多参考最小二乘复频域法的数值问题分析及优化
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TB122;TU311.3

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国家自然科学基金资助项目(51705114);浙江省自然科学基金资助项目(LQ16E080009);浙江省教育厅一般科研资助项目(Y201430581);浙江省水利科技计划项目(RC1807);杭州市科技计划项目(20191203B72)


Numerical analysis and optimization of poly⁃reference least-squares complex frequency-domain method
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    摘要:

    分析多参考最小二乘复频域法在实际应用中的数值问题,提出一种多参考最小二乘复频域优化方法。由于实际系统阶次未知,为了避免模态遗漏,需先过估计系统阶次。通过理论与数值分析发现:由于系统阶次过估计,识别过程需要对奇异矩阵进行伪逆计算,伪逆计算方法和参数的选择对识别结果有很大影响。利用特征值分解计算奇异矩阵 Ro的伪逆矩阵,通过奇异值分解计算奇异矩阵 Msub的伪逆矩阵,以能量为指标自动确定阶次,在不失精度的前提下可自动得到清晰稳定图。利用优化多参考最小二乘复频域法对一个 7 自由度线性时不变系统和葡萄牙Infante D. Henrique 大桥辨识,实验结果表明本文方法可以在保持精度的前提下容易地识别系统模态。

    Abstract:

    This paper analyzes the numerical problems in practical application of polyreference least-squares complex frequency-domain method,and proposes an optimization algorithm of polyreference least-squares complex frequency-domain method. The order of a real structure that cannot be estimated accurately is always overestimated to find all physical modes. Theoretical and numerical analyses show that pseudo-inverse calculation of some singular matrixes is required in the analyses process due to the overestimation of the order of the system and the selection of pseudo-inverse calculation method and parameters has a great influence on the recognition results. Eigenvalue decomposition is used to calculate the pseudo-inverse matrix of the singular matrix Ro,singular value decomposition is used to calculate the pseudo-inverse matrix of the singular matrix Msub,and the order is automatically determined by energy index. A clear stabilization diagram can be obtained automatically without losing accuracy. The proposed method is applied on the parameter estimation of a linear time-invariant system of 7 degrees of freedom and of the Infante D. Henrique bridge located at the North of Portugal,it is demonstrated that the proposed method can identify physical modes easily without losing accuracy.

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章国稳,汤宝平,陈 卓.多参考最小二乘复频域法的数值问题分析及优化[J].振动工程学报,2021,34(4):690~696.[ZHANG Guo-wen, TANG Bao-ping, CHEN Zhuo. Numerical analysis and optimization of poly⁃reference least-squares complex frequency-domain method[J]. Journal of Vibration Engineering,2021,34(4):690~696.]

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  • 在线发布日期: 2022-09-30
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