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Structural health monitoring (SHM) is a multidisciplinary damage detection technique that incorporates various mechanisms, of which guided waves (GWs) -based damage detection is one of the critical fields of research. To realize the complete process of SHM, research on GWs has concentrated on diagnosis and localization. GWs-based damage detection technology is widely used in plate structure, combining different sensor placement algorithms and equipment such as scanning laser doppler vibrometry (SLDV) to achieve accurate damage location. Simultaneously, developing the finite element method (FEM) allows for precise simulation in discontinuous media and complex sharp structures. Therefore, this paper combines the theoretical calculation approach of elastic wave propagation with the orthogonal matching pursuit (OMP) algorithm, using the excitation signal and signal reflected by damage as the input matrix and target matrix, respectively. Thus, the reflection-waves coefficient matrix (RCM) containing damage information could be obtained after calculation by the OMP algorithm. Besides, a prediction approach of reference reflected signal based on four-layers recurrent neural networks (RNNs) is proposed with experiments data to reduce the difficulty of expanding a dictionary matrix in a plate with multiple defects, which allows for predicting the damage reflection signal under different distances with 88.14% accuracy. And finally, considering the aluminum plate with hole damage as an example, the experiment results show that the proposed approaches are effective for the localization of single damage and muti-damage. Meanwhile, the prospects and limitations of the algorithm for precise localization are also addressed in the last. [ABSTRACT FROM AUTHOR]

The Hankel matrix of type B Narayana polynomials was proved to be totally positive by Wang and Zhu, and independently by Sokal. Pan and Zeng raised the problem of giving a planar network proof of this result. In this paper, we present such a proof by constructing a planar network allowing negative weights, applying the Lindström-Gessel-Viennot lemma and establishing an involution on the set of nonintersecting families of directed paths. • Providing a combinatorial proof of the Hankel total positivity of type B Narayana polynomials. • Allowing negative weights in the construction of planar networks. • Establishing an elegant sign-reversing involution on families of nonintersecting lattice paths. [ABSTRACT FROM AUTHOR]