基于AR模型与Prony法的结构模态参数识别

【作者】 贾承林；

【导师】 黄方林；

【作者基本信息】 中南大学 ， 固体力学， 2009， 硕士

【摘要】 振动模态参数识别是结构动力学中一个十分重要的课题,在结构建模、模型修正、灵敏度分析、振动控制、损伤识别以及状态监测等方面起着重要的作用。本文研究了基于AR模型和Prony法的模态参数识别,主要内容如下:(1)回顾了时间序列参数模型类型的识别、模型阶数的确定以及模型参数的估计方法。理论上,不同类型的模型都可以用足够高阶的AR模型来表示。通过数字仿真,验证了传统的模型类型识别、模型阶数确定以及参数估计方法的正确性。(2)应用AR模型法和Prony法对线性时不变振动系统进行模态参数识别,提出了有效剔除虚假模态的方法。仿真算例和试验结果表明了本文提出的剔除虚假模态方法的有效性,同时也表明Prony法识别的模态参数精度比AR模型法识别的精度高。(3)研究了能够处理非平稳信号的时变Prony法以及确定模型阶数和基函数维数的最大似然准则。仿真算例表明不同基函数下时变Prony法参数估计和模态参数识别的性能不一样,基于DCT基的时变Prony法估计的参数以及识别的模态参数比其它基函数下的时变Prony法要精确。(4)研究了基于DCT(离散余弦)基时变Prony法的频率分辨率以及抗噪性能。以一附加质量可调的悬臂梁进行实验,时变Prony法识别的模态参数与指定状态下梁的模态参数以及有限元分析结果进行比较,结果表明基于DCT基的时变Prony法在实际应用中是可行的。更多还原

【Abstract】 Modal parameter identification of vibration systems is one of the most important subjects in structural dynamics, which plays significant roles on structure modeling, model updating, sensitivity analysis, vibration control, damage detection and state monitoring, etc. In this paper, modal parameter identification by AR model and Prony method are studied and the main contents are detailed as following:(1) The identification of parameter model type, the determination of the model order and the estimation of model parameter are reviewed. Different types of models can be expressed as the AR model with sufficient high orders. The correctness of the identification method for model type, the criteria of order determination and the parameter estimation methods are investigated by digital simulation examples.(2) The AR model and the Prony method are applied to identify the modal parameters of the linear time-invariant vibration system. An approach to effectively remove the false modal is put forward. Simulation examples and experiments show the efficiency of the method. In addition, it is indicated that the Prony method has higher precision than that of the AR model to identify the parameters.(3) The time-variant Prony method to process non-stationary signals, the maximum likelihood criterion to determine the model order and the basis function dimension are studied. Simulation examples show that for different basis functions the precisions of parameter estimation and model parameter identification are different. The discrete cosine time (DCT) basis function is more precise than other functions.(4) Based on the DCT basis function, the frequency resolution and the anti-noise performance of the Prony method are researched. The experimental device comprising a cantilever beam and an adjustable additive mass is designed. The experiment on a cantilever beam with an adjustable mass are conducted. The modal parameters identified by the time-variant Prony method are compared with the modal parameters on the designated status and obtained by finite element analysis. It is indicated that the Prony method based on the DCT basis function is feasible in practice.更多还原