## 5 Analysis of Industrial Field Application Results
According to the error analysis in Figure 20, it can be concluded that the maximum width detection error is 2 mm, the minimum is \(-2\) m, and most of the detection accuracy is \(\leq\)\(\pm 1\), which meets the requirements for on-site production. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Board Number** & \begin{tabular}{c} **Theoretical** \\ **Values/mm** \\ \end{tabular} & \begin{tabular}{c} **Manually Measured** \\ **Values/mm** \\ \end{tabular} & \
\begin{tabular}{c} **System Values/mm** \\ \end{tabular} &
\begin{tabular}{c} **Error** \\ **Error** \\ \end{tabular} \\ \hline
1 & 1585 & 1585 & 1585 & 0 \\
2 & 1585 & 1584 & 1584 & 0 \\
3 & 1585 & 1586 & 1585 & \(-1\) \\
4 & 1585 & 1585 & 1585 & 0 \\
5 & 1585 & 1584 & 1584 & 0 \\
6 & 1585 & 1583 & 1585 & 2 \\
7 & 1585 & 1584 & 1584 & 0 \\
99 & 1585 & 1585 & 1585 & 0 \\
100 & 1585 & 1585 & 1585 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Measurement results of the width of 100 cross-cutting boards. Figure 17: Error in length detection of cross-cutting boards. Figure 19: Analysis of the comparison of cross-cutting board widths. Figure 20: Error in width detection of cross-cutting boards. Figure 18: Live equipment diagram. Diagonal detection result of the cross-cutting boards  
Based on the above measurements of length and width, it can be concluded that the overall accuracy of the measurement system is good. Therefore, for 100 cross-cutting boards on site, the difference between two diagonals is measured to evaluate their quality. The evaluation criterion is a diagonal difference of \(<\)\(\pm\)5 mm for qualified and \(\geq\)\(\pm\)5 mm for unqualified, as shown in Table 5.  
The curve in Figure 21 shows the variation of diagonal difference values for 100 cross-cutting boards. Diagonal detection error: maximum of 2 mm, minimum of \(-\)1 mm. Based on the quality evaluation in Figure 22, it can be concluded that out of the one hundred boards, four boards were found to be defective, which is consistent with the on-site production quality inspection results, which meets the requirements for on-site production. Figure 21: Result of the difference between the diagonals of cross-cutting boards. \begin{table}
\begin{tabular}{c c c c} \hline
**Board Number** &
\begin{tabular}{c} **Manually Measured** \\ **Values/mm** \\ \end{tabular} & **System Values/mm** & **Quality Evaluation** \\ \hline
1 & 11 & 9 & Unqualified \\
2 & 1 & 1 & Qualified \\
3 & 1.2 & 1.2 & Qualified \\
4 & 1.5 & 1.5 & Qualified \\
5 & 2.3 & 2 & Qualified \\
6 & 1.5 & 1.6 & Qualified \\
7 & 0 & 0.2 & Qualified \\ \(\ldots\ldots\ldots\) & & \(\ldots\ldots\ldots\) & \(\ldots\ldots\) \\
99 & 1 & 0.9 & Qualified \\
100 & 6 & 7 & Unqualified \\ \hline \end{tabular}
\end{table} 
Table 5: Measurement results of the diagonal of 100 cross-cutting boards. The requirements for industrial production sites are as follows: (1) achieve online real-time detection of the length, width, and diagonal of the cross-cut board; (2) detection accuracy: length \(\leq\pm\)50 mm, width \(\leq\pm\)2 mm, diagonal difference \(\leq\pm\)5 mm. Based on the above industrial application scenarios, it can be concluded that the maximum length detection error is 18 mm and the minimum is \(-\)21 mm, with an overall error of \(\leq\)\(\pm\)50 mm; the maximum width detection error is 2 mm and the minimum is \(-\)2 mm, while most of them have an accuracy of \(\leq\)\(\pm\)1 mm; the diagonal detection error ranges from a maximum of 2 mm to a minimum of \(-\)1 mm, with an overall error of \(\leq\)\(\pm\)2 mm. By comparison, it can be seen that all measured data from the measurement system meet the requirements in industrial production sites.