## 2 Materials and Methods
### Construction of NOx Simulation Model  
The marine diesel engine is a MISO system when NOx is the object of study. This is because the NOx output is influenced not only by the parameters associated with the current cycle but also by those of the previous cycle. Therefore, the complexity and diversity of the physical model and its parameters make it difficult to be simulated and controlled in \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Component**} \\ \hline
**Factors** & **1** & **2** & **3** & **4** & **5** & **6** & **7** \\ \hline P\_CR & 0.163 & 0.153 & 0.086 & \(-\)0.093 & 0.754 & 0.211 & \(-\)0.142 \\ Inj\_D & \(-\)0.238 & 0.824 & 0.426 & 0.013 & \(-\)0.155 & \(-\)0.065 & 0.153 \\ P & \(-\)0.764 & \(-\)0.277 & 0.051 & \(-\)0.324 & 0.160 & \(-\)0.031 & \(-\)0.277 \\ T\_max & \(-\)0.238 & \(-\)0.072 & 0.345 & \(-\)0.260 & \(-\)0.078 & 0.563 & 0.098 \\ Q\_HR & \(-\)0.417 & 0.001 & 0.139 & 0.746 & 0.004 & 0.277 & \(-\)0.241 \\ HRR & \(-\)0.398 & 0.067 & \(-\)0.585 & 0.339 & 0.421 & \(-\)0.116 & 0.175 \\ PFP\_C & \(-\)0.034 & \(-\)0.301 & 0.018 & \(-\)0.052 & 0.128 & 0.402 & 0.762 \\ PFP & 0.011 & \(-\)0.119 & 0.488 & 0.139 & 0.407 & \(-\)0.498 & 0.012 \\ CA50 & \(-\)0.348 & \(-\)0.407 & 0.556 & 0.556 & 0.071 & 0.128 & \(-\)0.025 \\ CA10 & 0.118 & 0.331 & \(-\)0.227 & 0.042 & 0.011 & 0.597 & \(-\)0.414 \\ IMEP & 0.963 & 0.021 & 0.122 & \(-\)0.079 & 0.112 & \(-\)0.039 & \(-\)0.082 \\ P\_exh & 0.956 & 0.027 & 0.139 & \(-\)0.061 & 0.095 & 0.002 & \(-\)0.102 \\ Tor & \(-\)0.672 & 0.554 & 0.371 & \(-\)0.089 & \(-\)0.100 & \(-\)0.037 & 0.102 \\ P\_sca & \(-\)0.921 & 0.169 & 0.207 & \(-\)0.158 & 0.018 & \(-\)0.072 & \(-\)0.090 \\ T\_oil & 0.871 & \(-\)0.231 & 0.206 & \(-\)0.158 & \(-\)0.198 & 0.060 & \(-\)0.133 \\ T\_exh & 0.304 & 0.592 & \(-\)0.315 & 0.211 & 0.010 & \(-\)0.034 & 0.101 \\ Ex\_o & 0.929 & 0.205 & 0.128 & 0.155 & 0.032 & 0.083 & 0.126 \\ Ex\_c & 0.855 & 0.164 & 0.166 & 0.172 & 0.167 & 0.043 & 0.136 \\ Inj & 0.395 & \(-\)0.169 & \(-\)0.059 & 0.322 & \(-\)0.560 & \(-\)0.127 & 0.001 \\ T\_sca & 0.963 & 0.021 & 0.122 & \(-\)0.079 & 0.112 & \(-\)0.039 & \(-\)0.082 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Component score coefficient matrix. Figure 5: Principal component analysis scree plot. real-time applications. The BPNN is a typical data-driven model that obtains information by simulating the forward and feedback transmission of signals between neurons and then calculates and predicts NOx. The GMDH is a heuristic self-organizing method to study the relationship between variables. It can be used to select and classify input parameters to reduce the dimension of input features. For example, when there are three layers and four inputs, the sample architecture of the GMDH algorithm is shown in Figure 6. In Figure 6, there are four inputs (X1, X2, X3, and X4). From these input variables, there are three (X1, X2, and X4) control systems. X3 does not affect classification. The GMDH algorithm selects the important features that have an impact on classification. The GMDH algorithm generates a series of active neurons by cross-combining various input units of the system. Each neuron has the function of selecting the optimal transfer function and then selects several neurons closest to the target variable from the generated generation of neurons. The selected neurons combine to create new ones again, repeating the process of dominance inheritance, survival competition, and evolution until the most complex model is chosen. The GMDH neural network has the following characteristics: the modeling process is self-organizing control without any initial assumptions; optimized complexity and high-precision prediction; the ability to use the optimal structure of each layer of the self-organizing multilayer neural network, that is, it can automatically retain useful variables and remove redundant variables; automatically selects the optimal number of network layers and the number of neurons per layer.