## 5 Results and Analysis
### Thermal Prediction Under Variable Speed Conditions
#### 5.2.2 Influence on Prediction Efficacy of Sample Size and Reference Node Numbers  
In the prediction model, the number of samples and reference nodes are the key factors determining the prediction accuracy. To analyze the influence on prediction efficacy of sample size and reference node numbers, real temperature datasets from the PEL are partitioned into two subsets: sample dataset simulating low-speed under low-risk behaviors and validation dataset representing high-speed under high-risk behaviors. The framework's predictive capability was evaluated by comparing validation temperatures against predictive temperatures of reference nodes across varying sample sizes, as depicted in Figure 13. Detailed scheme specifications and maximum temperature errors at reference nodes are quantitatively contrasted in Tables 5 and 6. Figure 12: Temperature prediction results and uncertainty analysis in rapid acceleration test (Tor: temperature of outer surface of the outer ring; Tir: temperature of inner surface of the inner ring). The digital twin-driven hybrid virtual-real framework was evaluated using five strategies: N_90, N_180, N_270, N_360, and N_450, corresponding to 90, 180, 270, 360, and 450 temperature sample data size, respectively. The N_90 strategy exclusively utilized temperature samples from the low-speed 1500 rpm, resulting in significant prediction deviations with maximum errors of 3.7 \({}^{\circ}\)C and 3.0 \({}^{\circ}\)C at reference nodes. In contrast, \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Scheme Code**} & \multicolumn{2}{c}{**Maximum Temperature Errors**} & \multicolumn{2}{c}{**Average Euclidean**} \\ \cline{2-4}  & \(T_{in}\)/\({}^{\circ}\)**C** & \(T_{off}\)/\({}^{\circ}\)**C** & **Distance of All Nodes/K** \\ \hline N90 & 3.74 & 3.03 & 39.2 \\ N180 & 1.23 & 1.45 & 7.8 \\ N270 & 0.64 & 1.34 & 4.9 \\ N360 & 2.21 & 2.93 & 25.8 \\ N450 & 1.18 & 1.74 & 9.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of predicted and validated data under varying sample sizes. Figure 13: Temperature comparison reference node under different sample sizes. other strategies incorporating multi-speed operation demonstrated improved predictive accuracy, highlighting the necessity of diverse speed-range samples for accurate thermal parameter identification. Notably, while increased sample size (e.g., N_360 and N_450) theoretically enhances data density, their prediction temperature in the prediction zone exhibited suboptimal alignment with validation temperatures. Conversely, the N_270 strategy achieved superior accuracy despite a moderate sample size, yielding maximum reference node errors of 0.6 \({}^{\circ}\)C and 1.3 \({}^{\circ}\)C. This conclusively demonstrates that the selection of sample data sizes significantly impacts the thermal prediction outcomes of the proposed framework. In practical implementations, priority should be given to datasets encompassing diverse speed-range operational conditions to ensure robust parameter identification and prediction accuracy. To comprehensively analyze the thermal prediction performance of the proposed framework, a Euclidean distance-based similarity assessment method [53] was employed to quantify the discrepancy between twin temperature datasets \(T_{TD1}\) encompassing all nodes and the aforementioned predicted temperatures, as illustrated in Figure 14.  
In Figure 14, numerical values and color gradients represent similarity levels, where smaller values or brown-dominated hues indicate higher congruence between predicted temperatures \(T_{PRE}\) and twin temperatures \(T_{TD1}\), signifying superior predictive accuracy. Table 6 quantifies the average Euclidean distances across all nodes for each scheme. Analysis of the numerical trends and color distributions across nodes T1-T13 reveals that the N_270 scheme achieves the lowest Euclidean distances at all nodes except T3 and T6, with the minimum value 0.5 K observed at node T13.