# A Vision-Based Bolt Looseness Detection Method for a Multi-Bolt Connection
## 4 Results and Discussion
### Comparison with Traditional Methods  
To gain a more intuitive understanding of the advantages of this method over traditional approaches, we conduct a performance comparison of these methods in Table 4 below.  
Figure 12: Confusion matrix of detection result of the new RNN model on the comprehensive dataset.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \begin{tabular}{c} **Time for One** \\ **Epoch** \\ **(Minute)** \\ \end{tabular} & \begin{tabular}{c} **Iterations** \\ **Required for** \\ **Convergence** \\ \end{tabular} & \
\begin{tabular}{c} **Time for a** \\ **Single Judgment** \\ **(Millisecond)** \\ \end{tabular} &
\begin{tabular}{c} **File Size of** \\ **Single Model** \\ **(Kilobyte)** \\ \end{tabular} \\ \hline MV model & 11.91 & 195,000 & 7.17 & 540,540 \\ \hline RNN & 4.23 & 30,000 & 4.70 & 221 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Property comparisons of the MV model and RNN model.  
Contacted sensor-based methods have been proved to be inconvenient in many cases and are vulnerable to environmental factors like temperature changes and humidity, potentially leading to inaccurate judgments. For example, method 5 in Ref. [13] attained a detection accuracy of 97.39% at 45 \(\pm\) 1 \({}^{\circ}\)C but achieved 95.43% at 35 \(\pm\) 1 \({}^{\circ}\)C for a four-bolt connection. Moreover, such methods are rarely able to identify all the looseness cases of multi-bolt connections.  
Traditional vision-based methods, as we illustrated in Section 1, take too much time on prep work such as recognizing bolts, correcting perspective distortion, or 3D reconstruction before they can detect bolt looseness. The distortion rectification procedure in Ref. [20] is shown in Figure 13, which is complex and is limited to rectangular-based bolt arrays. Another limitation for these methods is the prerequisite of the initial angle of the bolts before loosening, significantly constraining the scenarios in which they can be effectively used.  
Our proposed method directly performs an image classification to detect loose bolts and only takes 4.70 milliseconds for a single detection of a multi-bolt connection, which is much faster than traditional methods. On the other hand, the proposed method does not require the prior information of the initial angles of the bolts, has strong robustness to the perspective angle, and can detect unseen bolts. These findings underscore the efficacy and simplicity of the proposed method. In conclusion, the proposed method has great potential in real-time bolt looseness detection for multi-bolt connections, even connections in complex structures.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \begin{tabular}{c} **Vision-Based or** \\ **Contact** \\ **Sensor-Based** \\ **Method** \\ \end{tabular} & \begin{tabular}{c} **Can Detect All** \\ **Looseness Cases** \\ **of Multi-Bolt** \\ **Connections** \\ \end{tabular} & \begin{tabular}{c} **Detection** \\ **Accuracy** \\ **Sine Judgment** \\ \end{tabular} \\ \hline \begin{tabular}{c} **The proposed** \\ **method** \\ \end{tabular} & \multirow{2}{*}{**Vision-based**} & \multirow{2}{*}{\begin{tabular}{c} **Yes** \\ **Yes** \\ **Yes** \\ **Yes** \\ \end{tabular} } & **Over 99\%** & **4.70 milliseconds** \\ \hline \
\begin{tabular}{c} Method 1 in \\ Ref. [21] \\ \end{tabular} & \multirow{2}{*}{**Vision-based**} & \multirow{2}{*}{Yes} & 92.13\% & 35 seconds \\ \cline{1-1} \cline{3-5} Method 2 in [23] & & & Yes & 91.65\% & - \\ \cline{1-1} \cline{3-5} Method 3 in [7] & & No & Over 99\% & - \\ \cline{1-1} \cline{3-5} Method 4 in [14] & \multirow{2}{*}{
\begin{tabular}{c} Contact \\ sensor-based \\ \end{tabular} } & \multirow{2}{*}{No} & \multirow{2}{*}{94.17\%} & \multirow{2}{*}{-} \\ \cline{1-1} \cline{3-5} Method 5 in [13] & & Yes & 96.69\% & - \\ \hline \hline \end{tabular}
\end{table}
Table 4: Performance comparisons of the proposed method and traditional methods.  
Figure 13: The procedure of distortion rectification in Ref. [20].