Underwater rotary body appearance multi-target transition delay optimization method based on NSGA-II

Abstract

The invention relates to an underwater rotary body appearance multi-target transition delay optimization method based on NSGA-II. The method comprises the following steps: establishing a multi-target optimization model; population initialization: selecting a plurality of known underwater revolving body appearances as a primary population; at multiple navigational speeds, predicting a natural transition position of a boundary layer at the head part of each appearance in the current population; performing non-dominated sorting; crowding degree calculation: the crowding distance is calculated according to the target value of each individual, and the individuals with the larger crowding distance are ranked in the front; generating a filial generation population: executing genetic operations of selection, crossover and variation on all shapes in the current generation population so as to generate the filial generation population; using an elitist strategy to mix the filial generations and the parent generations, performing non-dominated sorting and crowding degree calculation, and taking the first N individuals as the next generation of individuals; and performing iterative evolution to obtain a shape Pareto solution set, namely a shape solution set with uniformly distributed transition position delay.

Description

Technical Field

[0001] The present invention relates to the technical field of hydrodynamic research, and particularly relates to a multi-objective transition delay optimization method for the underwater body of revolution shape based on NSGA-II. Background Art

[0002] The boundary layer at the head of the underwater body of revolution is divided into a laminar section, a transition section and a turbulent section from front to back. The laminar section is relatively quiet with a small noise intensity; the turbulent section is relatively noisy; the noise intensity in the transition section is very large, even exceeding that in the turbulent section. Therefore, the transition position of the boundary layer at the head of the underwater body of revolution has an important influence on the flow noise. The transition position of the boundary layer of the underwater body of revolution will vary significantly with the change of the head shape. Therefore, by changing the head shape of the underwater body of revolution, the transition position of the boundary layer at the head can be effectively affected, thereby improving the detection ability of its head sonar.

[0003] To optimize the shape of the head of an underwater body of revolution to delay the transition position, it is necessary to know the transition positions of different body-of-revolution shapes, that is, to predict the transition. Regarding this, the eN method has been proposed by some people (Liu, J., Chu, X., Zhang, Y., 2021. Numerical investigation of natural transitions of bow boundary layers over underwater axisymmetric bodies. Phy. Fluids 33, 074101.). In addition, some people have previously optimized with the single goal of delaying the transition at a certain ship speed (Lv, J., Liu, J., Zhang, Y., Liu, J., 2024. Optimization design of forebody shape of an underwater axisymmetric body for transition delay using a genetic algorithm. Ocean Engineering 301, 117529.). However, in actual engineering, an underwater vehicle has to sail at multiple speeds. Therefore, in engineering, it is necessary to find the shape with the best comprehensive performance at multiple typical ship speeds. Existing research has shown that when the ship speed changes, the Reynolds number effect will be exhibited (Liu, J., Liu, J., Zhang, Y., 2023. Influence of Reynolds number on the natural transition of boundary layers over underwater axisymmetric bodies. Phy. Fluids 35, 044107.), that is, the change in ship speed (the Reynolds number changes accordingly) will cause irregular changes in the order of transition positions between different shapes. If the single-objective optimization method is used separately at different ship speeds, the optimal shapes obtained are different. Therefore, it is necessary to use a multi-objective optimization algorithm to solve this multi-objective optimization problem. At present, it seems that multi-objective intelligent optimization algorithms have been applied to the optimization problem of underwater vehicles. However, most of them are applications with the goals of drag reduction, pressure reduction, and efficiency improvement. No multi-objective optimization work on the shape of an underwater body of revolution with the goal of delaying the transition position at multiple ship speeds has been seen yet. Summary of the Invention

[0004] The purpose of the present invention is to overcome the deficiencies of the prior art and provide a feasible method for delaying the transition of the boundary layer of an underwater body of revolution at multiple ship speeds, and to delay the transition through the intelligent optimization of the shape. The technical solution is as follows:

[0005] A multi-objective transition delay optimization method for underwater rotating body shape based on NSGA-Ⅱ includes the following steps:

[0006] Step 1: Establish a multi-objective optimization model as follows:

[0007] 1) Gene encoding

[0008] Using real number coding and NURBS method, the genes of the external shape are represented by the coordinates of the control points, and the mapping from the control point coordinates to the transition position is the mapping from genotype to phenotype;

[0009] 2) Determine multiple optimization goals

[0010] Determine a plurality of ship speeds that need to be delayed in a specific category, and use delaying transition positions at the plurality of ship speeds as a plurality of optimization targets;

[0011] 3) Determine genetic parameters, variables and constraints

[0012] Determine the population size N, crossover probability, and mutation probability parameters in the genetic algorithm; determine the constraints and the range of variation of the design variables, that is, the range of variation of the control point position coordinates;

[0013] Step 2: Population initialization: select several known underwater rotating body shapes as the initial population;

[0014] Step 3, predicting the natural transition position of the bow boundary layer of each shape in the contemporary population at the plurality of speeds;

[0015] Step 4: Non-dominated sorting: if all the target values ​​of an individual are better than those of another individual, that is, the individual dominates the other individual, and the individuals without dominated relationships constitute the first-level solution set, namely the Pareto solution set. Similarly, several levels of solution sets are sorted. The genes of individuals in the top-ranked solution sets are more likely to be inherited to the next generation.

[0016] Step 5: Calculate the crowding degree. Calculate the crowding distance of each individual according to its target value. Individuals with larger crowding distances are ranked higher.

[0017] Step 6, generate offspring population: perform genetic operations of selection, crossover and mutation on all appearances in the contemporary population to generate offspring population;

[0018] Step 7: Use the elite strategy to mix the offspring and parents, perform non-dominated sorting and crowding calculation, and take the first N individuals as the next generation of individuals;

[0019] Step eight, iterative evolution, repeating steps three to seven until convergence and meeting the optimization goal, obtaining the shape Pareto solution set, that is, the shape solution set with uniform distribution of transition position delay.

[0020] In Step 1, the method for determining the variation range of the position coordinates of the control points is as follows:

[0021] Set the weights of each control point to be fixed at 1. The method for selecting the control points on one side of the underwater body of revolution is as follows: ① The first point is used as the leading edge of the body of revolution, and its position is set; ② The axial coordinate of the second point is the same as that of the first point, but its radial coordinate is different from that of the first point to ensure that the leading edge is blunt; ③ According to the head-body junction, select the control point n at the head-body junction. Its radial coordinate is fixed at the radius of the body of revolution, and its axial coordinate is variable to control the position of the head-body junction; ④ The radial coordinate of the (n - 1)th point is the same as that of the nth point to ensure a smooth transition at the head-body junction; ⑤ The axial and radial coordinates of the third to (n - 2)th points can both vary to control the shape of the head of the body of revolution.

[0022] In Step 3, the method for predicting the natural transition position of the boundary layer at the head of a known underwater body of revolution is as follows: Numerically solve the dimensionless incompressible steady N - S equations to obtain the laminar basic flow of the underwater body of revolution; Use numerical methods to solve the linear stability equations in an incompressible orthogonal curvilinear coordinate system for stability analysis; Use the eN method to predict the natural transition position of the boundary layer at the head of the underwater body of revolution.

[0023] In Step 5, the calculation formula for the crowding distance is as follows:

[0024]

[0025] CD im represents the crowding degree of the i-th individual in the m-th objective function, f m represents the m-th objective function, x max represents the maximum value among all individuals under the m-th function, x min represents the minimum value.

[0026] Advantages of the present invention compared with the prior art:

[0027] 1) Compared with the existing single-objective optimization method (Tianjin University. "Transition Delay Optimization Method for the Head Shape of an Underwater Body of Revolution Based on Genetic Algorithm.", 202410227673.4. 2024), the present invention conducts comprehensive optimization at multiple speeds and can better meet the actual engineering needs.

[0028] 2) The present invention uses a multi-objective genetic algorithm based on non-dominated sorting and crowding degree calculation to generate an optimal Pareto solution set containing multiple shapes, rather than just one optimal shape. Brief Description of the Drawings

[0029] Figure 1 is the step block diagram of the present invention

[0030] Figure 2 Schematic diagram of the control point position and the shape of the rotating body (the rotating body is symmetric, only the upper half needs to be expressed)

[0031] Figure 3 Non-dominated sorting diagram of the first-generation individuals (the first-level solution set represented by red is the optimal level, i.e., the Pareto solution set, and the seventh level represented by purple is the worst level)

[0032] Figure 4 Number of individuals in the Pareto solution set for each generation

[0033] Figure 5 Non-dominated sorting diagram of the 14th-generation individuals

[0034] Figure 6 Maximum, average, and minimum values of the transition positions of individuals in the Pareto solution set for each generation at a speed of 3.087 m / s

[0035] Figure 7 Maximum, average, and minimum values of the transition positions of individuals in the Pareto solution set for each generation at a speed of 5.144 m / s

[0036] Figure 8 Maximum, average, and minimum values of the transition positions of individuals in the Pareto solution set for each generation at a speed of 12.347 m / s Specific implementation manners

[0037] The present invention will be described in detail below in conjunction with specific implementation manners and the accompanying drawings. In the following description, for the purpose of explanation rather than limitation, specific details are set forth to help fully understand the present invention. However, it will be apparent to those skilled in the art that the present invention may also be practiced in other embodiments without these specific details.

[0038] It should be noted here that in order to avoid obscuring the present invention with unnecessary details, only the device structures and / or processing steps closely related to the solution according to the present invention are shown in the drawings, while other details less related to the present invention are omitted.

[0039] An embodiment of the present invention provides a multi-objective transition delay optimization method for the underwater rotating body shape based on NSGA-II, as Figure 1 shown, including the following steps

[0040] The multi-objective transition delay optimization method for the underwater rotating body shape based on NSGA-II of the present invention includes the following steps:

[0041] Step 1, establish a multi-objective optimization model, the method is as follows:

[0042] 1) Perform gene coding

[0043] Using real - number coding, the NURBS method is adopted, and the genes representing the shape are in the form of control - point coordinates (for the specific method, refer to Tianjin University. "Transition Delay Optimization Method for the Forebody Shape of an Underwater Revolving Body Based on Genetic Algorithm.", 202410227673.4, 2024). Then, the mapping from the control - point coordinates to the transition position is the mapping from genotype to phenotype. The control - point positions and the schematic diagram of the revolving - body shape are shown in Figure 2 . Among them, x * , r * are the axial and radial coordinates in the cylindrical - coordinate system respectively.

[0044] 2) Determine multiple optimization objectives

[0045] Taking the transition positions at three speeds as three optimization objectives. In this embodiment, the transition positions under the working conditions of 3.087 m / s, 5.144 m / s, and 12.347 m / s are taken as the optimization objectives, that is

[0046]

[0047] 3) Determine genetic parameters, variables, and constraints

[0048] The population size of each generation is 32, the crossover probability is 0.95, and the mutation probability is 0.1.

[0049] The value range of the control points refers to the reference document (Lv, J., Liu, J., Zhang, Y., Liu, J., 2024. Optimization design of forebody shape of an underwater axisymmetric body for transition delay using a genetic algorithm. Ocean Engineering 301, 117529.)

[0050] In this step, the weights of each control point are all fixed at 1, and the functions of each control point are as follows: ① The first point is the leading edge of the revolving body, and its position is fixed at (0 m, 0 m). ② The axial coordinate of the second point is the same as that of the first point, but its radial coordinate is different from that of the first point to ensure a blunt head at the leading edge. ③ The 18th point is the head - body junction, and its radial coordinate is fixed at the radius r of the revolving body *= 5.8315 m; its axial coordinate is variable to control the position of the head-body joint. ④ The radial coordinate of the 17th point is the same as that of the 18th point to maintain a smooth transition at the head-body joint. ⑤ The axial and radial coordinates of the 3rd - 16th points can both vary to control the shape of the head of the of the body of revolution. According to the above settings, the total number of variable variables is 31, including the axial and radial coordinates of the 3rd - 16th points, the radial coordinate of the 2nd point, and the axial coordinates of the 17th and 18th points. The range of variation of each control point taken in the present invention is shown in Table 1.

[0051] Table 1 Range of values of each control point (unit: m)

[0052]

[0053] Step 2, population initialization: Take several classical shapes existing in current engineering or research as the initial population.

[0054] In this step, take the 7 shapes (SUBOFF, LYW1, LYW2, LYW3, LYW4, Ellipse, and LGLS) in Liu et al. (2023) as the initial population. For a detailed introduction to the shapes, see the literature (Liu, J., Liu, J., Zhang, Y., 2023. Influence of Reynolds number on the natural transition of boundary layers over underwater axisymmetric bodies. Phys. Fluids 35, 044107.).

[0055] Step 3, predict the natural transition position of the boundary layer at the head of each shape in the current population at three ship speeds.

[0056] In this step, numerically solve the dimensionless incompressible steady N - S equations to obtain the laminar basic flow of the underwater body of revolution; use numerical methods to solve the linear stability equations in an incompressible orthogonal curvilinear coordinate system for stability analysis; use the eN method to predict the transition position of the underwater body of revolution.

[0057] Step 4, non - dominated sorting. If all the objective values of an individual are better than those of another individual, that is, this individual dominates the other individual, the individuals without a domination relationship form the first - level solution set (Pareto solution set), and so on to sort out several levels of solution sets. The probability that the genes of the individuals in the solution set with a higher ranking are inherited to the next generation is greater. The non - dominated sorting of all individuals in the initial population is as Figure 3 shown, where the 1st level shown in red is the optimal - level solution set, that is, the Pareto solution set, and the 7th level shown in purple is the worst level.

[0058] Step 5: Calculate the crowding degree. Calculate the crowding distance of each individual based on its target value. Individuals with larger crowding distances are ranked higher.

[0059] In this step, the calculation formula of crowding distance is as follows:

[0060]

[0061] CD im represents the crowding degree of the ith individual in the mth objective function, f m represents the mth objective function, x max represents the maximum value of all individuals under the m function, x min Indicates the minimum value.

[0062] Step 6: Generate offspring population: Perform genetic operations of selection, crossover and mutation on all appearances in the current population to generate offspring population.

[0063] Step 7: Use the elite strategy to mix the offspring and parents, perform non-dominated sorting and crowding calculation, and take the first 32 individuals as the next generation population.

[0064] Step eight, iterative evolution, repeating steps three to seven until convergence and meeting the optimization goal, obtaining the shape Pareto solution set, that is, the shape solution set with uniform distribution of transition position delay.

[0065] In this step, after 14 iterations, the optimization effect gradually increases, and the number of individuals in the Pareto solution set of each generation gradually increases. Figure 4 As shown. By the 14th generation, all individuals in the population are in a non-dominant relationship and the transition position has a delayed effect compared with the first generation, as shown Figure 5 As shown. The maximum and average values ​​of the transition positions of individuals in the Pareto solution set of each generation at the three speeds gradually increase, as shown in the figure. The average value at 3.087m / s increases from 4.97185m in the first generation to 5.450072m in the 14th generation; the average value at 5.144m / s increases from 3.874923m in the first generation to 4.070525m in the 14th generation; the average value at 12.347m / s increases from 2.09733m in the first generation to 2.506413m in the 14th generation.

[0066] Features described and / or illustrated above for one embodiment may be used in the same or similar manner in one or more other embodiments, and / or combined with or used in place of features in other embodiments.

[0067] It should be emphasized that the term "comprising / including", as used herein, refers to the presence of features, whole units, steps or components, but does not exclude the presence or addition of one or more other features, whole units, steps, components or combinations thereof.

[0068] The above-mentioned apparatus and method of the present invention can be implemented by hardware, or can be implemented by a combination of hardware and software. The present invention relates to such a computer-readable program that, when executed by a logic component, can enable the logic component to implement the above-mentioned apparatus or constituent components, or enable the logic component to implement the above-mentioned various methods or steps. The present invention also relates to a storage medium for storing the above program, such as a hard disk, a magnetic disk, an optical disk, a DVD, a flash memory, etc.

[0069] Many features and advantages of these embodiments are apparent from this detailed description, and thus the appended claims are intended to cover all such features and advantages of these embodiments that fall within their true spirit and scope. In addition, since many modifications and changes are readily envisioned by those skilled in the art, the embodiments of the present invention are not to be limited to the exact structures and operations illustrated and described, but may cover all suitable modifications and equivalents that fall within their scope.

[0070] The parts not detailed in the present invention are well-known technologies to those skilled in the art.

Claims

1. A multi-objective transition delay optimization method for underwater rotating body shape based on NSGA-Ⅱ, comprising the following steps: Step 1: Establish a multi-objective optimization model as follows: 1) Gene encoding Using real number coding and NURBS method, the genes of the external shape are represented by the coordinates of the control points, and the mapping from the control point coordinates to the transition position is the mapping from genotype to phenotype; 2) Determine multiple optimization goals Determine a plurality of ship speeds that need to be delayed in a specific category, and use delaying transition positions at the plurality of ship speeds as a plurality of optimization targets; 3) Determine genetic parameters, variables and constraints Determine the population size N, crossover probability, and mutation probability parameters in the genetic algorithm; determine the constraints and the range of variation of the design variables, that is, the range of variation of the control point position coordinates; Step 2: Population initialization: select several known underwater rotating body shapes as the initial population; Step 3, predicting the natural transition position of the bow boundary layer of each shape in the contemporary population at the plurality of speeds; Step 4: Non-dominated sorting: if all the target values ​​of an individual are better than those of another individual, that is, the individual dominates the other individual, and the individuals without dominated relationships constitute the first-level solution set, namely the Pareto solution set. Similarly, several levels of solution sets are sorted. The genes of individuals in the top-ranked solution sets are more likely to be inherited to the next generation. Step 5: Calculate the crowding degree. Calculate the crowding distance of each individual according to its target value. Individuals with larger crowding distances are ranked higher. Step 6, generate offspring population: perform genetic operations of selection, crossover and mutation on all appearances in the contemporary population to generate offspring population; Step 7: Use the elite strategy to mix the offspring and parents, perform non-dominated sorting and crowding calculation, and take the first N individuals as the next generation of individuals; Step eight, iterative evolution, repeating steps three to seven until convergence and meeting the optimization goal, and obtaining the shape Pareto solution set, that is, the shape solution set with uniform distribution of transition position delay.

2. The multi-objective transition delay optimization method for underwater rotating body shape based on NSGA-Ⅱ according to claim 1 is characterized in that: In step 1, the method for determining the range of change of the control point position coordinates is as follows: The weight of each control point is set to 1. The method for selecting the half-side control points of the underwater rotating body is as follows: ① The first point is taken as the front edge of the rotating body and its position is set; ② The axial coordinate of the second point is the same as that of the first point, but its radial coordinate is different from that of the first point, so as to ensure that the front edge is a blunt head; ③ The control point n of the head-to-body junction is selected according to the head-to-body junction, and its radial coordinate is fixed as the radius of the rotating body, and its axial coordinate is variable, which is used to control the position of the head-to-body junction; ④ The radial coordinate of the n-1th point is the same as that of the nth point, so as to maintain a smooth transition of the head-to-body junction; ⑤ The axial and radial coordinates of points 3 to n-2 can be changed to control the shape of the head of the rotating body.

3. The multi-objective transition delay optimization method for underwater rotating body shape based on NSGA-Ⅱ according to claim 1 is characterized in that: In step three, the method for predicting the natural transition position of the boundary layer at the bow of a known underwater rotating body shape is as follows: numerically solve the dimensionless incompressible steady-state NS equations to obtain the laminar basic flow of the underwater rotating body; use a numerical method to solve the linear stability equations in the incompressible orthogonal curvilinear coordinate system to perform stability analysis; use the eN method to predict the natural transition position of the boundary layer at the bow of the underwater rotating body shape.

4. The multi-objective transition delay optimization method for underwater rotating body shape based on NSGA-Ⅱ according to claim 1 is characterized in that: The calculation formula for the crowding distance in step 5 is as follows: CD im represents the crowding degree of the ith individual in the mth objective function, f m represents the mth objective function, x max represents the maximum value of all individuals under the m function, x min Indicates the minimum value.

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