CN115600311A - Ship trim optimization method and system - Google Patents

Ship trim optimization method and system Download PDF

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CN115600311A
CN115600311A CN202211151944.XA CN202211151944A CN115600311A CN 115600311 A CN115600311 A CN 115600311A CN 202211151944 A CN202211151944 A CN 202211151944A CN 115600311 A CN115600311 A CN 115600311A
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ship
target
trim
determining
optimization
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秦尧
房新楠
樊翔
黄建涛
侯良生
汤瑾璟
顾一清
李鑫
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Shanghai Merchant Ship Design and Research Institute
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Abstract

The invention provides a ship trim optimization method and a system, comprising the following steps: determining a target navigational speed, a target draught and a target sea state of the ship for trim optimization based on the navigation plan; inputting the target navigational speed, the target draft and the target sea state into a pre-trained trim optimization mathematical model, and outputting a plurality of trimmings of the ship and a plurality of corresponding host powers; the trim optimization mathematical model is obtained by taking operation data acquired during the actual ship navigation of the ship as a training set and a verification set and taking preset environment variables and ship parameters as training parameters for training; the environmental variable includes wave height; determining the trim corresponding to the main machine power with the minimum power in the plurality of trimmings and the plurality of main machine powers as a target trim; the current trim of the vessel is adjusted based on the target trim. Based on the operation data acquired during the actual ship navigation, the method for obtaining the pitch optimization scheme with the minimum power by sending the operation data to the pitch optimization mathematical model improves the accuracy of the pitch optimization scheme.

Description

Ship trim optimization method and system
Technical Field
The invention relates to the technical field of ships, in particular to a ship trim optimization system method and system.
Background
With the development of intelligent ships, more and more software related to ship energy conservation optimization follows. Among them, the trim optimization has received much attention as a core function of the energy saving optimization. Corresponding programs are developed by software which emphasizes the improvement of the operating energy efficiency of the ship at home and abroad, and the energy efficiency is improved by optimizing the trim of the ship.
The common method for saving energy through trim optimization of a ship comprises the steps of calculating energy consumption of the ship through a traditional empirical formula and further adjusting trim of the ship, wherein operation data used for calculating the energy consumption of the ship in the method are obtained through numerical simulation calculation under still water, and the problems that the accuracy of simulation operation data is low, the error is large, and the accuracy of a trim optimization result is difficult to guarantee exist.
Disclosure of Invention
In view of this, the present invention provides a method and a system for optimizing a trim of a ship, which are based on operational data acquired during a real ship voyage period, and obtain a trim optimization scheme with minimum power by sending the operational data to a trim optimization mathematical model, thereby improving accuracy of the trim optimization scheme.
In a first aspect, an embodiment of the present invention provides a ship trim optimization method, including: determining a target navigational speed, a target draft and a target sea state of the ship based on the navigation plan; inputting the target navigational speed, the target draft and the target sea state into a pre-trained trim optimization mathematical model, and outputting a plurality of trimmings of the ship and a plurality of corresponding host powers; the trim optimization mathematical model is obtained by taking operation data acquired during the actual ship navigation of the ship as a training set and a verification set and taking preset environment variables and ship parameters as training parameters; the environmental variables include wave height; determining a trim corresponding to a main machine power with the minimum power in the plurality of trimmings and the plurality of main machine powers as a target trim; the current trim of the vessel is adjusted based on the target trim.
Further, after the step of adjusting the current trim of the vessel based on the target trim, the method further comprises: determining an initial trim of the vessel based on the target draft; determining initial host power corresponding to the initial trim based on the plurality of trimmings and the plurality of host powers; and calculating the trim optimization rate of the ship based on the initial host power and the host power with the minimum power, and taking the trim optimization rate as an energy-saving index of the trim optimization method.
Further, the creating step of the pitch optimization mathematical model comprises the following steps: acquiring operation data of a ship during sailing; selecting data of ships belonging to constant-speed straight line navigation in the operational data as a training set, and training a plurality of preset mathematical models; selecting operation data under different ship types and sea conditions from the operation data as a verification set, and calculating respective parameter errors of the trained mathematical models based on the verification set; sea state includes the mean value of the mean wave height of the flight line; the parameter errors comprise average absolute error, mean square error and root mean square error; determining the mathematical model corresponding to the minimum parameter error in the calculated parameter errors as a trim optimization mathematical model of the ship; wherein the operational data comprises environmental variables and vessel parameters; the environment variables are meteorological forecast data, and the meteorological forecast data comprise wind speed, wind direction, flow speed, flow direction, wave height, wave direction and wave period; the ship parameters comprise ship measurement data, and the ship measurement data comprise ship type, water depth, draft, trim, navigational speed, host power, host rotating speed, slewing rate and host oil consumption.
Further, the mathematical models include an integrated regression model of the tree, a K-nearest neighbor regression model, and a random forest model.
Further, in selecting the operation data, the data that the ship belongs to the constant speed straight line navigation is taken as a training set, and the step of training a plurality of mathematical models comprises the following steps: using operation data with water depth larger than 100 meters as a first training set; determining operation data that the standard deviation of the host power in the first training set is smaller than a first preset standard deviation and the standard deviation of the slew rate is smaller than a second preset standard deviation as a second training set; and taking the wave height, the draught and the navigational speed in the second training set as input, taking the trim and the corresponding host power as output, and training the tree integration regression model, the K neighbor regression model and the random forest model.
Further, the step of obtaining the target navigational speed of the ship comprises: determining departure time, arrival time and voyage of the ship based on the voyage plan; based on the range, departure time and arrival time, the average speed of the ship is calculated, and the average speed is determined as the target speed.
Further, the step of obtaining the target sea state comprises: determining a course of the ship and a segmentation waypoint of the course based on the navigation plan; determining the wave height of the split waypoints when the ship reaches each split waypoint based on the weather forecast database and the target speed; and calculating the average wave height on the route based on the wave heights of the plurality of split route points, and determining the average wave height as a target sea state.
In a second aspect, an embodiment of the present invention provides a ship trim optimization system, including: the data acquisition module is used for determining a target navigational speed, a target draft and a target sea state of the ship based on the navigation plan; the range determining module is used for inputting the target navigational speed, the target draft and the target sea state into a pre-trained trim optimization mathematical model and outputting a plurality of trimmings of the ship and a plurality of corresponding host powers; the trim optimization mathematical model is obtained by taking operation data acquired during the actual ship navigation of the ship as a training set and a verification set and taking preset environment variables and ship parameters as training parameters for training; the environmental variables include wave height; the target pitch determining module is used for determining the pitch corresponding to the host power with the minimum power in the plurality of pitches and the plurality of host powers as the target pitch; a trim optimization module to adjust a current trim of the vessel based on the target trim.
In a third aspect, an embodiment of the present invention provides an electronic device, which includes a memory and a processor, where the memory stores a computer program that is executable on the processor, and the processor implements the method described above when executing the computer program.
In a fourth aspect, the embodiments of the present invention provide a computer-readable storage medium, on which a computer program is stored, where the program code causes the processor to execute the method described above.
The embodiment of the invention provides a ship trim optimization method and a system, which comprise the following steps: determining a target navigational speed, a target draught and a target sea state of the ship for trim optimization based on the navigation plan; inputting the target navigational speed, the target draft and the target sea state into a pre-trained trim optimization mathematical model, and outputting a plurality of trimmings of the ship and a plurality of corresponding host powers; the trim optimization mathematical model is obtained by taking operation data acquired during the actual ship navigation of the ship as a training set and a verification set and taking preset environment variables and ship parameters as training parameters for training; the environmental variable includes wave height; determining a trim corresponding to a main machine power with the minimum power in the plurality of trimmings and the plurality of main machine powers as a target trim; the current trim of the vessel is adjusted based on the target trim. In the method, the operating data are sent to the trim optimization mathematical model to obtain the trim optimization scheme with the minimum power, so that the accuracy of the trim optimization scheme is improved, and the energy conservation of the ship is improved; meanwhile, the wave height is increased in the environment variable, so that the rationality of the pitching optimization is improved.
Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings.
In order to make the aforementioned and other objects, features and advantages of the present invention comprehensible, preferred embodiments accompanied with figures are described in detail below.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the embodiments or the prior art descriptions will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings can be obtained by those skilled in the art without creative efforts.
Fig. 1 is a flowchart of a ship trim optimization method according to an embodiment of the present invention;
fig. 2 is a flowchart for acquiring a target speed of a ship according to a first embodiment of the present invention;
fig. 3 is a flowchart of obtaining a target sea state according to an embodiment of the present invention;
FIG. 4 is a flowchart illustrating a creation process of a pitch optimization mathematical model according to an embodiment of the present invention;
fig. 5 is a schematic view of a ship trim optimization system provided in the second embodiment of the present invention.
Icon: 1-a data acquisition module; 2-a range determination module; 3-a target pitch determination module; 4-trim optimization module.
Detailed Description
To make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings, and it is apparent that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, belong to the protection scope of the present invention.
For the understanding of the present embodiment, the following detailed description will be given of the embodiment of the present invention.
The first embodiment is as follows:
fig. 1 is a flowchart of a ship trim optimization method according to an embodiment of the present invention.
Referring to fig. 1, a ship trim optimization method includes:
and S101, determining a target navigational speed, a target draft and a target sea state of the ship for trim optimization based on the navigation plan.
Here, the target draft is set according to the ship parameters.
In an embodiment, referring to fig. 2, the step of acquiring the target speed of the ship in step S101 includes:
step S201, determining departure time, arrival time and voyage of the ship based on the voyage plan.
And S202, calculating the average navigational speed of the ship based on the course, the departure time and the arrival time, and determining the average navigational speed as the target navigational speed.
Here, the first and second liquid crystal display panels are,
Figure BDA0003856794610000051
in an embodiment, referring to fig. 3, the step of acquiring the target sea state in step S101 includes:
step S301, determining the course of the ship and the segmentation waypoints of the course based on the navigation plan.
Step S302, determining the wave height of the split waypoints when the ship reaches each split waypoint based on the weather forecast database and the target speed.
And searching the wave height of the whole route through a weather forecast database so as to determine the wave height of the split route point of the ship.
Step S303, calculating the average wave height on the route based on the wave heights of the plurality of split route points, and determining the average wave height as a target sea state.
Here, the average wave height is an average value of all the split waypoint wave heights.
Step S102, inputting a target navigational speed, a target draft and a target sea state into a pre-trained trim optimization mathematical model, and outputting a plurality of trimmings of the ship and a plurality of corresponding host powers; the trim optimization mathematical model is obtained by taking operation data acquired during the actual ship navigation of the ship as a training set and a verification set and taking preset environment variables and ship parameters as training parameters for training; the environmental variable includes a wave height.
In an embodiment, referring to fig. 4, the creating step of the pitch optimized mathematical model in step S102 includes:
step S401, operation data during the ship voyage is acquired.
The operation data is acquired by a real ship navigation device of the ship and comprises environment variables and ship parameters; the environment variables are meteorological forecast data, and the meteorological forecast data comprise wind speed, wind direction, flow speed, flow direction, wave height, wave direction and wave period; the ship parameters comprise ship measurement data, and the ship measurement data comprise ship type, water depth, draft, trim, navigational speed, host power, host rotating speed, slewing rate and host oil consumption.
And S402, selecting the data of the ship belonging to the constant-speed straight line navigation in the operation data as a training set, and training a plurality of preset mathematical models.
Here, the mathematical models include an Extra Trees Regressor (tree integrated regression model), knoeghbors Regressor (K neighbor regression model), and Random Forest Regressor (Random Forest model).
In an embodiment, in step S402, selecting, as a training set, data of a ship that belongs to a constant-speed straight line voyage from operation data, and training a plurality of mathematical models, includes:
and taking the operation data with the water depth of more than 100 meters as a first training set.
Here, to avoid the shallow water effect, the operation data with water depth greater than 100m is learned as the first training set.
And determining the operation data that the standard deviation of the host power in the first training set is smaller than a first preset standard deviation and the standard deviation of the slew rate is smaller than a second preset standard deviation as a second training set.
Here, the first preset standard deviation and the second preset standard deviation are set according to actual conditions. The data in the second training set are the operation data of the ship with the constant-speed linear course.
And taking the wave height, the draught and the navigational speed in the second training set as input, taking the trim and the corresponding host power as output, and training the integrated regression model, the K nearest neighbor regression model and the random forest model of the tree.
Step S403, selecting operation data under different ship types and sea conditions from the operation data as a verification set, and calculating respective parameter errors of the trained mathematical models based on the verification set; sea state includes the mean value of the mean wave height of the flight line; the parameter errors include mean absolute error, mean square error, and root mean square error.
After a plurality of mathematical models are trained, the three mathematical models are newly verified through a verification set according to the ship type and the meteorological characteristics of the sea area.
And S404, determining the mathematical model corresponding to the minimum parameter error in the calculated parameter errors as the trim optimization mathematical model of the ship.
Here, a model in which MAE (mean absolute error), MSE (mean square error), and RMSE (root mean square error) are all the smallest is selected as the ship's trim optimization mathematical model.
In step S103, the pitch corresponding to the host power having the smallest power among the plurality of pitches and the plurality of host powers is determined as the target pitch.
Here, among the plurality of pitches and the plurality of corresponding main machine powers, the pitch corresponding to the main machine power having the smallest power is selected as the target pitch.
Step S104, adjusting the current trim of the ship based on the target trim.
In an embodiment, after the step of adjusting the current trim of the vessel based on the target trim, the method further comprises:
based on the target draft, an initial trim of the vessel is determined.
Based on the plurality of pitches and the plurality of host powers, an initial host power corresponding to the initial pitch is determined.
And calculating the trim optimization rate of the ship based on the initial host power and the host power with the minimum power, and taking the trim optimization rate as an energy-saving index of the trim optimization method.
Here, the first and second liquid crystal display panels are,
Figure BDA0003856794610000081
the pitch optimization rate is in the range of 0 to 100%.
The embodiment of the invention provides a ship trim optimization method, which comprises the following steps: determining a target navigational speed, a target draught and a target sea state of the ship for trim optimization based on the navigation plan; inputting the target navigational speed, the target draft and the target sea state into a pre-trained trim optimization mathematical model, and outputting a plurality of trimmings of the ship and a plurality of corresponding host powers; the trim optimization mathematical model is obtained by taking operation data acquired during the actual ship navigation of the ship as a training set and a verification set and taking preset environment variables and ship parameters as training parameters; the environmental variable includes wave height; determining a trim corresponding to a main machine power with the minimum power in the plurality of trimmings and the plurality of main machine powers as a target trim; the current trim of the vessel is adjusted based on the target trim. In the mode, the trim optimization scheme of the ship is determined based on the real ship operation data and the actual marine environment, so that the accuracy and the practicability of the trim optimization scheme are improved.
Example two:
fig. 5 is a schematic view of a ship trim optimization system provided in the second embodiment of the present invention.
Referring to fig. 5, the ship trim optimization system includes:
and the data acquisition module 1 is used for determining the target navigational speed, the target draught and the target sea state of the ship for the trim optimization based on the navigation plan.
The range determining module 2 is used for inputting the target navigational speed, the target draft and the target sea state into a pre-trained trim optimization mathematical model and outputting a plurality of trimmings of the ship and a plurality of corresponding host powers; the trim optimization mathematical model is obtained by taking operation data acquired during the actual ship navigation of the ship as a training set and a verification set and taking preset environment variables and ship parameters as training parameters for training; the environmental variable includes a wave height.
And a target pitch determining module 3 configured to determine, as the target pitch, a pitch corresponding to a host power having a smallest power among the plurality of pitches and the plurality of host powers.
And a trim optimization module 4 for adjusting the current trim of the vessel based on the target trim.
The embodiment of the invention provides a ship trim optimization system, which comprises: determining a target navigational speed, a target draft and a target sea state of the ship based on the navigation plan; inputting the target navigational speed, the target draft and the target sea state into a pre-trained trim optimization mathematical model, and outputting a plurality of trimmings of the ship and a plurality of corresponding host powers; the trim optimization mathematical model is obtained by taking operation data acquired during the actual ship navigation of the ship as a training set and a verification set and taking preset environment variables and ship parameters as training parameters; the environmental variable includes wave height; determining a trim corresponding to a main machine power with the minimum power in the plurality of trimmings and the plurality of main machine powers as a target trim; the current trim of the vessel is adjusted based on the target trim. In the mode, the operating data are sent to the trim optimization mathematical model to obtain the trim optimization scheme with the minimum power, so that the accuracy of the trim optimization scheme is improved.
The embodiment of the present invention further provides an electronic device, which includes a memory, a processor, and a computer program stored in the memory and capable of running on the processor, and when the processor executes the computer program, the steps of the ship trim optimization method provided in the above embodiment are implemented.
Embodiments of the present invention further provide a computer-readable storage medium, where a computer program is stored on the computer-readable storage medium, and the computer program is executed by a processor to perform the steps of the ship trim optimization method according to the above embodiments.
The computer program product provided in the embodiment of the present invention includes a computer readable storage medium storing a program code, where instructions included in the program code may be used to execute the method described in the foregoing method embodiment, and specific implementation may refer to the method embodiment, which is not described herein again.
It is clear to those skilled in the art that, for convenience and brevity of description, the specific working processes of the system and the apparatus described above may refer to the corresponding processes in the foregoing method embodiments, and are not described herein again.
In addition, in the description of the embodiments of the present invention, unless otherwise explicitly specified or limited, the terms "mounted," "connected," and "connected" are to be construed broadly, e.g., as meaning either a fixed connection, a removable connection, or an integral connection; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
The functions may be stored in a computer-readable storage medium if they are implemented in the form of software functional units and sold or used as separate products. Based on such understanding, the technical solution of the present invention may be embodied in the form of a software product, which is stored in a storage medium and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and other various media capable of storing program codes.
In the description of the present invention, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc. indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, and are only for convenience of description and simplification of description, but do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus, should not be construed as limiting the present invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
Finally, it should be noted that: although the present invention has been described in detail with reference to the foregoing embodiments, it should be understood by those skilled in the art that the following descriptions are only illustrative and not restrictive, and that the scope of the present invention is not limited to the above embodiments: any person skilled in the art can modify or easily conceive the technical solutions described in the foregoing embodiments or equivalent substitutes for some technical features within the technical scope of the present disclosure; such modifications, changes or substitutions do not depart from the spirit and scope of the embodiments of the present invention, and they should be construed as being included therein. Therefore, the protection scope of the present invention shall be subject to the protection scope of the appended claims.

Claims (10)

1. A method of vessel trim optimization, comprising:
determining a target navigational speed, a target draft and a target sea state of the ship based on the navigation plan;
inputting the target navigational speed, the target draught and the target sea state into a pre-trained trim optimization mathematical model, and outputting a plurality of trimmings of the ship and a plurality of corresponding host powers; the trim optimization mathematical model is obtained by training by taking operation data acquired during actual ship navigation of the ship as a training set and a verification set and taking preset environment variables and ship parameters as training parameters; the environmental variable comprises a wave height;
determining the trim corresponding to the main machine power with the minimum power in the plurality of trimmings and the plurality of main machine powers as a target trim;
adjusting a current trim of the vessel based on the target trim.
2. The method of claim 1, further comprising, after the step of adjusting the current trim of the vessel based on the target trim:
determining an initial trim of the vessel based on the target draft;
determining an initial host power corresponding to the initial pitch based on the plurality of pitches and the plurality of host powers;
and calculating the trim optimization rate of the ship based on the initial host power and the host power with the minimum power, and taking the trim optimization rate as an energy-saving index of the trim optimization method.
3. The method according to claim 1, wherein the creating step of the pitch optimized mathematical model comprises:
acquiring operation data of a ship during sailing;
selecting data of the ship which belongs to constant-speed straight line navigation from the operation data as a training set, and training a plurality of preset mathematical models;
selecting operation data under different ship types and sea conditions in the operation data as a verification set, and calculating respective parameter errors of the trained mathematical models based on the verification set; the sea state comprises an average of the wave heights in the airlines; the parameter errors comprise mean absolute error, mean square error and root mean square error;
determining the mathematical model corresponding to the minimum parameter error in the parameter errors obtained by calculation as a trim optimization mathematical model of the ship;
wherein the operational data comprises the environmental variables and the vessel parameters; the environment variables are meteorological forecast data, and the meteorological forecast data comprise wind speed, wind direction, flow speed, flow direction, wave height, wave direction and wave period; the ship parameters comprise ship measurement data, and the ship measurement data comprise ship type, water depth, draft, trim, navigational speed, host power, host rotating speed, slewing rate and host oil consumption.
4. A method according to claim 3, characterized in that the mathematical model comprises an integrated regression model of a tree, a K-nearest neighbor regression model and a random forest model.
5. The method according to claim 4, wherein the step of selecting the data of the operation data, which belongs to the constant-speed straight-line navigation, as a training set to train a plurality of mathematical models comprises:
taking the operation data with the water depth of more than 100 meters as a first training set;
determining operation data in the first training set, wherein the standard deviation of the host power is smaller than a first preset standard deviation, and the standard deviation of the slew rate is smaller than a second preset standard deviation, as a second training set;
and taking the wave height, the draught and the navigational speed in the second training set as input, taking the trim and the corresponding host power as output, and training the integrated regression model of the tree, the K nearest neighbor regression model and the random forest model.
6. The method of claim 1, wherein the step of obtaining the target speed of the vessel comprises:
determining a departure time, an arrival time, and a voyage of the vessel based on the voyage plan;
based on the range, the departure time, and the arrival time, calculating an average speed of the ship, and determining the average speed as the target speed.
7. The method of claim 6, wherein the step of obtaining the target sea state comprises:
determining a course of the ship and a segmentation way point of the course based on the navigation plan;
determining the wave height of the split waypoints when the ship reaches each split waypoint based on a weather forecast database and the target speed;
and calculating the average wave height on the route based on the wave heights of the plurality of split route points, and determining the average wave height as the target sea state.
8. A vessel trim optimization system, comprising:
the data acquisition module is used for determining a target navigational speed, a target draught and a target sea state of the ship for trim optimization based on the navigation plan;
the range determining module is used for inputting the target navigational speed, the target draught and the target sea state into a pre-trained trim optimization mathematical model and outputting a plurality of trimmings of the ship and a plurality of corresponding host powers; the trim optimization mathematical model is obtained by training by taking operation data acquired during actual ship navigation of the ship as a training set and a verification set and taking preset environment variables and ship parameters as training parameters; the environmental variable comprises a wave height;
a target pitch determining module, configured to determine, as a target pitch, a pitch corresponding to a host power with a minimum power among the plurality of pitches and the plurality of host powers;
a trim optimization module for adjusting a current trim of the vessel based on the target trim.
9. An electronic device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor implements the method of any of claims 1-7 when executing the computer program.
10. A computer-readable storage medium, on which a computer program is stored, characterized in that the computer program executes the steps of the method according to any one of claims 1 to 7.
CN202211151944.XA 2022-09-21 2022-09-21 Ship trim optimization method and system Pending CN115600311A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117634317A (en) * 2023-12-26 2024-03-01 华中科技大学 Dragon boat athlete intelligent ranking method, device and system based on optimal pitching

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117634317A (en) * 2023-12-26 2024-03-01 华中科技大学 Dragon boat athlete intelligent ranking method, device and system based on optimal pitching

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