PSI - Issue 77

H. Lopes et al. / Procedia Structural Integrity 77 (2026) 673–680 H. Lopes/ Structural Integrity Procedia 00 (2026) 000 – 000

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Fig. 2. Experimental setup for the measurement of the plate’s strain using shearography.

2.3. Methodology The raw phase maps acquired by the DS system capture the strain field developed in the plate due to the external loading. The plate generally exhibits a non- uniform strain field resulting from the combined effects of the plate’s uniform geometry, non-homogeneous material, boundary conditions, and non-uniform load, among others. Additionally, the maps are corrupted by high-frequency noise primarily caused by speckle decorrelation. Detecting internal damage is difficult because the small strain variations they induce often fall in the mid-range of the strain spectrum. This makes it challenging to isolate from the background strain caused by the structure's global response. Conventional methods attempt to amplify the damage signature by first filtering, unwrapping, and scaling the phase maps, followed by smoothing and numerical differentiation (Aebischer and Waldner, 1999). The core challenge, however, lies in a critical trade-off: finding the optimal balance between suppressing high-frequency noise and preserving the subtle strain variations induced by damage. This complex, multi-step process involves the sequential application of several low-pass filters, combined with numerical differentiation, making it both computationally intensive and complex. Furthermore, the inherent smoothing from the filtering process causes damage signatures to propagate to adjacent areas, resulting in poorly defined contours. Consequently, accurately determining the true size and precise location of the damage becomes severely compromised. The present work employs a simpler approach, which involves extracting damage signatures typically located in the mid-frequency range by applying a band-pass filter to the raw phase maps. These signatures are further enhanced relative to the background noise by summing multiple filtered phase maps. This band-pass filtering, is efficiently implemented by subtracting a low-pass filtered map, Δ ( , ) with a lower cutoff frequency from a second low-pass filtered map, Δ ℎ ℎ ( , ) with a higher cutoff frequency. This operation simultaneously isolates mid-frequency damage signatures by suppressing both the global background strain and the high-frequency noise. The necessary low-pass filtering is achieved by iteratively applying a common sine/cosine average filter with a 2D kernel to the raw phase maps (Aebischer and Waldner, 1999). This approach inherently manages phase discontinuities and ± signal modulation. The filter's cutoff frequency is controlled by adjusting the kernel size and the number of passes. The following empirical expression for the normalized cutoff frequency (0 ≤ f cutoff ≤ 0.5) in any direction is derived by considering the effects of multi -pass of the moving average filtering and the standard −3 dB amplitude attenuation criterion (Smith, 1997): ≈ 0 . 4×6√0 6 (1) where is the kernel size (window width) of the moving average filter and is the number of times the filter is applied (multi-pass). The flowchart in Figure 3 shows the application of the band-pass filter to a single raw phase map by subtracting two filtered phase maps with different cutoff frequencies. Specifically, the filtered phase map Δ ℎ ℎ

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