Sensitivity analysis of frequency response functions with imaginary parts decoupling based on multicomplex-step perturbation

被引:0
|
作者
Qian, Hui [1 ]
Li, Ang [1 ]
Tian, Yu [1 ]
Wang, Yusheng [1 ]
Cao, Zhifu [2 ]
Liu, Qinghua [1 ]
Jiang, Dong [1 ]
机构
[1] Nanjing Forestry Univ, Sch Mech & Elect Engn, Nanjing 210037, Jiangsu, Peoples R China
[2] Chongqing Univ, Coll Aerosp Engn, Chongqing 400044, Peoples R China
基金
中国国家自然科学基金;
关键词
Sensitivity analysis; Multicomplex-step perturbation; Frequency response function; Complex variable decoupling; Hessian matrix; OPTIMIZATION;
D O I
10.1016/j.apm.2024.115669
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
Imaginary perturbation is used in the complex step differentiation method to compute first-order derivatives, widely known as an effective approach for sensitivity analysis in structural dynamics. However, coupling of imaginary parts occurs in the damped frequency response functions when employing this method. To mitigate this coupling, a novel approach for sensitivity analysis based on multicomplex-step perturbation is proposed in this paper, for sensitivity analysis of Frequency Response Functions in structural dynamics. The structural parameters are perturbed in multicomplex domain, the dimensions of structural matrices are expanded using the Cauchy Riemann matrix representation, the equation of motion for sensitivity analysis in frequency domain is transformed to matrix operation in field of real numbers, imaginary term will not exist in the equation of motion for sensitivity analysis, the imaginary part of the frequency response function and the imaginary part of the perturbation are decoupled, the structural frequency response functions and the corresponding sensitivities are obtained from the dimension-expanded equation of motion. A truss structure and a solar wing are adopted to verify the accuracy of the proposed method. Results show that the sensitivity of FRFs can be effectively calculated using the proposed method. Compare to the finite difference method, the proposed method is not depended on the step-size selection procedure. The multi-order and mixed-order sensitivity matrices, especially Hessian matrix can also be obtained using the proposed method.
引用
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页数:20
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