PSI - Issue 80

Yuhang Pan et al. / Procedia Structural Integrity 80 (2026) 43–52 YuhangPan / Structural Integrity Procedia 00 (2023) 000–000

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successfully detects the occurrence of a 0.7 mm crack at approximately 92,000 cycles. This demonstrates that the proposed DPL-based approach not only enables accurate stage segmentation but also provides a reliable way for early crack detection. Such results further validate the e ff ectiveness and robustness of the method in identifying critical transitions in the fatigue process, which are essential for structural integrity monitoring. Although our previous studies have demonstrated that the third harmonic parameter γ ′ can achieve in service baseline-free crack detection, some limitations remain to be addressed. In particular, the critical point between the second and third stages is located very close to the actual crack initiation point, which pro vides valuable reference for identifying crack onset and for early prognosis. However, the transition between the first and second stages exhibits more uncertainty. For example, in specimen T1 this transition occurred around the 12,000 cycles, the underlying mechanism of which is not yet fully understood. Based on exten sive experimental observations, this critical point appears to correspond not to crack initiation, but rather to the transition of the bonding condition—from the initial adjustment at the start of the fatigue test to a more stable state during cyclic loading. This interpretation is also supported by previous studies that reported similar observations in related fatigue experiments (Wang et al. (2023); Yue et al. (2018)). In addition, the inherent fluctuations of γ ′ may a ff ect the stability and robustness of the monitoring process, especially in practical applications where signal variability is inevitable. Therefore, it is necessary to further investigate alternative or complementary features that exhibit improved stability in order to achieve more reliable and robust crack monitoring under varying operational and environmental conditions. To address these limita tions, the RMS value of the time-domain signals was extracted as an alternative feature. The RMS parameter, which inherently reflects the energy content of the measured signal, is expected to provide a more stable and robust indicator of structural changes compared with the higher-order harmonic parameters. To evaluate its e ff ectiveness, the same DPL method was applied to the RMS data, and the results are summarised in Fig. 6. Fig. 6(a) illustrates the change of the RMS values throughout the fatigue experiment for specimen T1. Compared with the third harmonic parameter γ ′ , the RMS demonstrates a markedly more stable trend. While γ ′ typically exhibits three stages, the RMS response can be broadly divided into two stages: an initial plateau at approximately 6, followed by a sharp decrease after about 90,000 cycles. Notably, this transition point closely coincides with the experimentally observed onset of crack initiation. The application of the DPL method to the RMS data is presented in Fig.6(b). In the vicinity of the stage transition, the fitting procedure produces multiple “spikes,” indicating the sensitivity of the method to abrupt changes in the signal. These spikes form the basis for defining a threshold, as shown in Fig.6(c), which enables automated identification of the critical transition point. The resulting two-stage segmentation obtained from the threshold-based DPL analysis is summarized in Fig. 6(d). The critical point was identified at approximately 92,000 cycles, corre sponding to a detectable crack length of 0.7 mm.This result is in full agreement with the detection outcome obtained using γ ′ , thereby validating the feasibility of RMS as an alternative feature for online crack de tection. Furthermore, the clear two-stage behavior of RMS o ff ers a more straightforward and interpretable characterization of fatigue crack initiation and propagation. The results obtained from another two specimens, T2 and T3 are summarized in Fig. 7. Fig. 7(a) presents the crack monitoring results for specimen T2. Similar to specimen T1, the fatigue process of T2 can be clearly divided into two stages based on the RMS evolution. By applying the proposed DPL method, the critical point was identified at approximately 95,000 cycles, corresponding to a detectable crack length of 1.4 mm. For specimen T3, as shown in Fig. 7(b), a comparable two-stage behavior is observed. The transition point was detected at around 115,000 cycles, corresponding to a crack length of 1.0 mm. This result further demonstrates the robustness of the RMS-based DPL approach, as it consistently identifies crack initiation points across di ff erent specimens with varying fatigue lives. Moreover, the close agreement between the detected crack sizes with physically measurable crack lengths provides strong evidence of the method’s feasibility for practical online crack detection applications.

4.4. The e ff ect of the sensor position

As illustrated in Fig.2(b), two PZT sensors were employed in the present experimental setup. The results presented in the previous sections were primarily obtained from Sensor 1, which consistently exhibited reli able crack detection performance and strong agreement with the observed crack growth. To further evaluate the potential influence of sensor location on the proposed approach, additional analysis was performed using