Comparative study of damped FE model updating methods

Most of finite element (FE) model updating techniques do not employ damping matrices and hence, cannot be used for accurate prediction of complex frequency response functions (FRFs) and complex mode shapes. In this paper, a detailed comparison of two approaches of obtaining damped FE model updating methods are evaluated with the objective that the FRFs obtained from damped updated FE models is able to predict the measured FRFs accurately. In the first method, damped updating FE model is obtained by complex parameter-based updating procedure, which is a single-step procedure. In the second method, damped updated model is obtained by the FE model updating with damping identification, which is a two-step procedure. In the first step, mass and stiffness matrices are updated and in the second step, damping matrix is identified using updated mass and stiffness matrices, which are obtained in the previous step. The effectiveness of both methods is evaluated by numerical examples as well as by actual experimental data. Firstly, a study is performed using a numerical simulation based on fixed–fixed beam structure with non-proportional viscous damping model. The numerical study is followed by a case involving actual measured data for the case of F-shaped test structure. The updated results have shown that the complex parameter-based FE model updating procedure gives better matching of complex FRFs with the experimental data.     

Finite element model updating based on eigenvalue and strain energy residuals using multiobjective optimisation technique

The numerical results from a finite element (FE) model often differ from the experimental results of real structures. FE model updating is often required to identify and correct the uncertain parameters of FE model and is usually posed as an optimisation problem. Setting up of an objective function, selecting updating parameters and using robust optimisation algorithm are three crucial steps in FE model updating. In this paper, a multiobjective optimisation technique is used to extremise two objective functions simultaneously which overcomes the difficulty of weighing the individual objective function of more objectives in conventional FE model updating procedure. Eigenfrequency residual and modal strain energy residual are used as two objective functions of the multiobjective optimisation. Only few updating parameters are selected on the basis of the prior knowledge of the dynamic behaviours of the structure and eigenfrequency sensitivity study. The proposed FE model updating procedure is first applied to the simulated simply supported beam. This case study shows that the methodology is robust with an effective detection of assumed damaged elements. The procedure is then successfully applied to the updating of a precast continuous box girder bridge that was tested on field under operational conditions.     

A method in model updating using Miscorrelation Index sensitivity

This paper presents a new model updating method based on minimization of an index called Miscorrelation Index (MCI), which is introduced to localize the coordinates carrying error in a finite element (FE) model. MCI can be calculated from measured frequency response functions (FRFs) and dynamic stiffness matrix of the FE model for each coordinate as a function of frequency. Nonzero numerical values for MCI of a coordinate indicate errors in one or more elements of the system matrices corresponding to this coordinate. The sensitivity-driven model updating method presented in this study (MCI Sensitivity Method) is based on minimization of MCI. The application of the method is illustrated with four case studies. In the first and second examples a discrete system is considered, and computationally generated and polluted FRFs are used as pseudo-test data. In the third and fourth case studies, real test data is used and the performance of the method in practical applications is demonstrated on the benchmark structure built to simulate the dynamic behavior of an airplane, namely, GARTEUR SM-AG19 test bed. It is concluded that MCI Sensitivity Method yields successful results even when the measured responses of only a few coordinates are used, especially when miscorrelation is due to local errors.     

内存数据库在移动计费系统中的应用

在移动计费系统中,实时话费更新,用户档案信息变更等操作对数据库的操作实时性要求相当高,尤其是批量添加,更新等操作。现有的关系型数据库Oracle,Sybase效率上不能完全满足移动计费系统的性能要求,而内存数据库却能在实时性和准确性上提供保证。本文研究了内存数据库在移动计费系统上的应用,实现了内存数据库的系统监控工具、DBMS工具、代码生成工具,同步工具等功能,并提供了与多种编程语言的接口。     

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。     

3D finite element simulation of temperature distribution,residual stress and distortion on 304 stainless steel plates using GTA welding

In the present study, the distortion induced in rectangular plate of AISI 304 SS during autogenous GTA welding process is measured experimentally and further validated using Finite element (FE) analysis. The thermal histories are measured at fixed locations over the surface of the plate and the results are compared with FE analysis. The Gaussian surface and Volumetric heat source models are simulated and transient heat transfer analysis is performed. The heat source models have been tested with two different speeds. The effectiveness of change in thermal histories of the heat sources have been studied and reported. In FE analysis, the sequentially coupled thermomechanical analysis is performed using the thermal histories as input and the distortion of the plates are predicted and compared with experimental measurements. The large and small displacement theories are employed for the above purpose and the effectiveness of the theories are reported. The edge deformation of the plates have been measured and validated for both the theories. The residual stress and distortion at the mid span are predicted and discussed. The results predicted using large displacement theory is in good agreement with measured values.     

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.     

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.     

Data fusion of acceleration and angular velocity for improved model updating

In the traditional finite element (FE) model updating, translational responses, such as acceleration, have generally been employed to identify the structural properties. However, the boundary conditions of a structure are associated with both translational and rotational DOFs. Thus, the combinational measurement of translational and rotational responses (e.g., angular velocity) would increase accuracy of FE model updating of structures, especially in identifying their boundary conditions. This paper proposes data fusion of translational and rotational responses for improved system identification using FE model updating technique. In the proposed method, the accelerometers and gyroscopes are installed in between and near the supports of a structure, respectively, and FE model updating is carried out using the natural frequencies, the translational mode shapes obtained from accelerations, and the rotational mode shapes obtained from angular velocities. Numerical and experimental verifications are carried out on simply-supported beam structures. The verifications show that the proposed FE model updating strategy based on the data fusion results in more accurate assessment of both structural properties and boundary conditions than the traditional FE model updating using translational responses only.     

Damage localization using experimental modal parameters and topology optimization

This work focuses on the development of a damage detection and localization tool using the topology optimization feature of MSC.Nastran. This approach is based on the correlation of a local stiffness loss and the change in modal parameters due to damages in structures. The loss in stiffness is accounted by the topology optimization approach for updating undamaged numerical models towards similar models with embedded damages. Hereby, only a mass penalization and the changes in experimentally obtained modal parameters are used as objectives. The theoretical background for the implementation of this method is derived and programmed in a Nastran input file and the general feasibility of the approach is validated numerically, as well as experimentally by updating a model of an experimentally tested composite laminate specimen. The damages have been introduced to the specimen by controlled low energy impacts and high quality vibration tests have been conducted on the specimen for different levels of damage. These supervised experiments allow to test the numerical diagnosis tool by comparing the result with both NDT technics and results of previous works (concerning shifts in modal parameters due to damage). Good results have finally been achieved for the localization of the damages by the topology optimization.     

Finite element model updating and structural damage identification using OMAX data

The main limitations in the finite element (FE) model updating technique lie in the ability of the FE model to represent the true behavior of the structure (modelling problem), and in the ability to identify enough modal parameters with sufficient accuracy, especially for large structures that are tested in operational conditions (identification problem). In this paper, the identification problem is solved with an OMAX approach, where an artificial force is used in operational conditions and a structural model is identified that takes both the forced and the ambient excitation into account. From an extensive case study on a real three-span bridge, it is observed that, while updating the FE model using the experimental output-only data yields a good fit, discrepancies show up when the more extensive set of OMAX data is used for validation, or even for updating. It can be concluded that an OMAX approach not only increases the well-posedness of the updating problem, it also allows to detect potential inaccuracies in the FE model.     

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.     

Parameter study for the finite element modelling of long bones with computed-tomography-imaging-based stiffness distribution

Four radii of different horses were tested in three-point bending and in pure torsion. Detailed finite element (FE) models of these long bones were established by means of computed-tomography (CT) images and tests simulated for both load cases. For the allocation of the local isotropic material stiffness, individual exponential functions were applied whose factor and exponent were determined solely by fitting them to the measured torsional stiffness and bending stiffness of the entire bones. These stiffness functions referring directly to the CT number and having exponents between 1.5 and 2 were in good agreement with Young's moduli subsequently measured from small samples cut from the investigated bones. Based on a model with local orthotropic material definition, an additional parameter study was conducted to verify the sensitivities of the FE analysis results on single variations in the orthotropic elastic constants. This study revealed that the bending test simulations could be enhanced by substantial reduction in Young's moduli in the directions perpendicular to the bone axis; thus, orthotropic material definition is preferable for the FE analysis of long bones.     

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.     

阀控缸系统有限时间滑模控制

针对阀控缸系统稳态跟踪误差的收敛时间均为非有限时间内收敛到0的问题，提出了一种终端滑模控制方法。解决了液压系统非有限时间收敛问题，使得跟踪误差在有限时间内收敛到0。首先，运用终端滑模控制方法通过构造终端函数方式引入非线性项，设计终端滑模面来保证系统的全局鲁棒性和稳定性；其次，基于Lyapunov稳定性理论设计终端滑模控制器，保证位置跟踪误差在有限时间内收敛到0并验证其稳定性；最后，利用阀控缸系统模型以正弦信号及其衍生信号为参考信号对控制策略进行Simulink仿真，表明了终端滑模控制方法的可行性与有效性。     

西文DOS下监控软件的C语言设计与实现

分析了实时监控系统软件的特点,提出了西方DOS下微机监控软件中一些关键技术的编程方法和程序实现,包括键盘输入、快速图形操作、过程数据趋势图显示、汉字显示等功能,以上程序实现简单,实现运行效果良好。     

基于矩阵逼近的模型修正方法的研究

提出一种新的以试验振动和参数辨识的数据为参数,进行有限元分析模型修正的方法。该方法基于矩阵最佳逼近理论,运用Ｂａｙｅｓ估计原理来处理试验结果误差带来的试验模态可信度问题,求取分析模对试验获得的不完备模态的谱点的最佳逼近结果,最后获得质量阵的最小修正模型。     

基于Excel工作表对静态网页进行更新的研究

针对普通文件服务器中静态网页没有后台支持更新比较麻烦的问题,本文通过简单的VBA代码编程,实现了在Excel工作表界面对静态网页的编辑更新,为静态网页的更新问题开辟了一条方便实用的途径。     

Studies in dynamic design of drilling machine using updated finite element models

The aim of the present work is to develop updated FE models of a drilling machine using analytical and experimental results. These updated FE models have been used to predict the effect of structural dynamic modifications on vibration characteristics of the drilling machine. Two studies have been carried out on the machine. In the first study, modal tests have been carried out on a drilling machine using instrumented impact hammer. Modal identification has been done using global method of modal identification. For analytical FE modeling of the machine, a computer program has been developed. The results obtained using FEM, have been correlated with the experimental ones using mode shape comparison and MAC values. Analytical FE model has been updated, with the help of a program, which has been developed using direct methods of model updating. In the second study, modal testing has been carried out using random noise generator and modal exciter. Global method has been used for modal identification. Analytical FE modeling has been done using I-DEAS software. Correlation of FE results with the experimental ones has been carried out using FEMtools software. Updating of the analytical FE model has also been done using the above software, based on an indirect technique viz. sensitivity based parameter estimation technique. The updated FE models, obtained from both the studies have been used for structural dynamic modifications (SDM), for the purpose of dynamic design and the results of SDM predictions are seen to be reasonably satisfactory.     

Wear modelling in mild steel orthogonal cutting when using uncoated carbide tools

Wear prediction in machining has been recently studied by FEM although the use of numerical methods for such applications is still a very challenging research issue. In fact, wear phenomenon involves many aspects related to process mechanics which require a very accurate modelling. In other words, only a very punctual code set-up can help the researchers in order to obtain consistent results in FE analysis. The high relative velocity between chip and tool requires effective material models as well as friction modelling at the interface. Moreover the prediction of temperature distribution is another critical task; in the paper some different procedures are discussed. Subsequently a wear model is presented and calibrated in order to obtain a suitable tool to be implemented in a FE code with the aim to describe the wear evolution during the simulation process.A proper designed experimental campaign supplied some reference data for model set-up and verify in the practical application.All these aspects are carefully discussed in the paper.