## 3 Optimization Models
### Crested Porcupine Optimizer (CPO) Optimization
\begin{array}{c}\overset{\rightarrow}{F_{i}^{t}}=\overset{\rightarrow}{ \tau_{6}}\times\frac{m_{i}\times(y_{i}^{t+1}-y_{i}^{t})}{\Delta t}\\ m_{i}=\frac{f(x_{i}^{t})}{\sum_{k=1}^{N}(r_{i}^{t})+\epsilon}\\ v_{i}^{t}=x_{i}^{t}\\ v_{i}^{t+1}=x_{r}^{t}\end{array}  \tag{12}\]where \(m_{i}\) is the mass of the ith individual (predator) at iteration \(t\), \(f(. )\) denotes the objective function, \(v_{i}^{l+1}\) is the final velocity of the \(i\)th individual at the next iteration \(t+1\), assigned according to a random solution chosen from the current population, \(\overrightarrow{v_{i}^{l}}\) is the initial velocity of the \(i\)th individual at iteration \(t\), \(\Delta t\) is the current number of iterations and \(\overrightarrow{v_{6}}\) is a vector including random values between 0 and 1. In the SCR system, the parameters affecting the NOx conversion efficiency are mainly the SCR inlet temperature, exhaust flow rate, SCR inlet NOx concentration and urea injection volume. Therefore, these four data points are selected as input parameters of the SVM model for each condition, and the output parameters are NOx conversion efficiency and NH\({}_{3}\) slip. The output parameter NH\({}_{3}\) slip is the NH\({}_{3}\) slip before ASC, and the NH\({}_{3}\) slip after ASC is not selected because it is more difficult to observe the NH\({}_{3}\) slip when the urea injection volume is low. in order not to affect the prediction accuracy of the SVM model for the NH\({}_{3}\) slip, the NH\({}_{3}\) slip before ASC is selected as the output parameter of the model. The NOx conversion efficiency is calculated by Equation (13). \[\eta_{NOx}=\frac{C_{NOx,in}-C_{NOx,out}}{C_{NOx,in}} \tag{13}\]  
where \(\eta_{NOx}\) is the NOx conversion efficiency, %, \(C_{NOx,in}\) and \(C_{NOx,out}\) are SCR inlet and outlet NOx concentrations, respectively, ppm. Of the 25 sets of data for each operating condition, a randomized division was used to divide the dataset in order to eliminate the subjective errors of manual division. A total of 70% of the data (18 sets) were selected to train the SVM model, and the remaining 30% (7 sets) were used to test it. Before training the model, the four input parameters have different magnitudes; in order not to affect the model training results and eliminate the effect of magnitude, the input parameters are normalized using Equation (14). Taking 1800 rpm-300 N\(\cdot\)m as an example, 25 sets of test data are shown in Table 5.  
\[x^{*}=\frac{x-x_{min}}{x_{max}-x_{min}} \tag{14}\]  
where \(x\) is the sample data, \(x_{max}\) is the maximum value of the sample data and \(x_{min}\) is the minimum value of the sample data. In support vector machines (SVMs), the penalty coefficient C and the kernel function coefficient gamma are the two most critical tuning parameters, both of which directly affect the classification performance and generalization ability of the model. The penalty coefficient C is defined to control the penalty strength of classification error and balance the model complexity and training error. The kernel coefficient gamma is defined to control the \"width\" of the Gaussian kernel function, which determines the influence of a single sample. Both parameters can be set when building the SVM model. In this paper, in order to find the optimal penalty coefficient C and kernel coefficient gamma, these two parameters are used as the parameters to be optimized; the empirical range of values for these two parameters is [10\({}^{-2}\), 10\({}^{3}\)]. Both parameters have an upper bound of 1000 and a lower bound of 0.01, and their values are real numbers. The population size for both optimizations was 20 and the number of iterations was 50. Finally, the model was evaluated using the coefficient of determination R\({}^{2}\) and Root Mean Square Error (RMSE). In order to compare the optimization of the two algorithms, three working conditions, 1200 rpm-75 N\(\cdot\)m, 1800 rpm-300 N\(\cdot\)m, 2400 rpm-450 N\(\cdot\)m, were selected to show the results of the optimization among all the working conditions.