## 5 Development of Accurate Oil Temperature Prediction Model Based on CAM
### CAM Development
The PRESS weighted averaging method proposed by [PERSON] et al. [27] allows the weighting factors for the sub-models to be calculated according to Formulas (25)-(27). \[E_{\text{avg}} =\frac{1}{m}\sum_{i=1}^{m}E_{i} \tag{25}\] \[w_{m-p}^{*} =\left(E_{i}+\alpha E_{\text{avg}}\right)^{\beta}\] (26) \[w_{m-p} =w_{m}^{*}/\sum_{i=1}^{m}w_{m-p}^{*} \tag{27}\]  
where \(E_{i}\) represents the error of the i-th submodel, \(E_{\text{avg}}\) represents the average error of the m submodels, \(w_{m-p}^{*}\) is the unnormalized weight factor, and \(w_{m-p}\) is the final normalized weight factor. \(\alpha\) and \(\beta\) are coefficients. [PERSON] et al. suggest setting \(\alpha\) = 0.05 and \(\beta\) = \(-1\). It has been determined that the weight ratio of the Kriging model to the SVM model is 56.68% and 43.32%, respectively. The coefficient of determination and root-mean-square error (RSME) are employed to assess the overall generalization capability of three models with varying sample-point numbers. A higher coefficient of determination indicates a stronger global generalization ability in agent models, thereby reflecting higher accuracy. With an increase in sample points, the coefficient of determination and RSME for all three agent models also increases, and the changing trend of the two parameters is illustrated in Figures 14 and 15. Once the number of sample points exceeds 260, the coefficient of determination stabilizes across all three agent models. Both the Kriging model and SVM model exhibit similar agent abilities, reaching maximum coefficients of determination at 0.832 and 0.818, respectively. Nevertheless, the CAM model demonstrates a notable advantage over its counterparts. At 200 sample points, its coefficient of determination can reach 0.831 and further increases to 0.935 at 300 sample points. With an increase in sample size, the RMSE exhibits a gradual decline. Notably, when the sample size of the CAM model surpasses 260, the RMSE stabilizes at approximately 1.5 \({}^{\circ}\)C. The data indicate that the CAM model exhibits superior fitting accuracy compared to both the Kriging and SVM models. It is important to recognize that the development of a CAM model entails greater complexity compared to that of a single-agent model. The procedures involved in computing the computational load and assigning the weight factors contribute significantly to the modeling time costs. To verify the effectiveness of optimizing CAM, 20 sample validation points are generated by the improved LHD method, their response values are calculated by the three agent models, and the true response values are obtained. The temperature solution results and errors are shown in Figures 16 and 17. Based on the temperature-solving data, the CAM model demonstrates a significantly higher solution accuracy and stability compared to the other two models. The standard deviations of the solution error data for the CAM model, Kriging model, and SVR model are 0.815, 1.678, and 1.832, respectively. Furthermore, the maximum solution errors for the CAM model, Kriging model, and SVR model are 1.49 \({}^{\circ}\)C, 2.94 \({}^{\circ}\)C, and 3.42 \({}^{\circ}\)C, correspondingly. A boxplot of the temperature error data shown in Figure 18 is constructed to facilitate a more rigorous and scientific analysis and resolution of errors. Figure 14: The coefficient of determination of the agent model changes with different sample sizes. Figure 15: The RMSE of the agent model changes with different sample sizes. In the boxplot, the gray dots depict the true distribution of the data, while the central line represents the mean of the group's data. The black squares denote the median of the group's data, and the upper and lower whiskers indicate its maximum and minimum values. The boundaries of the box represent its upper and lower quartiles. From this visualization, it is evident that the error distribution range for the CAM model is narrower compared to wider ranges observed for the other two models, suggesting superior accuracy representation.