PSI - Issue 80

60 8 Haomiao Fang et al. / Procedia Structural Integrity 80 (2026) 53–64 H. Fang et al./ Structural Integrity Procedia 00 (2025) 000 – 000 ℎ ( ) = 1 (2 1 + 2 − 1 2 ) [ ( ) − ( − ℎ )] ( ) = 0.5 2 [ ( ) − ( − )](1−cos( 2 )) sin(2 ) Where = 200 is the duration window, 1 =5 is the amplitude, = 50 kHz , = 5 cycles .

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Figure 7: The geometry and PZTs distribution.

4.2. Comparative analysis based on PDI results. This section provides a comparative analysis of the proposed K-SVD baseline-free method against the Time Reversal (TR), Instantaneous Baseline (IB), and reciprocity approaches based on probability-based diagnostic imaging (PDI) results from various damage s cenarios. Notably, IB exploits an ‘in - situ baseline’ from the responses of undamaged paths, and compares them with the responses of equivalent paths with the same distances and angles [17]. However, this technique highly relies on sensor configurations. Due to the lack of sufficient equivalent paths, IB could lead to a larger localization error compared with other baseline-free approaches [29]. Therefore, a refined IB approach is utilized in this study comparing the normalized first wavepacket of each path with the analytical toneburst, which is assumed as a perfect baseline. This post processing and indirect comparison with a surrogate reference reduce the reliance on having sufficient equivalent paths, which is well-suited for sensor networks with limited coverage.

Figure 8: Damage localization of scenario 1 based on different baseline-free techniques: (a) TR, (b) reciprocity, (c) IB, (d) the proposed K-SVD dictionary learning framework.