## 5 Development of Accurate Oil Temperature Prediction Model Based on CAM
### CAM Development  
There are two primary categories of agent models, namely interpolation-based models, such as radial basis function and Kriging models, and fitting-based models, such as response surface and SVM models. Nevertheless, no single model can universally outperform others in all domains, and there is a dearth of mature and effective theories to guide the selection of agent models. A single-agent model is insufficient to meet the accuracy requirements for the multi-input highly nonlinear problem of HCS oil temperature prediction. CAM can effectively harness the strengths of various sub-models to enhance the global accuracy of the agent model. The Kriging model is an interpolation model based on unbiased estimation, consisting of a global trend function and a random process [25]. The Kriging model can be represented by Formula (19). \[\hat{y}=\sum_{i=1}^{k}\beta_{i}f_{i}(x)+z(x) \tag{19}\]  
where \(f_{i}(x)\) is the basis function for the linear regression part, \(\beta_{i}\) is the coefficient of the i basis function, and \(z(x)\) is the random process term that satisfies the following Formulas (20)-(22). \[E[z(x)] =0 \tag{20}\] \[\text{Var}[z(x)] =\sigma^{2} \tag{21}\] \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Number** & **A** & **B** & **C** & **D** & **E** & **F** & **G** \\ \hline
1 & 11.660 & 59.436 & 231.757 & 5.398 & 1.107 & 0.767 & 0.792 \\
2 & 11.535 & 62.015 & 211.514 & 5.537 & 0.872 & 0.862 & 0.803 \\
3 & 14.647 & 51.478 & 176.577 & 4.803 & 0.940 & 0.841 & 0.868 \\
4 & 10.339 & 49.784 & 176.960 & 5.502 & 0.914 & 0.811 & 0.813 \\
5 & 11.272 & 50.943 & 297.763 & 5.707 & 1.037 & 0.871 & 0.762 \\ \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) \\
300 & 8.098 & 53.124 & 201.751 & 5.152 & 1.132 & 0.832 & 0.822 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Sample space of LHD (300, 7). Figure 13: Correlation coefficients between different dimensions. \[\text{Cov}\left[z\left(x^{i}\right),z\left(x^{i}\right)\right]=\text{Var}[z(x)]R \left(\theta,x^{i},x^{i}\right)=\sigma^{2}\prod_{l=1}^{n}R_{l}(\theta_{l},d_{l}) \tag{22}\]  
where \([z(x)]\), \(\text{Var}[z(x)]\), and \(\text{Cov}\left[z\left(x^{i}\right),z\left(x^{i}\right)\right]\), respectively, represent the expected value, variance, and covariance of the random process term \(z(x)\), \(R(\theta,x^{i},x^{i})\) represents the sample data-correlation function, \(\theta\) is the parameter of the correlation function, \(n\) is the dimension of the sample data, and \(d_{l}\) is the distance between sample points \(x^{i}\) and \(x^{i}\). The SVM model is grounded on the principle of minimizing structural risk [26]. In contrast to other agent models, the SVM model can accommodate a permissible error, disregarding regression errors falling within this range and thereby effectively simplifying solution computation. The expression for the SVM model is provided by Formula (23). \[\hat{f}(x)=\mu+\sum_{i=1}^{k}\left(\alpha^{+i}-\alpha^{-i}\right)\psi(\parallel x -x_{i}\parallel) \tag{23}\]  
where \(\psi(\parallel x-x_{i}\parallel)\) is the core function, \(\alpha^{+i}\) and \(\alpha^{-i}\) denote the support vector, and \(\mu\) is a constant. The common kernel functions utilized in SVM models encompass polynomial, Gaussian, and sigmoid kernels, as well as radial basis functions. Excluding the kernel function, the SVM model possesses only one hyperparameter, which is called the penalty coefficient. A larger penalty coefficient renders the model less tolerant to errors and more susceptible to overfitting. Conversely, a smaller penalty coefficient increases the error tolerance and raises the likelihood of underfitting. CAM can be expressed by Formula (24). \[\left\{ \begin{array}{l}\hat{f}(x)_{z}=\sum_{i=1}^{m}w_{i}\hat{f}_{m}(x)\\ \sum_{i=1}^{m}w_{i}=1\end{array} \right. \tag{24}\]  
where \(\hat{f}(x)_{z}\) is a CAM, \(\hat{f}_{m}(x)\) is the sub-model, \(w_{i}\) is the weight factor of the sub-model, and m represents the number of sub-models. Here, m = 2.