基于曲线拟合的改进型FDD算法ImCFDD

Improved frequency domain decomposition algorithm ImCFDD based on curve-fitting

提出了一种基于曲线拟合的改进型FDD算法Im CFDD,以加速度自功率谱矩阵的SVD分解得到的主奇异值为对象,推导了主奇异值与模态参数间的关系。推导表明:主奇异值与加速度自功率谱函数是等价的,奇异值可以分解为关于频率ω的分子和分母均为4阶的比值形式。据此建立了求解模态参数的表达式,并给出了迭代拟合算法。所提算法同频域分解算法FDD、增强型的频域分解算法EFDD、曲线拟合频域分解算法CFDD、频域空间分解算法FSDD有着本质的不同,在公式的推导上做了最小的简化,同时考虑了负频率部分和共轭极点部分的贡献,得到的模态参数求解方程是非线性的,需要迭代求解。最后,采用数值模型验证了新算法的有效性。

This paper presents an improved curve-fitting frequency domain decomposition algorithm（ImCFDD） and also derives the relationship between modal parameters and singular values which comes from SVD of a PSD matrix of acceleration. The derivation shows that the main singular value is equal to PSD of acceleration, singular values can be decomposed into an fractional form which numerator and denominator are the 4th order of jω. On those grounds, the author derived the expression to solve modal parameters and its nonlinear iterative solution algorithm. The new improved algorithm--ImCFDD is not the same as frequency domain decomposition（FDD） , enhanced fre- quency domain decomposition （ EFDD ）, curve-fitting frequency domain decomposition （ CFDD ）, frequency-spatial domain decomposition（FSDD） in essence. It is based on the least simplification in formula derivation and contains the contributions from negative frequency parts and conjugate poles. Also the equations obtained is nonlinear, it needs iterative solution. In the end of this paper, a numerical modal is used to test the validity of the new algorithm.