A modelling framework for ultrasonic inspection of waveguides with arbitrary discontinuities, excited using piezoelectric transducers, is developed. The framework accounts for multi-modal, dispersive and damped one dimensional propagation over long distances. The proposed model is applied to simulate a realistic guided wave-based inspection of a welded rail. The framework models the excitation, propagation and scattering of guided waves from welds by respectively employing a hybrid model that couples a 3D FEM model of a piezoelectric transducer with a 2D SAFE model of the rail; a 2D SAFE model of the rail; and another hybrid method which couples a 3D FEM model of the arbitrary discontinuity (weld) with two SAFE models of the rail to represent the semi-infinite incoming and outgoing waveguides. Optimal damping parameters for hysteretic and viscous damping, respectively, are determined using a model updating procedure to approximate attenuation in the rail. Good agreement between the experimental measurement and simulation is demonstrated, even for weld reflections originating over 640 m from the transducer location. The proposed physics-based framework can be used to efficiently perform multiple analyses considering different numbers and locations of welds, different excitation signals or to investigate the effects of changes in parameters such as transducer geometry, or material property variations caused by temperature fluctuations. The framework could therefore be used in future to set up a digital twin of a section of rail track, or in the development of a rail monitoring system by predicting reflections from defects which cannot readily be measured, but which can be simulated.

中文翻译：

---

基于超声波导波的焊接铁轨检测仿真建模框架

开发了一种建模框架，用于对具有任意不连续性的波导进行超声波检测，使用压电换能器激励。该框架考虑了长距离的多模态、色散和阻尼一维传播。所提出的模型用于模拟真实的基于导波的焊接钢轨检测。该框架通过分别采用将压电换能器的 3D FEM 模型与轨道的 2D SAFE 模型耦合的混合模型，对来自焊缝的导波的激发、传播和散射进行建模；轨道的二维安全模型；另一种混合方法将任意不连续（焊缝）的 3D FEM 模型与轨道的两个 SAFE 模型相结合，以表示半无限输入和输出波导。分别使用模型更新程序来确定磁滞阻尼和粘性阻尼的最佳阻尼参数，以近似轨道中的衰减。证明了实验测量和模拟之间的良好一致性，即使对于源自换能器位置超过 640 m 的焊缝反射也是如此。考虑到不同数量和位置的焊缝、不同的激励信号，所提出的基于物理的框架可用于有效地执行多重分析，或研究参数变化的影响，例如换能器几何形状或由温度波动引起的材料特性变化。因此，该框架将来可用于建立一段铁路轨道的数字孪生，