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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results of baseline-free techniques considering the temperature variations and the dual damages, while conclusions are drawn in the final part. 2. Investigated Baseline-free Techniques In this paper, the accuracy and reliability of 3 different baseline-free methods for detecting single and multiple damages in a composite plate is investigated. A brief introduction of each method is presented first. 2.1. TR and its extensions The standard TR process is comprised of the following procedures (Huang, Zeng, Lin, et al., 2018; Liu et al., 2015; Wang & Shen, 2019). • Signal actuation and sensing: ( ) = ( ) ( , ) (1) where , represent the actuator and sensor in a transducer path, represents the frequency spectrum of signals, is the angular frequency of guided waves, and is a transfer function of the signal path − , which is reliant on and the path distance . • Time-reversal of guided wave responses: ′ ( ) = ∗ ( ) ሺʹሻ where ′ ( ) is the time-reversed response signal and ∗ ( ) is the complex conjugate form of ( ) . • Re-emission of the time-reversed response ′ ( ) = ′ ( ) ( , ) ሺ͵ሻ where ′ ( ) represents the frequency spectrum of the reconstructed excitation signal by the time-reversed response and other variables remain the same as above. Furthermore, the VTR reduces the hardware requirements of the standard TR (Liu et al., 2015) and can be easily implemented in a pitch-catch configuration. The VTR improves the standard TR by the following operation (Liu et al., 2015). ( , ) = ( ) ( ) ሺͶሻ When plugging the formula (2) and (4) into (3), the reconstructed excitation signal is yielded as follows. ′ ( ) = ∗ ( ) ∗ ( , ) ( , ) ሺͷሻ where ∗ ( ) represents the complex conjugate form of the excitation signal. Finally, a damage index (DI) based on the VTR method is shown as (Wang & Shen, 2019) = 1 − ∫ ( ) ′ ( ) 2 1 √∫ 2 ( ) 2 1 ∫ ′2 ( ) 2 1 ⁄ (6) In the formula (6), and ′ are the excitation signal and the reconstructed counterpart in the time domain, where the latter is obtained by implementing the inverse Fourier transform (IFFT) on (5). Meanwhile, 1 and 2 define a fixed interval for comparing and ′ .