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。     

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.     

基于广义动态缩聚法的脉冲推力器固有模态分析

对用于飞行器姿态控制和弹道修正的脉冲推力器进行了有限元模态分析,给出脉冲推力器壳体的前5阶固有频率和振型,对模态分析结果进行分析,找出容易产生共振和有害振型的频率,为进一步进行脉冲推力控制器的动力学分析奠定基础.同时,用广义动态缩聚法对模型进行固有模态分析,与精确模型计算结果进行比较,证明了用广义动态缩聚法进行固有模态分析得可行性.最后,分析了广义动态缩聚法对计算时间的影响.     

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.     

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.     

Damage identification by response surface based model updating using D-optimal design

Statistical tools, as well as mathematical ones, have been widely adopted and their performance has been shown in different engineering problems where randomicity usually exists. In the realm of engineering, merging statistical analysis into structural evaluation and assessment will be a tendency in the future. As a combination of mathematical and statistical techniques, response surface methodology has been successfully applied to design optimization, response prediction and model validation. This methodology provides explicit functions to represent the relationships between the inputs and outputs of a physical system, which is also a desirable advantage in damage identification. However, so far little research has been carried out in applying the response surface methodology to structural damage identification. This paper presents a damage identification method achieved by response surface based model updating using D-optimal designs. Compared with some common designs constructing response surfaces, D-optimal designs generally require a minimum number of numerical samples and this merit is quite desirable when analysts cannot obtain enough samples. In this study, firstly D-optimal designs are used to establish response surface models for screening out non-significant updating parameters and then first-order response surface models are constructed to substitute for finite element models in predicting the dynamic responses of an intact or damaged physical system. Three case studies of a numerical beam, a tested reinforced concrete frame and a tested full-scale bridge have been used to verify the proposed method. Physical properties such as Young’s modulus and section inertias were chosen as the input features and modal frequency was the only response feature. It has been observed that the proposed method gives enough accuracy in damage prediction of not only the numerical but also the real-world structures with single and multiple damage scenarios, and the first-order response surface models based on the D-optimal criterion are adequate for such damage identification purposes.     

轿车白车身有限元模型修正研究

有限元模型与实际结构的一致性影响着CAE分析的可靠性。以典型点焊薄板件为例,分别采用刚性梁单元和等效板两种方式对结合面连接刚度进行了修正方法研究,并将研究方法成功应用于某轿车白车身的有限元模型上。修正后有限元模型的分析结果与试验结果基本一致。     

Model updating of locally non-linear systems based on multi-harmonic extended constitutive relation error

Improving the fidelity of numerical simulations using available test data is an important activity in the overall process of model verification and validation. While model updating or calibration of linear elastodynamic behaviors has been extensively studied for both academic and industrial applications over the past three decades, methodologies capable of treating non-linear dynamics remain relatively immature. The authors propose a novel strategy for updating an important subclass of non-linear models characterized by globally linear stiffness and damping behaviors in the presence of local non-linear effects. The approach combines two well-known methods for structural dynamic analysis. The first is the multi-harmonic balance (MHB) method for solving the non-linear equations of motion of a mechanical system under periodic excitation. This approach has the advantage of being much faster than time domain integration procedures while allowing a wide range of non-linear effects to be taken into account. The second method is the extended constitutive relation error (ECRE) that has been used in the past for error localization and updating of linear elastodynamic models. The proposed updating strategy will be illustrated using academic examples.     

Stochastic model updating: Part 2—application to a set of physical structures

The application of a stochastic model updating technique using Monte-Carlo inverse propagation and multivariate multiple regression to converge a set of analytical models with randomised updating parameters upon a set of nominally identical physical structures is considered. The structure in question is a short beam manufactured from two components, one of folded steel and the other flat. The two are connected by two rows of spot-welds. The main uncertainty in the model is concerned with the spot-weld but there is also considerable manufacturing variability, principally in the radii of the folds.     

Statistical updating of finite element model with Lamb wave sensing data for damage detection problems

Health monitoring of large structures with embedded, distributed sensor systems is gaining importance. This study proposes a new probabilistic model updating method in order to improve the damage prediction capability of a finite element analysis (FEA) model with experimental observations from a Lamb-wave sensing system. The approach statistically calibrates unknown parameters of the FEA model and estimates a bias-correcting function to achieve a good match between the model predictions and sensor observations. An experimental validation study is presented in which a set of controlled damages are generated on a composite panel. Time-series signals are collected with the damage condition using a Lamb-wave sensing system and a one dimensional FEA model of the panel is constructed to quantify the damages. The damage indices from both the experiments and the computational model are used to calibrate assumed parameters of the FEA model and to estimate a bias-correction function. The updated model is used to predict the size (extent) and location of damage. It is shown that the proposed model updating approach achieves a prediction accuracy that is superior to a purely statistical approach or a deterministic model calibration approach.     

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.     

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.     

基于贝叶斯更新的机电作动器健康因子构建方法

机电作动器(EMA)由于重量轻、体积小、可靠性高等优势成为多电/全电飞机的核心部件,逐步广泛应用于各类多电/全电飞机中。然而,EMA动态变化的运行模式和载荷工况给其退化建模和健康因子(HI)估计带来较大挑战。因此,提出一种基于贝叶斯更新的EMA HI构建方法。首先基于历史监测数据构建HI先验模型,在此基础上,结合贝叶斯更新理论和实时监测数据对EMA HI先验模型参数分布进行迭代更新,最终实现不同运行模式和载荷工况下EMA退化状态的准确表征。为解决变工况条件下EMA HI构建模型失配问题提供了一种新颖的思路,并基于NASA公开数据集进行了实验验证。结果表明,与基于模型辨识的EMA HI构建方法相比,基于贝叶斯更新的EMA HI构建方法具有更强的工况适应能力,能够在变工况条件下有效地构建出EMA HI。     

特征融合和模型自适应更新相结合的相关滤波目标跟踪

提出了一种基于自适应特征融合和自适应模型更新的相关滤波跟踪算法(CFT)。该算法在跟踪的训练阶段利用损失函数计算特征的自适应权重,在检测阶段对不同特征的响应图进行加权求和,从而实现了响应图层面的自适应特征融合。设计了自适应的模型更新策略,采用响应图的峰值旁瓣比判断是否发生遮挡或错误跟踪,据此决定是否在当前帧更新目标模型。在11个视频序列上对所提算法进行了实验,验证了所采用的自适应特征融合策略和自适应模型更新策略的有效性。与多个传统的采用单特征的相关滤波跟踪算法进行了比较,结果显示,所提算法的跟踪精度和成功率典型值分别提升了18.2%和11.5%。实验结果验证了特征融合和自适应模型更新对跟踪算法的改进具有指导意义。     

Model error correction from truncated modal flexibility sensitivity and generic parameters: Part I—simulation

A great advantage of the flexibility based method is the availability of the large amount of measured information from a few lower modes which can be practically measured. But the modal truncated errors would be significant for a structure with high modal density, and this poses a limitation on the usage of existing flexibility methods. This paper presents the truncated modal flexibility sensitivity with respect to the generic parameters, and a model updating method is proposed based on this sensitivity and incomplete measurement. The loss of contribution from the higher modes to the modal flexibility will not be a source of error in the proposed method. The effect of spatial incompleteness and measurement noise is investigated with numerical studies. The proposed approach is found capable of updating both the systematic model error and local stiffness error separately in a single or two stages under noisy environment.     

Interval model updating with irreducible uncertainty using the Kriging predictor

Interval model updating in the presence of irreducible uncertain measured data is defined and solutions are made available for two cases. In the first case, the parameter vertex solution is used but is found to be valid only for particular parameterisation of the finite element model and particular output data. In the second case, a general solution is considered, based on the use of a meta-model which acts as a surrogate for the full finite element mathematical model. Thus, a region of input data is mapped to a region of output data with parameters obtained by regression analysis. The Kriging predictor is chosen as the meta-model in this paper and is found to be capable of predicting the regions of input and output parameter variations with very good accuracy. The interval model updating approach is formulated based on the Kriging predictor and an iterative procedure is developed. The method is validated numerically using a three degree of freedom mass-spring system with both well-separated and close modes. A significant advantage of Kriging interpolation is that it enables the use of updating parameters that are difficult to use by conventional correction of the finite element model. An example of this is demonstrated in an experimental exercise where the positions of two beams in a frame structure are selected as updating parameters.     

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。     

一种夹层板结构车厢的有限元简化模型及模态分析

以某型车的车厢夹层复合板结构为例,研究了夹层板结构的有限元建模方法,建立了车厢的有限元简化模型并进行了模态分析。与传统上使用的板梁单元相比,单元自由度数减少了66.7%,大大缩短了分析时间,提高了计算效率。     

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.