PSI - Issue 77

Andrzej Katunin et al. / Procedia Structural Integrity 77 (2026) 18–25 Author name / Structural Integrity Procedia 00 (2026) 000–000

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50% burst random signal was generated and, before delivered to the shaker, amplified using the TIRA ® BAA 500 shaker amplifier (Schalkau, Germany). The modal analysis was performed in the frequency band of 0÷300 Hz with a frequency resolution of 0.25 Hz to ensure high precision in determining the natural frequency of vibrations of the tested plates. It was decided to limit the study to a single natural frequency, since the higher modes of vibrations were characterized by low magnitudes of vibration velocity, which is crucial for further excitation of a specimen in the second step. The determined natural frequencies for the scenarios of 10%, 25%, and 50% of thickness reduction were 62.25 Hz, 61.75 Hz, and 64.25 Hz, respectively. In the second step, the specimens were loaded by harmonic signals corresponded to the first bending natural frequency to excite the self-heating effect. The acquisition of thermograms was performed using the Infratec VarioCam ® hr infrared camera (Dresden, Germany) with a resolution of 640×480 pixels. The registration was performed with a framerate of 1 Hz for a period of ca. 5 minutes. In each tested case, the self-heating temperature measured on the surfaces of the tested specimens did not exceeded 2°C, which confirms the non-destructive character of SHVT technique (see (Katunin, 2018b) for more details). 3. Damage identification and quantification 3.1. Selection of the best raw thermogram Due to the large number of thermograms acquired during SHVT testing, it is essential to identify the most informative raw thermogram for accurate damage detection and quantification with a minimal boundary distortions and measurement noise contamination. To this end, a two-step algorithm was developed to systematically select the optimal raw thermogram for each tested scenario. The first step involves identifying the thermographic time interval in which the thermal contrast between damaged and undamaged regions is most pronounced. This is defined as the Boundary of Effective Thermograms (BET), which is established in a manner similar to the thermal time constant principle. Two alternative criteria were used: • when the surface temperature reaches approximately 63.2% of its maximum value max , defined as: − − ≥ 1 , (1) • when the surface temperature reaches approximately 63.2% of its stabilized value s , defined as: − − ≥ 1 . (2) Here, represents the instantaneous surface temperature, is the initial (ambient) temperature, and is the base of the natural logarithm. The resulting BET defines the set of thermograms acquired at the highest temperature gradient during the test, before temperature stabilization causes a loss of contrast. After defining the BET interval, the second step involves evaluating each thermogram within this range to identify the one with the highest damage visibility. This is achieved by computing a temperature ratio for each thermogram: = − − , (3) where D is the mean temperature of the damaged region, is the minimum temperature of the damaged region, is the mean temperature obtained by subtracting the values in the damage region from the values of the plate area for each thermogram, and m in is the minimum value of this subtraction across the entire sequence. The optimal raw thermogram is identified as the one that yields the highest temperature ratio, i.e., max( ) . This metric effectively enhances thermal contrast between damaged and undamaged regions, thereby facilitating more accurate detection. This two-step approach ensures that thermogram selection is both time-efficient and data-driven,