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中文核心期刊

基于频响特征图的稳健有限元模型修正

ROBUST FINITE ELEMENT MODEL UPDATING METHOD BASED ON THE FEATURE MAP OF FREQUENCY RESPONSE FUNCTIONS

  • 摘要: 航空航天工程领域对飞机的性能指标和技术要求越来越苛刻, 传统方法在处理大规模、多工况的有限元模型修正问题时面临诸多挑战, 当前深度学习技术的快速发展为有限元模型修正提供了新的思路. 频响函数(FRF)囊括了结构的所有动态特性信息, 基于频响函数的方法是当前有限元模型修正研究的热点问题. 传统的基于频响函数的模型修正方法存在频率点选择、灵敏度矩阵数值异常、抗噪性差、耦合模态难以处理等问题, 为此本文提出一种基于频响特征图的稳健模型修正方法(FMFRF). 该方法借助贝叶斯卷积神经网络(BCNN), 将模型修正转化为正问题进行研究. BCNN的输入为若干条频响函数经处理和整合形成的频响特征图, 其输出为需要修正的模型参数. 贝叶斯框架能够减少神经网络在小数据集上的过拟合现象, 使训练具有更强的鲁棒性, 进而增强了频响特征图和模型参数之间复杂映射关系的拟合准确性. 基于频响特征图的方法不仅具备传统基于频响函数的方法的优点, 如无需模态识别和模态匹配, 可同时修正结构参数和阻尼等, 还显著地提升了修正效率和抗噪性. 本文首先以数值仿真为例, 证明了该方法相较于经典的基于频响的迭代方法具有更准确的修正精度和更强的抗噪性, 且对于多钟不同工况的修正更具有效率. 然后以包含六根加强肋的钛合金壁板为例对该方法进行实验验证, 证明了该方法在工程复杂结构中的有效性.

     

    Abstract: As the performance metrics and technical requirements in aerospace engineering become increasingly stringent, traditional methods face numerous challenges in addressing large-scale, multi-condition finite element model updating problems. The rapid development of deep learning technologies provides new perspectives for finite element model updating. The frequency response function (FRF) contains all the dynamic information of a structure, making FRF-based methods a popular topic in current finite element model updating research. However, traditional FRF-based model updating methods suffer from several issues, such as the selection of frequency points, numerical instability in the sensitivity matrices, poor noise resistance, and difficulties in handling coupled modes. To address these challenges, we propose a robust model updating method based on the feature map of frequency response functions (FMFRF). This approach treats the model updating as a forward problem by using a Bayesian Convolutional Neural Network (BCNN). The FRFs of multiple sensors are combined and transformed into feature maps, which are then used as inputs to the BCNN. The output of the BCNN is a vector composed of uncertain model parameters. The Bayesian framework helps mitigate overfitting in neural networks when dealing with small datasets, thus enhancing training robustness and improving the accuracy of mapping the relationship between FMFRFs and model parameters. This method retains the advantages of traditional FRF-based methods, such as eliminating the need for mode identification and mode matching, and allows for simultaneous updating of structural parameters and damping. Moreover, it significantly improves both efficiency and noise immunity. This paper first demonstrates, through numerical simulation, that the proposed method achieves higher accuracy and stronger noise immunity compared to the classical frequency response-based iterative method, and is more efficient in updating under multiple operating conditions. Then, the method is experimentally validated using a titanium alloy wall plate with six reinforcing ribs, proving its effectiveness in complex engineering structures.

     

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