The target ship is a 6,800TEU container, which is driven by one 69MW MAN B&W diesel engine and consists of four 3,000kW generators. The specifications of the target ship are shown in Table 1.

We used data measured at an interval of 10 minutes from 2014.11 to 2015.12. The data used is shown in Table 2.

The power consumption of a ship depends on the operation mode and environment of the ship. The operation mode of the ship is divided into voyage, entry and departure, and anchoring, and the equipment used in the ship differs according to each operation mode. For example, a large amount of power is consumed with the use of the bow thruster and winch for entry, and departure. Therefore, in this study, we divide the measurement data into the integer data of 0~2 depending on the operation mode of the ship. In addition, the external environment of the ship affects the main engine and how each device operates. This is because the parallel operation of equipment or cascade control under low loads is utilized as the environment outside the ship changes. In this study, we use the values such as the wind speed, wind angle, and water speed in Table 2 as the external environmental data that is used as training data. Since the use of the main engine affects the use of the air compressor and auxiliary blower, this can represent the load of the main engine by utilizing the vessel speed and the Revolution Per Minute (RPM) of a main engine. Therefore, we use the operation mode, external environment, and the load of main engine of the ship as the XGBoost and LGBM models.

XGBoost applies the boosting technique to the decision tree model. The boosting technique is an algorithm that produces robust models with the capability of complex prediction by combining weak models suitable for simple classification. After training the given data through the weak classifier, we can reduce errors by training the errors present in the trained result through another weak classifier.

XGBoost gives high scores to the tree model of high importance by assigning different weights to each model when integrating the models through the boosting technique. The weight of the previous model depends on the current error. The objective function for training consists of the loss function and normalization term between the true and predicted values, and the model is trained by obtaining the weight that minimizes this objective function.

LGBM is an algorithm for improving low efficiency and scalability when the data of the high dimensional variable of the conventional gradient boosting technique is large, and uses GOSS and a new algorithm called EFB. GOSS takes configuration that data entities with large gradients can play an essential role in calculating information acquisition by excluding data with small gradients among data entities. Therefore, GOSS can estimate information acquisition very accurately even with a small amount of data. EFB binds mutually exclusive variables through the greedy algorithm to reduce the number of variables. Therefore, it can effectively reduce the number of variables without significantly compromising the accuracy of split point determination.

A hyperparameter usually refers to a variable that is directly tuned by the user when training any arbitrary model in machine learning. The optimized hyperparameter will change depending on the given data. Therefore, it can be determined by experience or confirmed through various search methods.

Table 3 shows the major hyperparameters by model. In this study, we optimize the prediction models by adjusting the key hyperparameters in Table 3.

The following is the description of the hyperparameters in Table 3.

• ‣ colsample_bytree: When training a tree, we do not use all training data, but only some of the data randomly extracted based on the column. This improves performance by reducing overfitting.
• ‣ subsample: When training a tree, we do not use all training data, but only some of the data randomly extracted based on the row. This improves performance by reducing overfitting.
• ‣ max_depth: We specify the maximum tree depth in the process of forming the tree model. A small value causes underfitting while a large one causes overfitting.
• ‣ n_estimators: It refers to the number of trees. Since increasing the value adds more trees to the ensemble, the complexity of the model increases. Therefore, the probability of correcting errors in training goes up. However, the large value means more memory and longer training time.
• ‣ gamma: It is a hyperparameter used for XGBoost, which limits the complexity of the tree model. If the value is large, the tree model does not create many leaf nodes easily.
• ‣ min_split_gain: It is a hyperparameter used for LGBM, and plays the same role as the gamma of XGBoost.
• ‣ num_leaves: It is a hyperparameter used in LGBM. It refers to the number of leaves of the entire tree, and is the main parameter that limits the complexity of the tree model. The large value improves accuracy but can lead to overfitting.

Hyperparameters are used to enhance prediction models, and is a variable that must be set directly by the user. The hyperparameters are not theoretically determined but must be set empirically. Finding optimal hyperparameter is essential for building high-performance prediction models.

There are three widely-known optimization methods of hyperparameters. That is, grid search, random search, and Bayesian optimization are typical methods. In this paper, we optimize hyperparameters using the grid search.

The grid search is a method of dividing hyperparameters into grids and then checking the model performance for all grid points. When searching hyperparameters in a grid form, a relatively even and global search is possible. However, if the gap is too tight or the number of hyperparameters increases, there is a drawback that the search time increases.

In this study, we use the grid search for hyperparameter optimization. To optimize hyperparameters, it is important to adjust the variables in Table 3 in order. We adjust variables in the order of colsample_bytree, subsample, gamma, max_depth, n_estimators. After adjusting the variables, we select the variable with the smallest Root Mean Square Error (RMSE).

3.3.3 gamma adjustment

gamma limits the complexity of the tree model, and is initially set to 0. While changing the gamma value from 0.4~0.8 by 0.1 with the colsample_bytree and subsample values fixed to 0.7, we verify RMSE using the validation function. Figure 1 shows the validation results according to the change of the gamma value. The results show that RMSE was the lowest with 0.10986 at the gamma value of 0.7.

Figure 1: 
score of gamma in XGBoost

3.3.4 max_depth

max_depth specifies the maximum tree depth, and is initially set to -1. While changing the max_depth value from 5~9 by 1 with the colsample_bytree, subsample and gamma values fixed to 0.7, we verify RMSE using the validation function. Figure 2 shows the validation results according to the change of the max_depth value. The results show that RMSE was the lowest with 0.1095133 at the max_depth value of 8.

Figure 2: 
score of max_depth in XGBoost

3.3.5 n_estimators

n_estimators refers to the number of trees, and is initially set to 100. While changing the n_estimators value from 95~99 by 1 with the colsample_bytree, subsample and gamma values fixed to 0.7 and the max_depth value to 8, we verify RMSE using the validation function. Figure 3 shows the validation results according to the change of the n_estimators value. The results show that RMSE was the lowest with 0.1094432 at the n_estimators value of 97.

Figure 3: 
score of n_estimators in XGBoost

LGBM also uses the grid search method just like the optimization of XGBoost. colsample_bytree, subsample, max_depth, and n_estimators are the same as XGBoost but min_split_gain and num_leaves are different. Thus, the grid search order of LGBM is different from that of XGBoost. The variable optimization order of LGBM is colsample_bytree, subsample, min_split_gain, max_depth, n_estimators, and num_leaves. Just like XGBoost, the validation function used for optimizing variables uses the k-fold cross-validation provided by the scikit-learn library.

3.4.2 min_split_gain

min_split_gain plays the same role as the gamma of XGBoost, and limits the complexity of the tree model. It is initially set to 0. While changing the min_split_gain value with the colsample_bytree and subsample values fixed to 0.7, we verify RMSE. Figure 4 shows the results of the validation function according to the change of the min_split_gain value. The results show that RMSE was the lowest with 0.1096191 at the min_split_gain value of 0.8.

Figure 4: 
score of min_split_gain in LGBM

3.4.3 num_leaves

num_leaves adjusts the number of leaves in the entire tree, and limits the complexity of the tree model. It is initially set to 31. While changing the num_leaves value from 7~11 by 1 with the colsample_bytree and subsample values fixed to 0.7 and the min_split_gain value to 0.8, we verify RMSE. Figure 5 shows the validation function results according to the change of the num_leaves value. The results show that RMSE was the lowest with 0.1095569 at the num_leaves value of 9.

Figure 5: 
score of num_leaves in LGBM

3.4.4 n_estimators

n_estimators refers to the number of trees, and is initially set to 100. While changing the n_estimators value with the colsample_bytree, subsample values fixed to 0.7, the min_split _gain value to 0.8, and the num_leaves value to 9, we verify RMSE using the validation function. Figure 6 shows the validation function results according to the change of the n_estimators value. The results show that RMSE was the constant with 0.1095569. Therefore, we use the initial setting value of 100.

Figure 6: 
score of n_estimators in LGBM

3.4.5 max_depth

max_depth specifies the maximum tree depth, and is initially set to -1. While changing the max_depth value from 1~5 by 1 with the colsample_bytree and subsample values fixed to 0.7, the min_split _gain to 0.8, the num_leaves to 9, and the n_estimators to 100, we verify RMSE using the validation function. Figure 7 shows the validation function results according to the change of the max_depth value. The results show that RMSE was the lowest with 0.1093323 at the max_depth value of 4.

Figure 7: 
score of max_depth in LGBM

To validate the models with optimized hyperparameters, we use RMSE that represents the difference between the predicted and actual values of the models, MAPE that can solve the drawbacks of size-dependent errors, and MASE that can represent the difference between the predicted and actual values as the mean variation.

In Equation (1), yl^ refers to a predicted value, y_i to an actual value, and n to the number of data.

In Equation (2), F_t refers to a predicted value, A_t to an actual value, and n to the number of data.

In Equation (3), e_j refers to the j_th error value, J to the number of predictions, Y_t to an actual value, and T to the number of data.

Furthermore, in order to increase the reliability of the model, we configure it to verify the accuracy of the model according to the amount of the training data by changing the amount of the training data to 20%, 40%, 60%, 80%.

Figure 11 and 12 show graphs comparing the training results using XGBoost and LGBM with the actual power data, respectively. As shown in the graphs and the evaluation of the models described in Section 4.2, the errors of the two models are not significantly different.

Figure 11: 
Comparison of data between real and predicted val-ues (XGBoost)

Figure 12: 
Comparison of data between real and predicted values (LGBM)