基于盲源分离的线性结构工作模态参数识别
发布时间：2018-08-18 08:53
【摘要】：工作模态分析(OMA)一直是国内外研究的重点对象。基于二阶盲辨识(SOBI)和独立成分分析(ICA)方法,本文分别提出了线性时不变结构、复杂三维连续体结构和线性时变结构工作模态参数识别方法,主要研究内容包括:(1)研究了基于SOBI和ICA的线性时不变结构工作模态参数识别方法。首先从理论上分析工作模态识别方法和盲源分离之间的相似之处,并得出了分离矩阵与模态振型之间、分离信号和模态坐标响应之间的一一对应关系,指出了基于盲源分离(BSS)工作模态参数识别方法识别模态顺序不确定、振型能量不确定、模态缺失的根本原因。其次,从目标函数和优化方法出发,比较不同ICA方法应用于时不变结构工作模态分析领域时的优缺点。最后,由于ICA方法使用的是高阶统计量,本文还研究基于二阶统计量的SOBI方法。在离散三自由度和简支梁上的线性时不变数值仿真验证中,对比和分析SOBI方法和各种ICA方法线性时不变结构工作模态参数识别的优缺点。(2)研究了基于SOBI的复杂三维连续体结构的工作模态参数识别方法。本文利用在笛卡尔坐标系下三维结构三个方向的模态坐标矩阵相同的特性,先使用SOBI方法识别出响应最大的那个方向的模态坐标响应,再利用最小二乘广义逆的方法将该模态坐标矩阵回代到其它两个方向上识别其它两方向的模态振型,最后完成三维模态振型组装。在三维圆柱壳上的仿真验证结果表明,基于SOBI和最小二乘广义逆的方法能有效地识别出三维圆柱壳上的模态参数。(3)研究了基于滑动窗SOBI的线性时变结构工作模态参数在线识别方法。此方法利用“短时时不变”理论,假设在一个很小的时间窗内,结构是时不变的,此时可以利用SOBI方法识别结构在中间时刻的工作模态参数,随着时间的推移,窗口也不断向前滑动,从而识别出每个时刻的模态参数,最后将每个时刻的模态参数连起来,从而形成时变结构的模态参数,并给出方法中滑动窗的选取规则和应用范围。在线性时变三自由度系统和时变悬臂梁上的仿真验证结果表明,在选择合适的滑动窗窗口的大小的情况下,基于滑动窗SOBI方法能有效地识别出时变结构的模态参数,识别效果比基于滑动窗ICA方法更好。
[Abstract]:Working mode analysis (OMA) has been the focus of research at home and abroad. Based on the second order blind identification (SOBI) and the independent component analysis (ICA) method, this paper presents the methods for identifying the operating modal parameters of linear time-invariant structures, complex three-dimensional continuum structures and linear time-varying structures, respectively. The main contents are as follows: (1) the identification method of working modal parameters of linear time-invariant structures based on SOBI and ICA is studied. Firstly, the similarities between the working mode identification method and blind source separation are analyzed theoretically, and the one-to-one correspondence between the separation matrix and the modal mode type, the separation signal and the modal coordinate response is obtained. The identification method of operating modal parameters based on blind source separation (BSS) is presented to identify the fundamental causes of modal sequence uncertainty, mode energy uncertainty and modal missing. Secondly, based on the objective function and optimization method, the advantages and disadvantages of different ICA methods in the field of time-invariant structure working modal analysis are compared. Finally, because the ICA method uses high order statistics, this paper also studies the SOBI method based on the second order statistics. In the linear time-invariant numerical simulation of discrete three-degree-of-freedom and simply supported beam, The advantages and disadvantages of SOBI method and ICA method are compared and analyzed. (2) the working modal parameter identification method of complex 3D continuum structure based on SOBI is studied. In this paper, using the same characteristic of modal coordinate matrix of three directions of three-dimensional structure in Cartesian coordinate system, we first use SOBI method to identify the modal coordinate response of the direction in which the maximum response is obtained. Then, the modal coordinate matrix is replaced by the least square generalized inverse method to identify the modal modes in the other two directions. Finally, the three-dimensional modal mode assembly is completed. The simulation results on a three-dimensional cylindrical shell show that, Based on SOBI and least square generalized inverse method, the modal parameters on three-dimensional cylindrical shells can be effectively identified. (3) the on-line identification method of working modal parameters of linear time-varying structures based on sliding window SOBI is studied. Using the theory of "short time invariance", this method assumes that the structure is time-invariant in a very small time window. At this time, the SOBI method can be used to identify the working modal parameters of the structure at the middle time. The window also slips forward continuously to identify the modal parameters at each moment. Finally the modal parameters of each moment are connected to form the modal parameters of the time-varying structure. The selection rules and application range of the sliding window in the method are given. The simulation results on linear time-varying 3-DOF system and time-varying cantilever beam show that the modal parameters of time-varying structures can be effectively identified based on sliding window SOBI method under the condition of selecting the appropriate sliding window size. The recognition effect is better than that based on sliding window ICA method.
【学位授予单位】：华侨大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TB12
[Abstract]:Working mode analysis (OMA) has been the focus of research at home and abroad. Based on the second order blind identification (SOBI) and the independent component analysis (ICA) method, this paper presents the methods for identifying the operating modal parameters of linear time-invariant structures, complex three-dimensional continuum structures and linear time-varying structures, respectively. The main contents are as follows: (1) the identification method of working modal parameters of linear time-invariant structures based on SOBI and ICA is studied. Firstly, the similarities between the working mode identification method and blind source separation are analyzed theoretically, and the one-to-one correspondence between the separation matrix and the modal mode type, the separation signal and the modal coordinate response is obtained. The identification method of operating modal parameters based on blind source separation (BSS) is presented to identify the fundamental causes of modal sequence uncertainty, mode energy uncertainty and modal missing. Secondly, based on the objective function and optimization method, the advantages and disadvantages of different ICA methods in the field of time-invariant structure working modal analysis are compared. Finally, because the ICA method uses high order statistics, this paper also studies the SOBI method based on the second order statistics. In the linear time-invariant numerical simulation of discrete three-degree-of-freedom and simply supported beam, The advantages and disadvantages of SOBI method and ICA method are compared and analyzed. (2) the working modal parameter identification method of complex 3D continuum structure based on SOBI is studied. In this paper, using the same characteristic of modal coordinate matrix of three directions of three-dimensional structure in Cartesian coordinate system, we first use SOBI method to identify the modal coordinate response of the direction in which the maximum response is obtained. Then, the modal coordinate matrix is replaced by the least square generalized inverse method to identify the modal modes in the other two directions. Finally, the three-dimensional modal mode assembly is completed. The simulation results on a three-dimensional cylindrical shell show that, Based on SOBI and least square generalized inverse method, the modal parameters on three-dimensional cylindrical shells can be effectively identified. (3) the on-line identification method of working modal parameters of linear time-varying structures based on sliding window SOBI is studied. Using the theory of "short time invariance", this method assumes that the structure is time-invariant in a very small time window. At this time, the SOBI method can be used to identify the working modal parameters of the structure at the middle time. The window also slips forward continuously to identify the modal parameters at each moment. Finally the modal parameters of each moment are connected to form the modal parameters of the time-varying structure. The selection rules and application range of the sliding window in the method are given. The simulation results on linear time-varying 3-DOF system and time-varying cantilever beam show that the modal parameters of time-varying structures can be effectively identified based on sliding window SOBI method under the condition of selecting the appropriate sliding window size. The recognition effect is better than that based on sliding window ICA method.
【学位授予单位】：华侨大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TB12
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