施袁锋, 朱正言, 陈鹏, 戴靠山. 基于EM算法和模态形式的状态空间模型自降阶工作模态分析[J]. 工程力学, 2021, 38(9): 15-25. DOI: 10.6052/j.issn.1000-4750.2020.08.0618
引用本文: 施袁锋, 朱正言, 陈鹏, 戴靠山. 基于EM算法和模态形式的状态空间模型自降阶工作模态分析[J]. 工程力学, 2021, 38(9): 15-25. DOI: 10.6052/j.issn.1000-4750.2020.08.0618
SHI Yuan-feng, ZHU Zheng-yan, CHEN Peng, DAI Kao-shan. OPERATIONAL MODAL ANALYSIS USING EM ALGORITHM AND MODAL-FORM STATE-SPACE MODEL WITH AUTO MODEL ORDER REDUCTION[J]. Engineering Mechanics, 2021, 38(9): 15-25. DOI: 10.6052/j.issn.1000-4750.2020.08.0618
Citation: SHI Yuan-feng, ZHU Zheng-yan, CHEN Peng, DAI Kao-shan. OPERATIONAL MODAL ANALYSIS USING EM ALGORITHM AND MODAL-FORM STATE-SPACE MODEL WITH AUTO MODEL ORDER REDUCTION[J]. Engineering Mechanics, 2021, 38(9): 15-25. DOI: 10.6052/j.issn.1000-4750.2020.08.0618

基于EM算法和模态形式的状态空间模型自降阶工作模态分析

OPERATIONAL MODAL ANALYSIS USING EM ALGORITHM AND MODAL-FORM STATE-SPACE MODEL WITH AUTO MODEL ORDER REDUCTION

  • 摘要: 工作模态分析具有试验简单、经济可行等优点,在工程实际中有广泛的应用。在基于状态空间模型的模态分析中,模型阶次的确定是获得准确和稳定的模态参数的关键问题之一。该文结合期望最大(EM)算法和模态形式状态空间模型来实现模型自降阶和模态参数估计。将状态空间模型变换到模态形式,使待估计参数量得到精简的同时,可直接估计各阶模态响应。引入表征各阶模态响应在实际响应中占比的模态贡献作为模型降阶的指标,在EM求解模型极大似然估计时实现模型降阶。同时结合频谱图分析和阻尼比阈值剔除虚假模态,以获得实际的结构模态信息。通过数值结构模拟和现场结构实测的数据分析,结果表明该文方法具有较好的适用性和有效性。

     

    Abstract: With advantages such as simplicity of testing, low cost and practical feasibility, etc., operational modal analysis has been widely used in engineering practice. In state-space model-based modal analysis, determination of the model order is one of the key problems to obtain accurate and stable modal parameters. A method for auto model order reduction and modal identification is proposed using expectation-maximization (EM) algorithm and modal-form state-space model. By transforming the general state-space model into a special modal-form, not only the parameter space is simplified, but the modal responses can be estimated. Modal contribution ratio which represents the importance of each mode to the total response is used as a criterion for auto order reduction in EM algorithm. Meanwhile, combined with spectrum analysis and damping ratio threshold, spurious modes are eliminated for the selection of practical structural modes. Through validation analysis of synthetic and field data, it is shown that the method is practically feasible and effective.

     

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