# A New Method for Detecting Weld Stability Based on Color Digital Holography
## 3 Experiments and Results
### Evaluation of Weld Stability  
Unwrapping the wrapped phase difference after noise reduction means that the three-dimensional deformation field of the aluminum alloy plate under different loads can be calculated using Equation (4). Figure 7a-c show the three-direction deformation field of the lap-jointed aluminum alloy plate with the load from 293.67 N to 297.59 N. The load is applied in the y-direction of the overlapped aluminum alloy plate, and the y-direction has the maximum deformation variable. Subsequently, we evaluate the weld stability of the lap-jointed aluminum alloy plate solely based on the deformation in the y-direction. Figure 7d shows the center section line of the y-direction deformation field with the load from 293.67 N to 301.50 N. When y changes from 0 to 630 pixels, the three curves have almost the same slope. According to [PERSON]'s law, the elastic modulus is constant, which is because it is composed of aluminum alloy plates with uniform materials. When y changes from 630 pixels to 720 pixels (red box), the slopes of all three curves show significant changes, which are caused by changes in the thickness and material of the weld, leading to changes in the elastic modulus. On the other hand, by calculating the holographic reconstruction images of the aluminum alloy plate [27,32], it can be seen that the thickness around the weld increases significantly (red box), and the position of the weld coincides with the range of significant changes in the slope of the three curves. Therefore, the position of the weld can be accurately determined by the center profile of the upward displacement field in the y-direction. To evaluate the weld stability of the lap-jointed aluminum alloy plate, the variance of the y-direction deformation field and the coefficient of variation at the weld were calculated. \[\mathrm{s}^{2}=\frac{\sum_{i=1}^{n}(\mathrm{x_{i}-\overline{x}})^{2}}{n}, \tag{5}\]  
\[\mathrm{c_{v}}=\frac{\mathrm{s}}{\overline{x}}, \tag{6}\]  
where \(\mathrm{s}^{2}\) represents variance, \(\overline{x}\) represents the mean deformation along the x-direction, \(\mathrm{s}\) represents the standard deviation and \(\mathrm{c_{v}}\) represents the coefficient of variation. The variance curves are shown in Figure 7e. Based on the weld position determined in Figure 7d, the coefficient of variation corresponding to the maximum variance near this position can be calculated. When y changes from 630 pixels to 720 pixels (red box), the variance has a peak value of \(1.528\times 10^{-4}\) mm\({}^{2}\) at \(\mathrm{y}=687\) pixel. Next, \(\overline{x}=0.3685\) mm can be obtained, and finally, the coefficient of variation \(\mathrm{c_{v}}=0.0335\) can be obtained from Equation (6). It was reported that a coefficient of variation greater than 0.36 indicates poor weld stability, while a coefficient of variation less than 0.36 indicates good weld stability [31]. The smaller the coefficient of variation, the better the weld stability. Hence, we can conclude that the weld stability of the lap-jointed aluminum alloy plate is good. \begin{table}
\begin{tabular}{l l l l} \hline \hline  & **BM3D** & **WFT2F** & **4f-CycleGAN** \\ \hline PSNR\_R & 10.15 & 43.22 & 44.97 \\ PSNR\_G & 10.61 & 42.87 & 52.00 \\ PSNR\_B & 11.03 & 36.57 & 45.94 \\ SUM & 31.79 & 122.66 & 142.91 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: PSNR (dB) of several algorithms for the defective butt-jointed aluminum alloy plate. Figure 8a-c show the three-direction deformation field of the butt-jointed aluminum alloy plate with the load from 293.67 N to 297.59 N. It can be seen that the deformation of the butt-jointed aluminum alloy plate mainly occurs in the y-direction, and the weld stability of the butt-jointed aluminum alloy plate would be evaluated only based on the deformation in the y-direction.