一种改进的识别结构模态参数的随机子空间法

doi:10.3969/j.issn.1001-2400.2017.06.005

摘要/Abstract

摘要：

随机子空间法可有效地从环境激励下的结构响应中获取结构的模态参数，但在识别过程中需要构造高维矩阵，对高维矩阵进行奇异值分解需要大量内存与计算时间，严重影响该算法的计算效率．针对该问题，文中通过研究协方差驱动随机子空间法中Toeplitz矩阵奇异值的分解过程，发现其中一个子矩阵对于模态参数识别结果无影响，故而提出一种新的构造Toeplitz矩阵的方法，从而降低了Toeplitz矩阵的维数，提高了计算效率．实例分析证明，改进的协方差驱动随机子空间法在保持计算精度的情况下，计算时间是原来的106％．

关键词: 随机子空间法, 计算效率, 数据驱动, 协方差, 模态参数

Abstract:

Stochastic subspace identification can be used to identify the modal parameters of a structure according to its dynamic response to ambient excitation. However, some high dimensional matrices (Toeplitz matrices) must be constructed in the process of identification, and lots of memory and computation time are cost to the singular value decomposition of these high dimensional matrixes. Stochastic subspace identification affects the computational efficiency seriously. Therefore, this paper investigates a new method for constructing lower-dimension Toeplitz matrices to improve the computing efficiency. Finally, a numerical simulation is presented to demonstrate the computing efficiency of the method. The result shows that the computing consumption of the proposed method is only 106％ the computing consumption of the traditional stochastic subspace identification while the identification accuracy is maintained.

Key words: stochastic subspace identification, computing efficiency, data-driven, covariance, modal parameters

李团结;刘伟萌;唐雅琼;高利强. 一种改进的识别结构模态参数的随机子空间法[J]. 西安电子科技大学学报, 2017, 44(6): 26-30+58.

LI Tuanjie;LIU Weimeng;TANG Yaqiong;GAO Liqiang. Improved stochastic subspace method for identifying structural modal parameters[J]. Journal of Xidian University, 2017, 44(6): 26-30+58.

参考文献

［1］ LIU X, LUO Y, KARNEY B W, et al. Virtual Testing for Modal and Damping Ratio Identification of Submerged Structures Using the PolyMAX Algorithm with Two-way Fluid-structure Interactions［J］. Journal of Fluids and Structures, 2015, 54(1): 548-565.
［2］ LE T P, ARGOUL P. Distinction between Harmonic and Structural Components in Ambient Excitation Tests Using the Time-frequency Domain Decomposition Technique［J］. Mechanical Systems and Signal Processing, 2015, 52-53(1): 29-45.
［3］ NASSER F, LI Z, MARTIN N, et al. An Automatic Approach towards Modal Parameter Estimation for High-rise Buildings of Multicomponent Signals under Ambient Excitations via Filter-free Random Decrement Technique［J］. Mechanical Systems and Signal Processing, 2016, 70-71(8): 821-831.
［4］ de VIVO A, BRUTTI C, LEOFANTI J L. Modal Shape Identification of Large Structure Exposed to Wind Excitation by Operational Modal Analysis Technique［J］. Mechanical Systems and Signal Processing, 2013, 39(1/2): 195-206.
［5］ LI P, HU S L J, LI H J. Noise Issues of Modal Identification Using Eigensystem Realization Algorithm［C］//Proceedings of the Procedia Engineering: 14. Oxford: Elsevier Ltd, 2011: 1681-1689.
［6］ REYNDERS E, MAES K, LOMBAERT G, et al. Uncertainty Quantification in Operational Modal Analysis with Stochastic Subspace Identification: Validation and Applications［J］. Mechanical Systems and Signal Processing, 2016, 66/67(4): 13-30.
［7］ YAN R Q, GAO R X, ZHANG L. In-process Modal Parameter Identification for Spindle Health Monitoring［J］. Mechatronics, 2015, 31(12): 42-49.
［8］ BELLERI A, MOAVENI B, RESTREPO J I. Damage Assessment through Structural Identification of a Three-story Large-scale Precast Concrete Structure［J］. Earthquake Engineering and Structural Dynamics, 2014, 43(1): 61-76.
［9］ LIU Y C, LOH C H, NI Y Q. Stochastic Subspace Identification for Output-only Modal Analysis: Application to Super High-rise Tower under Abnormal Loading Condition［J］. Earthquake Engineering and Structural Dynamics, 2013, 42(4): 477-498.
［10］ NAGARAJAIAH S, BASU S. Output Only Modal Identification and Structural Damage Detection Using Time Frequency & Wavelet Techniques［J］. Earthquake Engineering and Engineering Vibration, 2010, 8(4): 583-605.
［11］徐亚兰, 马娟, 陈建军, 等. EMD和小波变换在结构模态参数辨识中的应用［J］. 西安电子科技大学学报, 2012, 39(2): 186-191.
XU Yalan, MA Juan, CHEN Jianjun, et al. Application of Empirical Mode Decomposition and Wavelet Transform in Structural Modal Parameter Identification［J］. Journal of Xidian University, 2012, 39(2): 186-191.
［12］ WANG Z C, CHEN G. Analytical Mode Decomposition with Hilbert Transform for Modal Parameter Identification of Buildings under Ambient Vibration［J］. Engineering Structures, 2014, 59(2): 173-184.
［13］常军, 张启伟, 孙利民. 随机子空间产生虚假模态及模态遗漏的原因分析［J］. 工程力学, 2007, 24(11): 57-62.
CHANG Jun, ZHANG Qiwei, SUN Limin. Analysis How Stochastic Subspace Identification Brings False Modes and Mode Absence［J］. Engineering Mechanics, 2007, 24(11): 57-62.
［14］ DOHLER M, MEVEL L. Efficient Multi-order Uncertainty Computation for Stochastic Subspace Identification［J］. Mechanical Systems and Signal Processing, 2013, 38(2): 346-366.
［15］章国稳, 汤宝平, 孟利波. 基于特征值分解的随机子空间算法研究［J］. 振动与冲击, 2012, 31(7): 74-78.
ZHANG Guowen, TANG Baoping, MENG Libo. Improved Stochastic Subspace Identification Algorithm Based on Eigendecomposition［J］. Journal of Vibration and Shock, 2012, 31(7): 74-78.
［16］常军, 孙利民, 张启伟. 随机子空间识别方法计算效率的改进［J］. 地震工程与工程振动, 2007, 27(3): 88-94.
CHANG Jun, SUN Limin, ZHANG Qiwei. Improvement in Stochastic Subspace Identification［J］. Journal of Earthquake Engineering and Engineering Vibration, 2007, 27(3): 88-94.

[1]	李翠芸;王精毅;姬红兵;王荣. 模型参数未知时的CPHD多目标跟踪方法[J]. 西安电子科技大学学报, 2017, 44(2): 37-41+184.
[2]	赵永红;张林让;刘楠;解虎. 采用协方差矩阵稀疏表示的DOA估计方法[J]. 西安电子科技大学学报, 2016, 43(2): 58-63+101.
[3]	杨杰;廖桂生;李军. 稳健的二级嵌套阵列自适应波束形成算法[J]. J4, 2015, 42(6): 30-36.
[4]	解虎;冯大政;虞泓波;袁明冬;聂卫科. 一种采用稀疏表示的快速空时自适应方法[J]. J4, 2015, 42(5): 55-62.
[5]	解虎;冯大政;袁明冬. 一种采用协方差矩阵稀疏表示的DOA估计方法[J]. J4, 2015, 42(1): 35-41.
[6]	高永婵;廖桂生;朱圣棋. 复合高斯噪声中知识辅助的贝叶斯Rao检测方法[J]. J4, 2013, 40(6): 46-51+173.
[7]	徐亚兰;马娟;陈建军;刘珍. EMD和小波变换在结构模态参数辨识中的应用[J]. J4, 2012, 39(2): 186-191.
[8]	曹向海;刘宏伟;吴顺君. 快速增量主分量算法的近似协方差矩阵实现[J]. J4, 2010, 37(3): 459-463.
[9]	黄庆东;张林让;卢光跃. 一种最小模级联相消器[J]. J4, 2010, 37(2): 204-209.
[10]	黄伯虎;段振华. 量子遗传算法在Web服务选择中的应用[J]. J4, 2010, 37(1): 56-61+67.
[11]	张怀根;吴顺君;张林让;刘寅. 基于协方差矩阵元素的多目标角跟踪方法 [J]. J4, 2008, 35(5): 785-792.
[12]	刘聪锋;廖桂生. 基于Bayes准则的STAP协方差矩阵估计算法 [J]. J4, 2008, 35(2): 223-227.
[13]	徐亚兰;陈建军;胡太彬. 系统模态参数辨识的小波变换方法[J]. J4, 2004, 31(2): 281-285.
[14]	李青山;陈平;褚华. 支持柔性机制的元数据驱动模型的研究与应用[J]. J4, 2002, 29(3): 319-324.
[15]	暂时无作者信息. 小波分析在Hurst指数估值中的应用[J]. J4, 2002, 29(1): 115-119.