## 2 Materials and Methods
### Experimental Methods
R\({}^{2}\) is a variance based evaluation index in the range of 0-1, as described in Equation (2). As it gets closer to 1, the accuracy improves and the influence of the data scale diminishes, making it possible to determine the relative performance. As the number of explanatory variables increases, R\({}^{2}\) approaches 1 and is affected by the number of data points and response variables [24; 30]. R\({}^{2}\)\({}_{\text{adj}}\) is the value obtained by correcting R\({}^{2}\) with the number of samples and the number of independent variables, as shown in Equation (3). It is smaller than or equal to  
Figure 1: Data preprocessing algorithm for the propulsion engine [3]. Figure 2: Simple linear regression model (source: own elaboration). \(\text{R}^{2}\), and the prediction accuracy improves as it approaches \(1\). Moreover, if \(\text{R}^{2}_{\text{adj}}\) is negative, the regression algorithm cannot be used. When \(\text{R}^{2}_{\text{adj}}\) is considerably smaller than \(\text{R}^{2}\), an unnecessary explanatory variable exists in the algorithm [24; 30]. \[\text{MAE}=\frac{1}{n}\sum\limits_{i=1}^{n}{{{\left|{{y_{i}}-{{\hat{y}}_{i}}} \right|}}}, \tag{1}\]  
\[R^{2}=1-\frac{\sum\limits_{i=1}^{n}{{{\left({{y_{i}}-{{\hat{y}}_{i}}}\right)}^{ 2}}}}{\sum\limits_{i=1}^{n}{{{\left({{y_{i}}-{{\overline{y}}_{i}}}\right)}^{2} }}}, \tag{2}\]  
\[R^{2}_{adj}=1-\frac{(n-1)}{(n-p)(1-R^{2})}, \tag{3}\]  
where \(n\) is the sampling number, \(y_{i}\) is the collected value, \({{\hat{y}}_{i}}\) is the predicted value, \({{\overline{y}}_{i}}\) is the collected value average, and \(p\) is the explanatory variable number. The machine learning algorithm was developed using PythonTM 3. Python is designed to easily use various libraries necessary for data loading and visualization, image processing, and statistics. Few errors occur due to complex code configurations with a simple grammar configuration, and library linkage with other programming languages is easy; thus, the efficiency of the developed algorithm is high [19; 31; 32]. The utilization of the entire dataset collected by the AMS for detecting anomalistic symptoms and determining maintenance requires considerable time and effort, from algorithm processing to the drawing of results. Moreover, unnecessary data are included in the data used to determine anomalistic symptoms. Therefore, the factors used to determine anomalistic symptoms and maintenance must be identified by considering propulsion engine characteristics. Abnormal operation issues that may occur during engine operation were analyzed by referring to propulsion engine related alarms and monitoring factors in the AMS, the propulsion engine related maintenance items of the planned management system, and the engine manual. Therefore, the item commonly considered to be the cause of abnormal operation was determined to be an exhaust system problem. An increase in the exhaust gas temperature is a major issue in abnormal engine operations, and the CET was selected for determining anomalistic symptoms of propulsion engines as the index that could directly determine the combustion state of the engine. In addition, the CCP was used to directly determine the combustion state in medium sized or large ships. Therefore, the CCP was also selected as a factor for determining the anomalistic symptoms of the propulsion engine. The CET and CCP were derived as the criteria for determining anomalistic symptoms. The maintenance of the propulsion engine tends to increase CET and decrease CCP during abnormal combustion due to problems related to fuel systems and exhaust valves. Therefore, a reference factor capable of easily confirming the tendency of variation in the two factors is required [17; 33; 34]. The increase in reference factors for determining anomalistic symptoms makes the machine learning algorithm complicated, reducing the effectiveness of predicting anomalistic symptoms for ships in real time.