基于频响函数截断奇异值响应面的有限元模型修正

发布时间：2018-03-19 16:57

本文选题：模型修正　切入点：频响函数　出处：《振动工程学报》2017年03期 　论文类型：期刊论文

【摘要】：考虑由于模型参数误差造成的有限元模型偏差的问题,提出一种基于频响函数截断奇异值响应面的模型修正方法。利用傅里叶反变换将结构频响函数变换为时域内的脉冲响应函数,通过延迟坐标法重构脉冲响应函数的相空间矩阵,进而对相空间矩阵进行截断奇异值分解,提取有限个较大的奇异值作为频响函数的特征量。以待修正模型参数为样本集输入,截断的奇异值为样本集输出,建立支持向量机响应面模型并进行训练,以逼近模型待修正参数与频响函数的特征量之间的非线性映射关系。以目标频响函数的特征量与支持向量机响应面模型输出的特征量之间的差值最小化为目标,利用遗传算法通过优化求解参数修正量。仿真计算表明:支持向量机的保留奇异值响应面能准确预报训练集以外样本的保留奇异值,具有较强的泛化能力;结合遗传优化算法能获得准确的参数修正量,算法对噪声有较强的鲁棒性。
[Abstract]:Considering the problem of finite element model deviation caused by model parameter error, A model modification method based on frequency response function truncating singular value response surface is proposed. The structural frequency response function is transformed into a pulse response function in time domain by Fourier inverse transform, and the phase space matrix of pulse response function is reconstructed by delayed coordinate method. Then the truncated singular value decomposition of the phase space matrix is carried out, and a finite number of singular values are extracted as the eigenvalues of the frequency response function. The parameters of the model to be modified are taken as the input of the sample set, and the truncated singular value is the output of the sample set. Support vector machine response surface model is established and trained. The objective is to minimize the difference between the eigenvalue of the target frequency response function and the output of the support vector machine response surface model. The genetic algorithm is used to optimize the parameter correction. The simulation results show that the support vector machine's reserved singular value response surface can accurately predict the reserved singular value of the samples outside the training set and has a strong generalization ability. Combined with genetic optimization algorithm, accurate parameter correction can be obtained, and the algorithm is robust to noise.
【作者单位】：清华大学汽车安全与节能国家重点实验室;
【基金】：科技部国际合作项目(2014DFG71590)
【分类号】：TB115;TP18

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