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Inhomogeneity reconstructions in tendon ducts via boundary integral equations

机译:基于边界积分方程的腱管非均匀性重建

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In this study, as an alternative to the formerly presented investigations, Newton-type numerical algorithms are proposed to find location and shape of an air void inside of a tendon duct and to identify gathered metallic bars in a concrete column. The simulated structures are illuminated by four acoustic sources at a fixed frequency such that the scattered field is measured in a near-field region at 128 points. According to the nature of physical problems, the Dirichlet boundary condition is employed to model air-filled cavities and transmission conditions are assumed for metallic objects. Additionally, conductive boundary conditions are suggested for a more realistic representation of the inhomogeneities for the rusty metallic skin of the duct. Potential approaches are used to derive boundary integral equations. The proper treatment of the ill-conditioned equations is established via Tikhonov regulariza-tion. Applicability of the proposed inversion algorithms is tested with realistic parameters for different scenarios using noisy scattered field data and accurate numerical results are presented at 10 kHz for the unknown physical properties of the duct's skin.
机译:在这项研究中,作为先前提出的研究的替代方法,提出了牛顿型数值算法,以查找腱管内部空隙的位置和形状,并识别混凝土柱中聚集的金属棒。模拟的结构由四个固定频率的声源照射,从而在128点的近场区域中测量散射场。根据物理问题的性质,采用Dirichlet边界条件对充气腔进行建模,并假设金属物体的传输条件。此外,建议使用导电边界条件来更真实地表示管道生锈的金属蒙皮的不均匀性。势方法用于导出边界积分方程。通过Tikhonov正则化可以确定对病态方程的正确处理。所提出的反演算法的适用性使用嘈杂的散射场数据在不同情况下使用实际参数进行了测试,并针对导管皮肤的未知物理特性在10 kHz处给出了精确的数值结果。

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