Estimating bulk carriers’ main engine power and emissions

Great importance is had in understanding the current situation of maritime transport and making predictions about its future. Maritime transport is an essential part of transportation, and correctly predicting installed main engine power has great significance in maritime transport with regard to fuel consumption and the generation of emissions. Nonlinear regression is a method with great potential in making predictions, as it allows for more realistic models to be developed using multiple variables. Vessels' dimensions of carrying capacity, gross tonnage, length, and breadth significantly impact the required main engine power. This article will calculate and estimate the installed main engine power for bulk carriers through nonlinear regression using data for the as yet highest number of bulk carriers ( n = 9,174 ships) and compare the results with the studies in the literature. The developed model has an accuracy of 93.2% for six different bulk carrier types (Small, Handysize, Handymax, Panamax, Capesize, and Large Capesize). In addition, the study calculates the emissions these ships produce (NOx, SO 2 , CO 2 , HC, PM), estimating and demonstrating a nonlinear linear regression model for these ships' emission amounts. The performed analyses have found the main engine power required per unit of load to decrease as ship size increases. However, these analyses also show the emissions generated per unit of load to decrease as size increases, with Large Capesize vessels being found to have the lowest fuel consumption and emission generation per unit of load.


Introduction
Calculating and estimating a ship's main engine power is essential in terms of economics, as well as for comprehensively calculating emissions and their various sub-components.The use of data in the literature for improving ship emission calculations significantly developed with Eyring et al.'s two-part study [1,2] that used 1950-2000 data to make short-term (until 2020) and long-term (until 2050) predictions.They estimated carbon emissions based on a technology-driven model and a business-as-usual model for an all-diesel fleet.In addition, Kalajdzic [3] investigated bulk carriers' power reduction concerns in light of the new energy efficiency rules.
Heating, ventilation, and air conditioning systems are significant power consumers on ships that run at a constant load, and using a variable speed compressor in its place has significantly reduced emissions [4].Başhan et al. [5] compared emissions versus fuel types for diesel generators used in crane operations and found them to have roughly 40% lower costs compared to Marine Gas Oil by calculating NOx, SO2, CO2, PM, and HC emissions.Engine power probabilities are used to calculate NOx emissions for bulk carriers, and the certified values are shown to require refinement by using weighted factors; doing this revealed 7% lower emissions at sea and 32% lower at port [6].The methods have also been shown to overestimate SO2 emissions.The recommendation is that onboard controls are more effective at reducing SO2 emissions due to the variable sulphur content found in marine fuels [7].Another issue regarding emission reduction is having ship designs satisfy current energy efficiency requirements [8].
Tasdemir et al. [9] used artificial neural networks (ANN) and a fuzzy expert system to predict performance and emissions for a gasoline engine.Their results showed ANN and fuzzy expert systems to be reliable for practical designs and experimental work in the automotive and engineering fields.Özener et al. [10] investigated the ANN approach for estimating engine emissions and performance of a turbocharged engine, showing both ANN to be effective and neural network performance to be increasable with the use of additional relevant input data.
Abramowski [11] used neural networks to apply a seven-variable solution vector for optimizing cargo ship design parameters.This parametric model is particularly suitable for determining effective ship power due to the model's simplicity.Gurgen et al. [12] used ANNs to estimate chemical tanker characteristics in the preliminary ship design stage, revealing ANNs to have prediction levels that significantly match the sample data for chemical tankers.Meanwhile, Jeon et al. [13] used ANN to predict ship fuel consumption using the vast volume of data collected from smart ships to streamline a model for predicting fuel consumption; this proved to be more accurate than the polynomial regressions, thus supporting vector machines.De Winter et al. [14] showed random forest regressors to provide better estimations than the empirical design equations, therefore demonstrating a practical application for naval architects.Okumuş et al. [15] studied main and auxiliary ship engine power using regression-based machine learning algorithms to increase the accuracy of ship engine power estimation and allow for the construction of more environmentally friendly ships.Due to their importance in providing data for fuel consumption and exhaust emissions, the Gaussian mixture model and deep neural network have also been studied over large vessels to predict main engine power [16].
Sahin et al. [17] set out to develop an ANN approach to forecast the Baltic Dry Index, a shipping sector indicator of global economic activity.Using Baltic Dry Index data from 2010-2016, they developed three ANN models: one involving weekly data from the Baltic Dry Index, one on weekly data regarding crude oil prices, and a combination of the two.Next, Cong et al. [18] looked at multivariate nonlinear regression to optimize emissions for a dual-fuel marine engine and showed this method to be applicable for optimizing engine parameters regarding various variables.Yang et al. [19] also used an ANN model to predict efficiency and emissions in a gasoline engine.Their results emphasized how one ANN model can take the place of several other traditional design testing methods to predict emissions and efficiency more accurately and cost-effectively.
Adamowski et al. [20] compared multiple linear and nonlinear regression with ANN, wavelet ANN, and autoregressive integrated moving average methods to predict water demands in Montreal.They found the wavelet ANN to have the best accuracy at predicting water demands based on daily data from 2001-2009 involving precipitation, temperature, and water demand.Adamowski et al. concluded this model to be particularly effective for estimates, which leads one to wonder about its effectiveness in other areas and fields.Gunes et al.'s [21] study also aimed to conduct nonlinear regression and ANN analyses to run estimates of tanker main engine power.Their regression analyses revealed one model to provide the best estimation for this, with the ANN analysis further improving its estimation strength.
One prolific set of studies in the literature involves Yildiz [22] developing a new model to predict the residual resistance of a trimaran vessel using an ANN and Cepowski's [23] development of a transfer function for bulk carriers to forecast added wave resistance from irregular head waves using an ANN with several inputs.Cepowski [24] then went on to use simple linear regression and multivariate linear regression analyses to approximate the preliminary parametric design of new container ships and the required main engine power based on data regarding the length between perpendiculars and the total number of containers to be carried for ships constructed between 2005-2015.Cepowski [25] used more comprehensive data for ships built between 2000-2018.He again used regression analyses to estimate total engine power, now using ship deadweight and TEU together with ship velocity for greater accuracy.Previous regressions [26] were found to be only accurate for medium-size ships or average speeds in the case of MAN Diesel's nominal engine power diagrams.The new estimator was accurate for contemporary ships, applicable to preliminary ship design, and able to help develop ship design theory.Cepowski [27] also used an ANN possessing a 6-neuron input (each with hidden layers) and a single-neuron output to again forecast ship addedresistance in normal head waves, this time involving the design elements of ship length, breadth, draught, and Froude number.Cepowski and Chorab [28] further studied ANNs for estimating engine power and fuel consumption of bulk carrier, tanker, and container ships' engines to update propulsion system design equations, with the inputs for the ANN being deadweight, TEU capacity, and ship speed.Meanwhile, Xhaferaj [29] compared the accuracy of a computer algorithm built to forecast ship resistance and power regarding standard hulls.
The present study looks at the most comprehensive analyses regarding calculations and estimations of ships' installed main engine power and performed nonlinear regressions to cover all ship types and sizes instead of just certain ones.Bejan et al.'s [30] study had previously presented the relationship between size (Dead Weight Ton, DWT) and main engine power by using a power law regression model for all ship types and sizes.This current study estimates main engine power and emission amount by considering not only DWT, but also many other main factors, including GT, L, B, T, an also computes emission amounts.

Database
This study uses the Marine Traffic Database [31], as it offers the most comprehensive data on ships, which is needed for conducting the analyses.The database contains over 80 technical specifications (e.g., type, shipbuilder, year built, draught, depth, DWT, Gross Tonnage [GT], engine power) of around 1 million ships and thus can be considered an up-to-date document regarding the world fleet.The database also has 75 subcategories for ships, with the Marine Traffic webpage showing 11,351 active bulk carriers, of which this paper uses 9,174 (80%) in the analysis, with bulk carriers categorized under six groups (i.e., Small, Handysize, Handymax, Panamax, Capesize, and Large Capesize) for making detailed analyses.The analyses only consider the ships with active statuses, ignoring those with under construction, cancelled order, decommissioned, lost, laid up, or under repair statuses.In addition, Very Large Bulk Carriers (VLBCs), these have been excluded from the analyses due to their small number.Table 1 provides scantling information regarding the bulk carrier types.Figure 4 shows the average speed of bulk carriers while underway.The ships can be seen to mainly operate between 7-13 knots, with most ships operating at a speed of 11 knots, followed by 12 and then 10 knots.The percentage of bulk carriers operating at speeds under 7 knots or over 13 knots is 11%.

Nonlinear Regression
Nonlinear regression examines data fitted to a mathematical model given as a function.Simple linear regression establishes a linear relationship between two variables, whereas nonlinear regression establishes nonlinear correlations [34].Cakici and Aydin used a nonlinear regression method for ship design and prediction [35].The model's objective is to minimize the residual sum of squares (RSS), a measure of the variance between the observations of Y and the nonlinear function used to forecast Y.A nonlinear regression equation has the following general form: Y(x) = f (xi, (c1 + c2 + …, + cn) + (a1 + a2 + …, + an)) (1) where Y is the estimate of the dependent variable (engine power), and Equation (1) has the coefficients c0, c1, …, cn as regression weight coefficients showing how the independent variables affect the dependent variable.
In Equation ( 2), all variables should be written as a matrix to calculate the regression coefficients.
Equation ( 3) shows the D matrix cannot be inverted because it is not square.To invert it, it is turned into a square matrix by adding the transpose of the D matrix (D T ) to both sides as: D T ΔA = D T R (4) where ∆A is the coefficient from the nonlinear regression, which is calculated as: ΔA = (D T ΔD) -1 D T R (5) Equation ( 4) allows the regression coefficients (c1 + c2 + …, + cn) and power coefficients (a1 + a2 + …, + an) to be calculated for the minimum RSS and high coefficient of determination (R 2 ).The least-squares method (LSM) is used to calculate the best algorithm of the RSS for the nonlinear regression.When finding the minimum RSS using LSM, all coefficients are calculated for this result.LSM asserts the curve that best fits a given set of observations to have the minimum RSS from the provided data points as shown in Equation ( 6).To find the best model, the study analyses the parameters in combination with DWT, Length, Draught, Breadth, and Gross Tonnage to find the best estimate of ship power.Table 3 shows the Pearson correlation for the ship particulars, with draught having the smallest correlation compared to all other parameters and as such has been removed from the models.To calculate the nonlinear problem, the study uses the Levenberg-Marquardt (L-M) algorithm [36], which combines the Gauss-Newton and steepest descent methods.The technique is effective in most situations and has become the standard for nonlinear least square routines.

Initial Values and Normalization
Choosing meaningful initial values (c1 or a1) is the essential part of the L-M algorithm, as the results are affected by the initial selected values.For this reason, a new algorithm was developed for identifying significant initial values.First, a power law fitting of the y-value was performed against each x-variable, using this on the fitted slope to provide the initial coefficient estimate for each x-variable.This method of defining the initial coefficient gives reasonable values for calculating all parameters in the nonlinear regression.
Several methods exist for normalizing data.In our analysis, all values are divided by their maximum value, thus converting the value from 0 to 1 in order to find a reasonable result from the analysis.Table 4 shows the normalization of the parameters and the derivative parameters.For weighting, the variance ~ yfit method is used due to the accuracy of current data trends.Equation (7) shows the calculation of annual emissions as follows: E = P×EPP×YWH×10 -6 (7) where E is emissions (tons), P is installed engine power (kW), EPP is emissions per unit of engine power (g/kWh), and YWH is yearly working hours (h).

Results and Discussion
Equation ( 8) defines the nonlinear model for estimating engine power and emissions for all sizes of bulk carrier types.
where β correlation function, ci, and ai are the respective regression and power coefficients.The individual correlation for engine power was analyzed with a single correlation.Engine power's relation with DWT / DWTmax is shown in Figure 5a, with GT / GTmax in Figure 5b, with L / Lmax in Figure 5c, and with B / Bmax in Figure 5d.The initial coefficient of the parameters shown in Figures 5a, 5b, 5c, and 5d are listed in Table 6.These initial values provided high correlation results in the nonlinear regression, with better nonlinear regression results depending on reasonable initial values.Tables 7 and 8 show the results of performing the nonlinear regression analysis over the model created according to Equation ( 8) covering all bulk carrier types (R 2 = 0.932).After finding power coefficients for the installed main engine power and emissions (Table 7) using Equation ( 8), regression coefficients for engine power were also found using nonlinear regression.Table 8 additionally shows the regression coefficients for the emission factors.All the coefficient in Table 7 and Table 8 can be used in Equation ( 8) to estimate main engine power and the amount of the emissions (NOx, SO2, CO2, HC and PM).The difference between the actual and estimated values shows the success of the nonlinear model.The present model also has very high prediction.As seen in Figure 6, the difference between the actual and estimated values is quite low.Error rates for 6,519 ships (71% of all ships) are less than 10% and between 10%-20% for 2,021 ships (22% of all ships).This model's estimations successfully estimate engine power using the ship parameters DWT, GT, L, and B. Table 9 shows the total emission amounts in bulk carriers as calculated using Tables 7  and 8.When examining the total emission amounts, the ships that cause the most emissions are seen to be Capesize-type ships, producing 37% of the total emissions from bulk carriers.After Capesize ships, Panamax ships cause the second highest total emissions at 32%, with Handymax-type ships in third at 14%, Handysize ships in fourth at 11%, and Large Capesize ships in fifth at 5%.The ship type that causes the least emissions overall is the small ship type at 0.1%.Table 10 shows bulk carriers' ratio of total emissions to load carried.While the ships with the lowest emissions per unit of load (DWT) are Small, the ships with the most emissions per unit load are the Large Capesize ships.Ship size increases are closely related to the energy demand per load unit, as studies have shown increased vehicle or animal size to decrease the energy demand per unit of load carried [27], [36].Therefore, as the power consumed per unit of load decreases, the amount of emissions generated per unit of engine power also decreases.Table 11 shows the average emissions bulk carriers generate.The table calculates the total emissions for each ship type by dividing by the total number of that ship.While small ships produce the fewest emissions on average, Large Capesize ships produce the most.As a result, average emissions increase in proportion with ship size, while the emissions produced per unit of load decrease.

Conclusions
Emissions have been a significant threat to the environment since the Industrial Revolution, and the most critical factor behind emissions is undoubtedly transportation.Maritime transport makes up a considerable part of all transportation activities, and the most crucial element in calculating marine emissions is the proper calculation of main engine power.
The main engine power of bulk carriers of known length, breadth, DWT, and GT can be calculated with a low error rate using nonlinear regression analysis by developing the calculations with data from the most extensive number of ships in the literature (N = 9,174).
This study has conducted a holistic assessment of bulk carrier emissions by calculating generated emissions in addition to bulk carriers' main engine power and uses the analyses performed herein to provide method of calculating the emissions of bulk carriers based on installed engine power.In addition, the effects of emissions have been calculated not only for general bulk carriers but also for six main groups based on ship size.
Power demand per unit of load is lower for larger ships than for smaller ships.Thus, smaller ships are used for domestic transportation, while bigger ships are used for international transport.Because bigger ships are more efficient than smaller ships, their travel range is greater than for small ships.This is also valid for emissions per unit of load.Therefore, bigger ships produce fewer emissions per unit of load compared to smaller ships.
Regarding average generated emissions, the biggest ships have the highest emissions, while the smallest ships have the lowest emissions.Capesize and very Large Capesize ships do not have suitable ports worldwide.Because a limited number of countries such as China, Singapore, the United States, and Italy have such ports, these countries and the cities and inland waters where these ports are located are exposed to more intense emissions.
Ships take up the largest share of transportation, and their volume of emissions is relatively high.Due to the carbon tax, ships now need to seek alternative fuels or improve their current emissions.In addition, they must reduce their emissions indirectly by slowing down due to engine power and shaft power limitations based on IMO's mandatory ruling for existing ships.Therefore, logistic time will take longer because of ships' decreased speeds.This article reveals the advantages and disadvantages of the various carrier ship types, and this information will be beneficial for those ordering ships to be newly built with regard to what would be the most advantageous.

Figure 1
Figure1shows the number of bulk carriers used in this analysis based on type.While Panamax is the most common type with 3,035 ships, the second most common is Capesize with 2,393.Handymax and Handysize types respectively number 1,651 and 1,647, while Large Capesize and Small ships have the lowest numbers with 246 and 158, respectively.

Fig. 1
Fig. 1 Number of bulk carriers Figure 2 lists the number of bulk carriers by ship's flag.Panama ranks first with 2,206 ships.The reason is the taxation advantage presented by ships bearing the Panama flag.The Marshall Islands rank second with 1,321 ships, and Liberia is third with 1,004.

Fig. 2
Fig. 2 Flags of the bulk carriers Figure 3 shows the bulk carriers' main engine RPM values.While ships operating in the 90-99 RPM range rank first with 1,703 ships, ships in the 120-129 RPM range rank second with 1,620.Third place sees 1,145 ships operating in the 100-109 RPM range, and fourth has 1,003 ships operating in the 110-119 RPM range.Fifth place has 835 ships operating in the 80-89 RPM range, and sixth place has 440 ships operating in the 130-139 RPM range.Ships operating in other RPM ranges correspond to 9.4% of all ships and have RPM values of less than 80 or greater than 140.RPM data directly affects a ship's economic navigation, slow steaming status, and produced power and therefore the amount of fuel it consumes.

Fig. 3
Fig. 3 RPM of the bulk carriers' main engine

Fig. 4
Fig.4 Average speed of the bulk carriers Table2contains the technical characteristics of the 9,174 bulk carriers used in this study.These characteristics include average GT, DWT, year of construction, breadth, installed engine power, and draught for each type of ship.This situation reveals the current state of the bulk carrier market and draws a projection of fleets' need to renovate their ships and what size to build new ships. 93

Fig. 6
Fig.6 The difference between the real engine power and the estimated values.

Table 2
Summary of bulk carriers' average technical information

Table 3
Pearson correlation for the ship's particular

Table 4
Normalization of the parameters [37]sion factors are required to calculate emissions.Table5shows the types of emissions generated in bulk carriers based on energy consumed (kWh).ENTEC[37]calculated the values in the table for 31,000 ships worldwide.

Table 6
Initial coefficients of the parameter

Table 7
(8)er coefficients of engine power emission factors based on Equation(8).

Table 8
Regression coefficients for engine power and emission factor based on Equation8.

Table 9
Total amount of annual emissions [tons] for the bulk carrier types

Table 10
Emissions per load (DWT) for the bulk carrier type

Table 11
Average amount of annual emissions (tons) by bulk carrier ship type