环境激励下结构模态参数自动识别与算法优化
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摘要
实验模态分析在结构的健康监测、损伤识别、动力特性分析等方面具有重要的工程应用价值，主要包括数据采集、数据处理、参数识别、模型验证等步骤，其中模态参数识别是其中的核心内容。在数据采集时，通常单次完成所有自由度数据采集，对于采集通道数小于结构自由度数的结构需进行多组分时测量。选用单组测量分析时域法中应用最为广泛的随机子空间识别法、多组分时测量分析中常用的特征系统实现算法以及善于低频密集模态分析的小波模态参数识别方法为研究对象。目前，随机子空间识别和特征系统实现算法需要人工参与定阶及模态拾取，存在自动化程度不高的问题，需要进行模态参数自动识别研究；另一方面，随着分析数据量的不断增大，基于数据驱动随机子空间识别法还存在效率低的问题，需要进行模态参数识别算法优化，以提高计算效率。在我国一些重要领域所应用的实验模态系统基本都是国外公司开发的，国内的实验模态系统还处于发展阶段，在各方面与国外成熟商业系统都有不小差距，需要研发具有自主产权功能完善的实验模态分析系统，以缩小与国外先进模态系统的差距。本文主要研究随机子空间识别法、特征系统实现算法等时域方法的模态参数自动识别及算法优化，研发具有自主产权功能完善的实验模态分析系统，主要工作和结论如下：
①研究了单组测量分析时域法中应用最为广泛的随机子空间识别法，针对其自动化不高的问题，提出利用模糊聚类算法进行模态参数自动拾取，以频率、阻尼比、模态振型、模态能量为聚类因子计算各模态之间的相似性，采用谱系聚类法根据模态之间的相似性将计算结果分成若干类，提取元素个数大于一定值的类作为拾取结果，实现模态参数自动识别；为了减少虚假模态对结果拾取的影响，提出了模态相似指数作为模态可靠性衡量指标，利用其可以有效剔除计算结果中的虚假模态；为了确定结构的主导模态，利用输出矩阵C、状态矩阵A的特征值与特征向量以及状态-输出协方差矩阵G计算随机子空间识别结果各模态对应的模态能量，从而确定结构中的主导模态；针对基于数据驱动随机子空间识别法计算效率低下的问题，提出了基于特征值分解的随机子空间算法，相比原始算法，无需对高维矩阵进行QR分解和SVD分解，在保证识别精度的条件下减少了计算量，尤其在对大数据量分析时可大幅度提高计算效率。
②研究了多组分时测量分析中常用的特征系统实现算法，针对其识别精度易受信号噪影响的问题，利用奇异值分解法（SVD）滤除信号中的部分噪声，减少噪声模态并提高识别精度。为了减少虚假模态对模态拾取的影响，利用输出矩阵C、状态矩阵A的特征值和特征向量以及输入分配矩阵B计算识别结果中各模态能量矩阵，对其进行奇异值分解得到最大奇异值，将其作为各模态对输出能量贡献的衡量指标，称之为模态能量水平，依据虚假模态模态能量为零的特点剔除计算结果中的虚假模态。以频率、阻尼比、模态振型为聚类因子，利用谱系聚类法实现模态参数自动识别。
③研究了善于低频密集模态分析的小波模态参数识别方法，针对其计算效率低下的问题，提出基于数据缩减的分频段小波模态参数快速识别算法。首先利用奇异值分解对协方差信号在保留数据信息量的情况下进行缩减以减少参与计算的数据量，由正功率谱密度矩阵的奇异值分解确定识别系统的模态阶数及相应的频率范围，利用小波变换对缩减后的数据进行各阶模态逐频段识别。相比原始算法在保持计算精度的情况下提高了计算效率，在多测点数据分析中可大幅度提高计算效率。
④成功研发了一套具有自主知识产权的实验模态分析系统，该系统包括数据采集、结构建模、数据处理、参数识别、模型验证、振型动画等模块，可以方便、快捷和高效地完成结构模态参数识别的全过程。对各个功能模块进行了详细的设计，并对系统实现的关键技术进行了讨论。系统包含了多种不同模态参数识别方法，它们可以互相校核，确保了识别结果的可靠性，最后将该系统进行了工程应用及对比试验。
最后对论文的工作进行了总结，并对基于环境激励的实验模态参数技术研究进行了展望。
Experimental modal analysis has important engineering application in structuralhealth monitoring, damage identification and dynamic characteristic analysis, etc. Itsanalyzing steps mainly includes data collection, data processing, parameteridentification, and model verification, in which the modal parameter identification isthe core content of the experimental modal analysis. During data collecting, the data ofall freedoms is usually collected at a single time, however the data should be collectedin different groups when the number of acquisition channels is less than the number ofstructure’s freedoms. SSI(Stochastic subspace identification) is the most widely usedtime-domain method in single measurement analysis; ERA(eigensystem realizationalgorithm) is a commonly used method in multi-component measurement analysis;while CWT (continuous wavelet transform)-based modal parameters identification isgood at identifying low-frequency close modal, all of them are studied detailedly inthis thesis. Today, order selection and modal selection for SSI and ERA needs manualparticipation, the automation degree is low, so the research about automatic modalparameter identification is urgently needed. Moreover, with the constantly increasingof analysis data amount, Data-SSI(data driven stochastic subspace identification) andCWT-based modal parameters identification exhibit a low efficiency in identification,so the algorithm of the modal parameter identification needs to be improved. Theexperimental modal systems used in some Chinese important domains are mainlydeveloped by foreign corporations, domestic experimental modal systems are still indevelopment stage, and the gap between domestic systems and foreign maturecommercial systems is still obvious, so developing experiment modal analysis systemwith self-propery right and perfect functions to narrow this gap is very important. Thisthesis studies the automatic modal parameter identification and algorithm optimizationfor some time-domain method such as stochastic subspace identification method, theeigensystem realization algorithm, and a analysis system with self-propery right andperfect functions has also been developed. The main contents and conclusions of thethesis are as follows:
①Stochastic subspace identification which is a most widely used time-domainmethod in single measurement analysis is studied. Due to its low automation degree,the hierarchical clustering method is adopted to automatically pick up modal. Automatic modal analysis is realized with the help of the hierarchical clusteringmethod, classify the results into several categories according the similarity between theresults with eigenfrequencies, damping ratios, mode shapes and mode energy, somecategories will be selected if the number of its elements is large enough. In order toreduce the influence by spurious modes on modal selection, a criterion named modelsimilarity index is proposed which can effectively indicate the spurious modesobtained by the stochastic subspace identification. The energy of each mode iscalculated by the selection matrices C, the eigenvalues and eigenvectors of the statematrix A and the state output covariance matrix G, then the contribution of differentorder modes to the structural response can be understood, which in turn can help toconfirm the dominate mode in the structure. An improved stochastic subspaceidentification algorithm based on eigendecomposition is introduced to solve its lowefficiency problem. Compared with the traditional algorithm, the proposed algorithmneed much less cost of memory and computing time as it doesn’t have a process of theQR decomposition of a high-dimensional matrix and SVD of the projection matrix,and the proposed algorithm improved the identification computational efficiencywithout losing the quality, especially when analyzing a large amount of data, thecomputational efficiency can be improved significantly.
②ERA(eigensystem realization algorithm) which is a commonly used method inmulti-component measurement analysis is studied. For the drawback that itsidentification precision is susceptible affected by the measurement noise, SVD isadopted to reduce measurement noise. In order to reduce the influence by spuriousmodes on modal selection, the energy matrix of each mode can be calculated by theselection matrices C, the eigenvalues and eigenvectors of the state matrix A and theinput distribution matrix B. The largest singular value of the energy matrix obtained bySVD is a measure for the energy contribution of each mode, which is named modalenergy level. Spurious modes resulting from noise or model redundancy are indicatedaccording their mode energy level. Take frequency, damping ratio, mode shape andmold the modal energy level as the clustering factor, automatic identification can berealized with the help of Hierarchical clustering method.
③CWT (continuous wavelet transform)-based modal parameters identificationwhich is good at identifying low-frequency close modal is studied. Attempting toovercome its low efficiency problem, a rapid modal identification algorithm usingwavelet based on data reduction is introduced. The SVD is firstly used to reduce the covarience signals on the premise of keeping data information amount, to decrease thedata needed in calculation. And then SVD is also applied to positive power spectraldensity matrix to identify modal order and its corresponding frequency range, then thewavelet transform is took to identify different order modes from one frequency toanother frequency after data reduction. Compared to the original algorithm, thismethod improves the identification computational efficiency without losing the quality,and the computational efficiency can be improved significantly especially whenanalyzing a large number of data.
④A modal analysis system with self-propery right is developed successfully inthis thesis. It contains data acquisition module, data process module, designs ofstructure model module, parameters identification module, modal validation module,and modal shaping module. The whole process of structural modal parametersidentification can be easily, quickly and efficiently completed by using this system.Each functional module is detailedly designed, and the key technologies of itsimplementation are also detailedly discussed. The system contains a variety of modalparameter identification methods, they can check each other to ensure the reliability ofthe identification results. At last, the system is used at some project applications andcomparative test, the results demonstrate that the modal analysis system designed inthis thesis has the value of engineering application.
Finally, the works of this thesis were summaried, and the future prospect ofambient excitation based experimental modal parameter technique is also discussed.
①研究了单组测量分析时域法中应用最为广泛的随机子空间识别法，针对其自动化不高的问题，提出利用模糊聚类算法进行模态参数自动拾取，以频率、阻尼比、模态振型、模态能量为聚类因子计算各模态之间的相似性，采用谱系聚类法根据模态之间的相似性将计算结果分成若干类，提取元素个数大于一定值的类作为拾取结果，实现模态参数自动识别；为了减少虚假模态对结果拾取的影响，提出了模态相似指数作为模态可靠性衡量指标，利用其可以有效剔除计算结果中的虚假模态；为了确定结构的主导模态，利用输出矩阵C、状态矩阵A的特征值与特征向量以及状态-输出协方差矩阵G计算随机子空间识别结果各模态对应的模态能量，从而确定结构中的主导模态；针对基于数据驱动随机子空间识别法计算效率低下的问题，提出了基于特征值分解的随机子空间算法，相比原始算法，无需对高维矩阵进行QR分解和SVD分解，在保证识别精度的条件下减少了计算量，尤其在对大数据量分析时可大幅度提高计算效率。
②研究了多组分时测量分析中常用的特征系统实现算法，针对其识别精度易受信号噪影响的问题，利用奇异值分解法（SVD）滤除信号中的部分噪声，减少噪声模态并提高识别精度。为了减少虚假模态对模态拾取的影响，利用输出矩阵C、状态矩阵A的特征值和特征向量以及输入分配矩阵B计算识别结果中各模态能量矩阵，对其进行奇异值分解得到最大奇异值，将其作为各模态对输出能量贡献的衡量指标，称之为模态能量水平，依据虚假模态模态能量为零的特点剔除计算结果中的虚假模态。以频率、阻尼比、模态振型为聚类因子，利用谱系聚类法实现模态参数自动识别。
③研究了善于低频密集模态分析的小波模态参数识别方法，针对其计算效率低下的问题，提出基于数据缩减的分频段小波模态参数快速识别算法。首先利用奇异值分解对协方差信号在保留数据信息量的情况下进行缩减以减少参与计算的数据量，由正功率谱密度矩阵的奇异值分解确定识别系统的模态阶数及相应的频率范围，利用小波变换对缩减后的数据进行各阶模态逐频段识别。相比原始算法在保持计算精度的情况下提高了计算效率，在多测点数据分析中可大幅度提高计算效率。
④成功研发了一套具有自主知识产权的实验模态分析系统，该系统包括数据采集、结构建模、数据处理、参数识别、模型验证、振型动画等模块，可以方便、快捷和高效地完成结构模态参数识别的全过程。对各个功能模块进行了详细的设计，并对系统实现的关键技术进行了讨论。系统包含了多种不同模态参数识别方法，它们可以互相校核，确保了识别结果的可靠性，最后将该系统进行了工程应用及对比试验。
最后对论文的工作进行了总结，并对基于环境激励的实验模态参数技术研究进行了展望。
Experimental modal analysis has important engineering application in structuralhealth monitoring, damage identification and dynamic characteristic analysis, etc. Itsanalyzing steps mainly includes data collection, data processing, parameteridentification, and model verification, in which the modal parameter identification isthe core content of the experimental modal analysis. During data collecting, the data ofall freedoms is usually collected at a single time, however the data should be collectedin different groups when the number of acquisition channels is less than the number ofstructure’s freedoms. SSI(Stochastic subspace identification) is the most widely usedtime-domain method in single measurement analysis; ERA(eigensystem realizationalgorithm) is a commonly used method in multi-component measurement analysis;while CWT (continuous wavelet transform)-based modal parameters identification isgood at identifying low-frequency close modal, all of them are studied detailedly inthis thesis. Today, order selection and modal selection for SSI and ERA needs manualparticipation, the automation degree is low, so the research about automatic modalparameter identification is urgently needed. Moreover, with the constantly increasingof analysis data amount, Data-SSI(data driven stochastic subspace identification) andCWT-based modal parameters identification exhibit a low efficiency in identification,so the algorithm of the modal parameter identification needs to be improved. Theexperimental modal systems used in some Chinese important domains are mainlydeveloped by foreign corporations, domestic experimental modal systems are still indevelopment stage, and the gap between domestic systems and foreign maturecommercial systems is still obvious, so developing experiment modal analysis systemwith self-propery right and perfect functions to narrow this gap is very important. Thisthesis studies the automatic modal parameter identification and algorithm optimizationfor some time-domain method such as stochastic subspace identification method, theeigensystem realization algorithm, and a analysis system with self-propery right andperfect functions has also been developed. The main contents and conclusions of thethesis are as follows:
①Stochastic subspace identification which is a most widely used time-domainmethod in single measurement analysis is studied. Due to its low automation degree,the hierarchical clustering method is adopted to automatically pick up modal. Automatic modal analysis is realized with the help of the hierarchical clusteringmethod, classify the results into several categories according the similarity between theresults with eigenfrequencies, damping ratios, mode shapes and mode energy, somecategories will be selected if the number of its elements is large enough. In order toreduce the influence by spurious modes on modal selection, a criterion named modelsimilarity index is proposed which can effectively indicate the spurious modesobtained by the stochastic subspace identification. The energy of each mode iscalculated by the selection matrices C, the eigenvalues and eigenvectors of the statematrix A and the state output covariance matrix G, then the contribution of differentorder modes to the structural response can be understood, which in turn can help toconfirm the dominate mode in the structure. An improved stochastic subspaceidentification algorithm based on eigendecomposition is introduced to solve its lowefficiency problem. Compared with the traditional algorithm, the proposed algorithmneed much less cost of memory and computing time as it doesn’t have a process of theQR decomposition of a high-dimensional matrix and SVD of the projection matrix,and the proposed algorithm improved the identification computational efficiencywithout losing the quality, especially when analyzing a large amount of data, thecomputational efficiency can be improved significantly.
②ERA(eigensystem realization algorithm) which is a commonly used method inmulti-component measurement analysis is studied. For the drawback that itsidentification precision is susceptible affected by the measurement noise, SVD isadopted to reduce measurement noise. In order to reduce the influence by spuriousmodes on modal selection, the energy matrix of each mode can be calculated by theselection matrices C, the eigenvalues and eigenvectors of the state matrix A and theinput distribution matrix B. The largest singular value of the energy matrix obtained bySVD is a measure for the energy contribution of each mode, which is named modalenergy level. Spurious modes resulting from noise or model redundancy are indicatedaccording their mode energy level. Take frequency, damping ratio, mode shape andmold the modal energy level as the clustering factor, automatic identification can berealized with the help of Hierarchical clustering method.
③CWT (continuous wavelet transform)-based modal parameters identificationwhich is good at identifying low-frequency close modal is studied. Attempting toovercome its low efficiency problem, a rapid modal identification algorithm usingwavelet based on data reduction is introduced. The SVD is firstly used to reduce the covarience signals on the premise of keeping data information amount, to decrease thedata needed in calculation. And then SVD is also applied to positive power spectraldensity matrix to identify modal order and its corresponding frequency range, then thewavelet transform is took to identify different order modes from one frequency toanother frequency after data reduction. Compared to the original algorithm, thismethod improves the identification computational efficiency without losing the quality,and the computational efficiency can be improved significantly especially whenanalyzing a large number of data.
④A modal analysis system with self-propery right is developed successfully inthis thesis. It contains data acquisition module, data process module, designs ofstructure model module, parameters identification module, modal validation module,and modal shaping module. The whole process of structural modal parametersidentification can be easily, quickly and efficiently completed by using this system.Each functional module is detailedly designed, and the key technologies of itsimplementation are also detailedly discussed. The system contains a variety of modalparameter identification methods, they can check each other to ensure the reliability ofthe identification results. At last, the system is used at some project applications andcomparative test, the results demonstrate that the modal analysis system designed inthis thesis has the value of engineering application.
Finally, the works of this thesis were summaried, and the future prospect ofambient excitation based experimental modal parameter technique is also discussed.
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