动力系统模型阶次的确定  

ORDER IDENTIFICATION OF DYNAMIC SYSTEM MODEL

作　　者：易伟建[1] 刘翔[1] 

机构地区：[1]湖南大学土木工程学院,长沙410082

出　　处：《振动与冲击》2008年第11期12-16,共5页Journal of Vibration and Shock

基　　金：国家自然科学基金(50678064);湖南省科技计划重点项目(06FJ3003)资助

摘　　要：为了判定状态空间方程的阶次,提出了一种新的动力系统模型定阶方法一残差期望法。该方法利用系统的脉冲响应函数建立Hankel矩阵,对其进行奇异值分解后,得到H_1和H_2两个矩阵。H_1和H_2分别为信号的主要组分和噪声。假设系统受到白噪声干扰,并利用白噪声的零均值特性,可以准确的辨识模型的阶次。在Hankel矩阵的大小满足一定要求的条件下,即使系统存在较大噪声,也能正确识别模型的阶次。对系统有较大噪声干扰的情况进行了数字仿真研究,并对一钢筋混凝土框架结构的实测数据进行了对比研究。A new method,called residual-difference-expectation method,was presented for determining the order of the state-space model of dynamic structural system.Impulse-response functions were employed to construct the Hankel matrices.The Hankel matrix was then decomposed into H_1 matrix and H_2 matrix by singular value decomposition,which describe the primary response signals and the noise respectively.Taking the signals of a dynamic system mixed with white noise only,and making use of the characteristic of zero-average-value of white noise,the order of state-space model could be determined correctly.If only the size of Hankel matrix is large enough and though the dynamic signals are mixed with strongly noise,the method can identify the model's order exactly.Numerical examples with response signals of a dynamic system mixed with strong noise were carried out and the results were compared with those from actual signals measured in an experimental investigation on a reinforced concrete frame structure.

关 键 词：状态空间模型 阶次辩识 残差期望 残差期望比 

分 类 号：TU317.1[建筑科学—结构工程]