A Ship Route Planning Method under the Sailing Time Constraint
Abstract
:1. Introduction
2. Dynamic Sea Environment Model
2.1. Three-Dimensional Sea Environment Model
- The ship should navigate in an area with sufficient water depth.
- The ship should not sail in dangerous wind and wave conditions.
- The route plan should consider dynamic meteorological and sea conditions for long-distance and long-term navigation.
2.2. Binarization of Navigation Area
3. Predictive Model for Ship Parameters
3.1. Pre-Processing of Data
- Remove anomalous records in which data are incomplete, such as missing latitude and longitude data.
- To reduce the complexity of the artificial neural network mentioned later, the absolute directions of weather are converted to the directions to the ship reference frame:
- According to this method [40], extract sequential records of approximately 10 min and combine them into one segment.
- Calculate the mean value of each type of data in a segment.For data that are not measured as angles, the mean for the N data points in a segment with values is computed byFor data that are measured as angles, the mean is computed by
- Calculate the standard error of the mean of each type of data in a segment. The standard error of the mean is computed byFor data not measured as angles, the difference is computed byFor data measured as angles, the difference is computed by
- Two thresholds are used to delete segments in which the standard error of the mean of certain data is too large. In particular, if the of RPM is greater than 3 min or the of SOG is greater than 0.5 kt, then all records in that segment are deleted. After this operation, several uniform sailing segments are obtained.
- We use Chauvenet’s criterion to determine if data are anomalous in each uniform sailing segment. Once a data point is identified as an outlier based on the criterion, it is removed. A new mean and standard error of the mean can be calculated based on the remaining values and the new sample size.The probability for the occurrence of any is computed byA datum is considered an outlier if Formula (10) is fulfilled.This method cleans the original voyages’ records to obtain several navigation segments with a duration of about 10 min and a uniform speed. The mean values of these segments’ data can be used for subsequent training and prediction of the model.
- The different types of input data have different units. It would reduce the performance and convergence of the predictive model if the filtered data of the segments were input into the neural network directly. Therefore, the z-score standardization method is adopted to standardize the data:
3.2. Predictive Model for Ship Parameters
3.2.1. Structure of the Predictive Model
3.2.2. Error Back-Propagation Algorithm
3.3. Selection of Model Variables
- They can represent the current navigation state or navigation environment of the ship.
- They can be obtained or predicted in some way in the route planning process.
- How the data are obtained or predicted cannot be too complex or take up too much running time.
4. Co-Optimization of Ship Course and Speed
4.1. Speed Configuration
5. Weather Route Optimization for Ships with Sailing Time Constraints
5.1. A* Algorithm
- The two-dimensional A* algorithm takes distance as the evaluation criterion. At the same time, ship fuel consumption and navigation time are the main factors to evaluate the navigation cost of a route, and taking distance as the evaluation criterion cannot accurately quantify the navigation cost.
- The two-dimensional A* algorithm does not consider speed. In contrast, the ship does not sail at a fixed speed over the whole voyage; dynamically adjusting speed according to the sea state is desirable.
- The two-dimensional A* algorithm does not consider dynamic unnavigable areas with heavy winds and waves, which will affect the safety and efficiency of the voyage.
5.2. Evaluation Functions Concerning Time and Fuel Consumption
5.3. Customized A* Algorithm with Time Constraint
- Initialize (the set of ext-nodes to be checked) and (the set of ext-nodes checked).
- All ext-nodes belonging to the start node S are added to the , and their and are set to 0, while the and are calculated and recorded.
- If it is judged that the is not empty, the operation goes to Step 4; otherwise, there is no solution to this problem, which means no available path exists between S and T, and the procedure is terminated.
- The total navigation time of each ext-node in the is calculated. If the total navigation time of one ext-node is greater than the pre-set ETA, the node is retained in the but will not be executed in the rest of this step. Then, the ext-node with the minimum fuel consumption of the whole voyage is found in these nodes which meet the time limit. And the ext-node will be removed from the and added into the , setting the SOG record to .
- Traverse all the adjacent nodes of the navigation node i. There are two situations for the ext-nodes of these adjacent nodes:
- If there is no ext-node of the adjacent node j in and , all ext-nodes of node j are added to , the G and H value of these ext-nodes are calculated and recorded, and the parent node of these ext-nodes is set as node .
- If there is an ext-node of the adjacent node j in the , and the and values of calculated in this step are both smaller than those stored in the , the G and H values of in the will be updated correspondingly in this step. Also, the ext-node ’s parent node is set as node . Conversely, all information of the ext-node stored in will remain unchanged.
- Check whether there is any ext-node in that is subordinate to the end node T. If not, repeat Step 3; if it already exists, a path composed of ext-nodes is found by querying the parent node of the current ext-node step by step until the starting node. The sailing route and speed configuration are obtained after mapping like in Section 4.1.
- The weather forecast data and navigation data at each ext-node on the route are extracted based on the waypoint sequence and speed configuration. Then, the RPM prediction model is called, and the above data are modified as the input of the prediction model to calculate the recommended RPM of each ext-node on the route. Then, the RPM recommendation scheme is output for the whole voyage.
5.4. Overall Optimization Flow
- The historical data processing part uses historical ship voyage records and corresponding meteorological historical data, etc. These data are standardized by pre-processing data methods, and the pre-processed data are used as input for the ship parameter prediction models.
- The ship parameter prediction model part is used to build two artificial neural network models with the same frame. The input contains eight variables: SOG, fore draft, aft draft, course, wind speed, wind direction, wave height, and wave direction; the output is fuel consumption rate or RPM. The trained models are used for calculating fuel consumption rate and RPM in the voyage afterward.
- The ship navigation data processing part obtains and divides the ship’s characteristics and the weather forecast data into eight input variables which meet the requirements of the ship parameter prediction model and are used in the route planning process afterward.
- The ship route optimization part is based on the customized A* algorithm, using the ship fuel consumption rate prediction model and the current sailing data to calculate the fuel consumption for all nodes to be checked in order to find the node with the minimum fuel consumption that satisfies the ETA constraint and thus obtain the optimal ship route. Finally, the RPM recommendation scheme for the whole range is obtained based on the sailing data and the generated route.
6. Simulation Experiment and Results Analysis
6.1. Performance Analysis of Ship Parameter Prediction Models
6.2. Simulation Experiment of Ship Weather Route Optimization System
6.2.1. Scenario 1: Voyage from Osaka to Los Angeles on 3 February 2021
6.2.2. Scenario 2: Voyage from Tainan to Los Angeles on 17 January 2021
6.2.3. Computational Complexity of This Method
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Parameter | Value |
---|---|
Ship type | Container ship |
Displacement (t) | 169,700 |
Length (m) | 348 |
Beam (m) | 51.2 |
Draft (m) | 13.5 |
Pitch (mm) | 8668 |
Parameters | Value |
---|---|
Number of neurons in hidden layer of fuel consumption rate model | 45 |
Number of neurons in hidden layer of RPM model | 140 |
Activation function of the hidden layer | Relu |
Optimizer | Levenberg–Marquardt |
Parameters | Value |
---|---|
Start | 35.5 N, 141 E |
End | 34 N, 120 W |
SOG range (knot) | [8, 19] |
Maximum allowable wind speed (m/s) | 20 |
Maximum allowable wave height (m) | 6 |
Minimum draught (m) | 14 |
Time (h) | Danger Time (h) | |
---|---|---|
Optimized route | 367.15 | 0 |
Great circle route | 361.38 | 26.26 |
Time (h) | FOC (t) | |
---|---|---|
Optimized route | 408.69 | 1674.27 |
Historical route | 404.34 | 1805.20 |
Computational Time (s) | Data Size (MB) | |
---|---|---|
Scenario 1 | 991.917 | 1.10 |
Scenario 2 | 731.639 | 1.04 |
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Li, Y.; Cui, J.; Zhang, X.; Yang, X. A Ship Route Planning Method under the Sailing Time Constraint. J. Mar. Sci. Eng. 2023, 11, 1242. https://doi.org/10.3390/jmse11061242
Li Y, Cui J, Zhang X, Yang X. A Ship Route Planning Method under the Sailing Time Constraint. Journal of Marine Science and Engineering. 2023; 11(6):1242. https://doi.org/10.3390/jmse11061242
Chicago/Turabian StyleLi, Yuankui, Jinlong Cui, Xinyu Zhang, and Xuefeng Yang. 2023. "A Ship Route Planning Method under the Sailing Time Constraint" Journal of Marine Science and Engineering 11, no. 6: 1242. https://doi.org/10.3390/jmse11061242
APA StyleLi, Y., Cui, J., Zhang, X., & Yang, X. (2023). A Ship Route Planning Method under the Sailing Time Constraint. Journal of Marine Science and Engineering, 11(6), 1242. https://doi.org/10.3390/jmse11061242