PSI - Issue 52

Hongmin Zhu et al. / Procedia Structural Integrity 52 (2024) 679–689 Zhu et al./ Structural Integrity Procedia 00 (2019) 000 – 000

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2.2. Reciprocity-based Method The DI based on the reciprocity principle is defined as (Huang, Zeng, & Lin, 2018) = 1 − |∫ ( ) ( ) 2 1 | √∫ 2 ( ) 2 1 ∫ 2 ( ) 2 1 ⁄ (7) where , are guided wave signals of the path − and − respectively, and 1 and 2 is defined for the same purpose as in (6). 2.3. IB method The IB technique operates by categorising the transducer paths into several groups which contain equivalent paths with nearly identical distances and propagation angles, and then identifying the damaged paths within each group of paths (Anton et al., 2009; Sun et al., 2019). For a transducer path in the group , the corresponding DI is formulated as (Sun et al., 2019) , =1− , (8) where , and are denoted as the signal energy of the -th signal and the maximum signal energy of the -th group respectively. The signal energy is then calculated as (Sun et al., 2019) = ∫ ( ) 2 2 1 (9) where ( ) is a guided wave signal in the time domain and the definition of 1 , 2 is similar to (6). 3. Experimental Setup The damage localisation performances of the VTR, IB and the reciprocity-based methods are validated on an anisotropic Carbon Fibre Reinforced Polymer (CFRP) coupon, which is monitored by the DuraAct (PI ceramic) PZT transducers in an active pitch-catch configuration. The integrity of the transducer bonding was assessed by the Electromechanical Impedance (EMI) technique (Yue et al., 2021). Moreover, a National Instrument (NI) signal generator and a − 5105 oscilloscope are employed separately for the signal actuation and sensing purposes. The 50 tone bursts are then obtained and processed by a 5 -cycle Hanning window together with signal denoising procedures. In order to avoid boundary-reflected modes, the first wave packets are isolated from the guided wave tone bursts following the formula below. 1 = , 2 = +1.1 ∙ (10) where 1 , 2 indicate the start and end of the truncated packets and are utilised in the formulae (6) - (8), represent the path distance, and are denoted as the number of tone burst cycles and the centre frequency of guided wave signals, which are determined as 5 and 50 respectively. is the group velocity varying along different paths on the anisotropic composite and is measured by experiment. In addition, the factor 1.1 is considered to cover a complete wave packet (Yue, 2019). In this paper, a CFRP plate (see Fig. 1) manufactured of 21/194/34%/ 800 laminates is analysed with simulated putty damages. The 12-sensors plate has the dimension of 400 × 400 × 2.2 ( × × ) with the stacking sequence as [±45/0 2 /90/0] . In terms of the damage localisation, the reconstruction algorithm for probabilistic inspection of defects (RAPID) (Zhao et al., 2007) is implemented based on the DI generated by (6)-(8). Afterwards the CFRP plate is segmented into 100×100 ( × ) pixels for damage imaging and the imaging parameter is adopted as 1.05 (Zhao et al., 2007).