A method, device and computer storage medium for optimizing approximate hull lines
By combining genetic algorithms, frog-jumping algorithms, and DBN approximate hull resistance prediction models, the main dimensional parameters of ships are optimized, solving the problem of low efficiency of CFD optimization algorithms under varying operating conditions, and achieving higher accuracy and efficiency in ship design.
Patent Information
- Application Number
- CN202310791025.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-06-30
- Publication Date
- 2025-01-14
- Estimated Expiration
- 2043-06-30
AI Technical Summary
Existing CFD deterministic optimization algorithms fail to effectively consider various changes in wind, waves, and draft in ship design, resulting in low optimization efficiency and making them unsuitable for ship design across the entire route.
A genetic algorithm and a frog-leapfrog algorithm are combined with a DBN approximate hull resistance prediction model. A sample set is generated through Latin hypercube design to optimize the ship's principal dimensional parameters and uncertainties. Interval analysis is used to improve prediction accuracy and optimization efficiency.
It improves the applicability and reliability of the ship type under various speeds, wave conditions, and wind and wave directions, reduces ship resistance, and enhances overall optimization efficiency.
Smart Images

Figure CN117113860B_ABST
Abstract
Description
Technical Field
[0001] The invention relates to a ship type optimization method, and in particular to an approximate hull type line optimization method, device and computer storage medium. Background Art
[0002] The appropriate hull shape can be subjected to less resistance during navigation, thereby achieving the purpose of reducing fuel consumption and reducing carbon dioxide emissions. At present, the ship type optimization method based on CFD technology (viscous fluid mechanics method) has become the main means of initial ship type design. However, this method often uses certain ship parameters and wind and wave conditions for optimization calculation. In fact, a large ship often has to travel continuously into multiple countries and multiple routes. Long-distance and multi-route driving will encounter a variety of changing winds and waves, and the driving conditions are ever-changing. The ship speed will continue to change with the sea conditions and the driver's habits, and the draft will change with the change of the load and cargo. However, the optimal solution obtained by the CFD optimization algorithm using a single working condition (determining the speed, draft, and sea conditions) cannot be applied to the entire route. Therefore, it is essential to consider the influence of uncertain factors in ship type optimization. In addition, if all these uncertain factors are taken into account in the ship type optimization design, a large number of CFD models will be calculated, which will lead to very low optimization efficiency considering uncertain factors. Summary of the invention
[0003] In view of the above-mentioned defects of the prior art, the present invention provides an approximate hull line optimization method, which increases the consideration of multiple uncertain factors in ship design and improves the adaptability of ships on the entire route. In addition, the present invention provides an approximate hull line optimization device and a computer storage medium.
[0004] The technical solution of the present invention is as follows: A method for optimizing approximate hull lines comprises the following steps:
[0005] (1) Using genetic algorithm to initialize population parameters, a group of individuals are randomly generated, each of which is composed of the main scale parameters of the ship;
[0006] (2) Fixing the main scale parameters of the ship of the genetic algorithm individual in step (1), optimizing the uncertain factors, and obtaining the total resistance of the corresponding genetic algorithm individual in waves;
[0007] (3) Perform selection, crossover, and mutation operations on the genetic algorithm population;
[0008] (4) When the genetic algorithm meets the termination condition, the optimization ends and the solution with the minimum total resistance is output. Otherwise, a new population is generated by evolution and the optimization is continued by returning to step (1).
[0009] The optimization of uncertain factors in step (2) includes the following steps:
[0010] (201), using a frog leaping algorithm to randomly generate a group of frog populations, wherein the frog individuals are a combination of the ship main scale parameters of the fixed genetic algorithm individuals and uncertain factors, wherein the uncertain factors include ship parameters and environmental parameters of the ship at sea;
[0011] (202) predict the total resistance of each frog individual under different working conditions;
[0012] (203), according to the predicted total resistance values of the frog individuals in different working conditions obtained in step (202), all frog individuals are arranged in order from large to small and allocated to four groups, and then the frog individuals are continuously updated to perform optimization calculation based on the minimum total resistance, and the total resistance corresponding to the optimal solution finally obtained is used as the left boundary value;
[0013] (204), repeating steps (201) and (202), according to the total resistance prediction values of the frog individuals in different working conditions obtained in step (202), all frog individuals are arranged in order from large to small and allocated to four groups, and then the frog individuals are continuously updated to perform optimization calculation based on the maximum total resistance, and the total resistance corresponding to the optimal solution finally obtained is used as the right boundary value;
[0014] (205) Calculate the total resistance of the corresponding genetic algorithm individual in the wave according to the left boundary value and the right boundary value obtained in steps (203) and (204).
[0015] Furthermore, in the step (202), when predicting the total resistance of each frog individual in the waves, a DBN approximate hull resistance prediction model is used for prediction. The method for obtaining the DBN approximate hull resistance prediction model is as follows: first, a sample collection including ship main scale parameters, ship parameters and environmental parameters is established by Latin hypercube design, and then a CFD method is used to calculate the total resistance of each sample in the sample collection to form a training sample set. The DBN algorithm is trained by the training sample set to obtain the DBN approximate hull resistance prediction model.
[0016] Furthermore, the step (205) uses the following formula to calculate the total resistance of the corresponding genetic algorithm individual in the wave according to the left boundary value and the right boundary value:
[0017] R i =0.5*[F(LL)+F(RR)]-0.4*F(LL)
[0018] Among them, R i is the total resistance of the corresponding genetic algorithm individual in the wave, F(LL) is the left boundary value of the total resistance value corresponding to the optimal solution obtained by step (203), and F(RR) is the right boundary value of the total resistance value corresponding to the optimal solution obtained by step (204).
[0019] Furthermore, the ship parameters include ship speed and draft, and the environmental parameters include wave parameters and wind parameters, the wave parameters are wavelength, wave height and wave direction angle, and the wind parameters are wind speed and wind direction angle.
[0020] The present invention also provides an approximate hull line optimization device, comprising:
[0021] Genetic algorithm initialization module: Genetic algorithm is used to initialize population parameters and randomly generate a group of individuals, each of which is composed of the main scale parameters of the ship;
[0022] Uncertain factors optimization module: used to fix the ship main scale parameters of the genetic algorithm individuals generated by the genetic algorithm initialization module, and perform uncertainty factor optimization to obtain the total resistance of the corresponding genetic algorithm individuals in waves;
[0023] Operation module: performs selection, crossover and mutation operations on the genetic algorithm population;
[0024] Loop output module: when the genetic algorithm meets the termination condition, the optimization ends and the solution with the minimum total resistance is output; otherwise, a new population is generated by evolution and the algorithm returns to the genetic algorithm initialization module to continue the optimization;
[0025] The uncertainty factor optimization module includes the following modules:
[0026] Frog leaping algorithm initialization module: a group of frog populations is randomly generated by using the frog leaping algorithm, and the frog individuals in the frog population are a combination of the ship main scale parameters of the fixed genetic algorithm individuals and uncertain factors, and the uncertain factors include ship parameters and environmental parameters of the ship at sea;
[0027] Total resistance prediction module: used to predict the total resistance of each frog individual under different working conditions;
[0028] Frog jumping optimization module: according to the total resistance prediction value of frog individuals in different working conditions obtained by the total resistance prediction module, all frog individuals are arranged in order from large to small and allocated to four groups, and then frog individuals are continuously updated to perform optimization calculation based on the minimum total resistance, and the total resistance corresponding to the optimal solution finally obtained is used as the left boundary value, and frog individuals are continuously updated to perform optimization calculation based on the maximum total resistance, and the total resistance corresponding to the optimal solution finally obtained is used as the right boundary value;
[0029] Interval conversion module: The total resistance of the corresponding genetic algorithm individual in the wave is calculated by using the left boundary value and the right boundary value obtained by the frog leap optimization module.
[0030] Furthermore, the total resistance prediction module predicts the total resistance of each frog individual in waves by using a DBN approximate hull resistance prediction model. The method for obtaining the DBN approximate hull resistance prediction model is as follows: first, a sample collection including ship main scale parameters, ship parameters and environmental parameters is established by using Latin hypercube design, and then the total resistance of each sample in the sample collection is calculated by using a CFD method to form a training sample set. The DBN algorithm is trained by using the training sample set to obtain the DBN approximate hull resistance prediction model.
[0031] Furthermore, the total resistance of the corresponding genetic algorithm individual in the wave is calculated by the left boundary value and the right boundary value obtained by the frog leap optimization module using the following formula:
[0032] R i =0.5*[F(LL)+F(RR)]-0.4*F(LL)
[0033] Among them, R i is the total resistance of the corresponding genetic algorithm individual in the wave, F(LL) is the left boundary value, and F(RR) is the right boundary value.
[0034] The present invention also provides a computer storage medium on which a computer program is stored. When the computer program is executed by a processor, the above-mentioned approximate hull line optimization method is implemented.
[0035] The advantages of the technical solution provided by the present invention are:
[0036] The advantage of the present invention is to provide an approximate ship type optimization method, which uses CFD technology as a basic hydrodynamic calculation tool and adopts a Latin hypercube design method to obtain a multidimensional space sample set. Compared with the traditional artificial neural network algorithm, the DBN algorithm has higher accuracy in the prediction of hull resistance, which can improve the prediction accuracy and overall optimization efficiency of the optimization method. Then, the interval analysis method and the DBN algorithm are combined to perform uncertain optimization calculations on the main scale of the hull, and the changes in draft, wind and wave parameters and ship speed during actual navigation are considered in the optimization, so as to improve the reliability and engineering practicality of the optimal ship type under multiple speeds, different wave conditions, different wind and wave directions and different drafts. In addition, the genetic algorithm is used to determine the optimization of the main scale parameters, and the algorithm can be effectively prevented from falling into local extreme values through crossover and mutation calculations. In the calculation of the uncertain optimization module, the sorting and recombining populations of the frog leaping algorithm can also well identify more excellent individuals. In general, the optimization of the ship parameters and environmental parameters of the method of the present invention can make the optimal ship type be subject to less resistance in different environmental parameters, drafts and ship speeds, and has stronger applicability. BRIEF DESCRIPTION OF THE DRAWINGS
[0037] Figure 1Schematic diagram of the process of optimizing the approximate hull lines in step (1) of the embodiment of the present invention.
[0038] Figure 2 Schematic diagram of the process of optimizing the calculation of uncertain factors in step (2) in an embodiment of the present invention.
[0039] Figure 3 It is a schematic diagram of the module of the device for optimizing approximate hull lines of the present invention. DETAILED DESCRIPTION
[0040] The present invention is further described below in conjunction with examples. It should be understood that these examples are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading this description, various equivalent modifications to this description by those skilled in the art fall within the scope defined by the claims attached to this application.
[0041] Please combine Figure 1 As shown, the approximate hull line optimization method of this embodiment includes the following steps:
[0042] (1) Use genetic algorithm to initialize population parameters, including the maximum number of iterations S max First, let the current iteration number s = 1. Then randomly generate a set of m individuals G = {g1, g2, g i ,...,g m}, where the i-th individual is represented by: g i ={D 1i ,D 2i ,D 3i ,D 4i}. 1i , D 2i , D 3i , D 4i represents the length, width and square coefficient C of the i-th individual respectively B , sonar cover coefficient C. Then the three-dimensional model drawing method is used according to different g i The value obtains a hull shape different from the parent ship.
[0043] (2) Fixed hull modification parameter individual g i , enter the uncertainty factor optimization calculation. Figure 2 As shown, the method for optimizing the calculation of uncertain factors is as follows:
[0044] (a) Establish a DBN approximate hull resistance prediction model: Consider the uncertain variable parameters in the optimization. Here, ship parameters, wave parameters and wind parameters are selected as the research objects. The specific set is expressed as: ship parameters U = {U1 (ship speed), U2 (draft)}; wave parameters T = {T1 (wavelength), T2 (wave height), T3 (wave direction angle)}; wind parameters W = {W1 (wind speed), W2 (wind direction angle)}. Then, the DOE method (Latin hypercube design) is used to establish a sample set Δ = {Δ1, Δ2, ..Δ i .,Δ 1000}, where Δ i ={D 1i ,D 2i ,D 3i ,D 4i ,U 1i ,U 2i ,T 1i ,T 2i ,T 3i ,W 1i ,W 2i}. Then the CFD method is used to calculate the resistance of the corresponding sample. Then a new sample set is constructed to train the DBN algorithm, and then the DBN approximate hull resistance prediction model is obtained.
[0045] (b) Initialize the uncertainty factor optimization calculation parameters, including the maximum number of iterations N max . First, let the current iteration number n = 1. First, use the frog leaping algorithm to randomly generate a group of frog populations GG = {gg1, gg2, gg i ,...,gg m}, for gg i = {g i ,U 1i ,U 2i ,T 1i ,T 2i ,T 3i ,W 1i ,W 2i Then, the DBN approximate hull resistance prediction model in step (a) is used to calculate the total resistance value R of the i-th frog individual Ti .
[0046] (c) Then according to each target value R Ti The size of the GG set is i Then divide the set GG into four groups, and then sort them in order of size. i Assign to each group.
[0047] (d) Let c=c+1.
[0048] (e) Use formula (1) to update the position of the individual frog with the largest total resistance.
[0049] S λ (c+1)=S λ (c)+r()*(S α -S x ) (1)
[0050] In the formula, c represents the current iteration number, S α and S x They represent the positions of the frog with the smallest resistance and the frog with the largest resistance respectively. r() represents a random number ranging from 0 to 1.
[0051] (f) Use the DBN approximate hull resistance prediction model to predict the total resistance of each frog individual after the update, and then determine whether the updated total resistance is less than the total resistance of all frog individuals in the first generation. If yes, use this frog individual to replace the original individual; if not, use the global extreme value to replace the individual extreme value to update the position.
[0052] (g) If c ≤ C (set in algorithm initialization), return to step (d) to continue optimization. If c > C, execute step (h).
[0053] (h) The updated population is formed into a new set θ = {}. Determine whether n>N is satisfied max If it is satisfied, the algorithm ends and the optimal solution of the total resistance left side value F(LL) is obtained, and step (i) is executed. If it is not satisfied, n=n+1 is used, and the DBN approximate hull resistance prediction model is used to calculate the total resistance value of each frog individual in the set θ={}, and then return to step (c) to continue the optimization calculation.
[0054] (i) Repeat steps (b) to (h) to perform maximization optimization calculation. The only difference is that the minimum resistance value is set as the worst value of the frog individual, and the individual with the largest resistance is the optimal value of the frog individual. The maximum and minimum values in steps (b) to (h) are all reversed for optimization calculation. The optimal solution of the right boundary value of the total resistance F(RR) is finally obtained through optimization.
[0055] (j) The Ri calculated by formula (2) is used as the solution corresponding to the i-th genetic individual, and then output to the genetic algorithm to continue the optimization calculation based on the main scale parameters of the ship type.
[0056] R i =0.5*[F(LL)+F(RR)]-0.4*F(LL) (2)
[0057] (3) The commonly used roulette algorithm is used to select individuals from the population.
[0058] (4) Chromosomes are exchanged with a probability of 0.95 to generate new chromosomes.
[0059] (5) The population is mutated with a probability of 0.05.
[0060] (6) Generate a new population and determine whether the algorithm satisfies s>S max If it is satisfied, the algorithm ends and outputs the optimal solution set D with the minimum total resistance. If it is not satisfied, another s=s+1 is set, a set of m individual sets containing certain variables is randomly generated and the algorithm returns to step (2) to continue the optimization calculation.
[0061] It should be noted that the specific methods of the above embodiments can form a computer program product. Therefore, the computer program product implemented by the present application can be stored on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.). In addition, the present application can be implemented in the form of hardware, software, or a combination of hardware and software, or constitute a computer device including at least one processor and a memory, the memory storing a computer program for implementing the above process steps, and the processor executing the computer program on the memory to form the method steps of the above embodiments.
[0062] like Figure 3 As shown, the approximate hull line optimization device of the embodiment includes:
[0063] Genetic algorithm initialization module 100: execute step (1) of the above embodiment, use genetic algorithm to initialize population parameters, and randomly generate a group of individuals, each of which is composed of the main scale parameters of the ship.
[0064] Uncertain factor optimization module 200: executes step (2) of the above embodiment, and is used to fix the ship main scale parameters of the genetic algorithm individual generated by the genetic algorithm initialization module, and perform uncertainty factor optimization to obtain the total resistance of the corresponding genetic algorithm individual in waves;
[0065] Operation module 300: executes steps (3) to (5) of the above-mentioned embodiment, and performs selection, crossover and mutation operations on the genetic algorithm population.
[0066] Loop output module 400: execute step (6) of the above embodiment, end the optimization and output the solution with the minimum total resistance when the genetic algorithm meets the termination condition, otherwise evolve and generate a new population and return to the genetic algorithm initialization module to continue optimization.
[0067] The uncertainty factor optimization module includes the following modules:
[0068] Frog leaping algorithm initialization module 201: execute step (b) of the aforementioned embodiment, and use frog leaping algorithm to randomly generate a group of frog populations, wherein the frog individuals in the frog population are a combination of the main scale parameters of the ship of the fixed genetic algorithm individuals and uncertain factors, and the uncertain factors include ship parameters and environmental parameters of the ship at sea.
[0069] Total resistance prediction module 202: executes step (a) of the above embodiment to predict the total resistance of each frog individual in different working conditions.
[0070] Frog jumping optimization module 203: executes steps (c) to (i) of the aforementioned embodiment, and arranges all frog individuals in order from large to small and distributes them into four groups according to the total resistance prediction values of frog individuals in different working conditions obtained by the total resistance prediction module, and then continuously updates frog individuals to perform optimization calculations based on the minimum total resistance, and finally obtains the total resistance corresponding to the optimal solution as the left boundary value, and continuously updates frog individuals to perform optimization calculations based on the maximum total resistance, and finally obtains the total resistance corresponding to the optimal solution as the right boundary value.
[0071] The interval conversion module 204 executes step (j) of the above-mentioned embodiment, and obtains the total resistance of the corresponding genetic algorithm individual in the wave by calculating the left boundary value and the right boundary value of the total resistance calculated by the frog leaping optimization module.
Claims
1. A method for optimizing approximate hull lines, characterized in that: The following steps are involved: (1) Using genetic algorithm to initialize population parameters, a group of individuals are randomly generated, each of which is composed of the main scale parameters of the ship; (2) Fixing the main scale parameters of the ship of the genetic algorithm individual in step (1), optimizing the uncertain factors, and obtaining the total resistance of the corresponding genetic algorithm individual in waves; (3) Perform selection, crossover, and mutation operations on the genetic algorithm population; (4) When the genetic algorithm meets the termination condition, the optimization ends and the solution with the minimum total resistance is output. Otherwise, a new population is generated by evolution and the optimization is continued by returning to step (1). The optimization of uncertain factors in step (2) includes the following steps: (201), using a frog leaping algorithm to randomly generate a group of frog populations, wherein the frog individuals in the frog population are a combination of the ship main scale parameters of the fixed genetic algorithm individuals and uncertain factors, wherein the uncertain factors include ship parameters and environmental parameters of the ship at sea; (202) predict the total resistance of each frog individual under different working conditions; (203), according to the predicted total resistance values of the frog individuals in different working conditions obtained in step (202), all frog individuals are arranged in order from large to small and allocated to four groups, and then the frog individuals are continuously updated to perform optimization calculation based on the minimum total resistance, and the total resistance value corresponding to the optimal solution finally obtained is used as the left boundary value; (204), repeating steps (201) and (202), according to the total resistance prediction values of the frog individuals in different working conditions obtained in step (202), all frog individuals are arranged in order from large to small and allocated to four groups, and then the frog individuals are continuously updated to perform optimization calculation based on the maximum total resistance, and the total resistance value corresponding to the optimal solution finally obtained is used as the right boundary value; (205) Calculate the total resistance of the corresponding genetic algorithm individual in the wave according to the left boundary value and the right boundary value obtained in steps (203) and (204).
2. The method for optimizing approximate hull lines according to claim 1, characterized in that: The step (202) predicts the total resistance of each frog individual in the waves by using a DBN approximate hull resistance prediction model. The method for obtaining the DBN approximate hull resistance prediction model is as follows: first, a Latin hypercube design is used to establish a sample collection, wherein each sample in the sample collection is a collection of definite variables and uncertain variables, wherein the definite variables are the ship length, ship width, square coefficient and sonar housing coefficient, and the uncertain variables are the ship speed, draft, wavelength, wave height, wave direction angle, wind speed and wind direction angle; then, a CFD method is used to calculate the total resistance of each sample in the sample collection to form a training sample set, and the DBN algorithm is trained by the training sample set to obtain the DBN approximate hull resistance prediction model.
3. The method for optimizing approximate hull lines according to claim 1, characterized in that: The step (205) is performed by using the following formula to calculate the total resistance of the corresponding genetic algorithm individual in the wave according to the left boundary value and the right boundary value: R i =0.5*[F(LL)+F(RR)]-0.4*F(LL) Among them, R i is the total resistance of the corresponding genetic algorithm individual in the wave, F(LL) is the total resistance value corresponding to the optimal solution obtained by step (203), and F(RR) is the total resistance value corresponding to the optimal solution obtained by step (204).
4. The method for optimizing approximate hull lines according to claim 1, characterized in that: The ship parameters include ship speed and draft, and the environmental parameters include wave parameters and wind parameters. The wave parameters are wavelength, wave height and wave direction angle, and the wind parameters are wind speed and wind direction angle.
5. An approximate hull line optimization device, characterized in that: include: Genetic algorithm initialization module: Genetic algorithm is used to initialize population parameters and randomly generate a group of individuals, each of which is composed of the main scale parameters of the ship; Uncertain factors optimization module: used to fix the ship main scale parameters of the genetic algorithm individuals generated by the genetic algorithm initialization module, and perform uncertainty factor optimization to obtain the total resistance of the corresponding genetic algorithm individuals in waves; Operation module: performs selection, crossover and mutation operations on the genetic algorithm population; Loop output module: when the genetic algorithm meets the termination condition, the optimization ends and the solution with the minimum total resistance is output; otherwise, a new population is generated by evolution and the algorithm returns to the genetic algorithm initialization module to continue the optimization; The uncertainty factor optimization module includes the following modules: Frog leaping algorithm initialization module: a group of frog populations is randomly generated by using the frog leaping algorithm, and the frog individuals in the frog population are a combination of the ship main scale parameters of the fixed genetic algorithm individuals and uncertain factors, and the uncertain factors include ship parameters and environmental parameters of the ship at sea; Total resistance prediction module: used to predict the total resistance of each frog individual under different working conditions; Frog jumping optimization module: according to the total resistance prediction value of frog individuals in different working conditions obtained by the total resistance prediction module, all frog individuals are arranged in order from large to small and allocated to four groups, and then frog individuals are continuously updated to perform optimization calculation based on the minimum total resistance, and the total resistance corresponding to the optimal solution finally obtained is used as the left boundary value, and frog individuals are continuously updated to perform optimization calculation based on the maximum total resistance, and the total resistance corresponding to the optimal solution finally obtained is used as the right boundary value; Interval conversion module: The total resistance of the corresponding genetic algorithm individual in the wave is calculated by using the left boundary value and the right boundary value obtained by the frog leap optimization module.
6. The device for optimizing approximate hull lines according to claim 5, characterized in that: The total resistance prediction module predicts the total resistance of each frog individual in the waves by using a DBN approximate hull resistance prediction model for prediction. The method for obtaining the DBN approximate hull resistance prediction model is as follows: firstly, a Latin hypercube design is used to establish a sample collection, wherein each sample in the sample collection is a collection of definite variables and uncertain variables, wherein the definite variables are the ship length, ship width, square coefficient and sonar housing coefficient, and the uncertain variables are the ship speed, draft, wavelength, wave height, wave direction angle, wind speed and wind direction angle; and then a CFD method is used to calculate the total resistance of each sample in the sample collection to form a training sample set, and the DBN algorithm is trained by the training sample set to obtain the DBN approximate hull resistance prediction model.
7. The device for optimizing approximate hull lines according to claim 5, characterized in that: The total resistance of the corresponding genetic algorithm individual in the wave is calculated by the left boundary value and the right boundary value obtained by the frog leap optimization module using the following formula: R i =0.5*[F(LL)+F(RR)]-0.4*F(LL) Among them, R i is the total resistance of the corresponding genetic algorithm individual in the wave, F(LL) is the left boundary value, and F(RR) is the right boundary value.
8. The device for optimizing approximate hull lines according to claim 5, characterized in that: The ship parameters include ship speed and draft, and the environmental parameters include wave parameters and wind parameters. The wave parameters are wavelength, wave height and wave direction angle, and the wind parameters are wind speed and wind direction angle.
9. A computer storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the approximate hull line optimization method according to any one of claims 1 to 4 is implemented.
Citation Information
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