一种确定自回归滑动平均模型最小阶次的新方法  

Novel Minimum Order Fixed Method for Autoregressive Moving Average Models

作　　者：邢铭宗[1] 赵飞[1] 姜歌东[1,2] 梅雪松[1,2] 

机构地区：[1]西安交通大学机械工程学院,西安710049 [2]西安交通大学机械制造系统工程国家重点实验室,西安710049

出　　处：《西安交通大学学报》2011年第12期99-103,共5页Journal of Xi'an Jiaotong University

基　　金：国家重点基础研究发展规划资助项目(2011CB706805);陕西省2009年重大科技创新专项资金资助项目(2009ZKC01-09)

摘　　要：针对经典Akaike信息准则(AIC)在模型定阶时缺少阶次范围下界而引起的模态遗漏问题,根据稳态图和AIC准则,提出了一种自回归滑动平均模型在模态参数辨识中的定阶方法.该方法先利用稳态图能够鉴别真假模态的特点,进行各阶模态频率的估计和均值的求取,进而根据模态稳定性判定准则计算出阶次范围下界,最后利用AIC准则确定最优的模型阶次.仿真结果表明,与经典AIC准则相比,所提出的方法定阶后进行模态参数的辨识,不仅识别出了经典AIC准则遗漏的第3阶模态参数(误差为0.18%),而且使第1、2阶模态参数的精度分别提高了2.31%和6.31%.对悬臂梁的模态实验结果表明:该方法不仅辨识出了经典AIC准则遗漏的第1阶模态参数,使其误差仅为0.62%,而且也大大提高了其他各阶模态参数的精度.To address the missing mode of the classical Akaike information criterion（AIC） caused by the lack of lower bound as determining the model order,a novel autoregressive moving average model order estimation method based on the stabilization diagram and AIC for modal parameter identification is proposed.Since stabilization diagram can distinguish true modes from the false ones,the initial modal frequencies and the modal frequency mean values are estimated and calculated using stabilization diagram.Then the lower bound of the modal order is evaluated according to the modal stability criterion.And the optimal model order is determined in the light of AIC.The simulation results show that the third-order missing mode in the classical AIC is identified with error of 0.18%,and the accuracy for the first-order and second-order modal parameters is improved by 2.31% and 6.31% respectively.The experiments on a cantilever beam show that the proposed method makes up the first-order missing mode in the classical AIC with error of 0.18%,and the accuracy for the other order modal parameters is perfect.

关 键 词：Akaike信息准则 自回归滑动平均模型 稳态图 模态参数 

分 类 号：TB114[理学—概率论与数理统计] O211.61[理学—数学]