PSI - Issue 71

Rakesh Kumar Sahu et al. / Procedia Structural Integrity 71 (2025) 203–209

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where, T h is Hanning window length that is determined by from number of cycles in tone burst (N b ).

Fig. 1. Five-cycle Hanning-window modulated tone burst signal at 175 kHz central frequency in time domain .

2.1. Mode purification ( A0 mode ) Lamb waves exist in multiple modes, such as symmetric and anti-symmetric modes. These modes act differently after interaction with damages and sometimes overlap. In this work, the pure anti-symmetric mode is actuated by using a two-point load at the same location but opposite in direction, as shown in Fig. 2. Two piezoelectric sensors are located on both surfaces of the plate and at a distance of 300 mm from the actuator. The symmetric and anti symmetric wave modes are extracted from the measured response at the top and bottom sensors Eq. 3 and 4 ((Mori et al., 2019). To resolve the complexity of multiple mode wave propagation, the pure anti-symmetric mode for feature extraction and damage detection. For the extraction of symmetric wave mode: (3)

For extraction of anti-symmetric wave mode:

(4)

2.2. Damage index The presence of damage is identified by comparing the measured response with the baseline response and quantified through the damage index. The damage index used in the present study to quantify the severity of damage is RMSD, which evaluates the change in amplitude and phase of the signals. Root mean square deviation (RMSD) (Agrahari and Kapuria, 2016) is used to calculate the average error between the magnitude of damaged and pristine signals at each corresponding data point. This RMSD compares the damaged and pristine signals as given in eq. (5), higher value of the DI indicates a significant error between signals.

(5)

Where, x i , y i , and N represent the pristine data, damaged data, and total number of data points, respectively. RMSD is the effective parameter to detect the presence of damage in case of a single defect, also applicable in case of multiple damages, but other information about damage (type, width, location and number of damages) cannot be obtained by analyzing the DI value. To address this problem, the neural network is adopted to predict the location, severity of damage and multiple damages. The details of the neural network are described in the next section.