## 3 Post-Rolling Online Ultrasonic Thickness Measurement Platform
### Experimental Verification  
(1) Single-Point Measurement  
A 2.5-m-long post-rolling copper tube was selected for single-point measurement. In the middle section of the tube, 20 groups of measurement points were taken at 5 cm intervals, with each group containing 4 points, resulting in a total of 80 wall-thickness data points. The sample tube was placed on an ultrasonic thickness measurement platform and the 20 groups of points were measured for offline verification experiments, as shown in Figure 7. The measurement results were recorded and the sample tube was sequentially cut into 10 sections. A micrometer was used to measure the wall thickness at the detection points and the ultrasonic measurement data were compared with the manual measurement data, as shown in Table 2.  
The results of the average absolute error between ultrasonic and manual measurements for the 20 groups of data are shown in Figure 8. The average absolute error across the four points ranged from 0.027 to 0.06.  
\begin{table}
\begin{tabular}{c c} \hline
**Item** & **Parameter** \\ \hline Probe Working Mode & Single Crystal \\ Damping & 50 \(\Omega\) \\ Frequency & 10 MHz \\ Probe Type & Water–Immersion Line–Focus Probe \\ Probe Angle & 90\({}^{\circ}\) \\ Channel Gain & 50 dB \\ \hline \end{tabular}
\end{table}
Table 1: Probe-related working parameter information.  
Figure 5: Thickness detection probe: (**a**) Lower thickness detection probe group; (**b**) upper thickness detection probe group.  
Figure 6: Thickness probe detection software.  
(2) Segmented Measurement  
During a 10-day wall thickness detection experiment, ultrasonic and manual measurement data were collected from 35 post-rolling copper tubes. The ultrasonic system recorded 400-450 groups of wall thickness data at various axial positions for each tube, with each group containing wall thickness data from 4 different detection points. After the ultrasonic  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Measurement**} & \multicolumn{2}{c}{**Location 1**} & \multicolumn{2}{c}{**Location 2**} & \multicolumn{2}{c}{**Location 3**} & \multicolumn{2}{c}{**Location 4**} \\ \cline{2-9}  & **Ultrasound** & **Manual Measure-** & **Ultrasound** & **Manual Measure-** & **Ultrasound** & **Manual Measure-** & **Ultrasound** & **Manual Measure-** \\  & **Data** & **mean Data** & **mean Data** & **mean Data** & **mean Data** & **mean Data** & **mean Data** \\ \hline \(1\) & 2.88 & 2.98 & 2.  
measurements, a 20 cm section of the tube was cut, and a micrometer was used to measure the wall thickness at different cross-sections. Since ultrasonic measurements produced 400-450 groups of data per tube while manual measurements were limited to the sampled section at the rear end, the average values of the ultrasonic and manual measurements at corresponding positions were computed using a mean function. As the wall thickness deviations at the same circumferential positions of the same billet were negligible, using the average value of each position to represent the wall thickness of the post-rolling copper tube was deemed feasible. The ultrasonic measurement range and manual measurement range of wall thickness for the tube were then compared, as shown in Table 3.  
Online ultrasonic measurement records data once per second, providing real-time detection. For each position, 400-450 groups of data can be obtained. In contrast, manual measurements using calipers provide a single wall thickness value for the sampled tube section, which is influenced by operational factors; therefore, a relative error between ultrasonic measurement data and manual measurement data for the sampled tube was calculated. The relative error between the ultrasonic and manual measurement averages for the 35 data sets ranged from 0.5% to 14.5%. Given the inevitable errors during sampling and measurement, the relative error was determined to be within the allowable engineering tolerance.