采用工作振动响应的机械结构的健康监测方法的研究
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摘要
目前,基于结构振动响应的结构健康监测方法一直是国内外科研机构研究的一个重要方向,且其中又以工作模态分析方法的研究最有价值。由于环境激励下的模态分析方法只利用结构工况下的振动响应数据进行在线分析,而不需要人工激励设备对结构进行激励,所以该类方法的分析结果更符合结构的工况边界条件。因此,该类分析方法已经在宇航、桥梁和机械制造等工程应用领域得到了广泛应用。
鉴于上述原因,本文主要对环境激励下的随机子空间识别法进行了探索性研究。在该方法研究过程中,我们主要做了以下工作:
⑴本文以悬臂梁结构为研究对象,利用有限元分析的方法对它们进行了理论模态分析,得出了它们的模态频率和模态振型。从而为实验分析提供了理论参考依据,并和利用随机子空间识别法所得的实验模态分析结果进行了对比分析,结果证明两者的模态识别结果吻合良好。
⑵在前人研究的基础上,本文对环境激励下的随机子空间识别法进行了深入的研究。随机子空间识别法主要有协方差驱动随机子空间识别法和数据驱动随机子空间识别法两种算法,其中前者主要利用输出协方差序列组成的Toeplitz矩阵块,通过奇异值分解(SVD)得到系统的可观矩阵和可控矩阵,然后利用它们来识别振动系统的模态参数(模态频率、模态阻尼比和模态振型);而后者则主要利用时域振动响应数据组成的Hankel矩阵,通过矩阵的QR分解减缩计算数据量,并依靠对投影矩阵的奇异值分解来消除噪声的影响,然后利用最小二乘法等矩阵运算来识别出系统矩阵和输出矩阵,最后利用求得的系统矩阵和输出矩阵识别出振动系统的模态参数(模态频率、模态阻尼比和模态振型)。
⑶针对基于随机子空间识别法的系统定阶方法研究不足的状况,本文进行了探索性研究。在文中,我们主要研究了基于随机子空间识别法的系统稳态图定阶法和系统奇异熵增量定阶法,其中前者主要利用LMS Test.lab模态应用分析软件在线分析完成,而后者则主要通过matlab应用程序来完成。结果表明两种方法的系统定阶结果吻合良好,且都比传统的奇异值分解系统定阶法更为可靠有效。
⑷在和有限元分析的理论结果进行了对比之后,本文仍以上述的悬臂梁结构为研究对象,通过一个随机白噪声激励信号来模拟它在环境激励下的工况,并分别利用随机子空间识别法和Polymax(最小二乘复频域法)两种识别方法对它进行了在线模态分析,对比结果进一步证明了随机子空间识别法的有效性和可靠性。
综上所述,本文利用有限元模态分析和Polymax模态分析的方法分别证明了随机子空间识别法的有效性和可靠性。此外,在系统定阶方面,本文研究了基于随机子空间识别法的两种系统定阶方法—系统稳态图定阶法和系统奇异熵增量定阶法,结果表明,两种系统定阶方法的定阶结果吻合良好。总之,由于随机子空间识别法是一种基于结构振动响应的模态识别方法,其识别效果稳定可靠,而且目前对基于随机子空间识别法的系统定阶方法研究较少,所以本文的研究对于机械结构的在线健康监测有着重要的意义。
At present,the structural health monitoring methods based on structural vibration response has been focused by the scientific research institutions at home and abroad,and the operational modal analysis methods are most valuable among them.Due to the operational modal analysis methods using only the structural vibration response data which is obtained in operating conditions for on-line analysis,and it does not require artificial motive equipment to incentive the structure,so the analyzed results of such methods more in line with the operating boundary conditions of the structure.Therefore,such analysis methods have been widely used in the aerospace、bridges and mechanical manufacturing engineering applications.
For these reasons,the stochastic subspace identification method relying on environmental excitation has been exploringly studied on this paper.During the research process,we have mainly done the following works:
⑴On the paper,we have studied cantilever by the finite element analysis method to conduct their theoretical modal analysis,and obtained their modal frequencies and modal shape.Thus it provides a theoretical frame of reference for the experimental analysis,and comparatively analysis the experimental modal analysis results by the stochastic subspace identification method and the theoretical results,and it shows that the two modal identification results are in good agreement.
⑵on the basis of previous studies,the stochastic subspace identification method which is inspired by the environment has been studied deeply on this paper.The stochastic subspace identification method mainly consists of two kinds of algorithms—the covariance-driven stochastic subspace identification method and data-driven stochastic subspace identification method,and the specific identification process of the two algorithms has been respectively discussed in detail on this paper.The former mainly uses the output covariance sequence to compose Toeplitz matrix blocks,by the singular value decomposition (SVD) to obtain the system matrix and control matrix,then it uses them to identify the modal parameters of vibrating system (modal frequencies、modal damping ratio and the modal shape); while the latter mainly uses Hankel matrix composed of the time-domain vibration response data,reduces the amount of the matrix calculations by QR decomposition,and eliminates the effect of noise by the singular value decomposition of the projection matrix,then it uses the matrix operations such as least-squares method to identify the system matrix and output matrix.Finally,it uses the system matrix and output matrix to identify the modal parameters of vibrating system (modal frequencies、modal damping ratio and modal shape).
⑶Because of researching less on the system-order determination method based on the stochastic subspace identification method,we conducted an exploratory study.On this paper,we mainly studied the system order determination method by the steady-state diagram or singular entropy increment,which are both based on the stochastic subspace identification method.The former has been on-line completed by LMS Test.lab modal analysis software,but the latter has been completed by the matlab application.The results show that the results of two order determination methods are in good agreement,and they are more reliable and effective than the traditional system fixed-order method which uses the singular value decomposition.
⑷After comparing with the theoretical results obtained by the finite element analysis method, we still take the cantilever structure as researched objects and incentive it by a random white noise signal to mimic its working state in the environmental conditions, with the random subspace identification method and Polymax (Least-Squares Complex Frequency-domain method) conducting on-line modal analysis for them.The results further proves the validity and reliability of the stochastic subspace identification method.
In summary, the finite element modal analysis and Polymax modal analysis method are adopted,and they respectively proved the validity and reliability of the stochastic subspace identification method.In addition,on the system order determination methods,we studied two kinds of system order determination methods based on the stochastic subspace identification method—the system steady-state diagram fixed-order method and system singular entropy increment order determination method,the results showed that the fixed-order results of two system order determination method are in good agreement.In short,because the stochastic subspace identification method is a kind of modal identification method based on the structure vibration response,and the identified results is stable and reliable,and currently the system fixed-order method based on the stochastic subspace identification method has been less studied,so it plays an important role in the mechanical On-line health monitoring studies.
鉴于上述原因,本文主要对环境激励下的随机子空间识别法进行了探索性研究。在该方法研究过程中,我们主要做了以下工作:
⑴本文以悬臂梁结构为研究对象,利用有限元分析的方法对它们进行了理论模态分析,得出了它们的模态频率和模态振型。从而为实验分析提供了理论参考依据,并和利用随机子空间识别法所得的实验模态分析结果进行了对比分析,结果证明两者的模态识别结果吻合良好。
⑵在前人研究的基础上,本文对环境激励下的随机子空间识别法进行了深入的研究。随机子空间识别法主要有协方差驱动随机子空间识别法和数据驱动随机子空间识别法两种算法,其中前者主要利用输出协方差序列组成的Toeplitz矩阵块,通过奇异值分解(SVD)得到系统的可观矩阵和可控矩阵,然后利用它们来识别振动系统的模态参数(模态频率、模态阻尼比和模态振型);而后者则主要利用时域振动响应数据组成的Hankel矩阵,通过矩阵的QR分解减缩计算数据量,并依靠对投影矩阵的奇异值分解来消除噪声的影响,然后利用最小二乘法等矩阵运算来识别出系统矩阵和输出矩阵,最后利用求得的系统矩阵和输出矩阵识别出振动系统的模态参数(模态频率、模态阻尼比和模态振型)。
⑶针对基于随机子空间识别法的系统定阶方法研究不足的状况,本文进行了探索性研究。在文中,我们主要研究了基于随机子空间识别法的系统稳态图定阶法和系统奇异熵增量定阶法,其中前者主要利用LMS Test.lab模态应用分析软件在线分析完成,而后者则主要通过matlab应用程序来完成。结果表明两种方法的系统定阶结果吻合良好,且都比传统的奇异值分解系统定阶法更为可靠有效。
⑷在和有限元分析的理论结果进行了对比之后,本文仍以上述的悬臂梁结构为研究对象,通过一个随机白噪声激励信号来模拟它在环境激励下的工况,并分别利用随机子空间识别法和Polymax(最小二乘复频域法)两种识别方法对它进行了在线模态分析,对比结果进一步证明了随机子空间识别法的有效性和可靠性。
综上所述,本文利用有限元模态分析和Polymax模态分析的方法分别证明了随机子空间识别法的有效性和可靠性。此外,在系统定阶方面,本文研究了基于随机子空间识别法的两种系统定阶方法—系统稳态图定阶法和系统奇异熵增量定阶法,结果表明,两种系统定阶方法的定阶结果吻合良好。总之,由于随机子空间识别法是一种基于结构振动响应的模态识别方法,其识别效果稳定可靠,而且目前对基于随机子空间识别法的系统定阶方法研究较少,所以本文的研究对于机械结构的在线健康监测有着重要的意义。
At present,the structural health monitoring methods based on structural vibration response has been focused by the scientific research institutions at home and abroad,and the operational modal analysis methods are most valuable among them.Due to the operational modal analysis methods using only the structural vibration response data which is obtained in operating conditions for on-line analysis,and it does not require artificial motive equipment to incentive the structure,so the analyzed results of such methods more in line with the operating boundary conditions of the structure.Therefore,such analysis methods have been widely used in the aerospace、bridges and mechanical manufacturing engineering applications.
For these reasons,the stochastic subspace identification method relying on environmental excitation has been exploringly studied on this paper.During the research process,we have mainly done the following works:
⑴On the paper,we have studied cantilever by the finite element analysis method to conduct their theoretical modal analysis,and obtained their modal frequencies and modal shape.Thus it provides a theoretical frame of reference for the experimental analysis,and comparatively analysis the experimental modal analysis results by the stochastic subspace identification method and the theoretical results,and it shows that the two modal identification results are in good agreement.
⑵on the basis of previous studies,the stochastic subspace identification method which is inspired by the environment has been studied deeply on this paper.The stochastic subspace identification method mainly consists of two kinds of algorithms—the covariance-driven stochastic subspace identification method and data-driven stochastic subspace identification method,and the specific identification process of the two algorithms has been respectively discussed in detail on this paper.The former mainly uses the output covariance sequence to compose Toeplitz matrix blocks,by the singular value decomposition (SVD) to obtain the system matrix and control matrix,then it uses them to identify the modal parameters of vibrating system (modal frequencies、modal damping ratio and the modal shape); while the latter mainly uses Hankel matrix composed of the time-domain vibration response data,reduces the amount of the matrix calculations by QR decomposition,and eliminates the effect of noise by the singular value decomposition of the projection matrix,then it uses the matrix operations such as least-squares method to identify the system matrix and output matrix.Finally,it uses the system matrix and output matrix to identify the modal parameters of vibrating system (modal frequencies、modal damping ratio and modal shape).
⑶Because of researching less on the system-order determination method based on the stochastic subspace identification method,we conducted an exploratory study.On this paper,we mainly studied the system order determination method by the steady-state diagram or singular entropy increment,which are both based on the stochastic subspace identification method.The former has been on-line completed by LMS Test.lab modal analysis software,but the latter has been completed by the matlab application.The results show that the results of two order determination methods are in good agreement,and they are more reliable and effective than the traditional system fixed-order method which uses the singular value decomposition.
⑷After comparing with the theoretical results obtained by the finite element analysis method, we still take the cantilever structure as researched objects and incentive it by a random white noise signal to mimic its working state in the environmental conditions, with the random subspace identification method and Polymax (Least-Squares Complex Frequency-domain method) conducting on-line modal analysis for them.The results further proves the validity and reliability of the stochastic subspace identification method.
In summary, the finite element modal analysis and Polymax modal analysis method are adopted,and they respectively proved the validity and reliability of the stochastic subspace identification method.In addition,on the system order determination methods,we studied two kinds of system order determination methods based on the stochastic subspace identification method—the system steady-state diagram fixed-order method and system singular entropy increment order determination method,the results showed that the fixed-order results of two system order determination method are in good agreement.In short,because the stochastic subspace identification method is a kind of modal identification method based on the structure vibration response,and the identified results is stable and reliable,and currently the system fixed-order method based on the stochastic subspace identification method has been less studied,so it plays an important role in the mechanical On-line health monitoring studies.
引文
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[3]何辉.多参考点最小二乘复频域法在飞行器模态参数识别中的应用[R].洛阳:中国空空导弹研究院,2008.
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[5]张笑华.结构环境振动模态参数识别随机子空间方法与应用[D].福州:福州大学,2005.
[6]陈锋,陈小安,孟杰.高速电主轴的工作模态实验分析[J].现代制造工程,2008,(8):1-4.
[7]姚志远,汪凤泉,刘艳.工程结构模态的连续型随机子空间分解识别方法[J].东南大学学报,2004,34(3):382-385.
[8]刘兴汉,王跃宇.基于Cholesky分解的改进的随机子空间法研究[J].宇航学报,2007,28(3):608-652.
[9]董宁娟.基于参数识别的往复压缩机气阀故障诊断方法的研究[D].哈尔滨:哈尔滨工业大学,2006.
[10]孙建刚.基于环境振动的实验模态分析方法研究[D].哈尔滨:哈尔滨工业大学,2006.
[11]张家滨,陈国平.基于随机子空间的递推在线模态识别算法[J].振动与冲击,2009,28(8):42-45.
[12]Paul Williams.Structural damage detection from transient responses using square root uns -cented filtering [J].Acta Astronautica,2008,63(2008):1259-1272.
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