Three-dimensional shape optimization method, three-dimensional shape optimization device and three-dimensional shape optimization program

Abstract

To provide a three-dimensional shape optimization method, a three-dimensional shape optimization device and an aerodynamic shape optimization program which can automatically compute an optimum three-dimensional shape of an object existing in a flow field.SOLUTION: A method which optimizes a three-dimensional shape of an object existing in a flow field includes: a three-dimensional shape creation process (#400) of creating the three-dimensional shape of each individual of a group of initial individuals of the object; an objective function calculation process (#500) of performing a numerical fluid analysis to the three-dimensional shape of each individual to calculate an objective function of each individual; a next-generation individual generation process (#600) of selecting an excellent individual by an evolutionary algorithm, on the basis of the objective function of each individual to generate a next-generation individual; and an optimization shape search process (#700) of searching for an optimization shape of the object, by repeating creation of the three-dimensional shape of the next-generation individual, calculation of the objective function, and generation of the next generation individual, up to a specific generation.SELECTED DRAWING: Figure 13

Description

Technical Field

[0001] The present invention relates to a three-dimensional shape optimization method, a three-dimensional shape optimization device, and a three-dimensional shape optimization program for optimizing the three-dimensional shape of an object existing in a flow field.

Background Art

[0002] In railway vehicles, various considerations are required, such as devising a shape that takes into account workability and designability while ensuring sufficient vehicle body strength and vehicle volume while suppressing air resistance, aerodynamic noise, and vehicle body vibration. These performances required for railway vehicles often have a trade-off relationship, and the design of an optimal shape considering each performance may sometimes rely on the experience and know-how of designers.

[0003] A conventional method for optimizing the shape of a pantograph component (hereinafter referred to as Conventional Technique 1) includes a step of executing a simulation of a flow field in which a shape defined by a predetermined curve is arranged, and a step of using an optimization method so that an objective function is minimized. By repeating the execution of this simulation and the use of the optimization method, a shape in which the objective function is minimized is obtained (see, for example, Patent Document 1). In Conventional Technique 1, hydrodynamic performances such as lift and drag are used as the objective function, and an optimal cross-sectional shape of the hull is obtained by using a predetermined optimization method that minimizes or maximizes this objective function.

[0004] The method for determining the airfoil of a conventional helicopter rotor blade (hereinafter referred to as Prior Art 2) includes the steps of determining the characteristic equations of the upper and lower airfoil surfaces based on randomly generated airfoil sample points, simulating the dynamic characteristics of the airfoil according to the characteristic equations of the upper and lower airfoil surfaces to obtain the flow field characteristics of the airfoil, establishing the mapping relationship between the airfoil sample points and the flow field characteristics to obtain the trained mapping relationship, determining the optimal airfoil sample points according to the trained mapping relationship, and determining the airfoil of the rotor blade from the optimal airfoil sample points (see, for example, Patent Document 2). In Prior Art 2, an optimized design of the aerodynamic characteristics of the airfoil in the state of variable inflow - variable angle of attack is realized, and the dynamic stall characteristics in this state are effectively reduced.

Prior Art Documents

Patent Documents

[0005]

Patent Document 1

[0006]

Patent Document 2

Summary of the Invention

Problems to be Solved by the Invention

[0007] In Prior Art 1, when obtaining the optimal shape by minimizing the objective function regarding the change in the angle of attack, only the lift coefficient is set as the objective function, and a predetermined optimization method for minimizing this objective function is used to obtain the optimal cross - sectional shape of the hull. Therefore, in Prior Art 1, since multiple objective functions cannot be set, the two performances to be obtained are expressed by one function, and there is a possibility that only a shape that satisfies only one performance is generated. Also, in Prior Art 1, only two - dimensional cross - sections are targeted, and it is not an optimization considering the three - dimensionality of the object, and an optimal cross - sectional shape of the hull considering three - dimensionality cannot be obtained.

[0008] In the prior art 2, although it is a method for optimizing the airfoil shape of a helicopter, the target airfoil shape is determined by an airfoil equation and is limited to shapes that satisfy the airfoil equation. Further, in the prior art 2, the aerodynamic characteristics of each shape are obtained as predicted values based on calculation results from a general shape, and there may be a lack of accuracy. Furthermore, in the prior art 2, as in the prior art 1, only two-dimensional cross-sections are targeted, and it is not an optimization considering the three-dimensionality of the object, and an optimal cross-sectional shape airfoil shape considering three-dimensionality cannot be obtained.

[0009] An object of the present invention is to provide a three-dimensional shape optimization method, a three-dimensional shape optimization device, and an aerodynamic shape optimization program that can automatically calculate an optimal three-dimensional shape of an object existing in a flow field.

Means for Solving the Problems

[0010] The present invention solves the above problems by the following means for solving. Note that reference numerals corresponding to embodiments of the present invention will be used for explanation, but the present invention is not limited to these embodiments. The invention according to claim 1 is a three-dimensional shape optimization method for optimizing the three-dimensional shape of an object (2a; 2b; 8) existing in a flow field, as shown in FIGS. 1, 3, 7, 8, 13, 15, and 19, wherein a three-dimensional shape creation step (#140) for creating a three-dimensional shape (S 2 ) of each individual in the population of initial individuals of the object, an objective function calculation step (#500) for performing numerical fluid analysis on the three-dimensional shape of each individual in the population of initial individuals of the object and calculating the objective function of each individual, and based on the objective function of each individual in the population of initial individuals of the object, selecting excellent individuals by an evolutionary algorithm and generating individuals of the next generation in a next generation individual generation step (#600), and repeating the creation of the three-dimensional shape of the individuals of the next generation, the calculation of the objective function of the individuals of the next generation, and the generation of individuals of the further next generation of the individuals of the next generation up to a specific generation, thereby obtaining the optimized shape (S 3It is a three-dimensional shape optimization method (#100) including an optimization shape search step (#700) for searching for ).

[0011] The invention according to claim 2 is the three-dimensional shape optimization method according to claim 1, wherein, as shown in FIG. 6, in the objective function calculation step, for each three-dimensional shape of each individual in the population of initial individuals of the object, a computational grid (G 0 ) generated by the orthogonal grid method is used to perform numerical fluid analysis to calculate the objective function of each individual.

[0012] The invention according to claim 3 is the three-dimensional shape optimization method according to claim 2, wherein, as shown in FIG. 6, in the objective function calculation step, among the grid points (P 0 ) of the computational grid common to each three-dimensional shape of each individual in the population of initial individuals of the object, based on the grid points (P 01 ) located outside the three-dimensional shape of each individual, numerical fluid analysis is performed to calculate the objective function of each individual.

[0013] The invention according to claim 4 is the three-dimensional shape optimization method according to claim 1, wherein, as shown in FIG. 1, the three-dimensional shape creation step includes creating a three-dimensional shape of each individual in the population of initial individuals of the boat body (8) of the current collector device (3), and the objective function calculation step includes calculating at least two objective functions among the objective functions representing the lift stability, noise performance, air resistance reduction performance, or target value of lift of the boat body.

[0014] The invention according to claim 5 is the three-dimensional shape optimization method according to claim 4, wherein, as shown in FIG. 9, the three-dimensional shape creation step includes creating a three-dimensional shape of each individual representing the worn shape of the slider (8a) supported by the boat body.

[0015] The invention according to claim 6 is the three-dimensional shape optimization method according to claim 1, wherein, as shown in FIG. 15, the shape creation step includes a step of creating a three-dimensional shape of each individual in a population of initial individuals of the front part (2a) of the moving body (2), and the objective function calculation step includes a step of calculating at least two objective functions among the micro-pressure wave reduction performance of the front part of the moving body, the air resistance reduction performance, or the objective function representing the volume of the front part of the moving body. This is a three-dimensional shape optimization method characterized by this.

[0016] The invention according to claim 7 is the three-dimensional shape optimization method according to claim 1, wherein, as shown in FIG. 19, the three-dimensional shape creation step includes a step of creating a three-dimensional shape of each individual in a population of initial individuals of the rear part (2b) of the moving body (2), and the objective function calculation step includes a step of calculating the air resistance reduction performance of the rear part of the moving body and the objective function representing the fluctuating aerodynamic force (F) acting on the rear part of this moving body. This is a three-dimensional shape optimization method characterized by this.

[0017] The invention according to claim 8 is the three-dimensional shape optimization method according to claim 1, wherein, as shown in FIG. 19, the three-dimensional shape creation step includes a step of creating a three-dimensional shape of each individual in a population of initial individuals of both ends (2a, 2b) of the moving body of the same shape, and the objective function calculation step includes a step of calculating at least one objective function among the micro-pressure wave reduction performance, the air resistance reduction performance, or the objective function representing the volume of both ends of the moving body, and a step of calculating at least one objective function of the air resistance reduction performance of both ends of the moving body or the objective function representing the fluctuating aerodynamic force acting on both ends of this moving body. This is a three-dimensional shape optimization method characterized by this.

[0018] The invention according to claim 9 is a three-dimensional shape optimization system for optimizing the three-dimensional shape of an object (2a; 2b; 8) existing in a flow field, as shown in FIGS. 1 to 3, FIGS. 7, 8, 14, 15, and 19, wherein the three-dimensional shape (S 2A three-dimensional shape creation unit (14) that creates 3 ), an objective function calculation unit (23) that performs numerical fluid analysis on the three-dimensional shape of each individual in the population of initial individuals of the object and calculates the objective function of each individual, and based on the objective function of each individual in the population of initial individuals of the object, a next-generation individual generation unit (15) that selects excellent individuals by an evolutionary algorithm and generates next-generation individuals, and creation of the three-dimensional shape of the next-generation individuals, calculation of the objective function of the next-generation individuals, and generation of individuals of the further next generation of the next-generation individuals are repeated up to a specific generation to search for the optimized shape (S

[0019] The three-dimensional shape optimization system (9) includes an optimization shape search unit (13).

[0020] The invention according to claim 11 is a three-dimensional shape optimization program for optimizing the three-dimensional shape of an object (2a; 2b; 8) existing in a flow field, as shown in FIGS. 1, 3, 7, 8, 14, 15, and 19. For each individual in the population of initial individuals of the object, the three-dimensional shape (S 2A three-dimensional shape creation procedure (S130) for creating

Effect of the Invention

[0021] According to this invention, the optimal three-dimensional shape of an object existing in a flow field can be automatically calculated.

Brief Description of the Drawings

[0022]

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BEST MODE FOR CARRYING OUT THE INVENTION

[0023] (First Embodiment) Hereinafter, a first embodiment of the present invention will be described in detail with reference to the drawings. The overhead wire 1 shown in FIG. 1 is an electric train wire erected above the railway track. The overhead wire 1 is supported at support points at predetermined intervals. The trolley wire 1a is a wire with which the sliding plate 8a of the current collector 3 comes into contact. The trolley wire 1a supplies a load current to the vehicle 2 as the sliding plate 8a makes contact and moves. The vehicle 2 is a moving body that moves along the railway track. The vehicle 2 is an electric vehicle such as an electric train or a locomotive, and is, for example, a railway vehicle that travels on the Shinkansen (registered trademark) at a high speed of 320 km / h or more.

[0024] The current collector 3 is a device for guiding electric power from the trolley wire 1a to the vehicle 2. The current collector 3 includes a pedestal frame 4, an insulator 5, a framework 6, a boat support portion 7, and a boat body (current collecting boat) 8. The pedestal frame 4 is a member that supports the framework 6. The insulator 5 is a member that electrically insulates between the vehicle body of the vehicle 2 and the pedestal frame 4. The framework 6 is a link mechanism that can operate in the vertical direction while supporting the boat body 8. The boat support portion 7 is a mechanism portion that pushes up the boat body 8 horizontally with respect to the overhead wire 1 and gives a buffering action by a spring, and is pushed up upward by a push-up spring provided in the pedestal frame 4. The current collector 3 shown in FIG. 1 is an asymmetric single-arm pantograph that can be used in one direction or both directions with respect to the traveling direction of the vehicle 2.

[0025] The boat body 8 is a member for attaching and supporting the wear plate 8a. The boat body 8 is generally an elongated metal plate-like member extending in a direction perpendicular to the trolley wire 1a. The boat body 8 shown in FIG. 1 is the current collector boat of the Shinkansen pantograph. The boat body 8 includes a wear plate 8a and a horn 8b. The wear plate 8a is a member that contacts the trolley wire 1a. The wear plate 8a is a metal or carbon plate-like member that is divided into a plurality of wear plate pieces along the length direction of the boat body 8. The horn 8b is a member for preventing the vehicle 2 from interrupting the trolley wire 1a in a direction different from the traveling direction of the vehicle 2 among the two trolley wires 1a that intersect above the branch when the vehicle 2 passes through the branch. As shown in FIG. 1(B), the horn 8b protrudes from both ends in the length direction of the boat body 8 and is a metal member with a curved tip.

[0026] The three-dimensional shape optimization system 9 shown in FIG. 2 is a system for optimizing the three-dimensional shape S of the boat body 8 existing in the flow field. 2 The three-dimensional shape optimization system 9 optimizes the three-dimensional shape S of the boat body 8 in order to stabilize the lift force of the boat body 8, reduce noise, reduce air resistance, or set the lift force to a specific target value. 2 The three-dimensional shape optimization system 9 explores the optimal three-dimensional shape S of the boat body 8 by a multi-objective optimization method that combines numerical fluid analysis and an evolutionary algorithm. 2 The three-dimensional shape optimization system 9 uses, for example, a shape deformation method, an air flow simulation, and an evolutionary algorithm to search for an optimal aerodynamic shape of the boat body 8 that satisfies arbitrary shape constraints and a plurality of aerodynamic characteristics. Here, the aerodynamic shape is a shape considering the forces of air such as air resistance acting on an object existing in the air.

[0027] As shown in FIG. 3, the three-dimensional shape optimization system 9 automatically performs the creation of the air flow simulator for the initial individuals, the calculation of the objective function, the creation of the next-generation individuals by evolutionary calculation, and the acquisition of the optimized shape S. 3 The three-dimensional shape optimization system 9 creates the design variables of each individual in the population of the initial individuals, and based on these design variables, the three-dimensional shape S of each individual of the boat body 82 is created. The three-dimensional shape optimization system 9 performs numerical fluid analysis on the three-dimensional shape S of each individual to calculate the objective function, selects excellent individuals (parent generation) from the values of the objective function of each individual, and generates the design variables of the individuals in the next generation (child initial generation). The three-dimensional shape optimization system 9 repeats the creation of the three-dimensional shape S of the hull 8, the calculation of the objective function, and the generation of the design variables of the individuals in the next generation, so as to converge to the optimal solution that inherits the characteristics of the excellent individuals with excellent performance. 2 For the three-dimensional shape S of the hull 8, the three-dimensional shape optimization system 9 performs numerical fluid analysis to calculate the objective function, selects excellent individuals (parent generation) from the values of the objective function of each individual, and generates the design variables of the individuals in the next generation (child initial generation). The three-dimensional shape optimization system 9 repeats the creation of the three-dimensional shape S of the hull 8, the calculation of the objective function, and the generation of the design variables of the individuals in the next generation, so as to converge to the optimal solution that inherits the characteristics of the excellent individuals with excellent performance. 2 By repeating the creation of the three-dimensional shape S, the calculation of the objective function, and the generation of the design variables of the individuals in the next generation, the three-dimensional shape optimization system 9 converges to the optimal solution that inherits the characteristics of the excellent individuals with excellent performance.

[0028] As shown in FIG. 2, the three-dimensional shape optimization system 9 includes computers 10 and 22 and a communication device 28. The three-dimensional shape optimization system 9 performs the creation of the three-dimensional shape S of the initial individuals and the generation of the individuals in the next generation by evolutionary calculation by the computer 10. The three-dimensional shape optimization system 9 performs the calculation of the objective function by the air flow simulator after the creation of the three-dimensional shape S by the computer 22. The three-dimensional shape optimization system 9 performs the creation of the individuals in the next generation by the computer 10 based on the objective function of each individual calculated by the air flow simulator. The three-dimensional shape optimization system 9 repeats the creation of the three-dimensional shape S of the individuals in the next generation, the calculation of the objective function by the air flow simulator, and the creation of the individuals in the next generation by the computers 10 and 22 until the specified generation, so as to obtain the optimized shape S 2 by the computer 10. 2 After the creation of the three-dimensional shape S, the three-dimensional shape optimization system 9 performs the calculation of the objective function by the air flow simulator by the computer 22. The three-dimensional shape optimization system 9 performs the creation of the individuals in the next generation by the computer 10 based on the objective function of each individual calculated by the air flow simulator. The three-dimensional shape optimization system 9 repeats the creation of the three-dimensional shape S of the individuals in the next generation, the calculation of the objective function by the air flow simulator, and the creation of the individuals in the next generation by the computers 10 and 22 until the specified generation, so as to obtain the optimized shape S 2 by the computer 10. 3 The computer 10 is a device that automatically performs various calculations and data processing. The computer 10 is for the three-dimensional shape S of the initial individuals

[0029] The computer 10 is a device that automatically performs various calculations and data processing. The computer 10 is for the three-dimensional shape S of the initial individuals 2Create and perform evolutionary calculations. The computer 10 is a small personal general-purpose computer such as a personal computer, and causes the computer to execute predetermined processing according to a three-dimensional shape optimization program. As shown in FIG. 2, the computer 10 includes an input unit 11, an initial individual generation unit 12, an optimization requirement setting unit 13, a three-dimensional shape creation unit 14, a next-generation individual generation unit 15, an optimized shape search unit 16, a transmission / reception unit 17, a data storage unit 18, a three-dimensional shape optimization program storage unit 19, a display unit 20, and a control unit 21. The computer 10 performs the creation of the three-dimensional shape S by the three-dimensional shape creation unit 14, the generation of the next-generation individuals by the next-generation individual generation unit 15, and the search for the optimized shape S by the optimized shape search unit 16. The computer 10 transmits data related to the three-dimensional shape S and data related to the calculation grid G common to each individual of the initial individual population of the hull 8 to the computer 22 as data necessary for the calculation of the objective function. 2 The creation of, the generation of the next-generation individuals by the next-generation individual generation unit 15, and the search for the optimized shape S by the optimized shape search unit 16. The computer 10 performs the creation of the three-dimensional shape S 3 The search for. The computer 10 performs the three-dimensional shape S 2 Data related to, and the calculation grid G common to each individual of the three-dimensional shape S of each individual of the initial individual population of the hull 8 2 To the computer 22 as data necessary for the calculation of the objective function. 0

[0030] The input unit 11 is a means for inputting various information necessary for optimizing the three-dimensional shape S of the hull 8. The input unit 11 is, for example, an input device or an auxiliary input device that inputs various information to the computer 10 by manual operation of the user. The input unit 11 inputs the feature points P of the initial shape S necessary for the generation of the initial individuals of the hull 8, generates the calculation grid G common to all the three-dimensional shapes S of the initial individuals, selects an arbitrary evolutionary algorithm from various evolutionary algorithms used for evolutionary calculations, inputs the objective function, design conditions, constraint conditions, etc. necessary for setting the optimization requirements, and inputs the control points P necessary for the deformation of the three-dimensional shape S. The input unit 11 outputs data related to the input information after input to the control unit 21 as input data. 2 1 Of, the calculation grid G common to all the three-dimensional shapes S of the initial individuals, selects an arbitrary evolutionary algorithm from various evolutionary algorithms used for evolutionary calculations, inputs the objective function, design conditions, constraint conditions, etc. necessary for setting the optimization requirements, and inputs the control points P necessary for the deformation of the three-dimensional shape S. The input unit 11 outputs data related to the input information after input to the control unit 21 as input data. 1 2 0 2 Of, the control points P necessary for the deformation of the three-dimensional shape S 2

[0031] The initial individual generation unit 12 is a means for generating a population of initial individuals of the hull 8. As shown in FIG. 4, the initial individual generation unit 12 extracts the characteristic points P 1 of the initial shape S 1 of the hull 8 as design variables. The initial individual generation unit 12 determines the design variables, for example, by the Latin hypercube method that divides the variation range of each design variable by the number of individuals and distributes the values of the divided design variables so that each value is used once, and generates a population of initial individuals of the hull 8 as shown in FIG. 5. Here, the design variable is a value to be changed when performing the optimal design and is a main parameter for determining the optimal design. The design variables are, for example, coordinate values, lengths, gradients, etc. that determine the characteristics of the initial shape S 1 . The initial individual generation unit 12 realizes sampling according to a given probability distribution with a small number of samplings. The initial individual generation unit 12, for example, varies each shape so as not to be biased toward a specific shape as shown in FIG. 5, and generates a large number of populations of initial individuals of the hull 8. The initial individual generation unit 12 stores the data regarding the design variables, etc. of the generated population of initial individuals of the hull 8 in the data storage unit 18 as initial individual data.

[0032] The initial individual generation unit 12 generates a computational grid G 2 common to the three-dimensional shapes S 0 of each individual in the population of initial individuals of the hull 8. As shown in FIG. 6, the initial individual generation unit 12 generates one computational grid G 2 common to all the three-dimensional shapes S 0 of the population of initial individuals of the hull 8. Here, the computational grid G 0 is an analysis region used for discretization in numerical analysis and is a partial region obtained by dividing a two-dimensional or three-dimensional geometric shape into a finite number of parts. In FIG. 6, for ease of understanding of the invention, the cross-sectional shape of the three-dimensional shape S 2 of the hull 8 is represented two-dimensionally. The initial individual generation unit 12, for example, generates one computational grid G 2A , S 2B common to different three-dimensional shapes S 0 in advance even if they have different shapes as shown in FIG. 6. The initial individual generation unit 12 is the optimized shape S as shown in FIG. 3 3The calculation of the objective function repeated until search and the next-generation three-dimensional shape S 2 In the generation of, the same computational grid G 0 is used, and all three-dimensional shapes S of the population of the initial individuals of the hull 8 2 A single computational grid G common to 0 is generated. The initial individual generation unit 12 stores data related to the computational grid G 2 common to the three-dimensional shape S of each individual after generation 0 in the data storage unit 18 as computational grid data.

[0033] The optimization requirement setting unit 13 shown in FIG. 2 is means for setting requirements for optimizing the three-dimensional shape S of the population of the initial individuals of the hull 8 2 The optimization requirement setting unit 13 is for the three-dimensional shape S of the population of the initial individuals of the hull 8 2Set an objective function, design conditions, and constraint conditions, which are requirements for optimization. Here, the objective function is a performance index that desires to be minimized or maximized in an optimization problem. The objective function is, for example, a value or function that desires to be minimized or maximized in an optimization problem such as air resistance, lift, or noise level. The design conditions are the specifications of the hull 8. The design conditions are, for example, the chord length of the hull 8 and the vertically symmetric structure. The constraint conditions are requirements that the hull 8 should satisfy. The constraint conditions are, for example, the design space that is the range in which the design variables of the hull 8 change, the minimum thickness, or the maximum volume. The optimization requirement setting unit 13 sets at least two objective functions among the objective functions representing the lift stability, noise performance, air resistance reduction performance, or target value of lift of the hull 8. The optimization requirement setting unit 13, for example, minimizes the change in the angle of attack, which is the angle formed by the longitudinal direction (width direction) of the hull 8 and the flow direction, and the change in lift due to the wear of the skid plate 8a to increase stability, and sets the lift stability and the noise performance that minimizes the aerodynamic noise generated from the hull 8 to reduce the aerodynamic noise as the objective functions. The optimization requirement setting unit 13, for example, as shown in Fig. 8(A), sets the cross-sectional shape of the hull 8 to be vertically symmetric, the chord length of the hull 8 (for example, 120 mm), and the amount of cut-off from the upper end (for example, 6 mm) of the wear shape of the skid plate 8a as shown in Fig. 9 as the design conditions. The optimization requirement setting unit 13 sets the minimum thickness of the hull 8 (for example, at least 50 mm) and the magnitude of the lift acting on the hull 8 as the constraint conditions. The optimization requirement setting unit 13 is the three-dimensional shape S of the hull 8 after setting 2 regards the data regarding the optimization requirements of as the optimization requirement data and stores it in the data storage unit 18.

[0034] The three-dimensional shape creation unit 14 shown in Fig. 2 is a means for creating the three-dimensional shape S of each individual in the population of the initial individuals of the hull 8. 2 As shown in Fig. 3, the three-dimensional shape creation unit 14 creates the three-dimensional shape S of each individual in the population of the initial individuals of the hull 8 generated by the initial individual generation unit 12 1 based on the design variables of the initial shape S of each individual, creates the three-dimensional shape S of each individual, and based on the design variables of the three-dimensional shape S of the next-generation individuals of the hull 8 generated by the next-generation individual generation unit 15 2 creates the three-dimensional shape S of each individual, and at the same time, 2 creates the three-dimensional shape S of each of these next-generation individuals based on the design variables of the three-dimensional shape S of the next-generation individuals of the hull 8.2 Create it. As shown in FIG. 7(A), for example, the three-dimensional shape creation unit 14 creates a control grid G that covers the hull 8 made of a mesh model (polygon mesh) M 1 and, as shown in FIG. 7(B), moves each control point P of the control grid G 1 in an arbitrary direction to deform the control grid G 2 and uses free-form deformation (FFD) to deform the mesh model M, thereby creating the three-dimensional shape S of each individual in the initial population from the initial shape S 1 of each individual. The three-dimensional shape creation unit 14 creates the three-dimensional shape S of each individual having the cross-sectional shape of the hull 8 as shown in FIG. 8 1 and creates the three-dimensional shape S of each individual representing the worn shape of the rubbing plate 8a of the hull 8 as shown in FIG. 9 2 . Here, in FIGS. 8 and 9, for ease of understanding of the invention, the cross-sectional shape of the three-dimensional shape S of the hull 8 shown in FIG. 7(B) is represented two-dimensionally 2 . The three-dimensional shape creation unit 14 makes the lower surface of the hull 8 symmetric with the upper surface with reference to an ellipse having a longitudinal direction of 120 mm and a height of 50 mm as shown in FIG. 8, and moves the five control points P on the upper surface of the hull 8 within a range of ±25 mm in the height direction to change the cross-sectional shape of the hull 8. The three-dimensional shape creation unit 14 sets the control point P of the control grid G moved by free-form deformation 2 as the design variable of the three-dimensional shape S 2 . The three-dimensional shape creation unit 14 stores data regarding the design variables of the three-dimensional shape S of each individual changed by the user using the input unit 11 in the data storage unit 18 as three-dimensional shape data 2 . 1 2 2 2

[0035] ​​​​The next-generation individual generation unit 15 shown in FIG. 2 is a means for selecting excellent solids by an evolutionary algorithm based on the objective function of each individual in the population of initial individuals of the hull 8 and generating the next-generation individuals. The next-generation individual generation unit 15 generates the next-generation individuals using an evolutionary algorithm, which is a type of evolutionary computation. Here, the evolutionary algorithm is an evolutionary computation method that mimics the process of biological evolution in which individuals suitable for the environment leave offspring, inherit characteristics from the genes of high-performance individuals, and generate the next-generation individuals. The evolutionary algorithm is an algorithm inspired by the mechanisms of evolution such as reproduction, mutation, genetic recombination, natural selection, and survival of the fittest. In the evolutionary algorithm, genes are replaced with design variables, and environmental adaptability is replaced with the objective function. The next-generation individual generation unit 15 generates the design variables of the next-generation individuals by multi-objective optimization using the evolutionary algorithm. Here, multi-objective optimization is a method of searching for an optimal solution that satisfies multiple performances even when the desired performances are in a trade-off relationship by setting multiple objective functions. The next-generation individual generation unit 15 gives a fitness value to each individual according to the objective function calculated by the objective function calculation unit 23 of the computer 22, generates a pair of parent individuals based on this fitness value, crosses the design variables of each individual to generate a child generation, and repeats the process of generating a grandchild generation from the generated child generation to search for better individuals. The next-generation individual generation unit 15 minimizes the objective function representing the lift stability of the hull 8, minimizes the objective function representing the noise performance, minimizes the objective function representing the air resistance reduction performance, or generates the design variables of the next-generation individuals such that the objective function representing the target value of the lift approaches the target value. The next-generation individual generation unit 15 repeats the generation of the design variables of the individuals until a specified generation while creating new shapes until the optimization converges. The next-generation individual generation unit 15 stores data regarding the design variables of the generated next-generation individuals, etc. in the data storage unit 18 as next-generation individual data (design variable data).

[0036] The optimization shape search unit 16 is a means for searching for the optimization shape S of the hull 8 3 as shown in FIG. 3, the three-dimensional shape S of the next-generation individuals 2By repeating the creation, the calculation of the objective function, and the generation of individuals in the next generation up to a specific generation, the optimized shape S of the hull 8 3 is searched for. The optimized shape search unit 16 searches for the optimized shape S 3 of the hull 8 as shown in FIGS. 10 and 11, for example. The optimized shape search unit 16 creates the three-dimensional shape S 2 of each individual in the next generation by the three-dimensional shape creation unit 14, calculates the objective function of this individual in the next generation by the objective function calculation unit 23, and generates the design variables of the individuals in the further next generation by the next generation individual generation unit 15, and sequentially repeats the above operations up to the specified generation to perform the optimization calculation, thereby searching for the optimized shape S 3 which is a better solution. The optimized shape search unit 16 stores the data regarding the optimized shape S 3 after the search in the data storage unit 18 as optimized shape data.

[0037] FIG. 10 is a graph showing an example of the objective function space of the optimization result. Here, the vertical axis shown in FIG. 10 is the standard deviation of the lift coefficient (noise performance), and the horizontal axis is the lift stability with respect to the angle of attack change and friction. FIG. 11 is a longitudinal sectional view showing an example of the result of the optimization calculation in the case of the number of individuals being 30 and the number of generations being 32. As shown in FIG. 10, the non-dominated solutions obtained at the final generation time point form a Pareto front. Here, the non-dominated solution means a solution (Pareto solution) that is not inferior to all other individuals. When comparing individual A and individual B, individual A is considered to be inferior to individual B when all the objective functions of individual A are inferior. As shown in FIG. 10, it is considered that the solution has advanced in the optimization direction compared to the initial individual, and the optimization calculation has been correctly performed. As shown in FIG. 11, individuals superior to the past optimal solutions have been generated. Compared with the past optimal solutions, a shape has been obtained in which the lift stability has been sufficiently improved while the noise performance remains equivalent to the non-dominated solutions.

[0038] The numbers in parentheses for each individual shown in Fig. 11 represent the ranking of the objective function. The smaller the number, the greater the stability but also the greater the noise. Conversely, the larger the number, the smaller the stability but also the smaller the noise. Individuals (1) to (9) that satisfy the minimum thickness are overall of a similar shape, and individual (6) has the best balance between lift stability and noise performance. As a characteristic of the shape, it was found that the tip bulges, the center is slightly concave, and the rear end is thinner than the tip. For individuals (1) to (9), the same negative pressure is generated on the upper and lower surfaces, making the lift change less sensitive to the angle of attack and wear, and it is considered that the stability is improved. Also, it is considered that by making the rear end thinner, the vortex scale generated in the wake is suppressed to be small, reducing the lift fluctuation. When compared with the past optimal solution, it was confirmed that the tip bulges and the rear end is thinner, but the center is closer to a streamline shape and has a different shape. Individuals (10) to (12) are the group of individuals with the best noise performance, but the entire hull is very thin and does not satisfy the minimum thickness of 50 mm. Note that individuals (10) and (11) are the initial individuals created without considering the thickness.

[0039] The transmission / reception unit 17 shown in Fig. 2 is a means for transmitting and receiving various information between the computer 10 and the computer 22. The transmission / reception unit 17, for example, transmits a numerical fluid analysis command signal for instructing the execution of numerical fluid analysis to each individual in the group of initial individuals of the hull 8 from the computer 10 to the computer 22, transmits the computational grid data generated by the initial individual generation unit 12 to the computer 22, transmits the three-dimensional shape data created by the three-dimensional shape creation unit 14 to the computer 22, and receives the objective function data after the computer 22 calculates the objective function.

[0040] The data storage unit 18 is a means for storing various data related to the three-dimensional shape optimization system 9. The data storage unit 18 is a storage device that stores, for example, the initial individual data and calculation grid data generated by the initial individual generation unit 12, the optimization requirement data set by the optimization requirement setting unit 13, the three-dimensional shape data created by the three-dimensional shape creation unit 14, the next-generation individual data generated by the next-generation individual generation unit 15, the optimized shape data searched by the optimized shape search unit 16, and the objective function data calculated by the objective function calculation unit 23, in correspondence with each individual of the population of initial individuals.

[0041] The three-dimensional shape optimization program storage unit 19 stores the three-dimensional shape S of the boat 8 existing in the flow field. 2 The three-dimensional shape optimization program storage unit 19 is a storage device or the like that stores a three-dimensional shape optimization program read from an information recording medium or a three-dimensional shape optimization program downloaded through an electric communication line.

[0042] The display unit 20 is a means for displaying various information related to the three-dimensional shape optimization system 9. For example, the display unit 20 displays the initial shape S of the boat 8 generated by the initial individual generating unit 12 as shown in FIG. 1 and the design variables and the three-dimensional shape S of the boat 8 set by the optimization requirement setting unit 13 2 The objective function and design conditions, which are the requirements for optimization, and the three-dimensional shape S of each individual of the initial individual of the boat 8 created by the three-dimensional shape creation unit 14 as shown in Figs. 2 , the cross-sectional shape and the wear shape, the design variables of the boat 8 of each generation generated by the next generation individual generating unit 15, and the optimized shape S searched by the optimized shape searching unit 16 as shown in FIG. 10 and FIG. 3 and a display device that displays design variables, etc. on a screen.

[0043] The control unit 21 shown in FIG. 2 is a central processing unit (CPU) that controls various operations related to the computer 10. The control unit 21 reads out the three-dimensional shape optimization program from the three-dimensional shape optimization program storage unit 19 and executes the three-dimensional shape optimization process according to this three-dimensional shape optimization program. The control unit 21, for example, commands the initial individual generation unit 12 to generate a population of initial individuals of the hull 8, or commands the optimization requirement setting unit 13 to set the requirements for optimizing the three-dimensional shape S 2 of the population of initial individuals of the hull 8, or commands the three-dimensional shape creation unit 14 to create the three-dimensional initial shape S 1 of each individual in the population of initial individuals of the hull 8, or commands the next-generation individual generation unit 15 to generate the design variables of the next-generation individuals of the hull 8, or commands the optimized shape search unit 16 to search for the optimized shape S 3 of the hull 8, or commands the transmission / reception unit 17 to cause the computer 22 to execute the calculation of the objective function of each individual in the population of initial individuals of the hull 8, or commands the data storage unit 18 to store the objective function of each individual in the population of initial individuals of the hull 8 received by the transmission / reception unit 17 from the computer 22, or outputs the objective function of each individual in the population of initial individuals of the hull 8 calculated by the computer 22 to the next-generation individual generation unit 15, or commands the data storage unit 18 to store various data, or commands the display unit 20 to display various information. The control unit 21 is communicably connected to the input unit 11, the initial individual generation unit 12, the optimization requirement setting unit 13, the three-dimensional shape creation unit 14, the next-generation individual generation unit 15, the optimized shape search unit 16, the transmission / reception unit 17, the data storage unit 18, the three-dimensional shape optimization program storage unit 19, and the display unit 20.

[0044] The computer 22 is a device that automatically performs various calculations and data processing. The computer 22 is, for example, a computer having a large-scale and high-speed computing ability such as a supercomputer. The computer 22 executes a predetermined process according to a command from the computer 10. The computer 22 is a large-scale computer mainly for scientific and technological calculations, and is equipped with hardware and software optimized for achieving large-scale and high-speed computing ability. The computer 22 includes an objective function calculation unit 23, a transmission / reception unit 24, a data storage unit 25, a numerical fluid analysis program storage unit 26, and a control unit 27. The computer 22 calculates the objective function by the objective function calculation unit 23. The computer 22 transmits the objective function data calculated by the objective function calculation unit 23 to the computer 10.

[0045] The objective function calculation unit 23 is a means for performing numerical fluid analysis on the three-dimensional shape S of each individual in the population of the initial individuals of the hull 8 and calculating the objective function of each individual. 2 The objective function calculation unit 23 calculates the objective function of each individual in the population of the initial individuals of the hull 8 by numerical fluid analysis (aerodynamic analysis) such as an air flow simulator. Here, numerical fluid analysis is an analysis method and simulation method using computational fluid dynamics (CFD) that observes the flow by solving equations related to the motion of the fluid by a computer using a numerical solution method of partial differential equations or the like. 2 The objective function calculation unit 23 executes a predetermined process according to a numerical fluid analysis program for performing numerical fluid analysis on the three-dimensional shape S of each individual in the population of the initial individuals of the hull 8, and based on the design variables of the three-dimensional shape S of each individual, 2 calculates the objective function for the three-dimensional shape S of each individual. The objective function calculation unit 23 calculates the objective function according to, for example, a finite difference method fluid analysis program based on the orthogonal grid method. 2 2

[0046] The objective function calculation unit 23 is for the three-dimensional shape S of each individual in the population of the initial individuals of the hull 82 The computational grid G generated by the orthogonal grid method 0 Based on this, numerical fluid analysis is performed to calculate the objective function of each individual. Here, the orthogonal grid method is a computational method for representing an arbitrary object shape on an orthogonal computational grid G 0 as shown in FIG. 6, and is a numerical simulation method applicable to flow phenomena with complex shapes. The objective function calculation unit 23 uses the prepared common computational grid G 0 previously prepared by the user using the input unit 11 to perform numerical fluid analysis and calculate the objective function of each individual.

[0047] The objective function calculation unit 23 calculates the objective function of each individual based on the grid points P 2 of the computational grid G 0 common to the three-dimensional shapes S 0 of each individual in the population of the initial individuals of the hull 8. Among the grid points P 2 of the computational grid G 01 common to the three-dimensional shapes S 2 of each individual in the population of the initial individuals of the hull 8, the objective function calculation unit 23 performs numerical fluid analysis based on the grid points P 0 of the computational grid G 0 that are located outside the three-dimensional shape S 2 of each individual, and calculates the objective function of each individual. The objective function calculation unit 23 automatically determines whether the grid points P 2 of the computational grid G 2 of each individual are located outside (for example, the light-colored part shown in FIG. 6) or inside (the dark-colored part shown in FIG. 6) the three-dimensional shape S 0 of each individual. The objective function calculation unit 23 uses the grid points P 01 of the computational grid G 2 located outside the three-dimensional shape S 0 of each individual for calculating the objective function, and does not use the grid points P 02 of the computational grid G

[0048] Figure 12 is a conceptual diagram showing, as an example, the computational grid by the airflow simulator developed by the Railway Technical Research Institute, a public interest incorporated foundation. As shown in Figure 12, the computational domain has the center of the hull as the origin, the representative length as the chord length L, with x = -10L to 20L in the flow direction, y = -0.5L to 0.5L in the width direction, and z = -10L to 10L in the vertical direction. The computational grid is an unequally spaced orthogonal grid, and the coarseness and fineness are smoothly set so that the grid resolution near the hull is maximized. The minimum grid interval is 0.01L. The white frame in the figure is the region of the minimum grid interval. The y direction is an equally spaced grid with a grid interval of 0.1L. The total number of grid points is 1,296,000. The basic equation is the Navier - Stokes equation for incompressible fluids. The turbulent flow analysis method was carried out by Large Eddy Simulation (LES). The numerical calculation was performed by discretizing the basic equation by the finite difference method using the supercomputer (Cray XC50) of the Railway Technical Research Institute, a public interest incorporated foundation. The coupling of velocity and pressure used the fractional step method. The time advancement used the third - order accurate Adams - Bashforth method, and the spatial difference used the second - order accurate central difference method. The solution method for the Poisson equation of pressure used the Jacobi method. The number of computational cells is 360×10×360 (= about 1.3 million), the minimum grid width is 1.2 mm, and the span direction has periodic boundary conditions. The computational conditions are that the Reynolds number Re is 3.3×10 5 , the representative length L is 0.12 m, and the wind speed U is 41.25 m / s.

[0049] The transceiver 24 shown in Figure 2 is a means for transmitting and receiving various information between the computer 22 and the computer 10. For example, after the computer 22 performs numerical fluid analysis on each individual of the initial population of the hull 8 and the computer 22 calculates the objective function, the transceiver 24 transmits the objective function calculation data from the computer 22 to the computer 10.

[0050] The data storage unit 25 is a means for storing various data related to the three-dimensional shape optimization system 9. The data storage unit 25 is, for example, a storage device that stores, in correspondence with each individual in the population of initial individuals, design variable data created by the three-dimensional shape creation unit 14, objective function data calculated by the objective function calculation unit 23, and the like.

[0051] The numerical fluid analysis program storage unit 26 is a means for storing a numerical fluid analysis program for performing numerical fluid analysis on the three-dimensional shape S of each individual in the population of initial individuals of the hull 8. 2 The numerical fluid analysis program storage unit 26 is a storage device or the like that stores a numerical fluid analysis program read from an information recording medium or a numerical fluid analysis program captured through a telecommunication line.

[0052] The control unit 27 is a central processing unit (CPU) that controls various operations related to the computer 22. The control unit 21 reads a numerical fluid analysis program from the numerical fluid analysis program storage unit 26 and executes numerical fluid analysis processing according to this numerical fluid analysis program. The control unit 27, for example, receives the execution of the calculation of the objective function of each individual in the population of initial individuals of the hull 8 from the transmission / reception unit 24, commands the objective function calculation unit 23 to calculate the objective function of each individual in the population of initial individuals of the hull 8, or commands the transmission / reception unit 24 to transmit the objective function of each individual in the population of initial individuals of the hull 8 calculated by the objective function calculation unit 23 to the computer 10. The control unit 27 is communicably connected to the objective function calculation unit 23, the transmission / reception unit 24, the data storage unit 25, and the numerical fluid analysis program storage unit 26.

[0053] The communication device 28 is a device for communicating between the computer 10 and the computer 22. The communication device 28 is a telecommunication line or the like that connects the transmission / reception unit 17 on the computer 10 side and the transmission / reception unit 24 on the computer 22 side so as to be mutually communicable by wire or wirelessly.

[0054] Next, the three-dimensional shape optimization method according to the first embodiment of the present invention will be described. The three-dimensional shape optimization process #100 shown in FIG. 13 is a method for optimizing the three-dimensional shape S of the boat body 8 existing in the flow field. 2 The three-dimensional shape optimization process #100 includes an initial individual generation process #200, an optimization requirement setting process #300, a three-dimensional shape creation process #400, an objective function calculation process #500, a next-generation individual generation process #600, an optimized shape search process #700, and a display process #800.

[0055] The initial individual generation process #200 is a process for generating a population of initial individuals of the boat body 8. In the initial individual generation process #200, for example, an initial shape S of a population of initial individuals of the boat body 8 as shown in FIG. 4 1 is generated. In the initial solid individual generation process #200, the characteristic points P 1 of the initial shape S 1 of the generated population of initial individuals of the boat body 8 are extracted as design variables of the initial shape S 1 .

[0056] The optimization requirement setting process #300 is a process for setting requirements for optimizing the three-dimensional shape S 2 of the population of initial individuals of the boat body 8. In the optimization requirement setting process #300, for example, objective functions such as the lift stability and noise performance of the boat body 8, design conditions such as the chord length of the boat body 8 and the up-down symmetric structure, and constraint conditions such as the minimum thickness of the boat body 8 are set.

[0057] The three-dimensional shape creation process #400 is a process for creating the three-dimensional shape S 2 of each individual in the population of initial individuals of the boat body 8. In the three-dimensional shape creation process #400, the initial shape S 1 of each individual in the population of initial individuals of the boat body 8 generated in the initial individual generation process #200 is deformed using free form deformation as shown in FIGS. 7 and 8, and the three-dimensional shape S 2 of each individual is created. As a result, a large number of populations of initial individuals of the boat body 8 are generated so as not to be biased toward a specific initial shape S 1 as shown in FIG. 5. In the three-dimensional shape creation process #400, design conditions such as the chord length, minimum thickness, and up-down symmetric shape of the boat body 8 are set, and the three-dimensional shape S 2is created. In the three-dimensional shape creation step #400, the control points P of the control grid G of each individual in the population of the initial individuals of the boat body 8 1 are extracted as the design variables of the three-dimensional shape S 2 . 2

[0058] The objective function calculation step #500 is a step of performing numerical fluid analysis on the three-dimensional shape S of each individual in the population of the initial individuals of the boat body 8 and calculating the objective function of each individual. In the objective function calculation step #500, for example, a large-scale and high-speed computer 22 such as a supercomputer calculates the objective function for the three-dimensional shape of each individual in the population of the initial individuals of the boat body 8 according to a numerical fluid analysis program. In the objective function calculation step #500, as shown in FIG. 6, a common calculation grid G is prepared in advance for the three-dimensional shape S of each individual in the population of the initial individuals of the boat body 8, and it is determined whether the grid point P is located outside or inside the three-dimensional shape S for each three-dimensional shape S. In the objective function calculation step #500, only the grid points P in the external (fluid region) of the three-dimensional shape S are used for the calculation of the objective function. 2 2 for the common calculation grid G 0 and prepared in advance, and for each three-dimensional shape S 2 it is determined whether the grid point P 0 is located outside or inside the three-dimensional shape S 2 . In the objective function calculation step #500, for the three-dimensional shape S 2 , only the grid points P in the external (fluid region) 01 are used for the calculation of the objective function.

[0059] The next-generation individual generation step #600 is a step of selecting excellent individuals by an evolutionary algorithm based on the objective function of each individual in the population of the initial individuals of the boat body 8 and generating the next-generation individuals. In the next-generation individual generation step #600, excellent individuals (parent generation) are selected from the values of the objective functions of each individual in the population of the initial individuals of the boat body 8 obtained in the objective function calculation step #500, and the design variables of the next-generation individuals (child generation) are generated. In the next-generation individual generation step #600, for example, the design variables of the next-generation individuals are generated so as to minimize the objective function representing the lift stability of the boat body 8 and minimize the objective function representing the noise performance.

[0060] The optimal shape search step #700 is the optimal shape S of the boat body 8 3 ​​This is the step of searching. In the optimization shape search step #700, as shown in FIG. 3, the three-dimensional shape S of the next-generation individual by the three-dimensional shape creation step #400 2 creation, the calculation of the objective function of the next-generation individual by the objective function calculation step #500, and the generation of the design variables of the individuals in the further next generation by the next-generation fixed generation step #600 are repeated until the specified generation. As a result, in the optimization shape search step #700, the characteristics of the individuals with good performance are inherited and converge to the optimal solution, and the optimized shape S 3 of the hull 8 is searched for.

[0061] The display step #800 is the step of displaying the optimization result. In the display step #800, for example, the objective function space of the optimization result as shown in FIG. 10, the non-dominated solution optimization result as shown in FIG. 11, etc. are visualized and displayed on the screen.

[0062] Next, the operation of the three-dimensional shape optimization system according to the first embodiment of the present invention will be described. Hereinafter, the operations of the control units 21 and 27 shown in FIG. 2 will be mainly described. In step (hereinafter referred to as S) 100, the control unit 21 reads the three-dimensional shape optimization program from the three-dimensional shape optimization program storage unit 19. When the control unit 21 reads the three-dimensional shape optimization program, the control unit 21 starts a series of three-dimensional shape optimization processes.

[0063] In S110, the control unit 21 commands the initial individual generation unit 12 to generate a population of initial individuals of the hull 8. When the user operates the input unit 11 and inputs the data necessary to generate the initial shape S 1 of the hull 8, the initial individual generation unit 12 generates the initial shape S 1 of the population of initial individuals of the hull 8 as shown in FIG. 4, and at the same time, the initial individual generation unit 12 extracts the feature points P 1 of the initial shape S 1 as design variables.

[0064] In S120, the three-dimensional shape S 2The control unit 21 commands the optimization requirement setting unit 13 to set requirements for optimization. When the user operates the input unit 11 to input the requirements necessary for optimizing the three-dimensional shape S of the initial population of the hull 8 2 the optimization requirement setting unit 13 sets the objective function, design conditions, and constraint conditions.

[0065] In S130, the control unit 21 commands the three-dimensional shape creation unit 14 to generate the three-dimensional shape S of each individual in the initial population of the hull 8. When the user operates the input unit 11 to move each control point P 2 of the control grid G 1 in an arbitrary direction as shown in FIGS. 7 and 8, the three-dimensional shape creation unit 14 creates the three-dimensional shape S of each individual in the initial population of the hull 8 from the initial shape S 2 by free-form deformation. As a result, the initial individual generation unit 12 generates a large number of initial populations of the hull 8 as shown in FIG. 5. 2 from the initial shape S 1 As a result, the initial individual generation unit 12 generates a large number of initial populations of the hull 8 as shown in FIG. 5.

[0066] In S140, the control unit 21 commands the transmission of data necessary for calculating the objective function of each individual in the initial population of the hull 8. As a result, data necessary for calculating the objective function of each individual in the initial population of the hull 8 is transmitted from the transmission / reception unit 17 on the computer 10 side to the transmission / reception unit 24 on the computer 22 side through the communication device 28.

[0067] In S150, the control unit 27 commands the reception of data necessary for calculating the objective function of each individual in the initial population of the hull 8. As a result, the transmission / reception unit 24 on the computer 22 side receives the data necessary for calculating the objective function of each individual in the initial population of the hull 8 transmitted from the transmission / reception unit 17 on the computer 10 side.

[0068] In S160, the control unit 27 reads the numerical fluid analysis program from the numerical fluid analysis program storage unit 26. When the control unit 27 reads the numerical fluid analysis program, the control unit 27 starts a series of numerical fluid analysis processes.

[0069] In S170, the control unit 27 commands the objective function calculation unit 23 to calculate the objective function for each individual in the population of initial individuals of the hull 8. As a result, as shown in FIG. 12, the three-dimensional shape S of each individual in the population of initial individuals of the hull 8 2 is subjected to numerical fluid analysis by the objective function calculation unit 23, and the objective function calculation unit 23 calculates the objective function for each individual in the population of initial individuals.

[0070] In S180, the control unit 27 commands the transmission of the objective function data for each individual in the population of initial individuals of the hull 8. As a result, the objective function data for each individual in the population of initial individuals of the hull 8 is transmitted from the transmission / reception unit 24 on the computer 22 side to the transmission / reception unit 17 on the computer 10 side through the communication device 28.

[0071] In S190, the control unit 21 commands the reception of the objective function data for each individual in the population of initial individuals of the hull 8. As a result, the transmission / reception unit 17 on the computer 10 side receives the objective function data for each individual in the population of initial individuals of the hull 8 transmitted from the transmission / reception unit 24 on the computer 22 side.

[0072] In S200, the control unit 21 commands the next-generation individual generation unit 15 to generate the next-generation individuals. Based on the objective function of each individual in the population of initial individuals of the hull 8, the next-generation individual generation unit 15 selects excellent individuals by an evolutionary algorithm, and the next-generation individual generation unit 15 generates the next-generation individuals. The next-generation individual generation unit 15 selects excellent individuals from the values of the objective function by an evolutionary algorithm. For example, the next-generation individual generation unit 15 generates the design variables of the next-generation individuals such that the objective function representing the lift stability of the hull 8 is minimized and the objective function representing the noise performance is minimized. The next-generation individual generation unit 15 repeats the generation of the design variables of the next-generation individuals while creating new shapes until the optimization converges.

[0073] In S210, the control unit 21 commands the optimization shape search unit 16 to search for the optimized shape S of the hull 8 3 As shown in FIG. 3, the three-dimensional shape S of the next-generation individuals by the three-dimensional shape creation unit 14 2By repeating the creation, the calculation of the objective function by the objective function calculation unit 23, and the generation of the individuals of the next generation by the next generation individual generation unit 15, the optimal shape S of the hull 8 3 is searched for by the optimal shape search unit 16.

[0074] In S220, the control unit 21 determines whether or not the optimal shape search unit 16 has repeated the generation of the individuals of the next generation of the hull 8 up to the specified generation. When the control unit 21 determines that the optimal shape search unit 16 has repeated the generation of the individuals of the next generation of the hull 8 up to the specified generation, the process proceeds to S230. On the other hand, when the control unit 21 determines that the optimal shape search unit 16 has not repeated the generation of the individuals of the next generation of the hull 8 up to the specified generation, the process returns to S130. As a result, until the generation of the individuals of the next generation reaches the specified generation, the three-dimensional shape S 2 of the individuals of the next generation is generated by the three-dimensional shape creation unit 14, the objective function of the individuals of the next generation is calculated by the objective function calculation unit 23, and the next generation individual generation unit 15 generates the individuals of the next generation.

[0075] In S230, the control unit 21 commands the display unit 20 to display the optimization result. As a result, as shown in FIG. 11, the optimal shape S of the hull 8 obtained by a series of three-dimensional shape optimization processes 3 and the like are visualized and displayed on the screen.

[0076] The three-dimensional shape optimization method, the three-dimensional shape optimization system, and the three-dimensional shape optimization program according to the first embodiment of the present invention have the following effects. (1) In this first embodiment, the three-dimensional shape S 2 of each individual in the population of the initial individuals of the hull 8 is created, and numerical fluid analysis is performed on the three-dimensional shape S 2 of each individual in the population of the initial individuals of the hull 8 to calculate the objective function of each individual. Further, in this first embodiment, excellent individuals are selected by an evolutionary algorithm based on the objective function of each individual in the population of the initial individuals of the hull 8, and the individuals of the next generation are generated. Furthermore, in this first embodiment, the three-dimensional shape S 2The creation of the objective function, the calculation of the objective function, and the generation of the next generation of individuals are repeated until a specific generation, and the optimized shape S of the boat 8 is obtained. 3 For this purpose, a three-dimensional shape S of the hull 8 that satisfies any shape constraint and multiple aerodynamic characteristics is searched for using a three-dimensional shape deformation method, an aerodynamic simulation, and an evolutionary algorithm. 2 It is possible to easily search for individuals of the same shape, and the optimized shape S of the boat 8 can be obtained. 3 As a result, by repeatedly performing individual generation, airflow analysis, and evolutionary calculation, various optimal three-dimensional shapes S of objects existing in the flow field can be calculated. 2 In addition, for example, a multi-objective optimization method using an evolutionary algorithm can be used to automatically calculate the three-dimensional shape S 2 Therefore, it is possible to suppress changes in lift caused by changes in the angle of attack of the boat 8 and wear of the slider 8a, and it is also possible to suppress noise caused by pressure fluctuations on the surface of the boat 8.

[0077] (2) In the first embodiment, the three-dimensional shape S 2 The computational grid G ​​generated by the Cartesian grid method 0 Based on this, computational fluid analysis is performed to calculate the objective function of each individual. For example, when calculating the objective function using a boundary connection grid that matches the shape of the object, all three-dimensional shapes S 2 It is necessary to generate a different boundary-connected grid for each shape, and the generation of the boundary-connected grid requires considerable cost and time. In addition, while it is possible to automatically generate a boundary-connected grid for a simple two-dimensional shape such as an airfoil, it is difficult to generate a boundary-connected grid for a three-dimensional shape S with complex irregularities. 2 In the first embodiment, the boundary joint grid is easily broken, making automation difficult. 2 Even if the 3D shape data is used, the computational grid G 0 It is possible to automatically generate the computational grid G 0 This can reduce the cost and time of production.

[0078] (3) In this first embodiment, for each individual in the population of initial individuals of the hull 8, a numerical fluid analysis is performed based on the lattice points P of the computational grid G common to the three-dimensional shapes S, and the objective function of each individual is calculated. Among the lattice points P located outside the three-dimensional shape S of each individual. For this reason, by generating in advance the computational grid G common to all the three-dimensional shapes S of the population of initial individuals of the hull 8, it is possible to automatically determine whether the lattice points P are located outside or inside the three-dimensional shape S of each individual. As a result, it is not necessary to generate the computational grid G for each three-dimensional shape S of each individual, and the labor of generating a large number of computational grids G can be omitted. Also, even for a complex three-dimensional shape S, the calculation of the objective function can be streamlined. For example, compared to the case of generating different boundary joining grids for all the three-dimensional shapes S of the population of initial individuals of the hull 8, the objective function can be calculated with the same accuracy as the boundary joining grid, and the cost and time for calculating the objective function can be reduced. 2 a common computational grid G 0 of the lattice points P 0 Among them, based on the lattice points P located outside the three-dimensional shape S of each individual, a numerical fluid analysis is performed to calculate the objective function of each individual. For this reason, by generating in advance the computational grid G common to all the three-dimensional shapes S of the population of initial individuals of the hull 8, it is possible to automatically determine whether the lattice points P are located outside or inside the three-dimensional shape S of each individual. As a result, it is not necessary to generate the computational grid G for each three-dimensional shape S of each individual, and the labor of generating a large number of computational grids G can be omitted. Also, even for a complex three-dimensional shape S, the calculation of the objective function can be streamlined. For example, compared to the case of generating different boundary joining grids for all the three-dimensional shapes S of the population of initial individuals of the hull 8, the objective function can be calculated with the same accuracy as the boundary joining grid, and the cost and time for calculating the objective function can be reduced. 2 the lattice points P located outside the three-dimensional shape S of each individual 01 Based on this, a numerical fluid analysis is carried out to calculate the objective function of each individual. Therefore, for all the three-dimensional shapes S of the population of initial individuals of the hull 8, by generating in advance the computational grid G common to all of them, it is possible to automatically determine whether the lattice points P are located outside or inside the three-dimensional shape S of each individual. As a result, there is no need to generate the computational grid G for each three-dimensional shape S of each individual, and the effort of generating a large number of computational grids G can be saved. Also, even for a complex three-dimensional shape S, the calculation of the objective function can be made more efficient. For example, compared to the case of generating different boundary joining grids for all the three-dimensional shapes S of the population of initial individuals of the hull 8, the objective function can be calculated with the same accuracy as the boundary joining grid, and the cost and time for calculating the objective function can be reduced. 2 a common computational grid G 0 By doing so, it can be automatically determined whether the lattice points P are located outside or inside the three-dimensional shape S of each individual. As a result, there is no need to generate the computational grid G for each three-dimensional shape S of each individual, and the labor of generating a large number of computational grids G can be omitted. Also, even for a complex three-dimensional shape S, the calculation of the objective function can be streamlined. For example, compared to the case of generating different boundary joining grids for all the three-dimensional shapes S of the population of initial individuals of the hull 8, the objective function can be calculated with the same accuracy as the boundary joining grid, and the cost and time for calculating the objective function can be reduced. 2 outside or inside the three-dimensional shape S of each individual 0 the lattice points P are located 2 For each three-dimensional shape S of each individual, the computational grid G 0 As a result, there is no need to generate the computational grid G for each three-dimensional shape S of each individual, and the labor of generating a large number of computational grids G can be omitted. Also, even for a complex three-dimensional shape S, the calculation of the objective function can be streamlined. For example, compared to the case of generating different boundary joining grids for all the three-dimensional shapes S of the population of initial individuals of the hull 8, the objective function can be calculated with the same accuracy as the boundary joining grid, and the cost and time for calculating the objective function can be reduced. 0 a large number of computational grids G 2 Even for a complex three-dimensional shape S, the calculation of the objective function can be made more efficient. For example, compared to the case of generating different boundary joining grids for all the three-dimensional shapes S of the population of initial individuals of the hull 8, the objective function can be calculated with the same accuracy as the boundary joining grid, and the cost and time for calculating the objective function can be reduced. 2 For all the three-dimensional shapes S of the population of initial individuals of the hull 8, compared to the case of generating different boundary joining grids, the objective function can be calculated with the same accuracy as the boundary joining grid, and the cost and time for calculating the objective function can be reduced.

[0079] (4) In this first embodiment, at least two objective functions among the objective functions representing the lift stability, noise performance, air resistance reduction performance, or lift target value of the hull 8 are calculated. For this reason, regarding the issues in the trade-off relationship such as lift stability, noise performance, air resistance reduction performance, or lift target value, an optimal three-dimensional shape S that satisfies a plurality of requirements simultaneously can be searched for. For example, by a simulator that combines individual generation, air flow analysis, and evolutionary calculation, based on the shape constraints of the hull 8, a three-dimensional shape S of the hull 8 that satisfies lift stability and low noise can be easily obtained. 2 an optimal three-dimensional shape S 2 Based on the shape constraints of the hull 8, a three-dimensional shape S of the hull 8 that satisfies lift stability and low noise can be easily obtained.

[0080] (5) In this first embodiment, a three-dimensional shape S of each individual representing the worn shape of the grinding plate 8a supported by the hull 8 is created. Thus, a population of individuals that satisfy the shape constraints can be automatically calculated. For example, an optimized three-dimensional shape S of the hull 8 that satisfies the constraint conditions such as the thickness of the hull 8 and the chamfering of the corners of the hull 8 can be searched for. 2 2 (6) In this first embodiment, the computer 10 performs the creation of the three-dimensional shape S by the three-dimensional shape creation unit 14, the generation of the next-generation individuals by the next-generation individual generation unit 15, and the search for the optimized shape S by the optimized shape search unit 16, and the computer 22 performs the calculation of the objective function by the objective function calculation unit 23. Also, in this first embodiment, the computer 10 transmits data regarding the three-dimensional shape S created by the three-dimensional shape creation unit 14 to the computer 22, and the computer 22 transmits data regarding the objective function calculated by the objective function calculation unit 23 to the computer 10. Therefore, for example, the free deformation of the three-dimensional shape can be performed by a multi-purpose personal computer or the like within the optimization system, and the large-scale three-dimensional airflow analysis can be performed by a large-scale and high-speed supercomputer or the like within the optimization system. As a result, it is possible to automatically perform, in a short time, the generation of the initial individuals of the hull 8 to the acquisition of the optimized population of individuals.

[0081] (6) In this first embodiment, the computer 10 performs the creation of the three-dimensional shape S by the three-dimensional shape creation unit 14, the generation of the next-generation individuals by the next-generation individual generation unit 15, and the search for the optimized shape S by the optimized shape search unit 16, and the computer 22 performs the calculation of the objective function by the objective function calculation unit 23. Also, in this first embodiment, the computer 10 transmits data regarding the three-dimensional shape S created by the three-dimensional shape creation unit 14 to the computer 22, and the computer 22 transmits data regarding the objective function calculated by the objective function calculation unit 23 to the computer 10. Therefore, for example, the free deformation of the three-dimensional shape can be performed by a multi-purpose personal computer or the like within the optimization system, and the large-scale three-dimensional airflow analysis can be performed by a large-scale and high-speed supercomputer or the like within the optimization system. As a result, it is possible to automatically perform, in a short time, the generation of the initial individuals of the hull 8 to the acquisition of the optimized population of individuals. 2 (6) In this first embodiment, the computer 10 performs the creation of the three-dimensional shape S by the three-dimensional shape creation unit 14, the generation of the next-generation individuals by the next-generation individual generation unit 15, and the search for the optimized shape S by the optimized shape search unit 16, and the computer 22 performs the calculation of the objective function by the objective function calculation unit 23. Also, in this first embodiment, the computer 10 transmits data regarding the three-dimensional shape S created by the three-dimensional shape creation unit 14 to the computer 22, and the computer 22 transmits data regarding the objective function calculated by the objective function calculation unit 23 to the computer 10. Therefore, for example, the free deformation of the three-dimensional shape can be performed by a multi-purpose personal computer or the like within the optimization system, and the large-scale three-dimensional airflow analysis can be performed by a large-scale and high-speed supercomputer or the like within the optimization system. As a result, it is possible to automatically perform, in a short time, the generation of the initial individuals of the hull 8 to the acquisition of the optimized population of individuals. 3 (6) In this first embodiment, the computer 10 performs the creation of the three-dimensional shape S by the three-dimensional shape creation unit 14, the generation of the next-generation individuals by the next-generation individual generation unit 15, and the search for the optimized shape S by the optimized shape search unit 16, and the computer 22 performs the calculation of the objective function by the objective function calculation unit 23. Also, in this first embodiment, the computer 10 transmits data regarding the three-dimensional shape S created by the three-dimensional shape creation unit 14 to the computer 22, and the computer 22 transmits data regarding the objective function calculated by the objective function calculation unit 23 to the computer 10. Therefore, for example, the free deformation of the three-dimensional shape can be performed by a multi-purpose personal computer or the like within the optimization system, and the large-scale three-dimensional airflow analysis can be performed by a large-scale and high-speed supercomputer or the like within the optimization system. As a result, it is possible to automatically perform, in a short time, the generation of the initial individuals of the hull 8 to the acquisition of the optimized population of individuals. 2 (6) In this first embodiment, the computer 10 performs the creation of the three-dimensional shape S by the three-dimensional shape creation unit 14, the generation of the next-generation individuals by the next-generation individual generation unit 15, and the search for the optimized shape S by the optimized shape search unit 16, and the computer 22 performs the calculation of the objective function by the objective function calculation unit 23. Also, in this first embodiment, the computer 10 transmits data regarding the three-dimensional shape S created by the three-dimensional shape creation unit 14 to the computer 22, and the computer 22 transmits data regarding the objective function calculated by the objective function calculation unit 23 to the computer 10. Therefore, for example, the free deformation of the three-dimensional shape can be performed by a multi-purpose personal computer or the like within the optimization system, and the large-scale three-dimensional airflow analysis can be performed by a large-scale and high-speed supercomputer or the like within the optimization system. As a result, it is possible to automatically perform, in a short time, the generation of the initial individuals of the hull 8 to the acquisition of the optimized population of individuals.

[0082] (Second Embodiment) Hereinafter, for parts that are the same as the parts shown in FIGS. 1 to 14, the same reference numerals are given and detailed descriptions are omitted. This second embodiment is an embodiment in the case of searching for an optimal three-dimensional shape S of the vehicle front portion 2a that can reduce the tunnel micro-pressure wave W as shown in FIGS. 15 to 17. 2 (Second Embodiment) 2 (Second Embodiment)

[0083] Here, the tunnel micro-pressure wave W 2 will be described. ​As shown in Fig. 15, when the vehicle 2 enters the tunnel portal T on the entrance side 1 a compression wave (in-tunnel compression wave) W is generated in the tunnel T 1 and the compression wave W 1 propagates through the tunnel T at the speed of sound and radiates a pulsed pressure wave to the outside at the opposite tunnel portal T 2 This pressure wave radiated to the outside is the tunnel micro-pressure wave W 2 and the magnitude of the tunnel micro-pressure wave W 2 is approximately proportional to the pressure gradient of the compression wave W 2 that reaches the opposite tunnel portal T 1 The tunnel micro-pressure wave W 2 causes environmental problems such as blasting sounds and shaking of doors and windows of houses, so countermeasures are essential.

[0084] The tunnel T shown in Fig. 15 is a fixed structure (civil engineering structure) for allowing the vehicle 2 to pass through by penetrating through the ground such as a mountainside. The tunnel T has tunnel portals T 1 , T 2 which are the entrances and exits where the vehicle 2 enters and exits. The tunnel buffer H is a fixed structure (civil engineering structure) that covers the tunnel portal T 2 to reduce the tunnel micro-pressure wave W 1 As shown in Fig. 15, the tunnel buffer H reduces the tunnel micro-pressure wave W 1 radiated to the outside from the tunnel portal (opposite portal) T 1 on the exit side of the tunnel T by gently reducing the pressure gradient (gradient of the wave front) of the compression wave W 2 generated when the front part 2a of the vehicle enters the tunnel portal T 2 on the entrance side of the tunnel T. The tunnel buffer H is constructed outside the tunnel portal T 1 so as to extend the tunnel T. The vehicle 2 is a moving body that moves along the track. The vehicle 2 is, for example, a railway vehicle that runs at a high speed of 320 km / h or more on a Shinkansen (registered trademark). The vehicle 2 includes a vehicle front part (front part of the leading vehicle) 2a that constitutes the leading part side of the vehicle 2.

[0085] The three-dimensional shape optimization system 9 shown in FIG. 2 is for reducing the tunnel micro-pressure wave W in the front part 2a of the vehicle, reducing air resistance, or making the volume of the front part 2a of the vehicle reach a specific target value, and optimizes the three-dimensional shape S of the front part 2a of the vehicle. 2 In order to reduce the tunnel micro-pressure wave W, reduce air resistance, or make the volume of the front part 2a of the vehicle reach a specific target value, the three-dimensional shape S of the front part 2a of the vehicle 2 is optimized. The initial individual generation unit 12 generates a population of initial individuals of the three-dimensional shape S of the front part 2a of the vehicle. 2 As shown in FIG. 16, the initial individual generation unit 12 extracts the characteristic points P of the initial shape S of the front part 2a of the vehicle input by the user using the input unit 11 1 as design variables. 1

[0086] The optimization requirement setting unit 13 shown in FIG. 2 sets requirements for optimizing the three-dimensional shape S of the population of initial individuals of the front part 2a of the vehicle. 2 The optimization requirement setting unit 13 sets requirements for optimizing the three-dimensional shape S of the front part 2a of the vehicle input by the user using the input unit 11. 2 The optimization requirement setting unit 13 sets the objective function, design conditions, and constraint conditions, which are the requirements for optimizing the three-dimensional shape S of the population of initial individuals of the front part 2a of the vehicle. 2 The optimization requirement setting unit 13 sets at least two objective functions among the objective functions representing the tunnel micro-pressure wave reduction performance of the front part 2a of the vehicle, the air resistance reduction performance of the front part 2a of the vehicle, or the volume of the front part 2a of the vehicle.

[0087] FIG. 17 is a graph showing an example of the objective function space of the optimization result. Here, the vertical axis shown in FIG. 17 is the volume, and the horizontal axis is the tunnel micro-pressure wave reduction performance. The optimization requirement setting unit 13, for example, as shown in FIG. 17, minimizes the tunnel micro-pressure wave W 2 to reduce the tunnel micro-pressure wave W, and makes the volume of the front part 2a of the vehicle approach a specific target value and minimizes the tunnel micro-pressure wave W 2 and sets the tunnel micro-pressure wave reduction performance and the volume of the front part 2a of the vehicle as objective functions. 2

[0088] The three-dimensional shape creation unit 14 shown in FIG. 2 creates the three-dimensional shape S of each individual in the population of initial individuals of the front part 2a of the vehicle. 2Create. The three-dimensional shape creation unit 14 creates the three-dimensional shape S of each individual in the population of the initial individuals of the vehicle front part 2a generated by the initial individual generation unit 12 1 based on the design variables of 2 and creates the three-dimensional shape S of the next-generation individuals of the vehicle front part 2a 2 based on the design variables of 2 and creates the three-dimensional shape S of each individual in this next generation. The three-dimensional shape creation unit 14 creates, for example, the three-dimensional shape S of each individual in the population of the initial individuals of the vehicle front part 2a by free form deformation 2 .

[0089] The next-generation individual generation unit 15 optimizes the three-dimensional shape S of the vehicle front part 2a using an evolutionary algorithm. The next-generation individual generation unit 15 minimizes the objective function representing the micro-pressure wave reduction performance of the vehicle front part 2a, minimizes the objective function representing the air resistance reduction performance of the vehicle front part 2a, and generates design variables of the next-generation individuals so that the volume of the vehicle front part 2a approaches a specific target value 2 .

[0090] As shown in FIG. 16, the optimized shape search unit 16 searches for the optimized shape S of the vehicle front part 2a 3 . The optimized shape search unit 16 repeats the creation of the three-dimensional shape S of each individual by the three-dimensional shape creation unit 14, the calculation of the objective function by the objective function calculation unit 23, and the generation of the design variables of the next-generation individuals by the next-generation individual generation unit 15 to search for the optimized shape S of the vehicle front part 2a 2 . 3

[0091] The three-dimensional shape optimization program storage unit 19 stores a three-dimensional shape optimization program for optimizing the three-dimensional shape S of the vehicle front part 2a existing in the flow field. The display unit 20 displays, for example, the initial shape S of the vehicle front part 2a generated by the initial individual generation unit 12 2 and the characteristic points P 1 , and the objective function and design conditions that are the optimization requirements of the three-dimensional shape S of the vehicle front part 2a set by the optimization requirement setting unit 13, and the three-dimensional shape S of each individual in the population of the initial individuals of the vehicle front part 2a created by the three-dimensional shape creation unit 14 1 2 ​​​2 and display on the screen the design variables of the vehicle front part 2a of each generation generated by the next-generation individual generation unit 15, the design variables of the optimized vehicle front part 2a, and the like.

[0092] The control unit 21, for example, commands the initial individual generation unit 12 to generate a population of initial individuals of the vehicle front part 2a, sets requirements for optimizing the three-dimensional shape S 2 of the population of initial individuals of the vehicle front part 2a to the optimization requirement setting unit 13, commands the three-dimensional shape creation unit 14 to create the three-dimensional shape S 2 of each individual in the population of initial individuals of the vehicle front part 2a, commands the next-generation individual generation unit 15 to generate design variables of the next-generation individuals of the vehicle front part 2a, commands the computer 22 from the transmission / reception unit 17 to execute the calculation of the objective function of each individual in the population of initial individuals of the vehicle front part 2a, and commands the optimization shape search unit 16 to generate the optimized shape S 3 of the vehicle front part 2a.

[0093] The objective function calculation unit 23 performs numerical fluid analysis on the three-dimensional shape S 2 of each individual in the population of initial individuals of the vehicle front part 2a and calculates the objective function of each individual. The numerical fluid analysis program storage unit 26 stores a numerical fluid analysis program for performing numerical fluid analysis on the three-dimensional shape of each individual in the population of initial individuals of the vehicle front part 2a.

[0094] The control unit 27, for example, receives from the transmission / reception unit 24 the execution of the calculation of the objective function of each individual in the population of initial individuals of the vehicle front part 2a, commands the objective function calculation unit 23 to calculate the objective function of each individual in the population of initial individuals of the vehicle front part 2a, and commands the transmission / reception unit 24 to transmit the objective function of each individual in the population of initial individuals of the vehicle front part 2a calculated by the objective function calculation unit 23 to the computer 10.

[0095] The three-dimensional shape optimization method, three-dimensional shape optimization device, and three-dimensional shape optimization program according to the second embodiment of the present invention have the following effects in addition to the effects of the first embodiment. In this second embodiment, at least two objective functions among the micro-pressure wave reduction performance of the vehicle front portion 2a, the air resistance reduction performance, or the objective function representing the volume of the vehicle front portion 2a are calculated. For this reason, for example, regarding the problem of the trade-off relationship between the reduction of the tunnel micro-pressure wave W 2 and the reduction of air resistance and the securing of the volume of the vehicle front portion 2a, an optimal three-dimensional shape S 2 that satisfies a plurality of requirements can be searched for. As a result, the vehicle front portion 2a can be made as long as possible to reduce the tunnel micro-pressure wave W 2 and air resistance, and while maintaining the volume of the vehicle front portion 2a, the number of passenger seats and the disguise space can be secured as much as possible. Further, by a simulator that combines the generation of individuals, the air flow analysis, and the evolutionary calculation, based on the shape constraints of the vehicle front portion 2a, the three-dimensional shape S 2 of the vehicle front portion 2a that satisfies the micro-pressure wave reduction performance, the air resistance reduction performance, and the volume of the vehicle front portion 2a can be easily obtained.

[0096] (Third Embodiment) As shown in FIGS. 18 and 19, this third embodiment is an embodiment in which an optimal three-dimensional shape S 2 of the vehicle rear portion 2b that can reduce the fluctuating aerodynamic force F that is the cause of the lateral shaking generated in the vehicle rear portion 2b when the vehicle travels in the tunnel T and can reduce the air resistance generated in the vehicle rear portion 2b is searched for. The vehicle 2 shown in FIG. 18 is composed of a plurality of vehicles, and as shown in FIG. 19, it is composed of a leading vehicle 2A located at the head of the formation, a trailing vehicle (last vehicle) 2B located at the tail of the formation, and an intermediate vehicle 2C located in the middle of the formation. The vehicle 2 includes a vehicle front portion 2a that constitutes the front end portion on the front side in the traveling direction of the leading vehicle 2A of this vehicle 2 shown in FIG. 19, a vehicle rear portion 2b that constitutes the rear end portion on the rear side in the traveling direction of the trailing vehicle 2B of this vehicle 2, side surfaces 2c that constitute both side portions of the vehicle body of this vehicle 2 shown in FIG. 18, and a bottom surface 2d that constitutes the lower portion of the vehicle body of this vehicle 2.

[0097] Here, the vehicle shaking in the tunnel will be described. As shown in FIGS. 18 and 19, when the vehicle 2 travels in the tunnel T, large pressure fluctuations occur on the side surface 2c of the vehicle 2 on the side facing the wall surface T of the tunnel T, and a fluctuating aerodynamic force F that swings the vehicle 2 in the left - right direction is generated by this large pressure fluctuation. As shown in FIG. 19, the meandering flow (turbulence of the air flow) generated near the bottom surface 2d of the vehicle 2 rolls up to the side surface 2c of the vehicle 2, and this rolled - up meandering flow spreads while moving toward the rear vehicle 2B. The pressure fluctuates greatly at the rear part 2b of the vehicle of the rear vehicle 2B, and a large fluctuating aerodynamic force F acts on the side surface 2c of the rear vehicle 2B. When looking at the entire formation, the magnitude of the pressure fluctuation on the side surface 2c of the vehicle 2 increases from the leading vehicle 2A to about the 6th to 8th vehicle, becomes constant up to the rear vehicle 2B, and then increases sharply at the rear part 2b of the vehicle of the rear vehicle 2B. Such a fluctuating aerodynamic force F has been clarified by numerical simulation to be caused by the separation of the flow from the rear part 2b of the vehicle of the rear vehicle 2B. In order to reduce the fluctuating aerodynamic force F, it is necessary to devise the shape of the rear part 2b of the vehicle of the rear vehicle 2B. 3 When the vehicle 2 travels in the tunnel T, large pressure fluctuations occur on the side surface 2c of the vehicle 2 on the side facing the wall surface T of the tunnel T, and a fluctuating aerodynamic force F that swings the vehicle 2 in the left - right direction is generated by this large pressure fluctuation. As shown in FIG. 19, the meandering flow (turbulence of the air flow) generated near the bottom surface 2d of the vehicle 2 rolls up to the side surface 2c of the vehicle 2, and this rolled - up meandering flow spreads while moving toward the rear vehicle 2B. The pressure fluctuates greatly at the rear part 2b of the vehicle of the rear vehicle 2B, and a large fluctuating aerodynamic force F acts on the side surface 2c of the rear vehicle 2B. When looking at the entire formation, the magnitude of the pressure fluctuation on the side surface 2c of the vehicle 2 increases from the leading vehicle 2A to about the 6th to 8th vehicle, becomes constant up to the rear vehicle 2B, and then increases sharply at the rear part 2b of the vehicle of the rear vehicle 2B. Such a fluctuating aerodynamic force F has been clarified by numerical simulation to be caused by the separation of the flow from the rear part 2b of the vehicle of the rear vehicle 2B. In order to reduce the fluctuating aerodynamic force F, it is necessary to devise the shape of the rear part 2b of the vehicle of the rear vehicle 2B.

[0098] FIG. 20 is a photograph showing, as an example, a model of the rear part 2b of the rear vehicle 2B. The "gable - type" shown in FIG. 20 has an end face of the rear part 2b that is a plane and is perpendicular to the side surface of the rear part 2b of the vehicle, and there is no shape - changing part in the rear part 2b of the vehicle, and it is shown for comparison with other shapes. The "two - dimensional type" is a shape in which the upper part of the rear part 2b of the "gable - type" is cut off obliquely. The "three - dimensional type" is a shape in which the side surface of the rear part 2b of the "two - dimensional type" is narrowed toward the tip. The "long type" has a long length of the shape - changing part of the rear part 2b of the vehicle, and the "short type" has a short length of the shape - changing part of the rear part 2b of the vehicle.

[0099] The three - dimensional shape optimization system 9 shown in FIG. 2 optimizes the three - dimensional shape S of the rear part 2b of the vehicle in order to reduce the air resistance of the rear part 2b of the vehicle as shown in FIG. 20 or to reduce the fluctuating aerodynamic force F acting on the rear part 2b of the vehicle. The initial individual generation unit 12 generates a population of initial individuals of the three - dimensional shape S of the rear part 2b of the vehicle as shown in FIG. 20. The initial individual generation unit 12 is based on the initial shape S of the rear part 2b of the vehicle input by the user using the input unit 11 2 to optimize the three - dimensional shape S of the rear part 2b of the vehicle shown in FIG. 20. The initial individual generation unit 12 generates a population of initial individuals of the three - dimensional shape S of the rear part 2b of the vehicle shown in FIG. 20. The initial individual generation unit 12 is based on the initial shape S of the rear part 2b of the vehicle input by the user using the input unit 11 2 to generate a population of initial individuals of the three - dimensional shape S of the rear part 2b of the vehicle shown in FIG. 20. The initial individual generation unit 12 is based on the initial shape S of the rear part 2b of the vehicle input by the user using the input unit 111 The characteristic point P 1 is extracted as a design variable.

[0100] The optimization requirement setting unit 13 shown in FIG. 2 sets requirements for optimizing the three-dimensional shape S of the population of initial individuals of the rear vehicle part 2b. 2 The optimization requirement setting unit 13 sets requirements for optimizing the three-dimensional shape S of the rear vehicle part 2b. The optimization requirement setting unit 13 sets an objective function, design conditions, and constraint conditions, which are requirements for optimizing the cross-sectional shape of the population of initial individuals of the rear vehicle part 2b. The optimization requirement setting unit 13 sets an objective function representing the air resistance reduction performance of the rear vehicle part 2b and the fluctuating aerodynamic force F acting on the rear vehicle part 2b. The optimization requirement setting unit 13 sets, for example, the air resistance reduction performance that minimizes the air resistance received by the rear vehicle part 2b and reduces this air resistance, and the fluctuating aerodynamic force F that minimizes the lateral shaking generated in the rear vehicle part 2b and reduces this lateral shaking as objective functions. 2 The optimization requirement setting unit 13 sets requirements for optimizing the three-dimensional shape S of the rear vehicle part 2b. The optimization requirement setting unit 13 sets an objective function, design conditions, and constraint conditions, which are requirements for optimizing the cross-sectional shape of the population of initial individuals of the rear vehicle part 2b. The optimization requirement setting unit 13 sets an objective function representing the air resistance reduction performance of the rear vehicle part 2b and the fluctuating aerodynamic force F acting on the rear vehicle part 2b. The optimization requirement setting unit 13 sets, for example, the air resistance reduction performance that minimizes the air resistance received by the rear vehicle part 2b and reduces this air resistance, and the fluctuating aerodynamic force F that minimizes the lateral shaking generated in the rear vehicle part 2b and reduces this lateral shaking as objective functions.

[0101] The three-dimensional shape creation unit 14 creates the three-dimensional shape S of each individual in the population of initial individuals of the rear vehicle part 2b. The three-dimensional shape creation unit 14 creates the three-dimensional shape S of each individual based on the design variables of the initial shape S of each individual in the population of initial individuals of the rear vehicle part 2b generated by the initial individual generation unit 12, and creates the three-dimensional shape S of each individual in the next generation of the rear vehicle part 2b based on the design variables of the three-dimensional shape S of each individual in the next generation. The three-dimensional shape creation unit 14 creates the three-dimensional shape S of each individual in the population of initial individuals of the rear vehicle part 2b by, for example, free form deformation. 2 The three-dimensional shape creation unit 14 creates the three-dimensional shape S of each individual in the population of initial individuals of the rear vehicle part 2b. The three-dimensional shape creation unit 14 creates the three-dimensional shape S of each individual based on the design variables of the initial shape S of each individual in the population of initial individuals of the rear vehicle part 2b generated by the initial individual generation unit 12, and creates the three-dimensional shape S of each individual in the next generation of the rear vehicle part 2b based on the design variables of the three-dimensional shape S of each individual in the next generation. The three-dimensional shape creation unit 14 creates the three-dimensional shape S of each individual in the population of initial individuals of the rear vehicle part 2b by, for example, free form deformation. 1 based on the design variables, creates the three-dimensional shape S of each of these individuals, 2 and based on the design variables of the three-dimensional shape S of the individuals in the next generation of the rear vehicle part 2b, 2 creates the three-dimensional shape S of each of these next-generation individuals. 2 The three-dimensional shape creation unit 14 creates the three-dimensional shape S of each individual in the population of initial individuals of the rear vehicle part 2b by, for example, free form deformation. 2 creates the three-dimensional shape S of each individual in the population of initial individuals of the rear vehicle part 2b.

[0102] The next-generation individual generation unit 15 generates design variables of the next-generation individuals that minimize the objective function representing the air resistance reduction performance received by the rear vehicle part 2b as shown in FIG. 20 and minimize the objective function representing the fluctuating aerodynamic force F acting on the rear vehicle part 2b. The optimization shape search unit 16 searches for the optimization shape S of the rear vehicle part 2b as shown in FIG. 20.3 Search for it. The optimization shape search unit 16 creates the three-dimensional shape S of the next-generation individual, calculates the objective function, and further repeats the generation of the individuals of the next generation until a specific generation, thereby searching for the optimized shape S of the vehicle rear portion 2b. 2 3

[0103] The three-dimensional shape optimization program storage unit 19 stores a three-dimensional shape optimization program for optimizing the three-dimensional shape S of the vehicle rear portion 2b existing in the flow field. The display unit 20 displays, for example, the initial shape S of the vehicle rear portion 2b generated by the initial individual generation unit 12 and the feature points P, 2 and the objective function and design conditions that are the requirements for optimizing the three-dimensional shape S of the vehicle rear portion 2b set by the optimization requirement setting unit 13, and the three-dimensional shape S of each individual in the population of the initial individuals of the vehicle rear portion 2b created by the three-dimensional shape creation unit 14, 1 1 and the design variables of the vehicle rear portion 2b generated by the next-generation individual generation unit 15 and the optimized design variables of the vehicle rear portion 2b, etc. on the screen. 2 2

[0104] The control unit 21 commands, for example, the initial individual generation unit 12 to generate a population of initial individuals of the vehicle rear portion 2b, commands the optimization requirement setting unit 13 to set the requirements for optimizing the three-dimensional shape S of the population of initial individuals of the vehicle rear portion 2b, commands the three-dimensional shape creation unit 14 to create the three-dimensional shape S of each individual in the population of initial individuals of the vehicle rear portion 2b, commands the next-generation individual generation unit 15 to generate the design variables of the next-generation individuals of the vehicle rear portion 2b, commands the computer 22 via the transceiver unit 17 to execute the calculation of the objective function of each individual in the population of initial individuals of the vehicle rear portion 2b, and commands the optimization shape search unit 16 to generate the optimized shape S of the vehicle rear portion 2b. 2 2 3

[0105] The objective function calculation unit 23 calculates the objective function for each individual in the population of initial individuals of the vehicle rear portion 2b based on the three-dimensional shape S of each individual. 2Perform numerical fluid analysis to calculate the objective function for each individual. The numerical fluid analysis program storage unit 26 stores a numerical fluid analysis program for performing numerical fluid analysis on the cubic shape of each individual in the initial population of the vehicle rear portion 2b. The control unit 27, for example, receives the execution of the calculation of the objective function for each individual in the initial population of the vehicle rear portion 2b from the transmission / reception unit 24, commands the objective function calculation unit 23 to calculate the objective function for each individual in the initial population of the vehicle rear portion 2b, or commands the transmission / reception unit 24 to transmit the objective function for each individual in the initial population of the vehicle rear portion 2b calculated by the objective function calculation unit 23 to the computer 10.

[0106] The three-dimensional shape optimization method, three-dimensional shape optimization device, and three-dimensional shape optimization program according to the third embodiment of the present invention have the following effects in addition to the effects of the first embodiment. In this third embodiment, an objective function representing the air resistance reduction performance of the vehicle rear portion 2b and the fluctuating aerodynamic force F acting on the vehicle rear portion 2b is calculated. For this reason, regarding the problem of the trade-off relationship between the reduction of the air resistance received by the vehicle rear portion 2b and the reduction of the fluctuating aerodynamic force F acting on the vehicle rear portion 2b, an optimal three-dimensional shape S 2 that simultaneously improves a plurality of requirements can be searched for. For example, by a simulator that combines individual generation, air flow analysis, and evolutionary calculation, a three-dimensional shape S 2 of the vehicle rear portion 2b that satisfies the reduction of air resistance and the fluctuating aerodynamic force F can be easily obtained while taking into account the shape constraints of the vehicle rear portion 2b.

[0107] (Fourth Embodiment) As shown in FIGS. 15 to 17, this fourth embodiment is an embodiment in which an optimal three-dimensional shape S 2 of the vehicle front portion 2a capable of reducing the tunnel micro-pressure wave W 2 is searched for. Further, as shown in FIGS. 18 and 19, this fourth embodiment is an optimal three-dimensional shape S 2This is an embodiment in the case of searching. In the vehicle 2, the front part 2a and the rear part 2b of the vehicle have the same shape. When the vehicle 2 travels from the starting point to the ending point and when it turns back at the ending point and travels from the ending point to the starting point, for example, the front part 2a of the leading vehicle 2A and the rear part 2b of the trailing vehicle 2B are swapped. The three-dimensional shape optimization system 9 shown in FIG. 2 is for reducing the tunnel micro-pressure wave W of the front part 2a and the rear part 2b of the vehicle shown in FIG. 19 2 In order to reduce the air resistance or make the volume reach a specific target value, the three-dimensional shape S of the front part 2a of the vehicle 2 is optimized. At the same time, in order to reduce the air resistance of the rear part 2b of the vehicle and reduce the fluctuating aerodynamic force F acting on the rear part 2b of the vehicle, the three-dimensional shape S of the rear part 2b of the vehicle 2 is optimized.

[0108] The three-dimensional shape optimization method, the three-dimensional shape optimization device, and the three-dimensional shape optimization program according to the fourth embodiment of the present invention have the following effects in addition to the effects of the first to third embodiments. In this fourth embodiment, at least one objective function representing the micro-pressure wave reduction performance, the air resistance reduction performance, or the volume of the front part 2a and the rear part 2b of the vehicle is calculated, and at least one objective function representing the air resistance reduction performance or the fluctuating aerodynamic force F of the front part 2a and the rear part 2b of the vehicle is calculated. Therefore, when the front part 2a and the rear part 2b of the vehicle have the same shape and the vehicle 2 turns back and the leading vehicle 2A and the trailing vehicle 2B are swapped, by searching for the optimized shape S of the front part 2a and the rear part 2b of the vehicle 3 the reduction effect of the tunnel micro-pressure wave W 2 and the reduction effect of the vehicle shake in the tunnel can be achieved.

[0109] (Other embodiments) The present invention is not limited to the embodiments described above, and various modifications or changes are possible as described below, and these are also within the scope of the present invention. (1) In this embodiment, the case where the moving body is a railway vehicle has been described as an example. However, the present invention can also be applied to other moving bodies such as maglev trains, automobiles, airplanes, or flying objects. Further, in this embodiment, the case where the vehicle 2 is a Shinkansen vehicle has been described as an example. However, the present invention can also be applied to conventional line vehicles running on conventional lines, or vehicles for new-conventional through operation that can run on both Shinkansen lines and conventional lines. Furthermore, in this embodiment, the case where the three-dimensional shape S such as the vehicle front part 2a, the vehicle rear part 2b, or the hull 8 is optimized as an object existing in the flow field has been described as an example. 2 However, the present invention can also be applied to the case of optimizing the three-dimensional shape S of other objects existing in the flow field. 2

[0110] (2) In this embodiment, the case where an object such as the vehicle front part 2a, the vehicle rear part 2b, or the hull 8 moves has been described as an example. However, the present invention can also be applied to the case where a stationary object receives a flow. Further, in this embodiment, the case where the optimization requirement setting unit 13 sets two objective functions has been described as an example. However, the present invention can also be applied to the case where the optimization requirement setting unit 13 sets three or more objective functions. Furthermore, in this embodiment, the case where aerodynamic analysis such as an air flow simulator is taken as an example of numerical fluid analysis has been described. However, the present invention can also be applied to calculation systems other than the air flow simulator.

[0111] (3) In this first embodiment, the case where the current collector 3 is a single-arm pantograph has been described as an example. However, the present invention can also be applied to other types of pantographs such as diamond pantographs or wing-type pantographs. Further, in this second embodiment and the third embodiment, the case where the tunnel T is taken as an example of a fixed structure that the vehicle 2 enters or runs through has been described. However, the present invention can also be applied to fixed structures such as overpasses, flyovers, elevated stations, snow sheds (avalanche protection works), snow shelters, rockfall covers (rockfall protection works).

Explanation of Reference Numerals

[0112] 1 Overhead line 2 Vehicle (Moving body (Object)) 2a Front part of vehicle (Front part (Object)) 2b Rear part of vehicle (Front part (Object)) 3 Current collector 8 Boat body (Object) 8a Washboard 9 Three-dimensional shape optimization system 10 Computer (First computer) 12 Initial individual generation unit 13 Optimization requirement setting unit 14 Three-dimensional shape creation unit 15 Next-generation individual generation unit 16 Optimization shape search unit 19 Three-dimensional shape optimization program storage unit 21 Control unit 22 Computer (Second computer) 23 Objective function calculation unit 26 Numerical fluid analysis program storage unit 27 Control unit 28 Communication device S 1 Initial shape S 2 Three-dimensional shape S 3 Optimized shape G 0 Computational grid G 1 Control grid P 0 Grid point P 01 Grid point (External grid point) P 02 Grid point (Internal grid point) P 1 Feature point (Design variable) P 2 Control point (Design variable) T Tunnel T 1 ,T 2 Tunnel portal T 3 Wall surface H Tunnel buffer W 1 Compression wave W 2 Tunnel micro-pressure wave F Fluctuating aerodynamic force

Claims

1. A three-dimensional shape optimization method for optimizing the three-dimensional shape of an object existing in a flow field, comprising: A three-dimensional shape creation step of creating a three-dimensional shape of each individual in a population of initial individuals of the object; An objective function calculation step of performing numerical fluid analysis on the three-dimensional shape of each individual in the population of initial individuals of the object to calculate the objective function of each individual; A next-generation individual generation step of selecting excellent individuals by an evolutionary algorithm based on the objective function of each individual in the population of initial individuals of the object and generating next-generation individuals; An optimization shape search step of searching for the optimized shape of the object by repeating the creation of the three-dimensional shape of the next-generation individuals, the calculation of the objective function of the next-generation individuals, and the generation of individuals of the further next generation up to a specific generation; A three-dimensional shape optimization method including the above.

2. In the three-dimensional shape optimization method according to Claim 1, the objective function calculation step includes a step of performing numerical fluid analysis based on a calculation grid generated by an orthogonal grid method for the three-dimensional shape of each individual in the population of initial individuals of the object and calculating the objective function of each individual; A three-dimensional shape optimization method characterized by the above.

3. In the three-dimensional shape optimization method according to Claim 2, the objective function calculation step includes a step of performing numerical fluid analysis based on grid points located outside the three-dimensional shape of each individual among the grid points of the calculation grid common to the three-dimensional shapes of each individual in the population of initial individuals of the object and calculating the objective function of each individual; A three-dimensional shape optimization method characterized by the above.

4. In the three-dimensional shape optimization method according to Claim 1, the three-dimensional shape creation step includes a step of creating a three-dimensional shape of each individual in a population of initial individuals of the boat body of a current collector; the objective function calculation step includes a step of calculating at least two objective functions among objective functions representing the lift stability, noise performance, air resistance reduction performance, or target value of lift of the boat body; A three-dimensional shape optimization method characterized by the above.

5. In the three-dimensional shape optimization method according to Claim 4, the three-dimensional shape creation step includes a step of creating a three-dimensional shape of each individual representing the worn shape of the slider supported by the boat body; A three-dimensional shape optimization method characterized by the above.

6. In the three-dimensional shape optimization method according to Claim 1, the shape creation step includes a step of creating a three-dimensional shape of each individual in a population of initial individuals at the front part of a moving body; The objective function calculation step includes a step of calculating at least two objective functions among the micro-pressure wave reduction performance, air resistance reduction performance, or volume of the front part of the moving body. A three-dimensional shape optimization method characterized by the above.

7. In the three-dimensional shape optimization method according to claim 1, the three-dimensional shape creation step includes a step of creating a three-dimensional shape of each individual in a population of initial individuals at the rear part of the moving body, the objective function calculation step includes a step of calculating an objective function representing the air resistance reduction performance of the rear part of the moving body and the fluctuating aerodynamic force acting on the rear part of the moving body. A three-dimensional shape optimization method characterized by the above.

8. In the three-dimensional shape optimization method according to claim 1, the three-dimensional shape creation step includes a step of creating a three-dimensional shape of each individual in a population of initial individuals at both ends of the moving body having the same shape, the objective function calculation step is a step of calculating at least one objective function among the micro-pressure wave reduction performance, air resistance reduction performance, or volume of both ends of the moving body, and a step of calculating at least one objective function among the air resistance reduction performance of both ends of the moving body or the objective function representing the fluctuating aerodynamic force acting on both ends of the moving body. A three-dimensional shape optimization method characterized by the above.

9. A three-dimensional shape optimization system for optimizing the three-dimensional shape of an object existing in a flow field, comprising a three-dimensional shape creation unit that creates a three-dimensional shape of each individual in a population of initial individuals of the object, an objective function calculation unit that performs numerical fluid analysis on the three-dimensional shape of each individual in the population of initial individuals of the object to calculate the objective function of each individual, a next-generation individual generation unit that selects excellent individuals by an evolutionary algorithm based on the objective function of each individual in the population of initial individuals of the object and generates next-generation individuals, an optimization shape search unit that repeats the creation of the three-dimensional shape of the next-generation individuals, the calculation of the objective function of the next-generation individuals, and the generation of the next-next-generation individuals up to a specific generation to search for the optimized shape of the object. A three-dimensional shape optimization system comprising the above.

10. In the three-dimensional shape optimization system according to claim 9, a first computer that performs the creation of the three-dimensional shape by the three-dimensional shape creation unit, the generation of the next-generation individuals by the next-generation individual generation unit, and the search for the optimized shape by the optimization shape search unit, and a second computer that performs the calculation of the objective function by the objective function calculation unit. The first computer transmits data necessary for the calculation of the objective function by the objective function calculation unit to the second computer, The second computer transmits data regarding the objective function calculated by the objective function calculation unit to the first computer, A three-dimensional shape optimization system characterized by the above.

11. A three-dimensional shape optimization program for optimizing the three-dimensional shape of an object existing in a flow field, A three-dimensional shape creation procedure for creating the three-dimensional shape of each individual in the population of the initial individuals of the object, An objective function calculation procedure for performing numerical fluid analysis on the three-dimensional shape of each individual in the population of the initial individuals of the object and calculating the objective function of each individual, A next-generation individual generation procedure for selecting excellent individuals by an evolutionary algorithm based on the objective function of each individual in the population of the initial individuals of the object and generating next-generation individuals, An optimized shape search procedure for searching for the optimized shape of the object by repeating the creation of the three-dimensional shape of the next-generation individuals, the calculation of the objective function of the next-generation individuals, and the generation of the individuals of the next generation after the next-generation individuals until a specific generation, A three-dimensional shape optimization program that causes a computer to execute the above.

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