# Design and Implementation of a Digital Twin System for Log Rotary Cutting Optimization
## 4 Discussion  
In this study, the point cloud information of logs with radii of 150 mm, 175 mm, and 200 mm was collected using the physical layer experimental platform. The system was validated and calibrated using standard log data. Taking the example of a standard log with a radius of 150 mm, the point cloud data was processed using the centering analysis module in the service system to solve for the maximum inscribed cylinder. The resulting fitting error for the dimensions was 0.12 mm, and the calculated error for the centroid position was 0.03 mm and \(-\)0.07 mm. Considering the negligible error in practical experiments, the system meets the requirements for standard logs.  
To verify the accuracy, 50 sets of experimental data were collected from logs with radii of 150 mm, 175 mm, and 200 mm, respectively, after modeling and fitting with the least squares method, shown in Table 1.  
By following the same procedure and collecting data with different starting angles for irregularly shaped logs, we obtained point cloud data for irregularly shaped logs. The point cloud data was then triangulated to reconstruct the surface mesh. It can be observed that the surface of the model exhibits distinct depressions and protrusions, and the trend of surface undulation is highly similar to the Solidworks model, indicating a high degree of resemblance. The point cloud information and surface reconstruction results for irregularly shaped logs are shown in Figure 9.  
Figure 10: Log rotary cutting simulation interface.  
Figure 9: Log centering analysis interface.  
The point cloud data can be analyzed, and a maximum inscribed cylinder can be solved through the centroid analysis module in the service system. The effect is shown in Figure 9.  
According to industry conventions, manual measurements of the centroid are conducted using selected cross-sections of irregular-shaped logs. From Table 2, it can be observed that when comparing the measurements with the Solidworks model as the reference, the system's volume calculation error decreased from 12.8% in manual measurements to 2.7%, and the yield calculation error decreased from 23.5% in manual measurements to 5.7%.  
To validate the stability of the equipment, a repeatability experiment was conducted on the collection of irregular-shaped logs for 30 repetitions. After data processing and reconstruction, the fitted centroid data exhibited an error distribution within a circle centered at (0, 0) with a radius of 0.75 mm, as shown in Figure 11. This result demonstrates the stability of the collection equipment and algorithm.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Log Size** & **150 mm** & **175 mm** & **200 mm** \\ \hline \(X\)-axis offset range (mm) & \(-\)0.39–0.63 & \(-\)0.23–0.95 & \(-\)0.21–0.88 \\ \(Y\)-axis offset range (mm) & \(-\)0.05–0.82 & \(-\)0.31–0.78 & \(-\)0.11–0.50 \\ Radius minimum (mm) & 148.73 & 172.55 & 198.36 \\ Radius maximum (mm) & 151.52 & 177.34 & 201.68 \\ \hline \end{tabular}
\end{table}
Table 1: Standard log centering results.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Data Sources** & **Solidworks Model** & \
\begin{tabular}{c} **System Measurement** \\ **Results** \\ \end{tabular} &
\begin{tabular}{c} **Manual Measurement** \\ **Results** \\ \end{tabular} \\ \hline Volume & 0.0842 m\({}^{3}\) & 0.0865 m\({}^{3}\) & 0.0950 m\({}^{3}\) \\ Volume error & - & 2.7\% & 12.8\% \\ Maximum inscribed & 150 mm & 154.23 mm & 166.27 mm \\ circle radius & & 5.7\% & 23.5\% \\ Yield error & - & 5.7\% & 23.5\% \\ \hline \end{tabular}
\end{table}
Table 2: Comparison of experimental results.  
Figure 11: Distribution of experimental results.