# Predicting Seagoing Ship Energy Efficiency from the Operational Data

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data Source and Data Preparation

^{−1}(normal continuous rating (NCR)), 85 min

^{−1}(required speed during charter navigation), and 75 min

^{−1}(economic speed above auxiliary blowers switching on pressure) at different loads of the main propulsion engine, resulting in approximately 54 million data points collected from the automation system (Table 1). To ensure repeatability and comparability of measurements, the cooling water temperature of the main propulsion machine is automatically controlled by a temperature controller at 89 °C, while the temperature of the lubricating oil is automatically controlled by a temperature controller between 45 °C and 47 °C.

#### 2.2. Evaluation Metrics

## 3. Results

## 4. Discussion

#### 4.1. The Analysis of the Influence of Input Variables on Prediction Accuracy

#### 4.2. The Selection of the Output Variables

_{c}of 0.9989, RMSE of 0.1542, and RAE 3.1917%.

_{CO2}is the mass of carbon dioxide (t), M

_{c}is the mass of the cargo carried (t), and d is the total distance (nm).

_{c}is the fuel consumption (t/hr), C

_{f}is the dimensionless coefficient for converting the consumption into the amount of CO

_{2}emitted, Mc is the mass of the transported cargo (t), and v is the speed of the ship (knot).

_{C}is fuel consumption (t) and FC

_{B}is initial or comparative fuel consumption. EnPI represents the difference (%) in fuel consumption according to a predetermined basic consumption. Results of $EnP{I}_{FC}$ prediction are equal to the results for main propulsion FOC alone.

_{C}of 0.9887, RMSE of 12.0096, and 9.4625% RAE. For classification purposes, SFOC is divided into four classes corresponding to the consumption according to the test drive results: a < 161, 161 ≤ b < 175, 175 ≤ c ≤ 189, d > 189. Classes can be optimized depending on the results comparison, such as the comparison with the targeted fuel consumption from the SEEMP, or the values measured on the factory test bench. The classification algorithm of the RF method built the model in 5.55 s with 17,962 out of 18,499, or 97.1% of, correctly classified instances, RMSE of 0.103, and the confusion matrix, as shown in the Appendix B, Table A2.

_{C}of 0.995, RMSE of 1.593, and 5.857% RAE. The apparent slip ratio for classification purposes is divided into four classes corresponding to the experimental data: a < 0, 0 ≤ b < 5, 5 ≤ c ≤ 10, d > 10. The RF classification algorithm built the model in 7.34 s with 16,933 out of 18,499, or 91.53% of, correctly classified instances, and RMSE of 0.1856. More information on the results of the classification can be seen in the confusion matrix (Appendix B, Table A3). Ship’s trim is used to optimize energy consumption, especially in larger vessels, where the energy savings are more significant (Figure 3). Trim is changed by ballasting or by longitudinally distributing the cargo within the ship cargo holds. In a period of 5 h, the ship’s trim was changed (by ballasting) from the initial 0 m to 1 m of immersion in the bow and back to 0 m. The ship was loaded with 48,394.6 MT of cargo, the weather conditions and the state of the sea did not change, and the control lever was set to 88 rpm and kept stable within 1 rpm. It can be concluded that the subject ship has a lower propulsion fuel consumption when the bow is immersed 1 m more than the stern.

_{C}of 0.9992, RMSE of 0.0499, and 2.2963% RAE. For classification, trim is divided into five classes corresponding to the limit values from experimental data: a < −1, −1 ≤ b < 0, 0 ≤ c < 1, 1 ≤ d ≤ 2, e > 2. As no measurements were recorded over the −1 m group (ship inclined longitudinally towards the bow over 1 m), the group was omitted from the classification evaluation table. The RF classification algorithm built the model in 4.09 s with 18,116 out of 18,499, or 97.93% of, correctly classified instances, and an RMSE of 0.0879. More information on the results of the classification can be seen in the confusion matrix (Appendix B, Table A4). The set ML model is capable of learning the trim on known data and adequately predicting trim that needs to be maintained in order to match the predicted consumption.

## 5. Conclusions

_{c}of 0.9989, RMSE of 0.1542, and RAE 3.1917%; main propulsion engine specific fuel oil consumption regression C

_{C}of 0.9887, RMSE of 12.0096, and RAE 9.4625%, and classification TPR 97.1% and RMSE of 0.103; ship’s slip regression C

_{C}of 0.995, RMSE of 1.593, and 5.857% RAE, and classification TPR 91.53% and RMSE of 0.1856; trim C

_{C}of 0.9992, RMSE of 0.0499, and 2.2963% RAE and classification TPR 97.93% and RMSE of 0.0879; need for reliquefication classification TPR 98.09% and RMSE of 0.103. It should be noted that the classification results are not fixed and vary depending on the number and type of classes.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

#### Overview of Used Machine Learning Methods

_{1}, y

_{1}),. . .,(x

_{n}, y

_{n})} with x ∈ Rd (d-dimensional input space) and y ∈ R, support vector tries to find the function f(x), which relates the measured input object to the desired output property of an object [25,24]. The parameters are learned using modifications to the Smola and Schölkopf’s SMO algorithm [26], which demands that the kernel matrix is computed and stored in memory. This requires large memory and involves expensive matrix operations such as Cholesky decomposition of a large submatrix of the kernel matrix [27]. Third, the coding of these algorithms is difficult. Therefore, using modifications to the SMO introduced by Shevade et al. significantly speeds up the SMO algorithm in most of the situations [28].

_{0}of the peak, and x represents the independent variable. The parameters $\sigma $ and $\omega $ control the half-width (also named Pearson width) and the tailing factor of the peak. The main reason to use the Pearson VII function for curve fitting is its flexibility to change, by varying the parameter $\omega $, from a Gaussian shape ($\omega $ approximates infinity). Compared to the commonly applied kernel functions, the use of the PUK has two main advantages: on the one hand, it does not require making a selection out of the kernel functions, which simplifies the model building process and saves computing time, and on the other hand, it has a stronger mapping power through which it can properly deal with a large variety of mapping problems.

## Appendix B

**Table A1.**The confusion matrix for main propulsion engine fuel oil consumption set as outlet variable.

Classified as | a | b | c | d | e |
---|---|---|---|---|---|

a = b | 3225 | 99 | 23 | 1 | 1 |

b = c | 104 | 6142 | 6 | 85 | 1 |

c = a | 12 | 3 | 6398 | 0 | 0 |

d = d | 0 | 120 | 4 | 2224 | 3 |

e = e | 2 | 1 | 2 | 14 | 29 |

**Table A2.**The confusion matrix for main propulsion engine specific fuel oil consumption set as outlet variable.

Classified as | a | b | c | d |
---|---|---|---|---|

a = c | 13,611 | 103 | 20 | 7 |

b = b | 130 | 1968 | 5 | 107 |

c = d | 29 | 7 | 310 | 15 |

d = a | 6 | 91 | 17 | 2073 |

Classified as | a | b | c | d |
---|---|---|---|---|

a = b | 6548 | 192 | 293 | 9 |

b = a | 286 | 1868 | 20 | 21 |

c = c | 288 | 29 | 5708 | 151 |

d = d | 11 | 22 | 244 | 2809 |

Classified as | a | b | c | d |
---|---|---|---|---|

a = e | 10,583 | 107 | 0 | 0 |

b = d | 73 | 1696 | 0 | 92 |

c = b | 0 | 0 | 207 | 20 |

d = c | 0 | 76 | 15 | 5630 |

Classified as | a | b | c |
---|---|---|---|

a = a | 6503 | 17 | 38 |

b = b | 80 | 600 | 118 |

c = c | 26 | 75 | 11,042 |

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**Figure 1.**Significance of individual variables (attributes) in the construction of random forest model.

**Figure 2.**(

**a**) Accurately classified instances (true positive rate (TPR)) and (

**b**) correlation coefficients (Cc) for regression.

No. | rpm (°/min) | Recording Start | Recording End | ||
---|---|---|---|---|---|

Latitude | Longitude | Latitude | Longitude | ||

1 | 87 | 9°30′59.19′′ | 311°30′27.36′′ | −2°15′47′′ | 72°7′4.76′′ |

2 | 82 | 19°21′15.06′′ | 252°59′6.36′′ | 29°26′3.25′′ | 264°56′7.43′′ |

3 | 86 | 29°26′3.25′′ | 264°56′3.45′′ | 23°21′27.48′′ | 180°40′20.4′′ |

4 | 79 | 23°36′35.64′′ | 179°48′55.26′′ | 35°9′43.68′′ | 129°28′12′′ |

5 | 77 | 34°30′24.24′′ | 129°3′44.46′′ | 23°35′16.14′′ | 179°50′17.58′′ |

6 | 73 | 23°24′39′′ | 180°33′23.88′′ | 12°1′51.9′′ | 237°55′41.1′′ |

7 | 86 | 21°54′55.5′′ | 113°12′43.02′′ | −4°49′34.44′′ | 325°16′18.24′′ |

No | Variable/Tag | Information/Unit |
---|---|---|

1 | Pickup11 | ME revolutions per minute (min^{−1}) |

2 | SFOC * | Specific fuel consumption (g/kWh) |

3 | ME_tot_FL * | ME total FO consumption (mT) |

4 | Nav_02 * | Ship’s speed over ground (knots) |

5 | Nav_04 | Wind speed from anemometer (knots) |

6 | Prop_slip * | Apparent slip ratio (%) |

7 | MSB0-TOT-LOAD * | Total load on busbars (kW) |

8 | MS114 | Ambient air temperature (°C) |

9 | MW014 | Sea water temperature (°C) |

10 | Trim in meters * | − fore, + aft (m) |

11 | List in degrees | (°) |

12 | Draft—mean | (m) |

No | Variable/Tag | Information/Unit |
---|---|---|

13 | ECDIS COG | course over ground (deg) |

14 | ECDIS wind direction | (deg) |

15 | Uwind | (m/s) |

16 | Vwind | (m/s) |

17 | Wind gust | (m/s) |

18 | Significant wave height | (m) |

19 | Wave direction | (°) |

20 | Wave period | (s) |

21 | Sea direction | (°) |

22 | Sea current speed | (m/s) |

23 | Sea | Douglas sea scale (DSS) (ship’s logbook) (the Douglas sea scale is a measure of the height of the waves and the state of the swell. The scale is expressed from 0 to 9)). |

24 | Swell | Douglas sea scale (ship’s logbook) (DSS) |

25 | Wind | Beaufort scale (Bft) (ship’s logbook) (the Beaufort scale is used to evaluate wind strength in the scale from 0 to 12)). |

Outcome | Actual (True/False) | |
---|---|---|

Predicted (positive/negative) | True positive (TP) | False positive (FP) |

False negative (FN) | True negative (TN) |

Regression Method | Correlation Coefficient (Cc) | Root Mean Square Error (RMSE) | Relative Absolute Error (RAE) (%) | Model Building Time (s) |
---|---|---|---|---|

Linear regression (GLM) | 0.8762 | 205.5833 | 36.8504 | 0.46 |

Multilayer perceptron (MLP) | 0.9907 | 58.3507 | 7.0284 | 120.53 |

Support vector machines (SVM) | 0.963 | 115.3915 | 2.2637 | 2012.82 |

Random forest (RF) | 0.9992 | 17.2632 | 2.304 | 6.03 |

No. | Input Variable | Unit | Groups | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | |||

1 | ME rpm | °/min | x | x | x | x | x | x | x | x | x | x | x |

5 | Wind speed | m/s | x | x | x | x | x | x | x | ||||

8 | Air temperature | °C | x | x | x | x | x | ||||||

9 | SW temperature | °C | x | x | x | x | |||||||

10 | Trim | m | x | x | x | ||||||||

11 | List | ° | x | x | |||||||||

12 | Draft—mean | m | x | ||||||||||

13 | COG | ° | x | x | x | x | x | x | |||||

14 | Wind direction | ° | x | x | x | x | x | x | x | ||||

15 | Uwind | m/s | x | x | x | x | x | x | x | x | x | ||

16 | Vwind | m/s | x | x | x | x | x | x | x | x | x | ||

17 | Wind gust | m/s | x | x | x | x | x | x | x | x | x | ||

18 | Significant wave height | m | x | x | x | x | x | x | x | x | x | ||

19 | Wave direction | ° | x | x | x | x | x | x | x | x | x | ||

20 | Wave period | s | x | x | x | x | x | x | x | x | x | ||

21 | Sea direction | ° | x | x | x | x | x | x | x | x | x | ||

22 | Sea current speed | m/s | x | x | x | x | x | x | x | x | x | ||

23 | Sea (ship’s logbook) | DSS | x | x | x | x | x | x | x | x | x | ||

24 | Swell (ship’s logbook) | DSS | x | x | x | x | x | x | x | x | x | ||

25 | Wind (ship’s logbook) (Bft) | Bft | x | x | x | x | x | x | x | x | x | ||

Total number of variables entering the prediction model | 1 | 4 | 9 | 12 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |

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**MDPI and ACS Style**

Vorkapić, A.; Radonja, R.; Martinčić-Ipšić, S. Predicting Seagoing Ship Energy Efficiency from the Operational Data. *Sensors* **2021**, *21*, 2832.
https://doi.org/10.3390/s21082832

**AMA Style**

Vorkapić A, Radonja R, Martinčić-Ipšić S. Predicting Seagoing Ship Energy Efficiency from the Operational Data. *Sensors*. 2021; 21(8):2832.
https://doi.org/10.3390/s21082832

**Chicago/Turabian Style**

Vorkapić, Aleksandar, Radoslav Radonja, and Sanda Martinčić-Ipšić. 2021. "Predicting Seagoing Ship Energy Efficiency from the Operational Data" *Sensors* 21, no. 8: 2832.
https://doi.org/10.3390/s21082832