## 3 Results & Discussion  
### Healthy Engine Conditions  
To simulate the engine performance for the baseline conditions, the coupled thermodynamic and crankshaft dynamics model was calibrated at 100% engine load using the measured in-cylinder pressure as described in Section 2.1. In specific, the calibration parameters employed were the start of injection (Equation (5)), duration of combustion and Weibe shape parameter (Equation (4)), as well as the scavenging mixing factor (Equations (11) and (12)). Subsequently, by comparing to the measured data, the coupled model was validated at 100%, 85%, 75%, and 55% engine loads as shown in Figure 3.  
The calibration process resulted to the simulated in-cylinder pressure having a Normalised Root Mean Square Error (NRMSE) of 9.2% at 100% engine load, as shown in Figure 3a. Through the validation of the in-cylinder pressure for the remaining three engine loads in Figures 3c,e,g, it is observed that the NRMSE is increasing to 10.8%, 11.8% and 13.9% respectively. This error increase occurs as these loads are further away from the calibration load of 100%. In addition, the simulated peak combustion pressure is close to the measurements, with a maximum difference of 2.3 bar which occurs at 85% engine load. Also, the crank angle corresponding to the simulated peak combustion pressure is always within 2 crank angle degrees from the measurements, with the exception at 85% engine load where the simulated peak pressure is at 3.5 crank angle degrees less than the measurements. Finally, it is observed that the compression part of the cycle is captured accurately by the simulated pressure. However the expansion from the peak pressure to approximately 60\({}^{\circ}\)CA, appears to occur quicker in the case of the simulated in-cylinder pressure as compared to the measurements, for all engine loads.  
The NRMSE error in the simulated flywheel ICT in Figure 3b,d,f,h is observed to follow the same pattern as the error for the in-cylinder pressure, since it steadily increases at the engine loads further way from the calibration load. Furthermore, the error in the simulated flywheel ICT is observed to be greater than that of the in-cylinder pressure for all loads, which is due to the assumptions made in the crankshaft dynamics model. In specific, since the in-cylinder pressure from only one cylinder was available, all the cylinders in the crankshaft dynamics model were set to have identical in-cylinder pressures, which would also represent best the healthy engine conditions. As a result, the flywheel ICT was simulated using identical in-cylinder pressures, whilst in the physical engine the in-cylinder pressures were most likely to be different [38], which would result to a larger error in the flywheel ICT. Further analysis on the errors induced in the simulated flywheel ICT can be found in [46].  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Malfunctioning Condition** & **Changed Parameter** & **Parameter Range** & **Parameter Step** \\ \hline Change in SOI & Start of Combustion (\(\theta_{SOI}\)) & \(\pm 2.5^{\circ}\) & 1.25\({}^{\circ}\) \\ Change in RHR & Weibe shape parameter (\(w\)) & \(\pm 0.5\) & 0.25 \\ Change in scavenge air pressure & Scavenge air pressure & \(\pm 0.3\) bar & 0.15 bar \\ Blowby & Blowby effective area & \(0\sim 28.5\) mm\({}^{2}\) & 7.12 mm\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Malfunctioning condition parameters variation.