# Phase Reversal Method for Damage Imaging in Composite Laminates Based on Data Fusion
## 3 Results  
### Numerical Analysis Results  
In the numerical analysis, an orthogonal anisotropic composite plate was used as a research object. The structural model is shown in Figure 2; the plate size was 200 mm \(\times\) 200 mm \(\times\) 1 mm. The excitation source was located in the center of the plate, and the sensors were set up as four orthogonal linear arrays. The through hole with a diameter of 10 mm was used as damage, and its positional coordinates were (50 mm, 70 mm). To improve the calculation efficiency, since the damage type was through-hole damage, the composite material was assumed to be a whole structure. The composite material plate adopted the integral-modeling method, and the specific parameters are given in Table 1.  
Figure 2: Schematic diagram of the composite laminate and sensor array. The commercial finite element software COMSOL was used to calculate the damage scattering model of composite plates. The grid was structured; the unit type was a uniform hexahedral grid with a size of 1 mm; the excitation source was a circular equipotent line model with a diameter of 7 mm; and a linear array measuring point denoted the sensors on the composite plate's surface. Due to the high sensitivity of the \(A_{0}\) mode guided wave to damage and the low complexity of signal analysis, this study used the anti-symmetric \(A_{0}\) mode guided wave excited in the center of the plate to realize phase-reversal damage imaging. The excitation signal was a five-peak wave modulated by the Hanning window, and its expression was as follows:  
\[S=\frac{A}{2}\left[1-cos\left(\frac{2\pi f_{c}}{n}\right)t\right]\cdot sin(2\pi f _{c}) \tag{11}\]  
where \(A\) is the amplitude of excitation signal, \(f_{c}\) is the center frequency which was chosen 100 kHz, \(t\) is the time duration, and \(n\) is the wave period which was chosen 5 in this study. The time domain and frequency domain of the excitation signal are shown in Figure 3.  
The wave field diagram of the orthotropic composite material plate obtained by the finite element calculation is displayed in Figure 4. As the orthotropic characteristics of the composite material led to the directional dependence of the guided wave's propagation velocity, the wave front has an approximately diamond shape. Four orthogonal linear sensors located on the coordinate axis were used to receive the damage scattering signals. The position and number of sensors are shown in Table 2. According to the theory of PRM, the spacing of sensors should meet the error requirements, and in this study, the sensors' spacing was set to 1 mm. Off-plane displacement signals of each measuring point were extracted, and signals of four typical measuring points are shown in Figure 5, where direct wave signals and damage-scattered wave signals can be clearly identified. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Thickness** & **E11** & **E22** & **G12** & **G23** & \(v\)**12** & \(v\)**23** \\ \hline \(1\) mm & \(178\) GPa & \(178\) GPa & \(5.2\) GPa & \(5.2\) GPa & \(0.34\) & \(0.34\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of the orthotropic composite. Figure 3: (**a**) Time-domain diagram of the excitation signal. (**b**) Frequency-domain diagram of the excitation signal. Figure 4: Wave-field diagram of the orthotropic composite. \begin{table}
\begin{tabular}{c c c c c} \hline  & \(x\)-Axis & \(x\)-Axis & \(y\)-Axis & \(y\)-Axis \\  & **(Positive)** & **(Negative)** & **(Positive)** & **(Negative)** \\ \hline Sensor location & 15–35 mm & (\(-\)15)–(\(-\)35) mm & 15–35 mm & (\(-\)15)–(\(-\)35) mm \\ Number of sensors & 21 & 21 & 21 & 21 \\ \hline \end{tabular}
\end{table} 
Table 2: Location and number of sensors of the four sensor arrays. Figure 5: Typical received signals, including the incident and reflected waves.