Multi-objective transition delay optimization method for underwater rotating body shape based on NSGA-Ⅱ

Abstract

The present invention relates to a multi-objective transition delay optimization method for underwater rotating body shapes based on NSGA-II, comprising the following steps: establishing a multi-objective optimization model; population initialization: selecting a plurality of known underwater rotating body shapes as an initial population; predicting the natural transition position of the bow boundary layer of each shape in the contemporary population at multiple ship speeds; non-dominated sorting; crowding calculation: calculating the crowding distance of each individual according to its target value, and sorting individuals with larger crowding distances higher; generating a child population: performing genetic operations of selection, crossover and mutation on all shapes in the contemporary population, thereby generating a child population; using an elite strategy, mixing the offspring and parent generations, performing non-dominated sorting and crowding calculation, and selecting the top N individuals as the next generation individuals; and iterative evolution to obtain a shape Pareto solution set, that is, a shape solution set with uniform distribution of transition position delay.

Description

Technical Field

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

[0002] The boundary layer at the bow of an underwater rotating vessel is divided into a laminar flow section, a transition section, and a turbulent section from front to back. The laminar flow section is relatively quiet and has low noise intensity; the turbulent flow section is relatively noisy; and the noise intensity of the transition section is very high, even exceeding that of the turbulent flow section. Therefore, the transition position of the boundary layer at the bow of an underwater rotating vessel has a significant impact on flow noise. This transition position varies significantly with the bow shape of the underwater rotating vessel. Therefore, by changing the bow shape of an underwater rotating vessel, the transition position of the bow boundary layer can be effectively influenced, thereby improving the detection capability of the bow sonar.

[0003] In order to optimize the bow shape of an underwater rotating body to delay the transition position, it is necessary to know the transition position of different rotating body shapes, that is, to predict the transition. For this, the eN method has been proposed (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 the shape of an underwater axisymmetric body for transition delay using a genetic algorithm at one speed (Lv, J., Liu, J., Zhang, Y., Liu, J., 2024. Optimization design of a body shape of an underwater axisymmetric body for transition delay using a genetic algorithm. Ocean Engineering 301, 117529.). However, in actual engineering, underwater navigation bodies have to sail at multiple speeds, so engineering needs to find the shape with the best comprehensive performance at multiple typical speeds. Studies have shown that when the speed changes, the Reynolds number effect will appear (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 speed (and the consequent change in Reynolds number) will cause irregular changes in the order of transition positions between different shapes. If single-objective optimization methods are used at different speeds, the optimal shapes obtained are different. Therefore, a multi-objective optimization algorithm is needed to solve this multi-objective optimization problem. At present, multi-objective intelligent optimization algorithms have been applied to underwater navigation body optimization problems, but most of them are applied with the goals of reducing drag, reducing pressure, and improving efficiency. There has been no multi-objective optimization work on the shape of underwater rotating bodies with the goal of delaying the transition positions at multiple speeds. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the existing technology and provide a feasible method for delaying the boundary layer transition of an underwater rotating body at multiple speeds. This method delays the transition by intelligently optimizing 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. 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] Determining a plurality of ship speeds requiring special delays, and taking delaying transition positions at the plurality of ship speeds as a plurality of optimization objectives;

[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. Individuals without a dominated relationship constitute the first-level solution set, namely the Pareto solution set. Several levels of solution sets are sorted in this way. 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 based on 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 current 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 top N individuals as the next generation;

[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 range of change of the control point position coordinates is as follows:

[0021] The weight of each control point is set to be fixed at 1. The method for selecting the control points of the half side of the underwater rotating body is as follows: ① Point 1 is used as the leading edge of the rotating body and its position is set; ② The axial coordinate of point 2 is the same as that of point 1, but its radial coordinate is different from that of point 1 to ensure that the leading edge is a blunt head; ③ The control point n at the head-to-body junction is selected according to the head-to-body junction. Its radial coordinate is fixed to the radius of the rotating body, and its axial coordinate is variable to control the position of the head-to-body junction; ④ The radial coordinate of point n-1 is the same as that of point n 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.

[0022] 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 equation in the incompressible orthogonal curve 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.

[0023] The calculation formula for the crowding distance in step 5 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 mth objective function, x max represents the maximum value of all individuals under the m function, x min Indicates the minimum value.

[0026] The beneficial effects of the present invention compared with the prior art are as follows:

[0027] 1) Compared with the existing single-objective optimization method (Tianjin University. "Transition delay optimization method of the bow shape of underwater rotating body based on genetic algorithm.", 202410227673.4.2024), the present invention performs comprehensive optimization at multiple speeds and can better meet actual engineering needs.

[0028] 2) The present invention uses a multi-objective genetic algorithm based on non-dominated sorting and congestion 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 A flowchart of the steps 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 symmetrical, so only the upper half needs to be expressed)

[0031] Figure 3 This is the non-dominated sorting diagram of the first generation of 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 is the number of individuals in the Pareto solution set of each generation

[0033] Figure 5 is the non-dominated sorting graph of individuals in the 14th generation

[0034] Figure 6 The maximum, average, and minimum values ​​of the individual transition positions in each generation of Pareto solution sets at a speed of 3.087 m / s are

[0035] Figure 7 The maximum, average, and minimum values ​​of the individual transition positions in each generation of Pareto solution sets at a speed of 5.144 m / s are

[0036] Figure 8 The maximum, average, and minimum values ​​of the individual transition positions in each generation of Pareto solution sets at a speed of 12.347 m / s are DETAILED DESCRIPTION

[0037] The present invention will be described in detail below in conjunction with specific embodiments and accompanying drawings. In the following description, for the purpose of explanation and not limitation, specific details are set forth to help a comprehensive understanding of 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 that depart from these specific details.

[0038] It should be noted that, in order to avoid obscuring the present invention due to unnecessary details, the accompanying drawings only show the device structure and / or processing steps closely related to the solution according to the present invention, while omitting other details that are not very relevant to the present invention.

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

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

[0041] Step 1: Establish a multi-objective optimization model as follows:

[0042] 1) Gene encoding

[0043] Using real number coding and the NURBS method, the control point coordinates are used to represent the genes of the shape (for specific methods, please refer to Tianjin University. "Transition delay optimization method for the bow shape of underwater rotating body based on genetic algorithm.", 202410227673.4.2024). 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 rotating 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 goals

[0045] The three optimization targets are to delay the transition positions at three speeds. This embodiment uses the transition positions at 3.087m / s, 5.144m / s and 12.347m / s as the optimization targets, 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] References for the range of control points (Lv, J., Liu, J., Zhang, Y., Liu, J., 2024. Optimization design of forebody shape of an underwater axisymmetric body for transition delay using agenetic algorithm. Ocean Engineering 301, 117529.)

[0050] In this step, the weight of each control point is fixed to 1. The functions of each control point are as follows: ① Point 1 is the leading edge of the rotation body, and its position is fixed to (0m, 0m). ② Point 2 has the same axial coordinate as point 1, but its radial coordinate is different from point 1 to ensure that the leading edge is blunt. ③ Point 18 is the head-body junction, and its radial coordinate is fixed to the radius of the rotation body r. *=5.8315m; its axial coordinate is variable, used to control the position of the head-body junction. ④ The radial coordinate of point 17 is the same as that of point 18 to maintain a smooth transition of the head-body junction. ⑤ The axial and radial coordinates of points 3-16 can be changed to control the shape of the head of the rotating body. According to the above settings, there are a total of 31 variable variables, including the axial and radial coordinates of points 3-16, the radial coordinate of point 2, and the axial coordinates of points 17 and 18. The variation range of each control point taken by the present invention is shown in Table 1.

[0051] Table 1 Value range of each control point (unit: m)

[0052]

[0053] Step 2: Population initialization: Use several classic shapes currently used in engineering or research as the initial population.

[0054] In this step, the seven shapes (SUBOFF, LYW1, LYW2, LYW3, LYW4, Ellipse, and LGLS) in Liu et al. (2023) are used as the initial population. A detailed introduction to the shapes can be found in the literature (Liu, J., Liu, J., Zhang, Y., 2023. Influence of Reynolds number on the natural transition of boundarylayers over underwater axisymmetric bodies. Phys. Fluids 35, 044107.).

[0055] Step 3: Predict the natural transition position of the bow boundary layer for each shape in the contemporary population at three speeds.

[0056] In this step, the dimensionless incompressible steady-state NS equations are numerically solved to obtain the laminar basic flow of the underwater rotating body; the linear stability equations in the incompressible orthogonal curvilinear coordinate system are solved numerically to perform stability analysis; and the eN method is used to predict the transition position of the underwater rotating body.

[0057] 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. Individuals without a dominated relationship constitute the first-level solution set (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. The non-dominated sorting of all individuals in the initial population is as follows: Figure 3 As shown, the first level represented by red is the optimal solution set, namely the Pareto solution set, and the seventh level represented by 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 the crowding distance is as follows:

[0060]

[0061] Among them CD im represents the crowding degree of the i-th individual in the m-th 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 in the figure. The maximum and average values ​​of the transition positions of individuals in the Pareto solution set at the three speeds gradually increase in each generation, as shown in the figure. The average value at 3.087 m / s increases from 4.97185 m in the first generation to 5.450072 m in the 14th generation; the average value at 5.144 m / s increases from 3.874923 m in the first generation to 4.070525 m in the 14th generation; and the average value at 12.347 m / s increases from 2.09733 m in the first generation to 2.506413 m 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 "include / comprises" when used herein refers to the presence of features, integers, steps or components, but does not exclude the presence or addition of one or more other features, integers, steps, components or combinations thereof.

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

[0069] The 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 the true spirit and scope thereof. Furthermore, since numerous modifications and changes will readily occur to those skilled in the art, it is not intended that the embodiments of the invention be limited to the exact construction and operation illustrated and described, but rather that all suitable modifications and equivalents be covered within the scope thereof.

[0070] Parts of the present invention that are not described in detail are well known 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. The mapping from the control point coordinates to the transition position is the mapping from genotype to phenotype. 2) Determine multiple optimization goals Determining a plurality of ship speeds requiring special delays, and taking delaying transition positions at the plurality of ship speeds as a plurality of optimization objectives; 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. Individuals without a dominated relationship constitute the first-level solution set, namely the Pareto solution set. Several levels of solution sets are sorted in this way. 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 based on 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 current 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 top N individuals as the next generation; 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.

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 control points on the half side of the underwater rotating body is as follows: ① The first point is used as the leading 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 leading edge is blunt; ③ The control point n at the head-to-body junction is selected according to the head-to-body junction. Its radial coordinate is fixed to the radius of the rotating body, and its axial coordinate is variable 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 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 equation in the incompressible orthogonal curve 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 i-th individual in the m-th 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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