基于本征正交分解与模态扩展的结构振动响应虚拟感知

VIRTUAL SENSING OF STRUCTURAL VIBRATION RESPONSE BASED ON PROPER ORTHOGONAL DECOMPOSITION AND MODAL EXPANSION

  • 摘要: 桁架结构健康监测过程中,传感器数量受限而无法对结构进行整体性监测。为此,发展了一种基于本征正交分解(Proper Orthogonal Decomposition, POD)与模态扩展(Modal Expansion, ME)相结合的POD-ME方法。该方法无需建立有限元模型获取先验信息,仅利用实测动响应数据训练反映结构特征的本征模态,通过选取本征模态构建表征桁架稀疏应变与未测点处应变映射关系的虚拟感知矩阵,并结合有限测点的动响应数据与虚拟感知矩阵,实现桁架结构从有限测点应变响应到未测点应变响应的有效估计。分别开展桁架结构数值模拟和车过桁架桥试验,验证了所发展方法的有效性和鲁棒性。进一步探讨了POD模态数量、不同噪声水平、不同传感器布置和不同激励情况对应变估计结果的影响。结果表明,所发展方法能够在仅有部分杆件可测的条件下有效估计未测点应变响应。

     

    Abstract: During health monitoring of truss structures, structural integrity monitoring is limited by the number of sensors. To solve this problem, a POD-ME method based on proper orthogonal decomposition (POD) and modal expansion (ME) is developed. In this method, it is not necessary to obtain prior information by establishing a finite element model, and the proper modes reflecting the structure feature are trained using the measured dynamic response data only. The proper modes are chosen to construct a virtual sensing matrix that characterizes the mapping relationship between the sparse strain of truss and the strain at the unmeasured points, combined with the virtual sensing matrix and the dynamic response data of finite measuring points, and then an effective estimation of the truss structure from the strain response of finite measuring points to the strain response of unmeasured points is realized. The numerical simulation of a truss structure and a vehicle-passing truss bridge test are carried out to verify the effectiveness and robustness of the developed method. The influences of the number of POD modes, noise levels, different patterns of sensor placement and different excitation conditions on the estimated results are discussed. The results show that the unmeasured response of the structure is effectively estimated by the developed method under the condition that only some elements can be measured.

     

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