## 2 Methods and Tools  
### Reference System & Methodology  
The reference system considered in this study is a 10-cylinder two-stroke diesel engine, driving a generator operating at a constant speed of 125 rev/min. This engine was utilised for the development of a coupled thermodynamics and crankshaft dynamics model, which provides the in-cylinders pressure and flywheel ICT as output. The technical characteristics and measured data used to develop and calibrate the coupled model were obtained from [18; 38]. In specific, the measured data include the in-cylinder pressure for a single cylinder and the flywheel ICT for four loads as shown in Figure 1, whilst a summary of the engine technical details is listed in Table 1.  
Initially, the engine thermodynamic model and the engine crankshaft dynamics model were developed and coupled with each other. These models and their coupling are described in Sections 2.2 and 2.3. Subsequently, the thermodynamic model parameters calibration was carried out by employing a nonlinear data-fitting Levenberg-Marquardt algorithm from MATLAB [39]. The objective employed was to minimise the least-squares  
\begin{table}
\begin{tabular}{c c} \hline \hline Maximum Continuous Rating & 15.50 MW \\ Number of cylinders & 10 \\ Nominal rotational speed & 125 rev/min \\ Piston bore & 0.67 m \\ Stroke & 1.70 m \\ Firing order & 1-9-4-6-3-10-2-7-5-8 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Reference system basic technical specifications [18].  
Figure 1: Measured (**a**) in-cylinder pressure and (**b**) flywheel ICT, at four engine loads of 100%, 85%, 75% and 55%. Firing cylinders are marked as C1, C2,... C10.  
difference between the measured and simulated in-cylinder pressure from the coupled model, by assuming that all cylinders have identical in-cylinder pressure. The state of the calibrated model was considered to represent the engine healthy conditions.  
Following the calibration process, four different engine malfunctioning conditions were examined at 100% load as listed in Section 1, and four corresponding parameters within the coupled model were used to simulate the engine malfunctioning operation. To test individually all malfunctioning conditions, one parameter was varied 6 times in equal steps from its minimum to its maximum values (defined in Section 2.4), while the rest of the parameters were assigned a constant value corresponding to the healthy engine conditions. The above procedure was performed for each cylinder for three model parameters that correspond to each of the following malfunctioning conditions; change in SOI, change of RHR, and blowby. The remaining parameter corresponding to the change in scavene air pressure malfunction, was varied for the entire engine and not for each individual cylinder, as a drop in the scavene air pressure affects all cylinders simultaneously. Therefore, a total of six parametric runs were performed for the three malfunctioning conditions of each cylinder, providing a total of 180 (\(3\times 6\times 10\)) parametric runs. In addition to these parametric runs, six parametric runs were performed for the scavene air pressure malfunction, which affects all cylinders uniformly, raising the total to 186 runs.  
For each parametric run, a frequency analysis by using a Fast Fourier Transform (FFT) was performed to the output of the engine ICT, and the top three most affected signal frequencies and phase angles where identified. These were utilised to map the relationship between the engine ICT and the specific malfunctioning conditions considered in this study.