基于Kriging形函数的线性时变结构模态参数辨识
收稿日期: 2014-04-09
修回日期: 2014-08-19
网络出版日期: 2014-09-05
基金资助
北京理工大学基础研究基金(20120142009)
Modal parameter identification of linear time-varying structures using Kriging shape function
Received date: 2014-04-09
Revised date: 2014-08-19
Online published: 2014-09-05
Supported by
Beijing Institute of Technology Foundation for Basic Research (20120142009)
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。
杨武 , 刘莉 , 周思达 , 马志赛 . 基于Kriging形函数的线性时变结构模态参数辨识[J]. 航空学报, 2015 , 36(4) : 1169 -1176 . DOI: 10.7527/S1000-6893.2014.0194
Recently, it is essential and imperative to conduct the study of the time-varying dynamic characteristic of aerospace flight vehicle. Due to representation parsimony, high accuracy and improved tracking, the output-only parametric time-domain time-dependent time series models become the research hotspot. Above all, the function series vector time-dependent autoregressive (FS-VTAR) models are applied. Yet, the conventional FS-VTAR model needs to choose a suitable type and quite high order of basis function to certify its merit, which is complex and time-consuming. Stemmed from the moving least square (MLS) method via shape function in the mesh free method, a modal parameter identification method of time-varying structures via Kriging shape function is presented. Firstly, Kriging shape function adaptive to the signals is introduced to this method. Then, the time-varying coefficients are expanded into a linear combination of the shape functions. Once the unknown coefficients of shape functions are obtained via least square (LS) method, the time-varying coefficients are known. Finally, modal parameters are extracted from a generalized eigenvalue problem, which is transformed from an eigenvalue equation of the time-varying model. The identification approach is validated by non-stationary vibration signals of a system with time-varying stiffness. Compared with the traditional FS-VTAR model, the FS-VTAR method based on Kriging shape function avoids the form choice and high order of basis functions as well as high efficiency and has high precision. Moreover, compared with MLS method, this method solves efficiently the numerical conditions problem and has higher modal parameter identification precision.
[1] Verboven P, Cauberghe B, Guillaume P, et al. Modal parameter estimation and monitoring for on-line flight flutter analysis[J]. Mechanical Systems and Signal Processing, 2004, 18(3): 587-610.
[2] Wilson H. Dynamics of variable mass flexible bodies with time varying mode shapes[D]. Huntsville: University of Alabama in Huntsville, 2007.
[3] Fujii H A, Watanabe T, Kojima H, et al. Control of attitude and vibration of a tethered space solar power satellite[C]//AIAA Guidance, Navigation, and Control Conference and Exhibit. Reston: AIAA, 2003.
[4] Thornton E A, Dechaumphai P. Coupled flow, thermal, and structural analysis of aerodynamically heated panels[J]. Journal of Aircraft, 1992, 25(11): 1052-1059.
[5] Poulimenos A G, Fassois S D. Parametric time-domain methods for non-stationary random vibration modelling and analysis—a critical survey and comparison[J]. Mechanical Systems and Signal Processing, 2006, 20(4): 763-816.
[6] Niedzwiecki M. Identification of time-varying processes[M]. New York: Wiley, 2000: 103-178.
[7] Kitagawa G, Gersch W. Smoothness priors analysis of time series[M]. Berlin: Springer, 1996: 27-88.
[8] Spiridonakos M D, Fassois S D. Parametric identification of a time-varying structure based on vector vibration response measurements[J]. Mechanical Systems and Signal Processing, 2009, 23(6): 2029-2048.
[9] Xu X Z, Zhang Z Y, Hua H X. Identification of time-variant modal parameters by a time-varying parametric approach[J]. Acta Aeronautica et Astronautica Sinica, 2003, 24(3): 230-233.
[10] Spiridonakos M D, Fassois S D. Output-only identification of time-varying structures via a complete FS-TARMA model approach[C]//IOMAC2011, International Operational Modal Analysis Conference, 2011.
[11] Spiridonakos M D, Fassois S D. Adaptable functional series tarma models for non-stationary signal modelling[C]//Proceeding of Preprints of the 16th IFAC Symposium on System Identification. Brussels: IFAC Technical Cornmittee, 2012: 1276-1281.
[12] Spiridonakos M D, Fassois S D. Adaptable functional series models for non-stationary signal representation and their application to mechanical random vibration modeling[J]. Signal Processing, 2014, 96: 63-79.
[13] Huang C S, Hung S L, Su W C. Identification of time-variant modal parameters using time-varying autoregressive with exogenous input and low-order polynomial function[J]. Computer-Aided Civil and Infrastructure Engineering, 2009, 24(7): 470-491.
[14] Su W C, Liu C Y, Huang C S. Identification of instantaneous modal parameter of time-varying systems via a wavelet-based approach and its application[J]. Computer-Aided Civil and Infrastructure Engineering, 2014, 29(4): 279-298.
[15] Liu G R. Mesh free methods: moving beyond the finite element method[M]. New York: CRC Press, 2003: 84-162.
[16] Simpson T W, Mauery T M, Korte J J, et al. Kriging models for global approximation in simulation-based multidisciplinary design optimization[J]. AIAA Journal, 2001, 39(12): 2233-2241.
[17] Sacks J, Welch W J, Mitchell T J, et al. Design and analysis of computer experiments[J]. Statistics Science, 1989, 4(4): 409-435.
[18] Reinsel G. Elements of multivariate time series analysis[M]. Berlin: Springer, 1993: 21-51.
/
| 〈 |
|
〉 |
CJA