ensemble empirical mode decomposition with adaptive noise-singular value decompose,简称CEEMDAN-SVD)降噪方法联合方差贡献率数据级融合算法,对正常运行工况下覆盖三跨槽身振测信号进行多通道融合处理以获取完整有效的实测频率,并以此为目标值对响应面模型进行最优化求解,实现多跨渡槽有限元模型的参数优化。结果表明,修正后的有限元模型计算出的频率与实测频率吻合较好,最大误差为-4.38%,有效解决了大型渡槽结构有限元模型的精度问题,为后续结构损伤诊断等仿真研究提供基准模型。     

基于模态综合技术的结构有限元模型修正

由于结构的动力分析需要大量的计算时间和占用大量的计算机内存,常规的数值迭代计算方法难以实现,提出了基于模态综合技术的模型修正方法。该方法首先得到缩减后结构模型的频率与振型,并将该振型转换为缩减前模型物理坐标下的振型。然后,用缩减后模型的频率和转换后的振型,共同构成模型修正的优化目标函数,进而通过优化求解实现结构的模型修正。该方法既保证了计算精度又提高了模型修正的计算效率,使大型复杂结构的模型修正成为可能。最后,对某吊杆拱桥模型进行了动态测试和模型修正,验证了该算法的有效性。