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近年来,对航空航天飞行器随时间变化的动力学特性研究需求越来越迫切。仅输出参数化时域的时变时间序列模型以其结构简约、精度高且跟踪能力强而成为研究热点,尤其是泛函向量时变自回归(FS-VTAR)模型已经得到了广泛应用。然而传统的FS-VTAR模型在保证其辨识优势的同时却需要针对不同时变结构选择合适的基函数形式及较高的基函数阶数,该过程相当复杂且耗时。本文借鉴无网格法中移动最小二乘(MLS)法构造形函数的思想,提出一种基于Kriging形函数的线性时变结构模态参数辨识方法。该方法首先引入自适应于辨识信号的Kriging形函数;再把时变系数在形函数上线性展开,利用最小二乘(LS)法得到形函数的展开系数;最后把时变模型特征方程转换为广义特征值问题提取出模态参数。利用时变刚度系统非平稳振动信号验证该方法,结果表明:基于Kriging形函数的FS-VTAR模型相比于传统的FS-VTAR模型能有效地避免基函数形式的选择和较高的基函数阶数,且精度相当;相比于移动最小二乘法能有效地解决其数值条件问题且具有更高的模态参数辨识精度。
In recent years, the research on the dynamic characteristics of aerospace vehicles over time has become more and more urgent. Only time-varying time-series model of parametric time domain has become a research hotspot due to its simple structure, high precision and strong tracking ability. Especially, the functional vector time-varying autoregression (FS-VTAR) model has been widely used. However, the traditional FS-VTAR model needs to select suitable basis function forms and higher basis function orders for different time-varying structures while ensuring its identification advantages. This process is rather complicated and time-consuming. Based on the idea of moving least square (MLS) method to construct shape function in meshless method, this paper proposes a method of linear time-varying structural modal parameter identification based on Kriging-shaped function. Firstly, the Kriging-type function adaptive to the identification signal is introduced. Then the time-varying coefficient is linearly expanded on the shape function, and the expansion coefficient of the shape function is obtained by the method of least squares (LS). Finally, the characteristic equation of the time-varying model is transformed into Generalized eigenvalue problem is extracted modal parameters. The results show that the FS-VTAR model based on Kriging-shaped function can effectively avoid the choice of basis function form and the higher basis function order compared with the traditional FS-VTAR model Compared with the moving least square method, it can effectively solve the problem of numerical conditions and has higher accuracy of modal parameter identification.