A genetic algorithm-based grey-box model for ship fuel consumption prediction towards sustainable shipping

Abstract

In order to enhance sustainability in maritime shipping, shipping companies spend good efforts in improving the operational energy efficiency of existing ships. Accurate fuel consumption prediction model is a prerequisite of such operational improvements. Existing grey-box models (GBMs) are found with significant performance potential for ship fuel consumption prediction, although having a limitation of separating weather directions. Aiming to overcome this limitation, we propose a novel genetic algorithm-based GBM (GA-based GBM), where ship fuel consumption is modelled in a procedure based on basic principles of ship propulsion and the unknown parameters in this model are estimated with a GA-based procedure. Real ship operation data from a crude oil tanker over a 7-year sailing period are used to demonstrate the accuracy and reliability of the proposed model. To highlight the contribution of this work, we compare the proposed model against the latest GBM. The results show that the fitting performance of the proposed model is remarkably better, especially for oblique weather directions. The proposed model can be employed as a basis of ship energy efficiency management programs to reduce fuel consumption and greenhouse gas (GHG) emissions of a ship. This is beneficial to achieve the goal of sustainable shipping.

Appendices

Appendix A

See Table 10.

Table 10 Beaufort number related to wind speed at the standard height (Townsin et al. 1975)

Appendix B

See Table 11.

Table 11 Data fields of noon reports that are related to this study

Appendix C: The detailed extraction processes of the research data

• 1. Fuel consumption rate

The fuel consumption rate reflects the ship’s daily fuel consumption of main engines. It is calculated based on the fields of “Main engine fuel consumption” and “Report duration” in the corresponding noon reports:

$$ r = 24 \times \frac{{{\text{Main}}\;{\text{engine}}\;{\text{fuel}}\;{\text{consumption}}}}{{{\text{Report}}\;{\text{duration}}}} $$

(C.1)

• 2. Ship speed

The speed through water (STW) is calculated by dividing “Distance through water” by “Report duration”. Therefore, it is an average value for the corresponding report duration. Another speed, known as speed over ground (SOG), is also commonly used in the shipping industry. It is derived from “Distance over ground” and “Report duration”. Here, in order to take the influences of current and tides into account, we choose STW as the ship speed:

$$ V = \frac{{{\text{Distance}}\;{\text{through}}\;{\text{water}}}}{{{\text{Report}}\;{\text{duration}}}} $$

(C.2)

• 3. Displacement

We cannot obtain the displacement from noon reports directly. However, a ship’s hydrostatic table is provided by the shipping company, in which the corresponding relationship between displacement and mean draft can be obtained. The mean draft can be calculated based on the fields of “Forward draft” and “Aft draft”:

$$ {\text{mean}}\;{\text{draft}} = \frac{{{\text{Forward}}\;{\text{draft}} + {\text{Aft}}\;{\text{draft}}}}{2} $$

(C.3)

• 4. Weather direction

The weather direction is derived from the wind/waves direction angle (with respect to the ship’s bow) and can be defined as four different directions depending on the angle degree: head sea, bow sea, beam sea and following sea, as presented in Fig. 1. In practice, loading due to wind and waves is assumed to be from the same angle with respect to the ship’s bow. Here, $\theta$ represents the wind/waves direction angle with respect to the ship’s bow. In noon reports, the field of “Wind direction” means the angle with respect to the True North, as well as the field of “Ship heading”. $\theta$ can be calculated according to the following logical statement (Bialystocki and Konovessis 2016):

$$ \theta = \left\{ \begin{aligned} & \left| {{\text{Wind}}\;{\text{direction}} - {\text{Ship}}\;{\text{heading}} - 360^\circ } \right|,\;{\text{IF}}\;{\text{Wind}}\;{\text{direction}} - {\text{Ship}}\;{\text{heading}} > 180^\circ \\ & \left| {{\text{Wind}}\;{\text{direction}} - {\text{Ship}}\;{\text{heading}} + 360^\circ } \right|,\;{\text{IF}}\;{\text{Wind}}\;{\text{direction}} - {\text{Ship}}\;{\text{heading}} < - 180^\circ \\ & \left| {{\text{Wind}}\;{\text{direction}} - {\text{Ship}}\;{\text{heading}}} \right|,\;{\text{Otherwise}} \\ \end{aligned} \right.$$

(C.4)

• 5. Beaufort number

The Beaufort number can be obtained directly from noon reports.