基于空间压缩感知理论的梁和板结构全场响应重构研究

FULL-FIELD RESPONSE RECONSTRUCTION OF BEAMS AND PLATES BASED ON SPATIAL COMPRESSIVE SENSING THEORY

  • 摘要: 该文提出了一种利用空间压缩感知理论从少量位移或加速度传感器的测量值重构梁和板结构全场响应的方法。基于正弦级数可快速逼近结构振型的特点,提出了梁和板结构的通用字典。传感器的数量通过初略分析逼近结构振型所需的正弦级数项来确定,而安装位置则通过拉丁超立方体采样算法确定。稀疏表示向量通过正交匹配追踪算法恢复,并用于结构全场响应的重构。通过参数研究评估了各种因素对所提方法的影响,并通过模型试验验证了方法的有效性。算例表明所提方法是一种具有广泛适用性的结构全场响应重构方法,有望大幅提高结构振动测试的效率和振动分析的精度。

     

    Abstract: This study proposed a method to reconstruct the full-field responses of beam and plate-type structures from measurements recorded by a limited number of displacement or by acceleration sensors using spatial compressive sensing theory. Based on the fact that sine series can quickly approximate structural mode shapes, general dictionaries for both beam and plate-type structures are constructed. The number of sensors is determined by analyzing the sine series terms needed to approximate the modal shapes, while their installation positions are determined by the Latin Hypercube Sampling algorithm. The sparse representation vector is solved using the Orthogonal Matching Pursuit algorithm and employed for full-field response recovery. The effects of various factors on the method proposed are assessed through a parametric study, followed by validation through a laboratory test. The presented examples indicate that the method proposed is a widely applicable approach for reconstructing the full-field response of structures, which is expected to significantly improve the efficiency of structural vibration tests and to enhance the accuracy of vibration analysis.

     

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