## 2 Related Works  
Predicting the propulsion power of a vessel at various operating conditions is considered a difficult problem because horsepower can be affected by several external factors such as wind, waves, and hull fouling. Those external factors would increase the vessel resistance, the force working against the vessel movement, requiring more propulsion power to maintain a certain vessel speed. Thus, several methodologies have analyzed the added resistance and speed loss to accurately predict the propulsion power. As previously noted, the conventional method estimates the added resistance of the vessel, and uses this value in prediction of the required propulsion power [15]. The standard model for measuring the total resistance of the vessel is determined by the following equation:  
\[R_{total}\ =\ R_{friction}+R_{residual}+R_{wind} \tag{1}\]  
where \(R_{friction}\), \(R_{residual}\) and \(R_{wind}\) are resistance induced by the friction of the hull, residual resistance, and wind, respectively. \(R_{friction}\) can be calculated by the following:  
\[R_{friction}\ =\ R_{hull}+R_{fouling}+R_{draft} \tag{2}\]  
where \(R_{hull}\) is the size of the hull's wetted area, \(R_{fouling}\) is fouling of the hull and \(R_{draft}\) is specific frictional resistance coefficient. The residual resistance \(R_{residual}\) is determined by the following:  
\[R_{residual}\ =\ R_{wave}+R_{ealty} \tag{3}\]  
where \(R_{wave}\) is the energy loss caused by waves created by the vessel during its propulsion through the water, while \(R_{eddy}\) is eddy resistance which refers to the loss caused by flow separation which creates eddies, particularly at the aft end of the ship. In calm weather, \(R_{wind}\) is proportional to the square of the ship's speed, and proportional to the cross-sectional area of the ship above the waterline. Air resistance normally represents about 2% of the total resistance. Finally, the efficient propulsion power (_EHP_) of the vessel at a certain speed is determined by the following:  
\[EHP\ =\ SPEED\cdot R_{total} \tag{4}\]  
where the \(SPEED\) is a specific vessel speed and \(R_{total}\) is total resistance obtained from the above equation. In ISO15016, several procedures are introduced to correct added resistance [12]. For example, the added resistance due to the effect of short crested irregular wave, \(R_{aw}\) can be calculated by the following:  
\[R_{aw}\ =\ 2\int_{0}^{2\pi}\int_{0}^{\infty}\frac{R_{wave}(\omega,\alpha;V_{S} )}{\zeta_{A}^{2}}E(\omega,\alpha)d\omega d\alpha \tag{5}\]  
where \(\zeta_{A}\) is wave amplitude, \(\omega\) is circular frequency of regular wave, \(\alpha\) is angle between ship heading and incident regular wave, \(\rm V_{S}\) is the vessel speed through the water, and E is directional spectrum. In calculation of \(R_{aw}\), several methods such as the STAWAVE-1, STAWAVE-2, theoretical methods or the Seakeeping model test were proposed in [12]. However, such methods proposed in ISO15016 may not be appropriate to predict the propulsion performance in the actual operating condition because it requires data from the speed trial environment and requires too many input parameters. Even if such big data from operational conditions are available, it would take too much time and cost because the analysis procedure consists of complex equations which are computationally expensive. Alternatively, [PERSON]'s method [16; 17; 18] is also widely used to estimate the resistance and propulsion power requirement during the vessel design phase. It is an empirical method that utilizes data accumulated from many model tests results. The model coefficient and equation are obtained from statistical analysis and regression applied to the data. Although this method requires less computation and numerical analysis, it only provides rough approximation of the resistance and propulsion power which may result in a less accurate result. Moreover, since data is obtained from the model experiments, prediction result cannot be applied to the actual operational condition.