Guided ultrasonic waves are attractive screening tools for elongated engineering structures due to their ability to propagate over long distances and flexibility in selecting mode-frequency combinations. Both computing dispersion solutions and accurately tracing them into dispersion curves are essential for guided waves’ non-destructive evaluation (NDE) and structural health monitoring (SHM) applications. Complex waveguide problems often require numerical methods to compute the eigen-solutions at discrete frequencies, and manual routines are usually adopted to trace different guided wave modes by directly comparing their mode shapes. However, challenges arise in intricate dispersion relations involving mode coupling, mode veering, and mode splitting. To address this, we propose an automated mode-tracing technique for guided waves via Affinity Propagation (AP) clustering. Upon solving the associated eigenvalue waveguide problem, physical field quantities are extracted to capture the alignment or dissimilarity features of different eigen-solutions. The physics-driven similarity matrix construction is performed by employing the weighted cosine distance and the similarity propagation in a high-dimensional feature space. High-quality set of exemplars and corresponding clusters (i.e. well traced guided wave modes) can be iteratively obtained using an optimized AP clustering algorithm. This paper presents the principles of the proposed technique, and then validates and illustrates its use through typical numerical examples. Accurate tracing of the dispersion curves has been achieved, independent of the eigenvalue computation procedures, and its robustness has also been manifested.

中文翻译：

---

通过物理驱动的亲和传播 (AP) 聚类自动模式追踪弹性波导中导波的色散关系


导超声波因其长距离传播的能力以及选择模频组合的灵活性而成为细长工程结构的有吸引力的筛选工具。计算色散解并将其准确地追踪为色散曲线对于导波的无损评估 (NDE) 和结构健康监测 (SHM) 应用至关重要。复杂的波导问题通常需要数值方法来计算离散频率下的本征解，并且通常采用手动例程通过直接比较不同的导波模式的振型来追踪不同的导波模式。然而，涉及模式耦合、模式转向和模式分裂的复杂色散关系带来了挑战。为了解决这个问题，我们提出了一种通过亲和传播（AP）聚类进行导波的自动模式跟踪技术。在解决相关的特征值波导问题时，提取物理场量以捕获不同特征解的对准或相异特征。通过利用高维特征空间中的加权余弦距离和相似性传播来执行物理驱动的相似性矩阵构造。使用优化的 AP 聚类算法可以迭代获得高质量的样本集和相应的聚类（即良好追踪的导波模式）。本文介绍了所提出技术的原理，然后通过典型的数值例子验证和说明了其使用。已经实现了色散曲线的精确追踪，与特征值计算过程无关，并且其鲁棒性也得到了体现。