基于频响函数奇异值的模型修正方法

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摘要为减少实测环境中噪声的干扰，提出了一种基于频响函数奇异值的模型修正方法。利用计算得到的频响函数重构吸引子矩阵，对其进行奇异值分解，并在受噪声影响时根据极值点数量突变原则选择保留主要特征信息的奇异值个数，然后确定待修正参数；采用拉丁超立方抽样抽取初始样本点，结合修正参数所对应的奇异值响应，用粒子群算法寻得最优相关系数，构建Kriging模型；以奇异值响应差的平方最小构造目标函数，利用布谷鸟算法求解参数修正值。仿真算例表明：以奇异值作为结构响应，构建Kriging模型能获得较高的修正精度；在频响函数中加入不同信噪比的高斯白噪声，仍能得到较满意的修正效果，证明了本文方法对噪声具有较强的鲁棒性。

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	曹明明
	彭珍瑞
	刘满东

关键词 ：模型修正, 频响函数, 奇异值分解, 极值点, 粒子群算法, Kriging模型

Abstract：In order to reduce noise interference in measurement environment, a model updating method based on singular value of frequency response function (FRF) was proposed. Firstly, FRF obtained with calculation was used to reconstruct the attractor matrix, and the singular value decomposition (SVD) was performed for it. Under influence of noise, the number of singular values containing the main characteristic information was selected according to the principle of sudden change in the number of extreme value points, and then parameters to be corrected were determined. Secondly, initial sample points were extracted with Latin hypercube sampling, and the particle swarm optimization algorithm was used to find the optimal correlation coefficient, it was combined with singular value response corresponding to parameters to be corrected to construct Kriging model. Then, the objective function was constructed using the least square of the response difference of singular value, and Cuckoo algorithm was used to solve parameter correction values. Simulation examples showed that Kriging model can obtain higher correction accuracy by using singular value as structural response; adding Gaussian white noise with different signal-to-noise ratios in FRF, a more satisfactory updating effect can be obtained to verify stronger robustness of the proposed method to noise.

Key words： model updating frequency response function (FRF) singular value decomposition (SVD) extreme value point particle swarm optimization algorithm Kriging model

收稿日期: 2019-09-09 出版日期: 2021-02-15

引用本文:

曹明明，彭珍瑞，刘满东. 基于频响函数奇异值的模型修正方法[J]. 振动与冲击, 2021, 40(3): 195-203.
CAO Mingming, PENG Zhenrui, LIU Mandong. Model updating method based on singular value of frequency response function. JOURNAL OF VIBRATION AND SHOCK, 2021, 40(3): 195-203.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2021/V40/I3/195

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