## 4 Results and Analysis
### The Combustion Fit Results of Engine Nominal Operating Point
#### 4.2.1 Four-Cylinder Averaged Pressure Signals  
According to definition of the basic and advanced Seiliger process presented in Section 3, the combustion fitting results of these two Seiliger process types are compared and analyzed in terms \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Fit Indicator** & **SSE** & **R-Square** & **Adjusted R-Square** & **DFE** & **RMSE** \\ \hline  & 0.4306 & 0.9921 & 0.9921 & 1025 & 0.0205 \\ Engine parameters & \(P_{max}\) (bar) & \(T_{max}\) (K) & \(P_{EO}\) (bar) & \(T_{EO}\) (K) & \(P_{i}\) (kW) \\ Raw data & 95.87 & 1569.70 & 8.95 & 1159.98 & 83.59 \\ Smoothed & 93.19 & 1513.58 & 8.61 & 1119.60 & 83.32 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The goodness of fit of the pressure signals. Figure 9: In-cylinder pressure of 4 cylinders: (**a**) The smoothed pressure signals; (**b**) Zoom in of peak pressure region. of the four-cylinder averaged pressure signals at engine nominal operating point. Table 4 shows the Seiliger parameters and engine performance parameters chosen in the system of equations as variables and equivalence criteria for basic and advanced Seiliger process models, which actually are the same as each other, although the engine performance parameter \(q_{in}\) includes a different heat input definition as explained in Section 3. Before combustion fitting numerical calculation, the Seiliger parameters \(n_{comp}\), \(r_{c}\) and \(\Delta EO\), which are not taken into account as the variables in the fitting process, have to be set as constants. Considering the engine operating conditions in reality, the \(n_{comp}\) is set to be 1.36 to indicate proper heat loss during engine compression process; the \(r_{c}\) 13.107 means constant volumetric process occurring at top dead centre and \(\Delta EO\) is 0 without regarding the effect of exhaust valve open. Then based on Equations (12)-(15), the system of equations of combustion fitting is set up. During the system of equations root finding procedure, the mathematic setting should be thought over, including initial values, iterations, termination criteria, etc. The termination criteria for the iteration in this paper, which affect the accuracy and the calculation speed, in both basic and advanced Seiliger process models fitting is set as follows:  
\[\mid p_{3}-p_{max}\mid\leq 1\;\text{bar},\]  
\[\mid T_{4}-T_{max}\mid\leq 1\;\text{K},\]  
\[\mid q_{in,Seilger}-q_{in,measured}\mid\leq 10\;\text{J}/\text{kg},\]  
\[\mid w_{i,Seilger}-w_{i,measured}\mid\leq 10\;\text{J}/\text{kg}.\]  
The combustion fitting results of both basic and advanced Seiliger process models are shown in Table 5, in which the Seiliger parameters values and heat input during the Seiliger parameters effect stages are compared. The values of \(a\) and \(b\) are the same of these two types, the latter's small difference is caused by the numerical calculation errors. The value of \(c\) is quite different between these two Seiliger process models, together with heat input ratio in Seiliger stage 4-5 (isothermal process) large differences. In the basic Seiliger process, besides in stage 1-2 (isochoric process), the heat input occurs in isothermal process and the ratio is 36.02%, but in the advanced Seiliger process model it is only 16.53% with the others at 19.51% in stage 5-6 (expansion process), which means there is a very late combustion during operation of the engine. Figure 10 illustrates the basic and advanced Seiliger process models of combustion fitting results compared with the measurements in diversified diagrams. Figure 10a,b presents the comparison \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Seiliger Parameters (Variables)** & **Engine Performance (Equivalence Criteria)** \\ \hline
**basic Seiliger process** & \(a\), \(b\), \(c\), \(n_{cap}\) & \(p_{max}\), \(T_{max}\), \(q_{in}\), \(w_{i}\) \\
**advanced Seiliger process** & \(a\), \(b\), \(c\), \(n_{cap}\) & \(p_{max}\), \(T_{max}\), \(q_{in}\), \(w_{i}\) \\ \hline \hline \end{tabular}
\end{table}