Nonlinear finite element model updating of an infilled frame based on identified time-varying modal parameters during an earthquake

A model updating methodology is proposed for calibration of nonlinear finite element (FE) models simulating the behavior of real-world complex civil structures subjected to seismic excitations. In the proposed methodology, parameters of hysteretic material models assigned to elements (or substructures) of a nonlinear FE model are updated by minimizing an objective function. The objective function used in this study is the misfit between the experimentally identified time-varying modal parameters of the structure and those of the FE model at selected time instances along the response time history. The time-varying modal parameters are estimated using the deterministic–stochastic subspace identification method which is an input–output system identification approach. The performance of the proposed updating method is evaluated through numerical and experimental applications on a large-scale three-story reinforced concrete frame with masonry infills. The test structure was subjected to seismic base excitations of increasing amplitude at a large outdoor shake-table. A nonlinear FE model of the test structure has been calibrated to match the time-varying modal parameters of the test structure identified from measured data during a seismic base excitation. The accuracy of the proposed nonlinear FE model updating procedure is quantified in numerical and experimental applications using different error metrics. The calibrated models predict the exact simulated response very accurately in the numerical application, while the updated models match the measured response reasonably well in the experimental application.     

Structural damage identification of the highway bridge Z24 by FE model updating

The development of a methodology for accurate and reliable condition assessment of civil structures has become very important. The finite element (FE) model updating method provides an efficient, non-destructive, global damage identification technique, which is based on the fact that the modal parameters (eigenfrequencies and mode shapes) of the structure are affected by structural damage. In the FE model the damage is represented by a reduction of the stiffness properties of the elements and can be identified by tuning the FE model to the measured modal parameters. This paper describes an iterative sensitivity based FE model updating method in which the discrepancies in both the eigenfrequencies and unscaled mode shape data obtained from ambient tests are minimized. Furthermore, the paper proposes the use of damage functions to approximate the stiffness distribution, as an efficient approach to reduce the number of unknowns. Additionally the optimization process is made more robust by using the trust region strategy in the implementation of the Gauss-Newton method, which is another original contribution of this work. The combination of the damage function approach with the trust region strategy is a practical alternative to the pure mathematical regularization techniques such as Tikhonov approach. Afterwards the updating procedure is validated with a real application to a prestressed concrete bridge. The damage in the highway bridge is identified by updating the Young's and the shear modulus, whose distribution over the FE model are approximated by piecewise linear functions.     

Model updating using uncorrelated modes

FE model updating techniques are used to update dynamic FE models of structures in the light of modal test data. Iterative methods of model updating that update a set of chosen parameters of the model, so as to reduce the difference between the natural frequencies and the mode shapes of the FE model and the corresponding quantities obtained through a modal test on the structure, are probably the most widely used methods. Once experimental modal data has been identified, a necessary prior step, before updating can be carried out, is that of establishing the correspondence between the FE model modes and the experimentally identified modes.     

Regularised finite element model updating using measured incomplete modal data

This paper presents an effective approach for directly updating finite element model from measured incomplete vibration modal data with regularised algorithms. The proposed method is based on the relationship between the perturbation of structural parameters such as stiffness change and the modal data measurements of the tested structure such as measured mode shape readings. In order to adjust structural parameters at detailed locations, structural updating parameters will be selected at critical point level to reflect the modelling errors at the connections of structural elements. These updating parameters are then evaluated by an iterative or a direct solution procedure, which gives optimised solutions in the least squares sense without requiring an optimisation technique. In order to reduce the influence of modal measurement uncertainty, the Tikhonov regularisation method incorporating the L-curve criterion is employed to produce reliable solutions for the chosen updating parameters. Numerical simulation investigations and experimental studies for the laboratory tested space steel frame structure are undertaken to verify the accuracy and effectiveness of the proposed methods for adjusting the stiffness at the joints of structural members. The results demonstrate that the proposed methods provide reliable estimates of finite element model updating using the measured incomplete modal data.     

Structural damage identification for railway bridges based on train-induced bridge responses and sensitivity analysis

A damage identification approach using train-induced responses and sensitivity analysis is proposed for the nondestructive evaluation of railway bridges. The dynamic responses of railway bridges under moving trains composed of multiple vehicles are calculated by a train-bridge dynamic interaction analysis. Using the stiffness variation of the bridge element as an index for damage identification, the sensitivities of train-induced bridge responses to structural damage are analyzed and the sensitivity matrices are formed. By comparing the theoretical measurement responses of one measurement point in two different states, the damage indices of all elements are updated iteratively, and finally the absolute or relative damage is located and quantified. A three-span continuous bridge numerical example proves that the proposed dynamic response sensitivity-based FE model updating damage identification method is not only effective to detect local damage of railway bridges, but also insensitive to the track irregularity and the measurement noise.     

A method for analyzing vibration power absorption density in human fingertip

In the current study, we hypothesize that the vibration power absorption density (VPAD) is a good measure for the vibration exposure intensity of the soft tissues of the fingers. In order to calculate the VPAD at a fingertip, we proposed a hybrid modeling approach, which combines a 2D finite element (FE) model with a lumped parameter model. Whereas the lumped components are used to represent the global biodynamic characteristics of the hand-arm system, the FE component is used to predict the detailed stresses, strains, and VPAD in the fingertip. The lumped parameters are determined by using the vibration transmissibilities measured at the fingertip, while the material parameters of the soft and hard tissues of the FE model are adopted from the published experimental data. The proposed model was applied to predict the distributions of dynamic displacement, velocity, and VPAD in the soft tissues of the fingertip. Furthermore, we have derived the frequency weighting based on the VPAD of the soft tissue. The preliminary analysis indicated that the VPAD-based frequency weighting is substantially different from the ISO weighting in that the ISO frequency weighting emphasizes the effect of the vibration at frequencies lower than 25 Hz whereas the VPAD-based weighting generally emphasizes the resonant responses of the finger. Our analysis indicated that the VPAD-based weighting was fairly consistent with the finger surface vibration transmissibility at frequencies greater than the first resonance, suggesting that the finger surface transmissibility may be used as an alternative frequency weighting for assessing the finger vibration exposure. The proposed method provides a practical and efficient tool to simulate the detailed biodynamic responses of a complex biological system to vibration.     

Modal Overlap Factor of a beam with an acoustic black hole termination

An Acoustic Black Hole (ABH) effect is a passive vibration reduction technique which takes advantage of properties of wave propagation in thin structures of varying thickness. A practical implementation of ABH on a uniform beam consists in an extremity whose thickness follows a power-law profile covered by a very thin layer of additional damping material. A modal analysis based on a High Resolution technique shows that the ABH significantly increases the Modal Overlap Factor (MOF) of the beam, thus reducing the resonant behaviour of the structure. Further investigations, including a two-dimensional numerical model of the structure based on the finite difference method, show that this MOF can be explained by an increase of the modal density and a high damping of a number of modes of the structure due to the ABH.     

响应面法的杆式超声电机有限元模型修正

现有杆式超声电机的有限元模型大都采用连续复合材料的简化结构形式,忽略了实际超声电机各部件间的接触特性,导致计算结果与实验结果具有较大偏差。针对该问题,提出了一种采用响应面法的杆式超声电机有限元模型修正方法,来获得高精度的有限元模型。该方法考虑了超声电机螺栓预紧力及各部件接触界面的法向接触刚度和摩擦系数,筛选出显著影响电机工作模态的参数,建立响应面模型替代超声电机的有限元模型实现快速计算结构响应的目的,并以实验模态分析结果为目标对模型进行修正。修正结果表明,修正后的模型模态频率的平均误差由修正前的1.20%降到0.21%,模型精度得到明显改善,表明以响应面的有限元模型修正方法对杆式超声电机以及类似夹心式压电振子的设计具有应用价值。      

Finite grade pheromone ant colony optimization for image segmentation

By combining the decision process of ant colony optimization (ACO) with the multistage decision process of image segmentation based on active contour model (ACM), an algorithm called finite grade ACO (FACO) for image segmentation is proposed. This algorithm classifies pheromone into finite grades and updating of the pheromone is achieved by changing the grades and the updated quantity of pheromone is independent from the objective function. The algorithm that provides a new approach to obtain precise contour is proved to converge to the global optimal solutions linearly by means of finite Markov chains. The segmentation experiments with ultrasound heart image show the effectiveness of the algorithm. Comparing the results for segmentation of left ventricle images shows that the ACO for image segmentation is more effective than the GA approach and the new pheromone updating strategy appears good time performance in optimization process.     

基于Pareto优化理论的多目标超椭梯度线圈设计

磁共振系统梯度线圈设计是一个多目标优化问题,在设计时需要综合考虑能耗、磁场能、线性度等设计要求.这些设计要求通常难以同时获得极小解,因此在设计梯度线圈时需要权衡线圈的各方面的设计需求.本文基于柱面可展性和流函数设计方法,结合Pareto优化方法实现了在超椭圆柱设计表面上梯度线圈的多目标设计.分别分析了磁场能、能耗目标对梯度线圈线性度、线圈构型的影响;并在Pareto解空间中分析各目标的相互变化关系,通过数值算例验证了该方法在超椭梯度线圈设计时的有效性与灵活性.优化结果显示,在满足线性度误差小于5%,能耗与磁场能分别小于用户设定值的设计约束下,梯度线圈的多目标设计存在多个局部优化解.该方法可以直观地比较相同目标函数值的情况下各单目标的具体表现,有利于实现不同的设计要求下梯度线圈的最终定型设计.     

Self-adaptive modal control for time-varying structures

For the past several years, modal controllers are widely studied and used in the field of vibration or vibro-acoustics control. They are efficient but not robust, because these methods involve a reconstructor based on a modal truncation. When the dynamic behavior of the structure change, the controller and reconstructor must be updated to cope with the changes in the structure behavior, in order to maintain both performance and robustness. A solution is adaptive control but this approach needs some specific information not generally available particularly in the case of undergone modifications. This paper deals with a self-adaptive modal control based on a real-time identifier, which avoid the need of specific information. The identifier permits to update the controller and the reconstructor according to the changes of modal characteristics of time-varying structures. A classical algorithm of identification is used to obtain a state space model with an unspecified state vector. Then, based on this model, a well adapted transformation is carried out to get the modal characteristics from the expression of complex modes, including the mode shapes. As a criterion of running identification, the value of “variance-accounted for” (VAF) is employed to carry out the identifier only when the initial or previous model is not enough exact. A Linear Quadratic Gaussian Algorithm is employed in such a way that the controller and observer can be optimized according to the updated modal model. By this way, a self-adaptive modal control is completed and can demonstrate some smart properties. The proposed methodology is carried out on a simple but representative time-varying mechanical discrete structure. An inertia modification leads not only to low modal frequency shifts but also to inversion of a mode shape which is shown to lead to unstable configuration when control system is not updated. The overall procedure will be described through simulations and performed for different operating conditions, which will prove that mode shapes have to be precisely determined and updated in the controller and observer to guarantee a robust modal control with high performance in spite of the changes of structure.     

用子结构模态综合法求解光学反射镜组件结构动响应

在航天光学成像仪器中光学反射镜组件结构复杂,相应的有限元分析模型大,因此分析效率较低。针对此问题,引入子结构模态综合法作为光学反射镜组件结构动响应的求解方法。具体讨论了子结构模态综合法求解结构动响应的基本原理,说明了该法在工程上的实现方法。以某反射镜组件为例进行了计算,结果表明,子结构模态综合法与经典的整体FE分析法比较,求解的前10个固有频率误差小于7%,计算时间前者为后者的2/3;加速度响应曲线符合良好,计算时间前者为后者的2/5,子结构模态综合法的计算效率明显提高,工程适用性良好。     

注射用头孢他啶中头孢他啶、水分和精氨酸近红外定量模型的更新

以注射用头孢他啶通用性定量分析模型为例,通过对新的预测样本光谱与原模型训练集光谱相似性的研究,寻找更为合理的用于判断模型更新的指标以及模型更新的一般方法。对注射用头孢他啶新的待测样品,首先使用聚类分析的方法将所有样品分成5类,依次加入每一类中代表性光谱到原模型中进行模型更新,计算模型更新前后的平均预测偏差,并以此作为评判模型更新是否有效的标准。同时以相似系数为指标探讨模型更新的一般方法。再应用注射用头孢他啶通用性定量分析模型(包括头孢他啶、水分及精氨酸的定量分析模型)以及新的预测样品对该方法进行验证。实验数据证明当新样本光谱与原模型训练集样本的平均光谱在原模型建模谱段上的相似系数(r_T)小于96.5%时,模型需要更新。使用上述判断指标对含碳酸钠为助溶剂的样品进行模型更新后,预测头孢他啶含量的平均偏差由8.1%变为2.3%,预测水分含量的平均偏差由2.2%变为0.3%;对含精氨酸为助溶剂样品,预测头孢他啶含量的平均偏差由7.0%变为1.9%,预测水分含量的平均偏差由0.6%变为0.3%,预测精氨酸含量的平均偏差由2.3%变为0.4%。经过更新的模型能够用于分析国内市场上常见的注射用头孢他啶中头孢他啶、水分及精氨酸含量。以r_T作为模型更新指标较为合理,必要时可以参考新预测样品光谱与原模型训练集光谱的PCA得分图进行判断,该模型更新方法具有一定的普适性,r_T=96.5%可以初步作为判断模型是否需要更新的阈值。     

考虑结合部特征的?150 mm口径反射镜模型修正

针对?150 mm口径反射镜受结合部的非线性因素影响导致结构分析模型精度较差的问题,提出了线性的动力学等效建模与参数修正方法。首先,在实际装配和约束环境下测试并获得了反射镜结构的试验模态参数。然后,根据界面结合部的动力学特征,对反射镜结构按照镜框固定连接模型、镜面螺钉夹持模型以及间隙等效模型进行了等效建模。最后,以试验模态参数为修正目标,采用优化方法对反射镜结构的动力学等效模型进行了参数修正,并采用模型分层和分步修正的思路,依据结合部特征将修正模型细分为两部分,提高模型参数的修正效率。结果表明,参数修正后的固有频率平均误差为1.5%,模态置信度均大于0.8,提升了反射镜结构的动力学模型精度,验证了线性化等效建模方法的正确性。     

An automatic mode pairing strategy using an enhanced modal assurance criterion based on modal strain energies

In the context of finite element model updating using output-only vibration test data, natural frequencies and mode shapes are used as validation criteria. Consequently, the correct pairing of experimentally obtained and numerically derived natural frequencies and mode shapes is important. In many cases, only limited spatial information is available and noise is present in the measurements. Therefore, the automatic selection of the most likely numerical mode shape corresponding to a particular experimentally identified mode shape can be a difficult task. The most common criterion for indicating corresponding mode shapes is the modal assurance criterion. Unfortunately, this criterion fails in certain cases and is not reliable for automatic approaches.In this paper, the purely mathematical modal assurance criterion will be enhanced by additional physical information from the numerical model in terms of modal strain energies. A numerical example and a benchmark study with experimental data are presented to show the advantages of the proposed energy-based criterion in comparison to the traditional modal assurance criterion.     

Analytic approach to dielectric optical bent slab waveguides

A rigorous classical analytic frequency domain model of confined optical wave propagation along 2D bent slab waveguides and curved dielectric interfaces is investigated, based on a piecewise ansatz for bend mode profiles in terms of Bessel and Hankel functions. This approach provides a clear picture of the behaviour of bend modes, concerning their decay for large radial arguments or effects of varying bend radius. Fast and accurate routines are required to evaluate Bessel functions with large complex orders and large arguments. Our implementation enabled detailed studies of bent waveguide properties, including higher order bend modes and whispering gallery modes, their interference patterns, and issues related to bend mode normalization and orthogonality properties.     

Inverse substructure method for model updating of structures

Traditional model updating of large-scale structures is usually time-consuming because the global structural model needs to be repeatedly re-analyzed as a whole to match global measurements. This paper proposes a new substructural model updating method. The modal data measured on the global structure are disassembled to obtain the independent substructural dynamic flexibility matrices under force and displacement compatibility conditions. The method is extended to the case when the measurement is carried out at partial degrees-of-freedom of the structure. The extracted substructural flexibility matrices are then used as references for updating the corresponding substructural models. An orthogonal projector is employed on both the extracted substructural measurements and the substructural models to remove the rigid body modes of the free–free substructures. Compared with the traditional model updating at the global structure level, only the sub-models at the substructural level are re-analyzed in the proposed substructure-based model updating process, resulting in a rapid convergence of optimization. Moreover, only measurement on the local area corresponding to the concerned substructures is required, and those on other components can be avoided. The effectiveness and efficiency of the proposed substructuring method are verified through applications to a laboratory-tested frame structure and a large-scale 600 m tall Guangzhou New TV Tower. The present technique is referred to as the inverse substructuring model updating method as the measured global modal data are disassembled into the substructure level and then the updating is conducted on the substructures only. This differs from the substructuring model updating method previously proposed by the authors, in which the model updating is still conducted in the global level and the numerical global modal data are assembled from those of substructures. That can be referred to as the forward substructuring model updating method.