# Maintenance Time Prediction for Predictive Maintenance of Ship Engines
## 2 Materials and Methods
### Experimental Methods
The temperatures of all the cylinders of GE no. 2 under normal operating conditions (VOYAGE 21101-21112) were analyzed (Table 4). The RGCCV temperature criterion for maintenance decisions was set to 550 \({}^{\circ}\)C based on the maximum temperature (549 \({}^{\circ}\)C) of cylinder no. 6, which had the highest exhaust gas temperature among all cylinders [4]. Then, the MCRG was set considering the normal operating temperature range per cylinder. The average temperature of cylinder no. 6 was 481 \({}^{\circ}\)C, deviating by approximately 70 \({}^{\circ}\)C from the temperature criterion for maintenance decisions of 550 \({}^{\circ}\)C, based on which the MCRG of cylinder no. 6 was set to 0. In other words, the maintenance time was reached when the average exhaust gas temperature of each cylinder rose by 70 \({}^{\circ}\)C (when the average temperature reached 550 \({}^{\circ}\)C, where the MCRG of cylinder no. 6 was 0). As the criterion for maintenance was the time the average exhaust gas temperature of each cylinder increased by 70 \({}^{\circ}\)C in normal operation, the MCRG was set differently per cylinder. Because anomalous symptoms were determined using the average data of the voyage, the MCRG was set based on the average exhaust gas temperature of the cylinders. The maintenance time (MCRG) must be determined according to the operating and maintenance standards and guidelines of each engine. Given the GE's current operating time (COT) and PTMRG, the proposed algorithm was developed to calculate the remaining operating time until maintenance, or the predicted time of remaining operation, using the PTMRG (PTRORG), as seen in Equation (3). \[PTROPRG=PTMRG-COT, \tag{3}\]  
* COT: current operating time The maintenance time predicted using the exhaust gas temperature (PTMET), or the time of generator maintenance predicted using only the exhaust gas temperature of the cylinder, was configured as follows using Equation (2). The MCRG value in Equation (2) was changed to the temperature criterion for maintenance (MCET), and the regression analysis of the engine operating time and cylinder exhaust gas temperature for VOYAGE 2113 was used to derive the regression coefficients. Here, the PTMET was defined as Equation (4), the remaining operating time until maintenance predicted using the PTMET (PTROPET) was defined as Equation (5), and the algorithm was constructed. \[PTMET=\frac{\left[\frac{\left(MCET-PIET\right)}{PSET}\right]}{3600}, \tag{4}\]  
* MCET: exhaust gas temperature as maintenance criterion
* PIET: prediction intercept by the exhaust gas temperature
* PSET: prediction slope by the exhaust gas temperature  
\[PTROPET=PTMET-COT, \tag{5}\]  
* COT: current operating time The MSE, RMSE, and MAE were compared for a quantitative evaluation of the validity of the algorithm for predicting the maintenance time using machine learning. Moreover, a \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Item** \textbackslash{} **Cylinder (\({}^{\circ}\)C)** & **1** & **2** & **3** & **4** & **5** & **6** \\ \hline Mean & 459.5 & 456.5 & 471.9 & 453.1 & 456.0 & 480.7 \\ Std & 22.1 & 22.4 & 19.0 & 19.6 & 19.2 & 19.2 \\ Min & 343.8 & 343.8 & 348.8 & 334.9 & 333.9 & 364.9 \\
25\% & 443.9 & 440.9 & 458.9 & 440.0 & 443.9 & 467.9 \\
50\% & 460.9 & 456.0 & 473.9 & 456.0 & 459.9 & 482.0 \\
75\% & 477.9 & 473.9 & 487.8 & 468.9 & 470.8 & 497.0 \\ Max & 523.0 & 524.9 & 536.9 & 511.8 & 515.0 & 549.0 \\ \hline \end{tabular}
\end{table} 
Table 4: Analysis data of cylinder exhaust gas temperature of GE no. 2.  
suitable performance metric was selected for assessing the GE maintenance time prediction algorithm by reviewing the characteristics of the data and the performance metrics. The MSE is an important loss function that squares and averages the error between recorded and predicted values. Thus, it is sensitive to outliers due to squaring and depends on the data scale, with errors tending to increase with the data scale, as defined in Equation (6) [17,18].