Predicting tanker main engine power using regression analysis and artificial neural networks

Abstract

Keywords: Artificial Neural Network; ANN; Ship; Main Engine; Power; Regression Analysis

Introduction

Ships are one of the least expensive logistics vehicles able to carry many different loads at once. Many technical parameters are taken into consideration when designing different types of ships. These parameters are vital to

a ship’s longevity and ability to safely navigate and must be determined very carefully and accurately. One of the most important of these parameters involves determining a ship’s energy requirements and selecting the appropriate

*Corresponding author. *E-mail address: ugunes@yildiz.edu.tr This paper was recommended for publication in revised form by Editor Abdelraheem Mahmoud Aly Published by Yıldız Technical University Press, İstanbul, Turkey Copyright 2021, Yıldız Technical University. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Sigma J Eng Nat Sci, Vol. 41, No. 2, pp. 216–225, April, 2023

main engine and auxiliary machinery. The main engine market for ships reached nearly $33 billion USD in 2020 and is forecasted to reach over $40 billion USD by 2026, which shows an expected compound annual growth rate of 3.18% between 2021-2026 [1]. When considered multidirectionally in this context, choosing the main engine for a ship should involve noting energy efficiency, global economy, fuel, and the related regulations, emissions, ship speed, operational economy, propeller, waste heat recovery systems, and many other technical details. The literature has many computational and experimental studies that have been done on these issues. With recent developments in artificial intelligence, researchers have started to carry out studies apart from these that will make estimation about ships’ various aspects using a multitude of methods. One of these is artificial neural networks (ANNs), which have been used successfully over a wide range of different areas beyond ships, such as in different branches of social and natural sciences and medical treatments Another additional important method involves the various linear and non-linear types of regression analyses. ANNs and regression analyses all provide specific valuable data to a forecast between the inputs and outputs. Barua et al. [2] developed machine learning models that can be applied to various aspects of international freight management and made certain operational predictions. Bodunov et al. [3] demonstrated an approach using geospatial data for port destination classification and estimated time of arrival (ETA) determinations. Bui-Duy and Vu-ThiMinh [4] used an algorithmic solution from an asymmetric traveling salesman problem (ATSP) in which the fuel consumption model for the route is estimated based on the deep machine learning method. In order to minimize fuel costs, they attempted to optimize route selection for container ships using five inputs: average speed, sailing time, ship capacity, wind speed, and wind direction. Cepowski and Chorab [5] developed a study based on data beginning in 2015 to estimate the main engine power requirements and fuel consumption needs for commercial cargo ships (bulk carriers, tankers, and container ships). The study is based on simple mathematical structures that can be easily applied in the design stage as well as in ecological studies. Cui et al. [6] performed bulk carrier structural design optimization, which uses machine learning for optimization and improves the optimization’s adaptability to the dynamic design environment. Jeong et al. [7] carried out a study with the help of the programs R and Python, estimating lead times for manufacturing, ship block assembly, reel fabrication, and dyeing using machine learning technology to propose a new management method for process lead time using a master data system for the time element in production data. Cepowski [8] presented a forecasting tool to predict the main engine power for container ships built between 2005 and 2015 using basic design variables. Cepowski [9] also

presented regression formulas for the preliminary design of tankers, bulk carriers, and container ships based on data from ships built between 2000-2018. The authors indicated the formulas to be able to be used for estimating total engine power using a ship’s deadweight or Twenty-Foot-Equivalent Unit (TEU) capacity. Moreover, Cepowski and Chorab [10] developed preliminary design formulas for container ships using a database of container ships built between 2015-2020. Uyanık et al. [11] carried out various prediction models such as multiple linear regressions, Ridge and LASSO regression, support vector regression, tree-based algorithms, and elevation algorithms in order to determine the relationships among parameters for fuel consumption in a container ship such as main engine speed, main engine cylinder values, scavenge air, and shaft indicators. Gkerekos et al. [12] used algorithms such as support vector machines (SVMs), random forest regressors (RFRs), extra tree regressors (ETRs), ANNs, and community detection algorithms to estimate ships’ main engine fuel consumption. [13] proposed an unconventional technique for estimating ship performance using noon reports as a decision support system (DSS) based on ANN multi-regression methods. Tarelko and Rudzki [14] applied ANN-based decision support systems that use certain operational data to predict ship speed, travel time, and fuel consumption for reaching a destination. Farag and Olcer [15] used a combination of ANN and multiple regression techniques to estimate ships’ power and fuel consumption. The model they proposed was developed by processing dense datasets instead of ships’ traditional noon reports. Peng et al. [16] discussed how to estimate ships’ energy consumption in the port of Jingtang, China using five different machine learning regression models and strategies for reducing ships’ energy consumption. Yan et al. [17] created a ship energy efficiency optimization model that takes into account multiple environmental factors by analyzing the energy transfers among the hull, propeller, and main engine. The results show the proposed method to be able to effectively reduce ships’ energy consumption and CO2 emissions. Yan et al. [18] proposed a two-stage estimation and reduction model for dry cargo ship fuel consumption, validating a fuel consumption prediction model based on random forest regression. The forecast model takes into account vessel sailing speed, total cargo weight, and sea/weather conditions and then estimates the main engine’s hourly fuel consumption. Yuan and Nian [19] also developed a Gaussian process meta model for predicting ships’ fuel consumption under different scenarios. Their model takes into account not only the effects of operating conditions such as speed and trim, but also the effects of weather conditions such as wind and wave effects. Tran [20] used the ANN method to run estimations for a bulk carrier’s main diesel engine belonging to a Vietnamese company and on low sulfur content fuel consumption in ECA zones as well as heavy fuel oil consumption on 2-year voyages [21].

Sigma J Eng Nat Sci, Vol. 41, No. 2, pp. 216–225, April, 2023

Several researchers have also applied ANN-based regression analyses in a variety of fields for predicting physics-based shaft power for large merchant ships [22], predicting main engine failures [23], predicting main engine fuel consumption for more efficient ship operations [24], assigning a simple process for pre-processing the huge amount of data collected from automated data logging & monitoring (ADLM) systems [25], estimating motor yacht weight displacement based on design variables, predicting emission analyses (NOX, SO2, CO2, VOC, PM, and CO) for Turkey’s Izmir and Mersin ports [26], and proposing a dynamic calculation method of ship exhaust emissions based on real-time ship trajectory data [27]. This study attempts to determine the power of ship main engines using parameters such as draught, depth, deadweight tonnage (DWT), gross tonnage (GT), and engine power. The results from the approach using ANNs have good agreement with the literature. Another approach was additionally taken using various regression analyses, the results from which showed positive effects in estimating ship main engine power.

Materials And Methods

Database Marine Traffic is an open, community-based project that provides real-time information about ship locations using a database of vessel-identifying information including International Maritime Organization (IMO) number. This study uses the Marine Traffic database as a data source. The database contains more than 80 technical specifications (e.g., type, shipbuilder, year built, draught, depth, DWT, GT, engine power) of more than 900,000 ships and can be considered an up-to-date document on the world fleet. Non-Linear Regression Nonlinear regression analyzes data fit to a model expressed as a mathematical function. Simple linear regression relates two variables in a linear relationship, while nonlinear regression relates them nonlinearly (curved). The goal of the model is to minimize the sum of the squares, being a measure tracking the Y observations’ variance from the nonlinear function used to predict Y. This is computed by first finding then squaring and adding the difference between the fitted nonlinear function and every Y datum in the set. The general form of a non-linear regression equation is: Y ( x ) = f ( xi , A0 + A1 + A2 + , + An )

where Y is the estimate of the dependent variable (engine power). Equation 1 has the coefficients A0, A1, …, An as regression weight coefficients showing how the independent variables affect the dependent variable.

Equation 2 shows R as the residual value, which is the difference between the actual value and the mean value that the model predicts for that actual value. In Equation 2, all variables should be written as a matrix in order to calculate the regression coefficients.  ∂f ∂f ∂f      ∂A ∂ A1m   i1 ∂ Ai 2  ∆A1   R1  ∂    ∂ f    f      ∆A2   R2  ∂ A2 m  ⋅  =  ∂ A21                 ∆Am   Rm   ∂f    ∂ ∂ f f R   ∆A  ∂ ∂ Anm   An1 ∂ An 2  

Equation 3 shows the B matrix cannot be inverted because it is not square. In order to invert it, it is turned into a square matrix by adding the transpose of B matrix (BT) to both sides as: BT ∆A = BT R

in which ∆A is the coefficient from the non-linear regression, calculated as: −1

Equation 4 allows the regression coefficients (A0, A1, A2, … An) to be calculated with respect to minimum total sum of squares (RSS) and the high coefficient of determination (R2). Eight different non-linear models are shown in Table 1. The models used the variables of DWT, L, B, and GT to estimate best Y value (engine power). Artificial Neural Network ANNs are an information processing technology inspired by the working logic of the human brain. The algorithm of the simple biological nervous system is modeled using ANN. In other words, it is the digital representation of biological neuron cells and the synaptic connections these cells have with one another. A layer perceptron is used in the ANN model structure [28]. The F function used for each output neuron in the perceptron layers can be defined as follows: N

where ϕ (ωiT x + bi ) is an alternating continuous function, Im is an m-dimensional unit hypercube of interval [0, 1]m, C

Sigma J Eng Nat Sci, Vol. 41, No. 2, pp. 216–225, April, 2023

A0 +A1 L / B + A2 L / DWT1/3 + A3 B / DWT1/3 + A4 GT / DWT + A5

(Im) is the space of continuous functions in Im, N is the limit, vi and bi are function coefficients and real vectors in R, and ωi is the weighing factor (in Rm, i = 1, …, N). The F function is independent from φ, and x ∈ Im. Thus, for any e > 0, the following expression holds: F (x) − f (x) < e

The ANN dataset was calculated using ship data base by 14 inputs and 1 output data. For validation, the dataset is divided into 134 samples for validation and testing and 568 samples for training. Trial results have shown the Levenberg–Marquardt method to perform better compared to other algorithms [29–31]. Some parameters have been excluded the data set for simplification, with only 8 input parameters being used. As a result, the output calculation convergence is adequate. The training, validation, and testing of the 8-input ANN system is then performed in order. Figure 2 shows the perceptron model that was used. The logsig activation function is employed in the hidden layer, and the purelin activation function is utilized in the output layer. General definitions are expressed in the following equations. The ANN’s inside activity Ui can be expressed as: Sigmoid : f ( x ) =

The mean square error (MSE) is determined as a network performance function. The statistical methods of mean absolute percentage error (MAPE) and coefficient

Figure 1. Flowchart of the ANN research framework. of determination (R2) are used for network comparisons. These are expressed as: MSE =

_ where t is the target value, o is the output, o is the mean of the output, and n is the number of samples.

Results And Discussion

The results from the 8 non-linear regression models are shown in Figure 3. While most non-linear regression models have high correlations, Models 2 (Figure 2b) and 3 (Figure 2c) have low correlations. The correlation has a relationship with R2. Regression coefficients and the R2 values are show in Table 2. In addition to the poor fitting distributions, Model 2 and Model 3 have the lowest R2 values. As such, they don’t provide good approximations. The R2 from Models 1, 4, and 5 are around 0.80 and are also able to be applied to the estimations. Models 6 and 8 have much better R2 results. The best estimation is in Model 7, with an R2 = 0.827; thus, it is

the most proper model for estimating engine power using vessels’ actual DWT, L, B, and GT values. Data are currently available for more than 10,000 ships. These data involve 33 different pieces of information: ship

Sigma J Eng Nat Sci, Vol. 41, No. 2, pp. 216–225, April, 2023

ID#, ship name, type, distance traveled, draft, recorded speed (max / average), speed / course, IMO, MMSI, call sign, flag, AIS vessel type, length overall, breadth extreme, year built, status (active / passive), owner, manager, shipbuilder,

Figure 2. The basic working principles and architectural structure of ANN.

Sigma J Eng Nat Sci, Vol. 41, No. 2, pp. 216–225, April, 2023

Figure 3. Non-linear regression models and the estimations from each model.

height, gross tonnage (GT), deadweight (DWT), displacement–lightship, displacement–summer, engine bore, engine builder, engine model, engine cylinders, engine

RPM, engine stroke, propeller, and fuel type. First of all, the tanker-type ships were separated from the data; 836 tanker-type ships were analyzed by separating ships with

Sigma J Eng Nat Sci, Vol. 41, No. 2, pp. 216–225, April, 2023

Data Availability Statement

The authors confirm that the data that supports the findings of this study are available within the article. Raw data that support the finding of this study are available from the corresponding author, upon reasonable request.

Conflict Of Interest

The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article. Figure 7. MSE for the training, validation, and testing results with the number of neurons in each hidden layer.

Ethics

the number of middle layers and neurons in the ANNs vary. The results from the mean squared error value according to the number of neurons in the ANN analysis code are shown in Figure 7. When considering the training, validation, and testing values, the best result was concluded to have been obtained using 35 neurons. As the number of neurons increased to 50, the accuracy sensitivity was seen to decrease. When considering the ANN literature for this problem, the result can be obtained using a medium-simple neural network structure.

Share and Cite