Cyclostationarity and the cepstrum for operational modal analysis of MIMO systems—Part II: Obtaining scaled mode shapes through finite element model updating

This paper presents a new technique for scaling mode shapes, obtained from cepstrum-based operational modal analysis (OMA) techniques, such as that described in the companion paper, using finite element model updating. This OMA technique estimated frequency response functions (FRFs) between a cyclostationary input and response measurements. If the input is frequentially white, the resulting FRFs can be obtained up to an overall scaling constant using the in-band poles and zeros identified in the OMA process and employing the response autospectrum as a reference to correct for the effect of out of band modes. In this way, the mode shapes would be scaled correctly relative to each other but would still have arbitrary overall magnitude. If the input is not white, then no reference is available to correct FRF regenerated from in-band poles and zeros, and so these FRFs will exhibit both an overall slope resulting from the effect of out-of-band poles and zeros, and an arbitrary magnitude. This overall slope will differ between measurement locations so even the relative scaling between the mode shapes will be lost. This paper describes a simple technique for recovering both the relative and overall scaling of the FRFs, and hence the mode shapes, based on finite element model updating.     

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.     

Operational modal analysis by updating autoregressive model

This paper presents improvements of a multivariable autoregressive (AR) model for applications in operational modal analysis considering simultaneously the temporal response data of multi-channel measurements. The parameters are estimated by using the least squares method via the implementation of the QR factorization. A new noise rate-based factor called the Noise rate Order Factor (NOF) is introduced for use in the effective selection of model order and noise rate estimation. For the selection of structural modes, an orderwise criterion called the Order Modal Assurance Criterion (OMAC) is used, based on the correlation of mode shapes computed from two successive orders. Specifically, the algorithm is updated with respect to model order from a small value to produce a cost-effective computation. Furthermore, the confidence intervals of each natural frequency, damping ratio and mode shapes are also computed and evaluated with respect to model order and noise rate. This method is thus very effective for identifying the modal parameters in case of ambient vibrations dealing with modern output-only modal analysis. Simulations and discussions on a steel plate structure are presented, and the experimental results show good agreement with the finite element analysis.     

The sensitivity method in finite element model updating: A tutorial

The sensitivity method is probably the most successful of the many approaches to the problem of updating finite element models of engineering structures based on vibration test data. It has been applied successfully to large-scale industrial problems and proprietary codes are available based on the techniques explained in simple terms in this article. A basic introduction to the most important procedures of computational model updating is provided, including tutorial examples to reinforce the reader’s understanding and a large scale model updating example of a helicopter airframe.     

Proximal-point method for finite element model updating problem

The problem of finding the optimal approximation to analytical stiffness matrix modeled by the finite element method is considered in this paper. Desired matrix properties, including satisfaction of the dynamic equation, symmetry, positive semidefiniteness and physical connectivity, are imposed as side constraints of the minimization problem. To the best of the author's knowledge, the finite element model updating problem containing all these constraints simultaneously has not been proposed in the literature earlier. By partial Lagrangian multipliers technique, the optimization problem is transformed into a matrix linear variational inequality and the proximal-point method is first used to solve the equivalent problem. The results of numerical examples show that the proposed method works well even for incomplete measured data.     

Iterative finite element model updating in the time domain

An iterative time domain formulation for finite element model updating in structural dynamics is presented. The approach is supported on a derivation showing that the discrepancy between observations and model predictions can be expressed as a convolution between the state of the system and a sequence of pseudo-Markov parameters which are linear in the change of the free parameters. The approach is illustrated by updating all the stiffness and damping parameters of a twenty degree of freedom shear beam using four noise contaminated measurements.     

重型汽车变速箱箱体有限元模态分析

变速箱是汽车传动系统的主要部件之一,它的振动必然带来汽车整车的振动和噪音,影响汽车的整车性能。以重型汽车变速箱箱体为研究对象,应用PRO/E软件建立箱体的三维实体模型,并利用ANSYS软件建立箱体的有限元模型,完成了箱体的有限元模态分析。分析结果可为寻找变速箱箱体产生振动的敏感部位和箱体的结构优化设计提供依据。     

基于ANSYS的汽车起重机吊臂的动态分析

基于ANSYS软件对汽车起重机整体吊臂进行了有限元模态分析,提取影响吊臂性能的模态振型和频率,从而了解各种工况不同频率载荷对整体吊臂的影响和吊臂整体动态刚度特点,为吊臂设计和改造提供理论依据。     

有限元模型BERMAN修正算法的改进

BERMAN修正方法基于无阻尼系统的模态正交条件 ,利用实验模态矩阵和特征值对有限元理论模型进行修正。指出该方法存在的 2个缺陷 ,给出一种改进后的BERMAN修正方法 ,并编写了相应的迭代程序。通过修正一个实际例子表明 ,改进后的BERMAN修正方法有可取之处。     

Adaptive regularization parameter optimization in output-error-based finite element model updating

In finite element (FE) model updating, regularization methods are required to alter the ill-conditioned system of equations towards a well-conditioned one. The present study addresses the regularization parameter determination when implementing the Tikhonov regularization technique in output-error-based FE model updating. As the output-error-based FE model updating results in a nonlinear least-squares problem which requires iteration for solution, an adaptive strategy that allows varying value of the regularization parameter at different iteration steps is formulated, where the optimal regularization parameter at each iteration step is determined based on the computationally efficient minimum product criterion (MPC). The performance of MPC in output-error-based FE model updating is examined and compared with the commonly used L-curve method (LCM) and the generalized cross validation (GCV) through numerical studies of a truss bridge using noise-free and noise-corrupted modal data. It is shown that MPC is effective and robust in determining the regularization parameter compared with the other two methods, especially when noise-corrupted data are used. The adaptive strategy is more efficient than the fixed strategy that uses a constant value of the regularization parameter throughout the iteration process.     

机车构架静强度及模态有限元分析

利用大型有限元分析软件ANSYS,对某新型机车转向架构架进行静强度及模态仿真计算,从理论上证明构架静强度足够,刚性满足要求,能保证构架良好的动态性能,为机车的可靠运行提供了保证。     

A new method for finite element model updating in structural dynamics

A method is propounded in this paper to update finite element models in the field of structural dynamics. It is especially intended to solve cases for which other methods either cannot be applied or are inefficient. It is posed as the minimization of an error function defined in the time domain. The minimization is carried out by a novel adaptive sampling algorithm, which constitutes the main contribution in this work. In this algorithm, the solution is searched by sampling the parameters to be updated within a bounded space in an iterative form. The Beta distribution, which is consistent with the bounded character of the search space, is chosen for the sampling. The characteristics of the distributions are changed in each step of the process depending on the results of the previous ones. The method has been tested through a simulated dynamic model and an experimental case. In these particular cases, the performance of the proposed adaptive algorithm was better than those of other related stochastic algorithms it was compared with.     

有限元法在机械结构模态分析中的应用

运用有限元法对机械结构进行模态分析可以求出结构的固有振动特性,获得避免共振现象产生的工作频率范围,同时提出改善结构模态特性的方法。文章运用有限元分析软件ANSYS分析了某机床床身的前8阶固有频率和振型,提出了适合加工的主轴转速范围和改善床身结构模态特性的方法。研究实例表明:有限元法具有简单、快速、直观的特点,是一种对机械结构进行模态分析的有效方法。     

基于HyperMesh的有限元建模及减速器模态分析

采用Altair公司的HyperMesh软件对减速器进行高速度、高质量的自动网格划分,极大地简化了复杂几何的有限元建模过程,得出相应的模态算法和结果。结果表明:采用该软件进行优化分析,可以提高产品性能和质量,大大降低成本。     

Model selection in finite element model updating using the Bayesian evidence statistic

This paper considers the problem of finite element model (FEM) updating in the context of model selection. The FEM updating problem arises from the need to update the initial FE model that does not match the measured real system outputs. This inverse system identification-problem is made even more complex by the uncertainties in modeling some of the structural parameters. Such uncertainty often results in a number of competing forms of FE models being proposed which leads to lack of consensus in the field. A model can be formulated in a number of ways; by the number, the location and the form of the updating parameters. We propose the use of a Bayesian evidence statistic to help decide on the best model from any given set of models. This statistic uses the recently developed stochastic nested sampling algorithm whose by-product is the posterior samples of the updated model parameters. Two examples of real structures are each modeled by a number of competing finite element models. The individual model evidences are compared using the Bayes factor, which is the ratio of evidences. Jeffrey's scale is then used to determine the significance of the model differences obtained through the Bayes factor.     

基于有限元模型修正的损伤识别方法研究

通过实验方法测得结构的模态参数,建立结构系统的有限元基准(未损)模型,同时为了避免将初始的有限元模型误差误判为损伤,需对原始的基准模型进行有限元修正,建立基准解析模型.由于系统质量参数可以准确获得且在模型修正过程中保持质量不变,因此可将刚度参数作为修正对象,通过改变弹簧刚度,使其有限元动力分析的结果与实测结果尽量吻合.随后定义损伤变量(损伤引起刚度的变化率即灵敏度),借助刚性灵敏度实现对结构损伤位置与损伤程度的识别.     

Crack detection in beams using experimental modal data and finite element model

In this paper, an analytical, as well as experimental approach to the crack detection in cantilever beams by vibration analysis is established. An experimental setup is designed in which a cracked cantilever beam is excited by a hammer and the response is obtained using an accelerometer attached to the beam. To avoid non-linearity, it is assumed that the crack is always open. To identify the crack, contours of the normalized frequency in terms of the normalized crack depth and location are plotted. The intersection of contours with the constant modal natural frequency planes is used to relate the crack location and depth. A minimization approach is employed for identifying the cracked element within the cantilever beam. The proposed method is based on measured frequencies and mode shapes of the beam.     

基于有限元法的直齿圆柱齿轮振动模态分析

主要研究直齿圆柱齿轮的固有振动特性,利用ANSYS有限元软件建立直齿圆柱齿轮的三维模型并对其进行动力学模态分析,通过求解分析得到齿轮的低阶固有频率、主振型以及相对位移和相对应力,为齿轮及其系统的动态设计提供参考依据。     

Finite element model updating of vibrating structures under free-free boundary conditions for modal damping prediction

A method to predict resonance frequencies and modal loss factors of bare and damped samples, using constrained layer damping treatment, under free-free boundary conditions is proposed. In a first phase, measurements of the frequency response functions of these two specimens are performed. In a second phase, a finite element model of the undamped sample is developed. The novelty lies in the consistent modelling of the suspension with spring-damper elements defined with stiffness and damping coefficients with fixed values over the whole considered frequency range. By updating these, the agreement between experiments and simulation is further improved. In a third phase, a finite element model of the damped sample, with constrained layer damping material, is realized. A good agreement with experimental results is obtained thanks to an optimization algorithm used to determine the material parameters of the viscoelastic layer at various frequency. A comparison with experimental results, from a Dynamic Mechanical Analysis, confirms the consistency of the results from the optimization process.     

提升机主轴的有限元模态分析和断轴的预防

针对服役期内提升机主轴出现断裂损伤的现象。现将主轴用Solid Works simulaton进行实体建模和模态分析,并进行从生产到使用的全程分析。Solid Works中可以直观的看到主轴在工作中受到的应力、应变、位移等参数的变化,从而评估出主轴在实际工作中的力学性能和安全性的表现。最后结合分析和实际情况总结预防主轴断裂方法。