PSI - Issue 80

Haomiao Fang et al. / Procedia Structural Integrity 80 (2026) 53–64 H. Fang et al./ Structural Integrity Procedia 00 (2025) 000 – 000

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extracted from the analytical excitation signal, which is assumed as a "perfectly healthy" state. The key hypothesis underlying the proposed approach is that the interaction of guided waves with damage has a much severer influence on signal characteristics than variations in material properties, temperature, specimen size, or sensor configuration. As a result, the shapelets derived from the analytical excitation signal are expected to generalize well across different coupon panels, even under varying EOCs. The overall schematic of the proposed K-SVD baseline-free method is illustrated in Figure 3. The dictionary generation process consists of three main steps: shapelet candidate generation, K-SVD dictionary learning, and dictionary compilation. Once the dictionary is compiled, it can be used for signal reconstruction and subsequent damage identification through sparse coding.

Figure 3: The overall illustration of the proposed methodology.

3.2.1 Candidates generation The analytical excitation signal is defined by (4). ( ) = 0.5 2 [ ( ) − ( − )](1−cos( 2 )) sin(2 )

(4)

The typical length of the shape candidates is one fifth of the whole excitation signal. In this study, the length of the shapelet candidates and the entire signal are 16 and 80, respectively. Based on the analytical excitation signal with 80 datapoints, a total of 65 shapelet candidates can be extracted. 3.2.2 K-SVD dictionary learning Online dictionary learning technique is implemented to learn the representative shapelets from these candidates. The K-SVD dictionary learning technique is typically employed to find an overcomplete dictionary and sparse representations of data. The operating process can be expressed as (5): , 1 ∑ ( 1 2 ‖ − ‖ 22 + ‖ ‖ 1 ) = 1 (5) Where represents the shapelet dictionary of size × , which starts with a random matrix 0 composed of k numbers of 2 normalized columns. represents sparse representation of size × . represents training shapelet candidate matrix. , , represents the shapelet dimension (length), the number of atoms in the dictionary, and the number of training samples, respectively. denotes the number of iterations with the start of 1. The algorithm iteratively alternates between sparse coding and dictionary update, until convergence or a stopping criterion is met. Given a fixed dictionary 0 , the algorithm starts to do the first sparse coding and the corresponding sparse representation 1 can then be calculated. This process can be expressed by (6):