# A Vision-Based Bolt Looseness Detection Method for a Multi-Bolt Connection
## 4 Results and Discussion
### Detection Result under Different Perspective Angles  
Moreover, to rigorously evaluate the robustness of the method to shooting perspective angles, supplementary experimental trials were executed under nonstandard perspective angles of 60\({}^{\circ}\) and 30\({}^{\circ}\). As delineated in Figure 10, the imaging apparatus was strategically positioned at perspective angles of 90\({}^{\circ}\), 60\({}^{\circ}\), and 30\({}^{\circ}\), respectively, to ensure a comprehensive analysis. These additional experiments involved the systematic acquisition of visual data for 16 distinct cases, which were subsequently utilized for both the training and the testing and validation phases of the model. These additional experiments were instrumental in ascertaining the versatility and adaptability of the method. Figure 11 displays a set of illustrative sample images captured from the specified angles, alongside counterparts taken at a 90\({}^{\circ}\) angle for reference. It becomes apparent upon examination that a reduction in the shooting angle leads to a gradual decline in image contrast, with the fringes becoming increasingly subtle and challenging to discern, which is especially noticeable at the 30\({}^{\circ}\) angle. Our investigation included training both the proposed RNN model and the modified VGG-16 model (referred to as the MV model) from our previous work, using images captured at perspective angles of 90\({}^{\circ}\), 60\({}^{\circ}\), and 30\({}^{\circ}\). We named the datasets collected at perspective angles of 90\({}^{\circ}\), 60\({}^{\circ}\), and 30\({}^{\circ}\) Dataset 1, Dataset 2, and Dataset 3, respectively. A comparative analysis of their detection accuracy on the corresponding validation dataset is presented in Table 2.  
Figure 10: The perspective angles of original and supplementary experiments: (**a**) original perspective angle at 90\({}^{\circ}\), (**b**) perspective angle at 60\({}^{\circ}\), and (**c**) perspective angle at 30\({}^{\circ}\). The MV model exhibited detection accuracies of 96.65% at 90\({}^{\circ}\), 94.34% at 60\({}^{\circ}\), and 90.76% at 30\({}^{\circ}\), while the RNN model detailed in this study achieved accuracies of 99.55% at 90\({}^{\circ}\), 99.49% at 60\({}^{\circ}\), and 99.38% at 30\({}^{\circ}\). It is noteworthy that the MV model's performance was sensitive to the shooting angle. As the angle decreased, image contrast was reduced, leading to less distinct fringe patterns and a consequent dip in detection precision, with the accuracy settling at 90.76% for the 30\({}^{\circ}\) angle. However, the RNN model proposed herein demonstrated remarkable resilience, with detection accuracies consistently above 99%, indicating a minimal impact from variations in the perspective angle on the detection outcomes. These outcomes indicate that the proposed method effectively detects the loose bolts in multi-bolt connections with precision. Importantly, the method eliminates the need for distortion rectification, which is a complex process for traditional machine vision methods, especially for irregular shapes. Moreover, we compared these two models in terms of the characteristics shown in Table 3. The MV model costed 11.91 min for a whole epoch and required 195,000 iterations for convergence. While the RNN model took only 4.23 min for one epoch, and only needed \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Perspective Angle** & **90\({}^{\circ}\)** & **60\({}^{\circ}\)** & **30\({}^{\circ}\)** \\ \hline Dataset & Dataset 1 & Dataset 2 & Dataset 3 \\ \hline Accuracy of the MV model & 96.65\% & 94.34\% & 90.76\% \\ \hline Accuracy of the RNN model & 99.55\% & 99.49\% & 99.38\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The detection accuracy on validation dataset of the MV model and RNN model at different perspective angles. Figure 11: Representative fringe patterns in Case 1–4 at different perspective angles. 30,000 iterations for convergence. Furthermore, the training process was faster than that for the MV model.