基于特征值分解的随机子空间算法研究  

Improved stochastic subspace identification algorithm based on eigendecomposition

作　　者：章国稳[1] 汤宝平[1,2] 孟利波 

机构地区：[1]重庆大学机械传动国家重点实验室,重庆400030 [2]重庆交通科研设计研究院桥梁结构动力学国家重点实验室,重庆400067

出　　处：《振动与冲击》2012年第7期74-78,共5页Journal of Vibration and Shock

基　　金：国家自然科学基金(50875272);高等学校博士点基金(20090191110005);重庆大学"211工程"三期建设研究生开放实验室(S-0916)

摘　　要：针对基于数据驱动的随机子空间法计算效率低下的问题,提出一种基于特征值分解的随机子空间算法,该方法通过对CH矩阵的特征值分解得到扩展可观测矩阵Tmi,进而识别出系统模态参数。相比于传统算法,该算法免去了对Hankl矩阵的QR分解及投影矩阵的SVD运算,从而大大节省了内存和计算时间。通过一个7自由度的数值仿真和重庆朝天门大桥模型的实例分析证明该方法在保持计算精度的情况下大幅度地提升了计算效率。An improved stochastic subspace identification （SSI） algorithm based on eigendecomposition was introduced to solve low efficiency problems of data-driven SSI. With the method, system modal parameters were identified with an extended observability matrix Tmi obtained through eigendecomposition of matrix CH. Compared with the traditional algorithm, it needed much less memory and computing time because it avoided QR decomposition of Hankel matrix and SVD of projection matrix. A numerical example of parameter estimation of a linear time-invafiant system of 7 degrees of freedom and one experimental example of parameter estimation of a bridge model named Chao Tian Men were presented to demonstrate that the method dramatically improves the computing efficiency and still keeps accuracy.

关 键 词：参数识别 随机子空间法 特征值分解 

分 类 号：TB122[理学—工程力学]