多元统计分析的模态参数辨识方法比较及应用

Comparison and Application of Modal Parameter Identification Methods in Multivariate Statistical Analysis

工作模态参数辨识是实现飞行器结构精细化设计和安全评估的关键基础问题。基于结构响应数据,利用盲源分离和流形学习的方法进行系统模态参数辨识,建立基于多元统计分析的工作模态参数辨识方法。首先,从主成分分析(PCA)、独立成分分析(ICA)和局部线性嵌入(LLE)算法出发,建立响应模态坐标表示与多元统计分析算法之间的内在联系,将模态参数辨识问题转化为基于结构响应数据的多元统计分析求解问题。然后,设计1个离散3自由度系统和搭建1个悬臂板典型实验结构系统,获取数值仿真和实验响应数据。最后,基于测量的响应数据,利用多元统计分析方法辨识系统参数,并分析比较3种不同方法的模态参数识别精度以及抗噪性能。数值仿真和实验结果表明,提出的多元统计分析方法能够有效识别出系统的模态振型和模态频率,且LLE算法较其他两种方法具有更高的识别精度和鲁棒性。

The operational modal parameters identification is the key issue for precise design and safety assessment of aircraft structures. Based on the structural response data, the blind source separation and manifold learning are utilized to identify modal parameters of systems. The operational modal parameter identification methods based on multivariate statistical analysis are established. First of all, starting from principal component analysis（PCA）, independent component analysis（ICA） and local linear embedding（LLE） algorithms, the internal relationship between response mode coordinate representation and the multivariate statistical analysis algorithm is established. And the modal parameter identification problem is translated to the solution problem of the multivariate statistical analysis based structural response data. Then, a discrete three degree-of-freedom system is designed and an experimental system of a typical cantilever plate is built to obtain the numerical simulation and experimental response data. Finally, based on the measured response data, the modal parameters are identified by multivariate statistical analysis, and the identification accuracy and anti-noise performance of the three different methods are analyzed and compared. Numerical simulation and experimental results show that the mode shapes and mode frequencies are effectively identified by the multivariate statistical analysis, and the LLE algorithm has higher identification accuracy and robustness than the other two methods.