An Energy Efficiency Optimization Strategy of Hybrid Electric Ship Based on Working Condition Prediction

Abstract

Optimizing the operational performance of green ships can further improve the energy saving and emission reduction effect of ships, and speed optimization is one of the more widely used and effective measures. It is a new challenge for the shipping industry to achieve speed optimization that simultaneously saves energy, reduces emissions and meets transportation requirements, while considering changes in the navigation environment. In this paper, a hybrid electric ship energy efficiency optimization strategy based on working condition prediction is proposed to solve the problem of navigation condition at a future moment, by making a time series prediction of energy efficiency influencing factors, such as wind speed and current speed. Further, on the basis of establishing the sailing speed prediction model and the real-time energy efficiency operation index (EEOI) model, the real-time EEOI deviation and the sailing speed deviation are adopted as the comprehensive objective function to establish a dynamic optimization model of hybrid electric ship energy efficiency, considering the time-varying environmental factors. Then, the fast Non-Dominated Sorting Genetic Algorithm II (NSGA-II) is applied to solve the bi-objective optimization problem and obtain the optimal ship engine speed in real time. Finally, experimental studies show that the proposed optimization model can improve the energy-saving and emission-reduction effect of the ship under the given speed limit requirements and working environment conditions, which can provide theoretical support for the optimal navigation of hybrid electric ships.

1. Introduction

According to the latest greenhouse gas study by the International Maritime Organization (IMO), the total greenhouse gas emissions from ships and the proportion of ships in global emissions increased by 9.6% and 4.7%, respectively, between 2012 and 2018, and CO₂ emissions are expected to increase by 50% in 2050 compared to 2018 if effective measures are not taken in a timely manner [1]. To promote energy efficiency and emission reduction in shipping, the IMO has proposed mandatory operational and technical measures, which include the Energy Efficiency Design Index (EEDI) for newly designed ships and the Ship Energy Efficiency Management Plan (SEEMP) for all ships [2].

Hybrid electric ships have attracted increasing attention as promising green vessels with the advantage of achieving the efficient use of multiple energy sources, thereby improving vessel economics and reducing emissions [3]. Studies have shown that hybrid electric ships not only save fuel consumption, but also improve the operational efficiency of the main engine [4]. In terms of ship operation, reducing the speed of ships to achieve energy conservation and emission reduction has proved to be an effective measure [5,6]. However, simple speed reduction in navigation may produce adverse effects in terms of transportation cost and transportation reliability [7]. Therefore, sailing speed should be reasonably optimized to meet the requirements of energy saving, emission reduction and transportation, which is to seek a dynamic balance between expected profits and expected losses.

At present, there have been some results in research on speed optimization. By studying a series of speed optimization models that take the sailing environment, fuel prices and other factors into account, Psaraftis shows that energy conservation and emission reduction in ships can be achieved by optimizing the ship speed [8]. Wen et al. incorporated ship load and fuel prices into fuel consumption models and studied speed optimization and cargo distribution for fleet transport [9]. Li established the minimum fuel consumption model to solve the speed optimization problem of a ship on a given route under the condition of irregular wind and waves, and significantly reduced the fuel consumption of the ship [10]. With the development of computer science and artificial intelligence, machine learning is increasingly being used to build models of ship energy efficiency. For example, Lin et al. obtained a real-time prediction model of ship fuel consumption through BP neural network training-related data, and further used it for ship speed optimization [11]. Tarelko et al. used artificial neural networks (ANNs) to build speed and fuel consumption models [12].

However, the above speed optimization research focuses on traditional single-powered ships, mainly considering fuel consumption, and there is a certain research gap in the speed optimization of hybrid electric ships. The author proposed a static speed optimization method for hybrid electric ships, which is a step forward in optimizing the energy efficiency of ships considering various sailing environments [13]. However, environmental factors are constantly changing during actual voyages, and these static optimization methods cannot ensure optimal energy efficiency in real time throughout the voyage. Meanwhile, in the actual voyage process, ship fuel saving and punctual arrival need to be comprehensively considered, and sometimes, their changes are completely contradictory. Sui et al. point out that the optimal combination of propulsion control and voyage planning can further reduce fuel consumption and carbon emissions in the shipping industry [14]. Wang pointed out that optimizing the ship engine speed is a direct and effective method for the rational selection of sailing speed [15].

Therefore, this paper takes the real-time energy efficiency operation index (EEOI) as the monitoring index of real-time energy efficiency and proposes a dynamic energy efficiency optimization method for hybrid electric ship based on sailing condition prediction. Compared with the existing research, this method fully considers the influence of environmental factors such as wind speed and water flow speed in the establishment of a real-time EEOI model; this makes the EEOI calculation more realistic and effectively improves the reliability of the speed optimization model by using data such as wind speed and water flow speed collected online by the sensor. At the same time, speed and real-time EEOI are taken as comprehensive optimization goals, which can ensure the change degree of the speed in the optimization, to prevent the ultimate arrival time from being affected by excessive speed reduction during real-time EEOI optimization. Further, the fast Non-Dominated Sorting Genetic Algorithm II (NSGA-II) is used to solve the problem of speed optimization of the hybrid electric ship in real time, so as to improve the energy-saving and emission-reduction effect of the ship under the given speed limit requirements and navigation environment conditions.

2. Model Construction

Traditional static speed-optimization methods are mainly based on weather forecast information, regardless of the continuously changing environment. When significant and frequent changes occur in the sailing environment, these methods cannot ensure the real-time optimization of the ship energy efficiency. Changes in environmental factors affect ship resistance, which in turn affects the ship energy efficiency, so predicting the working conditions of short-distance voyages ahead of the ship is one of the keys to ensuring the reliability of the real-time EEOI model. This study also establishes a speed prediction model. On the one hand, the relationship between the engine speed and the ship speed can be established, which lays the foundation for the bi-objective optimization of the ship speed and EEOI. On the other hand, the ship speed change affects the ship resistance, and thus, affects the ship energy efficiency, so the speed prediction can improve the accuracy of the subsequent EEOI model.

The real-time prediction of working condition and ship speed is a dynamic system. The Elman neural network algorithm is a dynamic type of neural network with many applications, and it can well-reflect the dynamic characteristics of the changes of navigation parameters and ship speed sequences; therefore, this paper adopts the Elman neural network algorithm to carry out the prediction aspect of research [16]. However, this algorithm has the problems of slow training speed and ease of falling into local minima, and it is difficult to reach the global optimum in the training of the neural network [17]. In this paper, Genetic Algorithm (GA) with global search capability is introduced to optimize the weights and thresholds of the Elman neural network, in order to achieve the construction of the time series prediction model of working condition and the ship speed prediction model [18].

2.1. GA–Elman Neural Network Prediction Model

Compared with the traditional Elman neural network, the GA–Elman algorithm has a faster convergence speed, reduced training time, and solves the problem of easily falling into local minima, so it has better prediction performance. Under the premise of obtaining the historical working parameters, which is the known historical sequence $Z_{1:k}$, it is first necessary to determine the optimal time window of the sequence based on Cao’s method $m$. Figure 1 shows the prediction flow chart of the proposed GA–Elman neural network prediction model. The steps of this prediction model are shown below.

Step 1: Obtain the data and perform sample pre-processing. Determine the basic structure of Elman neural network and related network parameters and determine the time window $m$ by Cao’s method.

Step 2: Initialization of genetic algorithm. Determine population size, termination evolution algebra, crossover probability, mutation probability and fitness function. The reciprocal of the sum of squares of errors between the actual output and the desired value is selected as the fitness function in this study, as is shown in Equation (1):

$$f(i)=\frac{1}{{\displaystyle \sum _{i=1}^a{(y(i)-y^{\prime }(i))}^2}}$$

(1)

where $f(i)$ is the fitness value of the $i$th particle, $y^{\prime }(i)$ is the expected output value of the $i$th particle, $y(i)$ is the actual output value of the $i$th particle and $a$ is the total number of input samples.

Step 3: Input the data and obtain the optimal weights and thresholds of the Elman neural network based on GA.

Step 4: Model training. The Elman neural network is trained by the optimal weights and thresholds obtained after optimization by GA. The training error is less than the set value. Then, stop training.

(1)

Working condition prediction model.

The influence of environmental factors on the energy efficiency of ships mainly depends on the ship resistance, which has a strong correlation with the current speed and wind speed [19]. In this study, the assumption is made that the direction of the wind and the current of water coincide with the ship’s course. Therefore, scalars are used instead of vector quantities, and the current speed and wind speed are selected as the characteristic parameters to describe the working condition of the ship. Based on the GA–Elman neural network, this study uses a time series forecasting strategy to predict the parameters of ship working condition [20]. At equal time intervals, the time series problem can be formulated as follows:

$$v_{k+h}=g(v_k,v_{k-1},\cdots ,v_{k-m+1})$$

(2)

where $g(\ast )$ is the GA–Elman neural network model; $v_k,v_{k-1},\cdots ,v_{k-m+1}$ denotes time series data points; $v_{k+h}$ refers to the predicted results; $m$ is the amount of data input, also known as the embedded dimension; the optimal embedding dimension can be determined by cao algorithm; and $h$ is the forecast step, selected as 1 in this article. Based on the GA–Elman neural network model, according to the wind speed and water flow speed data collected by the sensor online, the above time series forecasting method is used, and the wind speed and water flow speed data for the previous $m$ moments before the moment $k$ are used as the input of the neural network model, which can be output as the wind speed and water flow speed at the moment $k+1$, respectively.

(2)

Ship speed prediction model.

Although reducing the speed can achieve the purpose of reducing the energy efficiency of the ship, in the actual transportation, the decrease in speed may cause adverse effects such as schedule delays. Therefore, it is necessary to consider the speed and EEOI as the optimization goal together, so it is necessary to establish a model of the relationship between the main engine speed, the working condition parameters and the ship speed. In the training process, the speed prediction model uses the actual navigation data based on the neural network model, and takes the main engine speed, wind speed and water flow speed at the current moment as the input, and the ship speed at the current moment as the output, so as to establish the relationship model between the main engine speed and the ship speed. During the actual voyage, the wind speed and water velocity data predicted at the next moment in real time are input into the speed prediction model, and the relationship between the main engine speed and the ship speed at the next moment can be obtained, laying a foundation for the subsequent speed optimization. Therefore, under the premise of obtaining the working condition parameters and the speed of the main engine during the voyage of the ship, the model can be used to predict the sailing speed of the ship online.

2.2. Ship Energy Efficiency Model

According to the guide adopted at the Marine Environment Protection Committee in 2009 [21], EEOI is used to measure the energy efficiency of ships, which expresses operational efficiency in terms of CO₂ emissions per unit of transport work. EEOI is defined as follows:

$$\mathrm{EEOI}=\frac{{\displaystyle \sum _{j}F{C}_j\times C_{carbon}}}{m_{c\arg o}\times D_S}$$

(3)

where $j$ is the fuel type, $F{C}_j$ is the total fuel consumption of the voyage, $C_{carbon}^{}$ is the carbon content of the fuel $j$, $m_{c\arg o}$ is the quantity of the goods transported, and $D_S$ is the sailing distance.

When the ship is sailing, the total resistance of the ship is $R$. In order to overcome this resistance, the main engine of the ship is required to send a certain power to turn the propeller, which produces the thrust to push the ship forward. Sailing resistance mainly includes hydrostatic resistance, wave resistance, wind resistance and shallow water resistance. Using the method in Holtrop and Mennen [22], the total resistance of the ship can be expressed by Equation (4):

$$R=R_T+R_{wave}+R_{wind}+R_{shallow}=F_R(V_S,V_a,V_w)$$

(4)

where $R$ denotes the total resistance to ship navigation, $R_T$ denotes the total hydrostatic resistance, $R_{wave}$ denotes the wave resistance, $R_{wind}$ denotes the wind resistance, $R_{shallow}$ denotes the shallow water resistance, $V_S$ denotes the ship sailing speed against the water, $V_a$ denotes the wind speed, $V_w$ denotes the current speed, and $V_g$ denotes the ship sailing speed against the ground, expressed as follows:

$$V_g=V_s+V_w$$

(5)

The main engine power $P_B$ can be calculated by Equation (6):

$$P_B=\frac{2\pi \rho D^5{n}^3{K}_Q}{{\eta }_S{\eta }_G{\eta }_R}$$

(6)

where $\rho$ denotes the water density, $n$ denotes the propeller speed, $D$ denotes the propeller diameter, $K_Q$ denotes the torque coefficient, ${\eta }_S$ denotes the shaft drive efficiency, ${\eta }_G$ denotes the gearbox efficiency, and ${\eta }_R$ denotes the relative rotational efficiency.

The fuel consumption per unit time is:

$$Q=P_B\cdot g_e=\frac{2\pi \rho D^5{n}^3{K}_Q{g}_e}{{\eta }_S{\eta }_G{\eta }_R}$$

(7)

where $g_e$ is the fuel consumption rate.

EEOI can be expressed as:

$$E=\frac{C_{carbon}}{m_{c\arg o}}{\displaystyle \int \frac{Q}{V_g\cdot t}}dt=\frac{C_{carbon}}{m_{c\arg o}}{\displaystyle \int \frac{q}{V_g}}dt$$

(8)

where $q$ is the equivalent fuel consumption per unit of time and $t$ is the sailing time. In order to dynamically grasp the energy efficiency level of the main engine during the ship voyage, Equation (8) is differentiated. The real-time EEOI model of the main engine is obtained by combining Equation (7), and the real-time energy efficiency level of the main engine during the navigation is measured by Equation (9):

$$dE=\frac{q\cdot C_{carbon}}{m_{c\arg o}{V}_g}=\frac{2\pi \rho D^5{n}^3{K}_Q{g}_e{C}_{carbon}}{{\eta }_S{\eta }_G{\eta }_R{m}_{c\arg o}{V}_g}$$

(9)

3. Real-Time Optimization Model of Ship Energy Efficiency

According to the actual voyage data of the hybrid electric ship studied in this paper, it can be seen that—except for the use of batteries in emergencies and berthing—the diesel generator is still used more than 85% of the time, so this paper mainly studies the PTH mode (only the diesel generator set operates).

In order to take the energy efficiency and arrival time of the ship into account synthetically, it is necessary to adopt an index that can reflect both parameters as the optimization target. Assuming that the speed in still water is the optimized speed for the voyage, the sum of the squares of the relative errors of the speed and real-time EEOI and their corresponding parameters in still water can be chosen as the comprehensive objective function for optimization, expressed as Equation (10):

$$\min Y={\lambda }_1\cdot {\left(\frac{V_g-V_{g0}}{V_{g0}}\right)}^2+{\lambda }_2\cdot {\left(\frac{E-E_0}{E_0}\right)}^2$$

(10)

$$n_{\min }\le n\le n_{\max }$$

(11)

$$V_{g\min }\le V_g\le V_g{}_{\max }$$

(12)

where $Y$ is the comprehensive optimization objective function; the main engine speed $n$ at different time steps is the optimization variable; $V_{g0}$ and $E_0$ are the ship speed and EEOI in still water at the specified speed, respectively; $M$ is the number of moments of total range; and ${\lambda }_1$, ${\lambda }_2$ are the weight factors to adjust the ratio of fuel ship speed and EEOI in the optimization objective function, which can be adjusted according to the actual demand, $0\le {\lambda }_1\le 1$, $0\le {\lambda }_2\le 1$, and ${\lambda }_1+{\lambda }_2=1$. Equations (11) and (12) are the physical limits corresponding to the engine speed and sailing speed, respectively, which can avoid overloading.

The objective of this study is to reduce the real-time EEOI while ensuring the navigation speed, which is a combinatorial optimization problem that is difficult to solve quickly by traditional optimization algorithms and is mostly solved by intelligent algorithms. The common methods for solving the bi-objective optimization include the ideal point method, the constraint method and the construction of Pareto solution sets [23]. The first two methods mainly transform the bi-objective problem into a single-objective problem, which reduces the difficulty of solving the algorithm to a certain extent but destroys the physical meaning of the bi-objective optimization problem itself. In contrast, the Pareto solution set can provide a variety of effective choices, which is more conducive for decision makers to make decisions according to different preferences. Therefore, the NSGA-II optimization algorithm is selected for this study.

The NSGA-II algorithm is widely used to solve multi-objective problems. It improves the sharing function adopted by the original NSGA algorithm to retain the diversity of solutions, adopts the crowding degree comparison operators, and introduces both elite strategy and non-dominated ranking algorithms, which have been successfully applied to the optimal design of energy systems been shown to provide a good trade-off between several different objectives [24]. Therefore, this algorithm will be used for the bi-objective optimization of real-time EEOI deviations and speed deviations.

The engine speed optimization method is shown in Figure 2. The whole optimization process mainly includes three parts: working condition prediction, solving real-time sailing speed and EEOI, and obtaining the optimal speed optimization of the main engine. The specific steps are:

(1)

Establish the prediction model of working condition parameters, real-time speed model and EEOI model.

(2)

Predict the wind speed and current speed at the next moment based on the working condition model and the historical data of the ship.

(3)

Substitute the predicted values of the working condition parameters into the real-time speed prediction model and the EEOI model as input to determine the relationship between the main engine speed and the ship speed, and the relationship between the main engine speed and EEOI at the next time.

(4)

The NSGA-II algorithm is used to solve for the optimal speed of the main engine, to calculate and obtain the main engine speed that minimizes the predicted value of the integrated objective function, and to set the main engine to operate at the optimized speed in real time to realize the real-time optimization of the hybrid electric ship.

4. Case Study

4.1. Data Acquisition

Data acquisition was carried out on an inland river fast official patrol vessel, as shown in Figure 3. It is seaworthy in Shanghai Dianshan Lake waters, and the navigation area is inland river class B. It is mainly used for daily river patrol, inspection, supervision and comprehensive command.

Table 1. Ship parameters.

Parameter	Value
Length	32.1 m
Width	7.3 m
Design draft	1.1 m
Rated power for propulsion motor	75 kW × 2
Total capacity of battery	387 kWh
Rated speed for propulsion motor	700 rpm
Rated power of diesel generator set	200 kW

gives the parameters of the ship.

Through the installation of a shaft power meter, fuel consumption meter and sensors, various data such as ship speed, shaft speed, fuel consumption, wind speed and current speed were collected. The data of the ship navigation were selected for more than 2 h in the afternoon of 2 December 2021 in Hongqitang, Jiashan County, Jiaxing District, Zhejiang province. The sampling period was 3 s, and a total of 3000 sets of data were collected. A time unit on the abscissa represents a sampling moment, i.e., 3 s. As recorded by relevant navigation software, the altitude was 14 m–15 m, the average speed was 14.137 km/h, and the maximum speed was 20.413 km/h.

4.2. Working Condition Prediction and Ship Speed Prediction

In this study, 80% of the working condition data set was used as the training set and 20% as the test set, and Mean Squared Error (MSE) and Root Mean Square Error (RMSE) were selected to evaluate the prediction performance of the proposed working condition prediction model and ship speed prediction model. MSE can evaluate the degree of change in the data, and RMSE is mainly used to describe the effect of samples with large errors, both of which are smaller values with a better prediction effect and higher prediction accuracy. The prediction results are shown in

Table 2. Predicted results of working condition.

Working Condition	MSE	RMSE
Wind speed	0.7401	0.8603
Current speed	0.0157	0.1253

. Figure 4 shows the prediction results of wind speed with the RMSE of 0.8603, and Figure 5 shows the prediction results of water velocity with the RMSE of 0.1253. Figure 6 shows the prediction results of ship speed. Figure 7 shows the absolute error of ship speed prediction. The simulation results show that although some errors still exist, the model is sufficient to provide information about the changes in working condition in practical applications.

4.3. Energy Efficiency Optimization Based on NSGA-II Algorithm

The objective of the simulation experiment is to optimize the engine speed for 15 moments at a fixed time interval. In order to determine the parameters in the comprehensive optimization objective function, it is first necessary to analyze the different values of the weight parameters ${\lambda }_1$ and ${\lambda }_2$.

Table 3. Optimization results under different parameter selection.

λ1	λ2	EEOI (g/t·n)	Ship Speed (m/s)
0	1	5.05	2.13
0.3	0.7	5.97	2.69
0.5	0.5	6.19	3.34
0.7	0.3	6.59	3.87
1	0	7.05	4.32

shows the optimization results of the selected real-time EEOI under different parameter selections at the same moment. As can be seen from Table 3, when ${\lambda }_1$ = 0, the optimization objective is only the EEOI deviation, which will greatly prolong the running time if the ship speed is reduced too much, and when ${\lambda }_1$ = 1, the optimization objective is only the speed deviation, without much optimization effect. When the weight coefficient ${\lambda }_1$ is large, the speed deviation plays a large role, which makes the optimized EEOI large—that is, the effect of energy saving and emission reduction is weak. Obviously, to minimize EEOI, the parameter ${\lambda }_1$ should be taken as small as possible. However, if the value is too small, the influence of speed deviation may also be too low, which will lead to the problem of adverse voyage time. In this study, we focus on environmental protection, and ${\lambda }_1$ takes a value of 0.3.

The information of the working condition during the optimization process is shown in Figure 8. Figure 9 shows the optimization results for 15 moments of fixed time interval, and Figure 10 shows the non-inferior solution distribution curve of the first moment. From Figure 9, the sailing speed after real-time optimization shows a trend of reduction, while the EEOI shows a more obvious improvement. Meanwhile, the non-inferior solution obtained by the optimization algorithm well-expresses the Pareto surface, which verifies the effectiveness of the proposed ship main engine speed-optimization method.

Compared with the traditional optimization strategy that takes economy or comprehensive energy efficiency level as a single optimization objective, this study ensures the best energy efficiency in real time during the whole voyage by realizing the prediction of real-time operating condition, and takes the speed deviation and EEOI deviation as the comprehensive objective function, which can reduce the EEOI and solve the possible delay of the ship caused by the drastic speed decrease. According to the bi-objective optimization model proposed in this study, a reasonable adjustment of the optimization target weights can substantially improve the overall comprehensive energy efficiency of the system on the premise of ensuring the speed deviation to a certain extent, thus, achieving the effect of energy saving and emission reduction.

5. Conclusions

In this paper, a hybrid electric ship energy efficiency optimization model considering time-varying environmental factors is proposed, which can optimize the EEOI for the ship in real time under wind and wave conditions, so that the optimized results are more in line with the actual sailing situation. Meanwhile, the speed and real-time EEOI are taken as the comprehensive optimization goals, which can ensure that the speed is limited during real-time optimization, so that it will not be excessively reduced and cause vessel duration delays. In this study, the proposed optimization method is verified by MATLAB simulation, and the results show that the fuel consumption per unit time of the target ship is reduced by an average of 13.4%, and the real-time EEOI is reduced by an average of 15.2%. Therefore, the speed optimization method proposed in this paper is a good energy efficiency practice, which has good reference value for the formulation of ship energy efficiency management strategies. At the same time, it also provides shipping companies with a new way for hybrid electric ships to reduce fuel consumption and reduce CO₂ emissions. At present, the energy efficiency management of hybrid electric ships is discussed, and further research can be made on the energy distribution after energy efficiency management in the future.