JP2016200902A - Method for generating approximation model of structure, device for generating approximation model of structure, and program - Google Patents

Abstract

A method of creating an approximate model of a structure, an apparatus for creating an approximate model of a structure, and a program capable of reducing the amount of calculation and calculation time with high accuracy of the approximate model. A method of creating an approximate model of a structure includes a plurality of types of design variables that define a structure and a material constituting the structure, and a plurality of characteristic values that define the structure and the material constituting the structure. It is targeted. A plurality of types of design variables, domain of each design variable, and a plurality of characteristic values are set, and a nonlinear response relationship between the plurality of types of design variables and the plurality of types of characteristic values is determined. Using nonlinear response relationships, calculate the output value in the characteristic value space consisting of multiple types of design variable values and characteristic values, set at least one output value, and perturb the input parameter value in the output value To obtain additional output values. An approximate model is created using the additional output value and the output value of the characteristic value space. A multi-objective optimization calculation is performed using an approximate model to obtain a Pareto solution. [Selection] Figure 1

Description

  The present invention relates to a structure approximation model creation method, a structure approximation model creation apparatus, and a program for creating an approximation model representing a relationship between a plurality of input values and a plurality of output values related to a structure. The present invention relates to a method of creating an approximate model of a structure, an apparatus for creating an approximate model of a structure, and a program that can reduce the calculation amount and the calculation time.

In the simulation, a predetermined design factor, a response to the design variable, and a characteristic value (objective function) for the design variable can be calculated. In the optimization, the value of a design variable for obtaining a desired characteristic value can be calculated.
In the simulation, the structure and the design variables of the materials that make up the structure are input values (input parameters), and multiple characteristic values (objective functions) of the structure and the materials that make up the structure are output values (output parameters). As a result, an approximate model representing the relationship between the design variable and the objective function has been created. Note that a response surface is created instead of the approximate model.
In multi-objective optimization that targets multiple characteristic values (objective functions), there is often a trade-off relationship between characteristic values. The divergence from may increase. Thus, various simulation methods have been proposed (see Patent Documents 1 and 2).

  In Patent Document 1, the response surface is divided based on an objective function (output value), and the response surface is sequentially updated while adding a sampling calculation to improve the accuracy of the response surface. It describes how to perform the calculation.

  In Patent Document 2, the first optimization calculation is performed using a stochastic method such as a genetic algorithm, and the range of design variables is narrowed down from the result, and the design used in the first optimization calculation is described. A technique for performing the second optimization calculation using a level narrower than the variable level is described. In Patent Document 2, a sufficiently wide level is set and random sampling is performed, and from this result, a response surface function is created, and optimization by a genetic algorithm is performed using the response surface function.

JP 2011-103036 A JP2013-242662A

In Patent Document 1, since the sampling calculation is repeated until the convergence condition is satisfied, there is a problem that it takes much time if the convergence condition is tightened.
In Patent Document 2, even when implemented at a sufficiently wide level, the random sampling may be biased when viewed in the design variable space. In addition, when using a sampling method that is uniformly distributed in the design variable space, such as the Latin hypercube, if the number of samplings is small, the point-to-point spacing in the design variable space increases, and the characteristic value space There is a high possibility that the characteristic peak is hidden between the points, that is, the multimodality of the solution cannot be expressed. Therefore, the tendency of the entire design variable space cannot be accurately expressed by the response surface function, and there is a possibility that the design variable and its value for improving the objective characteristic cannot be derived with high accuracy. On the other hand, if the number of samplings in the design variable space is increased in order to improve the accuracy of the response surface function, the calculation amount becomes enormous. As described above, in both Patent Document 1 and Patent Document 2, it is enormous if an important region in the characteristic value space is accurately determined from the entire design variable space and the approximation accuracy of the calculated optimal solution is improved. Having the amount of calculation was a problem.

  An object of the present invention is to solve the above-described problems based on the prior art, and to provide an approximate model creation method and an approximate model creation method for a structure capable of reducing the amount of computation and calculation time with high accuracy of the approximate model. To provide an apparatus and a program.

  In order to achieve the above object, according to a first aspect of the present invention, there are provided a plurality of input parameters defined as design variables among parameters defining a structure and a material constituting the structure, and the structure and the structure. A method for creating an approximate model of a structure for two types of data with a plurality of output parameters defined as characteristic values among parameters defining a constituent material, the plurality of types of design variables and each design variable A first step of setting a plurality of types of characteristic values, a second step of determining a nonlinear response relationship between a plurality of types of design variables and a plurality of types of characteristic values, and a second step A third step of calculating an output value in a characteristic value space composed of a plurality of types of design variable values and characteristic values, and at least one output value in the characteristic value space is set using a predetermined nonlinear response relationship And set output The characteristic is obtained by perturbing the input parameter value in the value, setting a plurality of input parameter values, obtaining the additional output value, and using the additional output value and the output value obtained in the third step. A method for creating an approximate model of a structure, comprising: a fifth step of creating an approximate model using a value as an objective function; and a sixth step of performing multi-objective optimization calculation using the approximate model Is to provide.

The step of obtaining the additional output value of the fourth step is to obtain a sparse region in the characteristic value space, select an output value from the sparse region, and perturb the input parameter value in the selected output value It is preferable to set a plurality of input parameter values and acquire additional output values.
In addition, the output value set in the fourth step is set as a reference value in the characteristic value space in the first step, and an output value in a region larger or smaller than the reference value or a reference value in advance. It is preferable to set to be set from output values within a predetermined distance region.

Also, between the fifth step and the sixth step, a verification calculation is performed on the approximate model created in the fifth step using the additional output value and the output value of the characteristic value space, and the result of the verification calculation is If the predetermined determination condition is satisfied, multi-objective optimization calculation is performed in the sixth step. If the verification result does not satisfy the predetermined determination condition, another additional output value is set in the fourth step. It is preferable to acquire and update the approximate model with another additional output value in the fifth step.
In addition, after the sixth step, there is a step of performing an actual calculation for verifying the error of the approximate model using the Pareto solution obtained by performing the multi-objective optimization calculation of the sixth step. If the result of the above satisfies the predetermined judgment condition, the Pareto solution obtained by performing the multi-objective optimization calculation obtained in the sixth step is set as the final Pareto solution, and the result of the actual calculation is the predetermined judgment. When the condition is not satisfied, it is preferable to acquire another additional output value in the fourth step and update the approximate model using the other additional output value in the fifth step.

  For example, the design variable is at least one parameter that changes the shape or structure of the tire, the characteristic value is at least one of the physical characteristic values of the tire, and the physical quantity of the tire is calculated by multi-objective optimization calculation. The

  According to a second aspect of the present invention, there are a plurality of input parameters defined as design variables among parameters defining a structure and a material constituting the structure, and parameters defining a material constituting the structure and the structure. A device for creating an approximate model of a structure for two types of data with multiple output parameters defined as characteristic values, including multiple types of design variables, domain of each design variable, and multiple types of data A condition setting unit that sets characteristic values and defines nonlinear response relationships between multiple types of design variables and multiple types of characteristic values, and consists of values and characteristic values of multiple types of design variables using nonlinear response relationships Calculate the output value in the characteristic value space, set at least one output value in the characteristic value space, perturb the input parameter value in the set output value, and set multiple input parameter values An operation that obtains additional output values, creates an approximate model using the additional output values and output values in the characteristic value space as characteristic functions, and performs multi-objective optimization calculations using the generated approximate models. And a Pareto solution search unit for extracting a Pareto solution. An apparatus for creating an approximate model of a structure is provided.

The calculation unit obtains a sparse region in the characteristic value space, selects an output value from the sparse region, and perturbs the input parameter value in the selected output value to set a plurality of input parameter values It is preferable to acquire an additional output value.
A reference value is set in the characteristic value space in the condition setting unit, and an output value to be set is set in the characteristic value space in the first step, and an output value in a region that is larger or smaller than the reference value, Or it is preferable to set from the output value in the area | region of the predetermined distance with respect to a reference value.

Let the computation unit perform a verification calculation using the additional output value and the output value of the characteristic value space in the approximate model, and if the result of the verification calculation satisfies a predetermined judgment condition, perform a multi-objective optimization calculation in the computation unit It is preferable that the Pareto solution is extracted by the Pareto solution search unit. On the other hand, when the result of verification does not satisfy the predetermined determination condition, it is preferable to have a control unit that causes the arithmetic unit to acquire another additional output value and update the approximate model using the other additional output value. .
When the arithmetic unit performs actual calculation for verifying the error of the approximate model using the Pareto solution obtained by performing the multi-objective optimization calculation, and the result of the actual calculation satisfies a predetermined determination condition, If the Pareto solution obtained by performing the multi-objective optimization calculation is the final Pareto solution, and the actual calculation result does not satisfy the predetermined judgment condition, the operation unit acquires another additional output value, It is preferable to have a control unit that updates the approximate model using the additional output value.

For example, the design variable is at least one parameter that changes the shape or structure of the tire, the characteristic value is at least one of the physical characteristic values of the tire, and the physical quantity of the tire is calculated by multi-objective optimization calculation. The
According to a third aspect of the present invention, there is provided a program for causing a computer to execute each step of the method for creating an approximate model of a structure according to the first aspect of the present invention as a procedure.

  According to the present invention, the accuracy of the approximate model of the structure can be increased, and the calculation amount and the calculation time can be reduced.

It is a schematic diagram showing an approximate model creation apparatus for a structure used in the approximate model creation method for a structure according to an embodiment of the present invention. It is a flowchart which shows the 1st example of the approximate model creation method of the structure of embodiment of this invention in process order. (A) is a graph which shows an example of a design variable, (b) is a graph which shows the relationship between the characteristic value 1 and the characteristic value 2, (c) typically shows the change method of a design variable value. It is a graph to show. (A) is a graph which shows the 1st example of the acquisition method of an additional output value, (b) is a graph which shows the 2nd example of the acquisition method of an additional output value, (c) is an addition It is a graph which shows the 3rd example of the acquisition method of an output value. (A) is a graph showing a first example of a reference point setting method, (b) is a graph showing a second example of a reference point setting method, and (c) is a graph of a reference point setting method. It is a graph which shows the 3rd example of a setting method. It is a flowchart which shows the 2nd example of the approximate model creation method of the structure of embodiment of this invention in process order. It is a graph which shows an example of a verification result. It is a flowchart which shows the 3rd example of the approximate model creation method of the structure of embodiment of this invention in process order. It is a graph for demonstrating an error. (A) is a graph which shows typically the change method of the design variable value of Example 1, (b) is a graph which shows the change method of the design variable value of the comparative example 2 typically. (A) is a graph which shows the set point of Example 1, (b) is a graph which shows the design point of the comparative example 1, (c) is a graph which shows the design point of the comparative example 2. . It is a graph which shows the characteristic value of Example 1, Comparative Examples 1 and 2, and a reference example.

Hereinafter, based on a preferred embodiment shown in the accompanying drawings, an approximate model creating method, an approximate model creating apparatus, and an approximate model creating method for a structure according to the present invention are executed by a computer or the like. Describe the program in detail.
FIG. 1 is a schematic diagram showing a structure approximate model creation apparatus used in the structure approximate model creation method of the embodiment of the present invention.
The structure approximate model creation apparatus 10 shown in FIG. 1 is used in the structure approximate model creation method of the present embodiment. Hereinafter, the approximate model creation apparatus 10 for a structure is referred to as an approximate model creation apparatus 10.
The approximate model creation apparatus 10 is configured using hardware such as a computer. As described above, the approximate model creation apparatus 10 shown in FIG. 1 is used in the approximate model creation method of the present invention. However, if the approximate model creation method can be executed using hardware such as a computer and software, the approximate model can be used. It is not limited to the creation device 10.

  In the present embodiment, as a characteristic value among a plurality of input parameters defined as design variables among the parameters defining the structure and the material constituting the structure, and among the parameters defining the structure and the material constituting the structure. A data set in which two types of data of a plurality of defined output parameters are grouped is targeted. For example, the design variable is displayed as visualization information such as a scatter diagram in the characteristic value space (objective function space).

The approximate model creation apparatus 10 includes a processing unit 12, an input unit 14, and a display unit 16. The processing unit 12 includes a condition setting unit 20, a model creation unit 22, a calculation unit 24, a Pareto solution search unit 26, a memory 28, a display control unit 30, and a control unit 32. In addition, although not shown, it has a ROM and the like.
The processing unit 12 is controlled by the control unit 32. In the processing unit 12, the condition setting unit 20, the model creation unit 22, the calculation unit 24, and the Pareto solution search unit 26 are connected to the memory 28, and the condition setting unit 20, the model creation unit 22, the calculation unit 24, and the Pareto Data of the solution search unit 26 is stored in the memory 28.
In the method of creating an approximate model of a structure described below, various processes are performed in each unit of the processing unit 12. In the following description, the description that various processes are performed by each unit of the processing unit 12 by the control unit 32 is omitted, but a series of processes of each unit is controlled by the control unit 32. The memory 28 also stores various determination conditions described later. The control unit 32 reads the determination condition from the memory 28, compares it with the result obtained by the calculation unit 24, determines the operation of each unit based on the determination result, and operates each unit based on the determined operation.

  The input unit 14 is various input devices for inputting various information such as a mouse and a keyboard in accordance with an operator instruction. The display unit 16 displays, for example, results obtained by the approximate model creation method, and various known displays are used. The display unit 16 also includes a device such as a printer for displaying various types of information on an output medium.

  The approximate model creation apparatus 10 executes a program (computer software) stored in a ROM or the like by the control unit 32, so that the condition setting unit 20, the model creation unit 22, the calculation unit 24, and the Pareto solution search unit 26 Each part is formed functionally. As described above, the approximate model creation apparatus 10 may be configured by a computer in which each part functions by executing a program, or may be a dedicated apparatus in which each part is configured by a dedicated circuit.

  The condition setting unit 20 inputs and sets various conditions and information necessary for displaying the Pareto solution as visualization information such as a scatter diagram in the objective function space by the method of creating an approximate model of the structure of the present embodiment. . Various conditions and information are input via the input unit 14. Various conditions and information set by the condition setting unit 20 are stored in the memory 28.

The condition setting unit 20 is set with a plurality of parameters determined as design variables among parameters defining the structure and the material constituting the structure. The design variable parameters may be set with variation factors such as load and boundary conditions, and in the case of products, constraints such as size and mass.
In addition, a plurality of parameters determined as characteristic values (objective functions) among the parameters defining the structure and the material constituting the structure are set. For the characteristic value, an index for evaluating the structure and the material constituting the structure other than physical and chemical characteristic values such as cost may be used.
The structure and the material constituting the structure may be the whole system including the structure such as the parts constituting the structure, the assembly form of the structure, or a part thereof, instead of the structure alone.

The plurality of types of characteristic values set in the condition setting unit 20 are physical quantities to be evaluated, that is, objective functions. The objective function has a preferable direction in terms of performance, and the value increases, decreases, or approaches a predetermined value. As for the objective function, there is an unfavorable direction opposite to the preferred direction in addition to the above-mentioned preferable direction.
When the structure is a tire, the characteristic value is a characteristic value of the tire. In this case, the characteristic value is a physical quantity to be evaluated as tire performance, for example, CP (cornering power) which is a lateral force in the vicinity of zero slip angle, which is an indicator of steering stability, and an indicator of riding comfort. Examples thereof include a primary natural frequency of a tire, rolling resistance as an index of rolling resistance, a lateral spring constant as an index of steering stability, wear energy of a tire tread member as an index of wear resistance, and fuel efficiency. Other than this, examples of the physical quantity of the tire include a shape and a dimensional value. The shape is, for example, a cross-sectional shape. Examples of the dimension value include a tire width and a tire outer diameter. Examples of the physical quantity of a tire include a deflection amount, contact pressure distribution, rolling resistance, cornering characteristics, and the like in addition to the shape or dimensional value.

The design variable defines the shape of the structure, the internal structure of the structure, the material characteristics, and the like. In the case of a tire, design variables are a plurality of parameters among a tire material behavior, a tire shape, a tire cross-sectional shape, a tire natural vibration mode, and a tire structure. Examples of the design variable include a radius of curvature that defines a crown shape in a tread portion of the tire, a belt width dimension of the tire that defines a tire internal structure, and the like. In addition to this, for example, a filler dispersion shape that defines material characteristics in the tread portion, a filler volume ratio, and the like can be given.
The constraint condition is a condition for constraining the value of the objective function to a predetermined range or constraining the value of the design variable to a predetermined range.
Also, when the structure is a tire, it is used for vehicle running simulation such as tire load load, running conditions such as tire rolling speed, road surface conditions where the tire runs, for example, uneven shape, friction coefficient, etc. Information on the vehicle specifications is set.

In addition, information for determining a nonlinear response relationship between a plurality of types of design variables and a plurality of types of characteristic values is set in the condition setting unit 20. This nonlinear response relationship includes, for example, a numerical simulation such as FEM, a theoretical formula, and the like.
The condition setting unit 20 sets a simulation condition and a constraint condition in the simulation when performing a numerical simulation such as a model generated by a nonlinear response relationship, a boundary condition of the model, and FEM. Furthermore, optimization conditions for obtaining a Pareto solution, such as conditions for searching for a Pareto solution, are set.

The conditions for the Pareto solution search are a method for searching for the Pareto solution and various conditions in the Pareto solution search. In the present embodiment, for example, a genetic algorithm (GA) can be used as a method for searching for a Pareto solution. In general, it is known that the search ability of a genetic algorithm decreases as the characteristic value (objective function) increases. One way to solve this is to increase the number of individuals.
In addition to this, a design variable definition area is set in the condition setting unit 20. The domain of the design variable may be a discrete level value or a constant. Since there are multiple types of design variables, discrete level values are set for all design variables, and the computer changes the combination of design variables with the domain defined as the constant for the remaining design variables. The characteristic value may be calculated while extracting a Pareto solution described later.

For example, the design variable is set by the condition setting unit 20 using, for example, a Latin hypercube method (Latin hypersquare method). The Latin hypercube method is a sample method that covers the design variable space discretely and uniformly. For this reason, design values can be set evenly in the design variable space. In addition to the Latin hypercube method, the value of the design variable can be set using, for example, an orthogonal table, a Monte Carlo method, or the like.
Since there are multiple types of design variables, discrete level values are set for some of the design variables, and the Pareto solution described later is extracted using the domain of the remaining design variables as constants. May be.
For multi-objective optimization calculations, either a method of searching sequentially using a nonlinear relationship (response surface) between input variables and output variables, or a method of searching by calculating output values while changing input variables according to an optimization algorithm May be used.

  The model creation unit 22 creates various calculation models based on the set nonlinear response relationship. As described above, the nonlinear response relationship includes a numerical simulation such as FEM. In this case, the model creation unit 22 generates a mesh model corresponding to a design parameter representing a design variable and a characteristic value parameter representing a characteristic value. Is done. Also in the case of a theoretical formula or the like, a theoretical formula or the like corresponding to the design parameter or characteristic value parameter is created. When the structure is a tire, a tire model is created. The calculation unit 24 performs a simulation calculation using the tire model.

The tire model created by the model creation unit 22 is created using each type of design parameters set by the condition setting unit 20, and a known creation method can be used for creating the tire model. . The tire model also generates at least a road surface model that is a target for rolling the tire model. A tire model that reproduces a rim on which a tire is mounted, a wheel, and a tire rotation axis may be used. Further, if necessary, a model that reproduces a vehicle to which a tire is attached may be incorporated into the tire model. At this time, a model in which the tire model, the rim model, the wheel model, and the tire rotation axis model are integrated based on a preset boundary condition can be created.
Moreover, the form of the tire model used for the analysis is not particularly limited, and may be a smooth tire without a groove, only a main groove, or with a pattern.

The tire model created by the model creation unit 22 is created using each type of design parameters set by the condition setting unit 20, and a known creation method can be used for creating the tire model. .
For example, a tire model is created by dividing a tire into a finite number of elements composed of a plurality of nodes. An analytical model may be used as a viscoelastic body, or an analytical model may be used as a rigid body.
The elements constituting the tire model are, for example, a quadrilateral element in a two-dimensional plane, a solid element such as a tetrahedral solid element, a pentahedral solid element, and a hexahedral solid element in a three-dimensional body, and a shell such as a triangular shell element and a rectangular shell element. Elements that can be analyzed by a computer, such as elements and surface elements. In the process of analysis, the elements divided in this way are identified one by one using three-dimensional coordinates in the three-dimensional model and using two-dimensional coordinates in the two-dimensional model.

  Each of these models may be a discretized model capable of numerical calculation, such as a finite element model for use in a known finite element method (FEM). In addition to the road surface model and the tire model, the inclusions existing on the road surface are reproduced, for example, when a tire design plan that optimizes tire performance such as tire wet performance is obtained using the tire model. Generate a model. For example, as an inclusion model, various models that reproduce water, snow, mud, sand, gravel, ice, and the like on the road surface may be generated as a discretized model that can be numerically calculated. The road surface model is not limited to a model that reproduces a road surface with a flat surface, and may be a model that reproduces a road surface shape having irregularities on the surface as necessary.

The calculation unit 24 calculates characteristic values using various models created by the model creation unit 22. Thereby, a characteristic value (output value) for the design variable is obtained. The obtained characteristic value (output value) is stored in the memory 28. The calculation unit 24 functions, for example, by executing a subroutine using a known finite element solver.
In addition, the calculation unit 24 calculates an output value (characteristic value) in a characteristic value space including a plurality of types of design variable values and characteristic values, using a nonlinear response relationship. Then, at least one output value is set in the characteristic value space composed of the characteristic values, the input parameter values in the set output values are perturbed, a plurality of input parameter values are set, and additional output values ( (Additional sampling point) is acquired, and an approximate model is created by using the additional output value and the output value of the characteristic value space, using the characteristic value as the output value as an objective function. Further, the calculation unit 24 performs multi-objective optimization calculation using the created approximate model.
The above approximate model (meta model) is a mathematical model that approximates the input / output relationship, and various input / output relationships can be approximated by adjusting parameters. For example, a polynomial model, kriging, a neural network, a radial basis function, or the like can be used as the above approximate model.

The calculation unit 24 also performs verification calculation such as cross-validation using the additional output value and the output value of the characteristic value space in the approximate model.
Moreover, the calculating part 24 performs the actual calculation using a finite element method using the Pareto solution obtained by implementing multiobjective optimization calculation. In addition to this, the calculation unit 24 calculates a characteristic value by a combination of a design variable and a characteristic value using a finite element method without using an approximate model.
The calculation unit 24 also performs multi-objective optimization calculation using an approximate model, and uses a specified nonlinear relationship using a Pareto solution extracted by the Pareto solution search unit 26 from the multi-objective optimization calculation result. It is also what causes the actual calculation to be executed. In addition to this, the calculation unit 24 calculates a characteristic value using a combination of a design variable and a characteristic value by using a finite element method without using an approximate model. As the multi-objective optimization calculation method, for example, a genetic algorithm (GA) which is one of evolutionary calculation methods is used. Genetic algorithms include, for example, DRMOGA (Divided Range Multi-Objective GA) or NCGA (Neighborhood Cultivation GA), which divides a solution set into a plurality of regions along an objective function and performs multi-objective GA for each divided solution set. , DCMOGA (Distributed Cooperation model of MOGA and SOGA), NSGA (Non-dominated Sorting GA), NSGA2 (Non-dominated Sorting GA-II), and SPEAII (Strength Pareto Evolutionary Algorithm-II) method are used. Can do.

The Pareto solution search unit 26 searches for a Pareto solution from the multi-objective optimization calculation result using the approximate model obtained by the calculation unit 24 according to the Pareto solution search conditions set by the condition setting unit 20, The solution is extracted. The obtained Pareto solution is stored in the memory 28.
Here, a Pareto solution cannot be said to be superior to any other solution in a plurality of characteristic values (objective functions) in a trade-off relationship, but a solution that has no other superior solution exists. Say. In general, there are a plurality of Pareto solutions as a set.
The Pareto solution search unit 26 searches for a Pareto solution using, for example, a Pareto ranking method.

  In the Pareto solution search unit 26, for example, selection using a vector evaluation genetic algorithm (VEGA), a Pareto ranking method, or a tournament method is performed. In addition to the genetic algorithm (GA), for example, annealing (SA) or particle swarm optimization (PSO) may be used as the same evolutionary calculation method.

  In the present invention, the non-linear response relationship defined between the design variable and the characteristic value, that is, the one used when the characteristic value is obtained using the design variable is not limited to the simulation such as FEM. A theoretical formula or the like can also be used.

The display control unit 30 causes the display unit 16 to display various parameters such as design variables and characteristic values set in the condition setting unit 20, the output value obtained by the calculation unit 24, and the Pareto solution. For example, the characteristic value and the Pareto solution are read from the memory 28 and displayed on the display unit 16. In this case, for example, the Pareto solution is displayed in the form of a scatter diagram with the characteristic value as an axis. That is, the design variable is displayed in the characteristic value space. In addition to the scatter diagram, it can be displayed in the form of a radar chart or a bubble chart.
The display control unit 30 can also cause the display unit 16 to display various types of information, tire models, numerical calculation results, and optimal solutions input via the input unit 14. For example, the tire model is read from the memory 28 and displayed on the display unit 16.

As described above, the control unit 32 controls the processing unit 12, and performs various processes performed by the approximate model creation method described below, including the model creation unit 22, the computation unit 24, and the Pareto solution of the processing unit 12. This is what the search unit 26 performs.
In the approximate model creation device 10, in the input file when changing the shape or structure, common portions such as boundary conditions and analysis steps, and portions that differ depending on individual shapes such as the node coordinate values, the placement angle of the reinforcing material, and the initial tension Can be automated by using a file format that can be divided into common parts, that is, by making individual information into an include file, it is easy to determine the tire shape even when many tire shapes are studied. Consideration is possible.

Next, a first example of a method for creating an approximate model of a structure according to the present embodiment will be described.
FIG. 2 is a flowchart showing a first example of the approximate structure creation method for a structure according to the embodiment of the present invention in the order of steps. FIG. 3A is a graph showing an example of a design variable, FIG. 3B is a graph showing a relationship between the characteristic value 1 and the characteristic value 2, and FIG. 3C schematically shows a method for changing the design variable value. FIG.

First, as shown in FIG. 2, optimization conditions such as design variables, characteristic values (objective functions), and constraint conditions are set for the target structure (step S10). For example, as the structure, a tire having a size of 195 / 65R15 can be given.
As design variables, for example, six design variables φ1 to φ6 that change the cross-sectional shape or structure of the tire are set. The design variable setting method is not particularly limited. For example, the design value of the design variable is set using the Latin hypercube method (Latin hypersquare method). In this case, for example, as shown in FIG. 3A, the design values of the design variables are set uniformly in the design variable space.
The characteristic values include, for example, tire rigidity, rolling resistance, air resistance, cornering performance, friction energy, and the like as tire physical characteristics. For example, two tire physical characteristics of characteristic value 1 and characteristic value 2 are set as objective functions. Two or more characteristic values may be set.

The design variable (input parameter) is a parameter of the tire cross-sectional shape, and the characteristic value (output parameter) is two characteristic values that are tire physical characteristics. Parameters for the tire cross-sectional shape and two characteristic values are set in the condition setting unit 20. For example, characteristic value 1 is a characteristic that requires a large value, and characteristic value 2 is a characteristic that requires a small value.
In the present embodiment, an approximate model is created by the approximate model creation method under such setting conditions. A change in the characteristic value 1 and the characteristic value 2 depending on the value of the parameter of the tire cross-sectional shape is obtained.

  Next, as shown in FIG. 2, a non-linear response used when obtaining characteristic values from design variables is set in the condition setting unit 20 (step S12). That is, the relationship between design variables and characteristic values is determined. The type of this nonlinear response is stored in the memory 28, for example. Specifically, the relationship between the tire cross-sectional shape parameter and the characteristic value 1 and characteristic value 2 is set. When a tire cross-sectional shape parameter is input and characteristic value 1 and characteristic value 2 are output, the relationship to be set is, for example, a nonlinear function such as a polynomial in which characteristic value 1 uses a tire cross-sectional shape parameter as a variable. It is expressed using. Further, the characteristic value 2 is expressed by using a nonlinear function such as a polynomial having a tire cross-sectional shape parameter as a variable.

Next, using the nonlinear response relationship set in step S12, an output value in a characteristic value space composed of a plurality of types of design variable values and characteristic values is calculated. That is, sampling calculation is performed to calculate a characteristic value that is an output when a design variable is input (step S14). Thereby, the position of the design value of the design variable in the characteristic value space composed of the characteristic value 1 and the characteristic value 2 can be known. FIG. 3B shows the result obtained using the design values of the design variables shown in FIG.
Reference numeral 40 shown in FIG. 3B indicates an output value (sampling point) represented by a combination of the characteristic value 1 and the characteristic value 2 obtained by the set nonlinear relationship. Reference numeral 42 indicates one characteristic value selected from among a plurality of output values 40 (sampling points). Reference numeral 44 indicates a plurality of output values (sampling points) set by setting a plurality of input parameter values by perturbing the input parameter values (values of the design variables φ1 to φ6) in the selected output value 42. .

Next, one output value 42 is set from the output values 40 shown in FIG. It should be noted that at least one output value 42 may be selected from the output values 40, a plurality of output values 40 may be selected, or all the output values 40 may be selected as the output values 42.
The method for setting the output value 42 is not particularly limited, and can be set randomly from the output value 40.

  In the present embodiment, the input parameter value at the output value 42 is perturbed, and a plurality of input parameter values are set to obtain a plurality of output values 44 (step S16). The output value 44 is a value represented by a combination of design variables φ1 to φ6 (input parameter values), for example. Variations are given to the design variables φ1 to φ6 with the values of the design variables φ1 to φ6 in the output value 44 of FIG. Specifically, in the design variable φ1, the variation of the predetermined width δ is allowed with respect to the point 46a. In the design variable φ2, the predetermined width δ is allowed to vary with respect to the point 46b. In the design variable φ3, the variation of the predetermined width δ is allowed with respect to the point 46c. In the design variable φ4, a predetermined width δ is allowed to vary with respect to the point 46d. In the design variable φ5, the fluctuation of the predetermined width δ is allowed with respect to the point 46e. In the design variable φ6, the fluctuation of the predetermined width δ is allowed with respect to the point 46f.

  At each point 46a to 46f of the design variables φ1 to φ6 of the output value 42, a combination in which the design variables are changed by a predetermined width δ is set. For example, a plurality of, for example, 10 combinations of design variables φ1 to φ6 are created for the combination of design variables in the output value 42 using the Monte Carlo method, and the output value 44 is set. Note that the number of output values to be added is not limited to 10 cases, and may be 50 cases, for example.

Further, as the values of the design variables φ1 to φ6 in the predetermined width δ, values obtained by equally dividing the value intervals may be used, and the distribution of the design variable values is set based on a probability distribution such as a Gaussian distribution. May be. For example, an output value 44 output by a combination of design variables using a Gaussian distribution has a high probability that an output value 44 having a value close to the output value 42 is added. These design variable values are preferably combined using a random sampling method such as the Monte Carlo method.
In the present invention, perturbation means that, in the characteristic values represented by a plurality of types of design variables, the value is varied within a predetermined width δ with respect to the value of each design variable serving as a median value. . By using a combination of these values, a combination of design variables similar to the combination of the design variables selected as the median value can be obtained, so that an output value near the output value indicated by the selected combination of design variables can be obtained. it can.

Next, an approximate model is created using the output value obtained in step S14 and the output value added in step S16 (step S18). That is, the relationship between the design variable and the characteristic value is expressed by an approximate model or an approximate expression.
Next, multi-objective optimization calculation using the approximate model is performed by the calculation unit 24 (step S20). Next, a Pareto solution is extracted by the Pareto solution search unit 26 from the multi-objective optimization calculation result to obtain a Pareto solution (step S22). In this way, a Pareto solution can be obtained using the approximate model. Note that the Pareto solution obtained using the approximate model as described above is an approximate prediction value.

A method for acquiring the additional output value (additional sampling point) in step S16 will be described.
The acquisition of the additional output value is performed by the calculation unit 24. In the characteristic value space, a region where the output value is sparse is obtained, the output value is selected from the sparse region, and the input parameter value in the selected output value is perturbed. It is preferable to set a plurality of input parameter values and acquire additional output values. More specific description will be given below.
4A is a graph showing a first example of an additional output value acquisition method, FIG. 4B is a graph showing a second example of an additional output value acquisition method, and FIG. FIG. 10 is a graph showing a third example of an additional output value acquisition method. FIG.

In step S16, the characteristic value space shown in FIG. 3B in step S14 is changed to an average value Pb of all output values (hereinafter referred to as an average value Pb of all output values) as shown in FIG. 4A, for example. Is simply referred to as an average value Pb), and is divided into _four regions D _{1 to} D ₄ . Each of the regions D _{1 to} D ₄ is a quadrangle. The distribution of the output values in the characteristic value space is examined, and the density of the output values in each region D _{1 to} D ₄ is examined. In the regions D _{1 to} D ₄ , at least one output value is set for the region having the lowest output value density, and the input parameter value in the output value is perturbed as described above, so that a plurality of input parameters are obtained. An additional output value is obtained by setting the value.
Of the regions D _{1 to} D ₄ , the region D ₁ has the lowest output value density, and at least one output value 42 is set out of the output values 40 of the region D ₁ . A plurality of input parameter values are set by perturbing the input parameter value at the set output value 42, and an output value is added.
Note that if the areas D _{1 to} D ₄ have the same area, it is possible to easily identify the areas with sparse output values by comparing the number of output values in each of the areas D _{1 to} D ₄ . For this reason, the average value Pb is preferably an output value calculated by a combination of medians in the design variable space or an output value calculated by a combination of reference values. The average value Pb is not limited to the output value described above as long as the areas of the regions D _{1 to} D ₄ are known.

In addition to this, as shown in FIG. 4B, an average value Pb may be set, and the regions D ₁₁ , D ₂₁ , and D ₃₁ may be divided into concentric circles centered on the average value Pb. In this case, the distribution of the output values in the characteristic value space is examined, and the density of the output values in each region D ₁₁ , D ₂₁ , D ₃₁ is examined. In the regions D ₁₁ , D ₂₁ , and D ₃₁ , characteristic values are added to the region having the lowest output value density. Of the regions D ₁₁ , D ₂₁ , and D ₃₁ , the region D ₃₁ has the lowest density of output values, and at least one output value 42 is set out of the output values 40 of the region D ₃₁ . Using the set output value 42, an output value is added as described above, and an additional output value is acquired.
When the regions D ₁₁ , D ₂₁ , and D ₃₁ are divided concentrically, the regions D _{1 to} D ₄ shown in FIG. 4A may be combined. As a result, it is possible to specify a region having a sparse output value in the characteristic value space with higher accuracy. Figure 4 (b), the areas of sparse output value is an area _{D 31} and region _{D 1.}
Further, as shown in FIG. 4C, the characteristic value space may be divided into a plurality of regions D having the same area, and a region having a sparse output value may be determined. In this case, if there is no output value in the region D, the output value is excluded from the target of density. Among the regions D, the region D ₄₀ has the lowest density of output values. Although there is only one output value ₄₀ in the region D ₄₀ , the output value 40 is set as the output value 42. Using the set output value 42, an output value is added as described above, and an additional output value is acquired.

In step S16, at least one output value for acquiring an additional output value is set from the characteristic value space. This setting method will be described.
Here, the characteristic value 1 and the characteristic value 2 have a preferable direction according to the required specifications and the like. As a preferable direction, the value increases, the value decreases, or approaches a predetermined value.
When selecting an output value, it is preferable to increase the density of the output values in a region where the two characteristic values 1 and 2 are preferable. Thereby, the accuracy of the approximate model in the vicinity of the Pareto solution can be improved, and the reliability of the obtained Pareto solution can be improved. The region in which the two characteristic values 1 and 2 are preferable can be set in step S10 and set in the condition setting unit 20.
FIG. 5A is a graph showing a first example of the reference point setting method, FIG. 5B is a graph showing a second example of the reference point setting method, and FIG. It is a graph which shows the 3rd example of the setting method of a point.

For example, as shown in FIG. 5A, the average value Pb is set to an output value calculated by a combination of median values in the design variable space, or as shown in FIG. When setting optimization conditions such as design variables, characteristic values (objective functions), constraint conditions, etc. for the target structure, the average value Pb in the characteristic value space is set. Further, as shown in FIG. 5C, the average value Pb is set to an arbitrary point.
Here, the characteristic value 1 and the characteristic value 2 have a preferable direction according to the required specifications. For example, the characteristic value 1 is a characteristic with a larger value, and the characteristic value 2 has a smaller value. It is a characteristic.
For example, when the reference point is set as shown in FIGS. 5A to 5C, the value of the characteristic value to be set is set with respect to the average value Pb, and a good characteristic can be obtained and a bad characteristic can be obtained. The direction and the direction of convergence to a predetermined characteristic can be set by a combination of the characteristic values. This setting can be set in the condition setting unit 20 via the input unit 14.
The direction in which a bad characteristic is obtained is, for example, a characteristic value having a larger value is better for characteristic value 1, but is set to a smaller value, and characteristic value 2 is a characteristic having a smaller value. However, it is to set the larger value. The direction of convergence to the predetermined characteristic is a direction from the reference point toward a predetermined value for the characteristic value 1, and a direction from the reference point toward a predetermined value for the characteristic value 2.

Next, a second example of the approximate model creation method of the structure according to the present embodiment will be described.
FIG. 6 is a flowchart showing a second example of the approximate structure creation method for a structure according to the embodiment of the present invention in the order of steps. FIG. 7 is a graph showing an example of the verification result.
In the second example of the approximate model creation method, detailed description of the same steps as those in the first example of the approximate model creation method is omitted.

  Compared to the first example of the approximate model creation method, the second example of the approximate model creation method includes a step (step S30) of performing verification calculation using the created approximate model. If the result does not satisfy the predetermined determination condition (step S32), the approximation model is created again, and the other steps are the same as those in the first example. Omitted. In the second example of the approximate model creation method, the approximate model accuracy at the output value (sampling point) in the characteristic value space can be improved, and thereby the accuracy of the optimization calculation result can be improved.

In the second example of the approximate model creation method, in step S30, the approximate predicted value is calculated by the calculation unit 24 using the approximate model created in step S18. In addition, the calculation unit 24 performs an actual calculation for calculating the characteristic value in order to verify the error of the approximate model with the combination of the design variable and the characteristic value using the nonlinear relationship defined without using the approximate model.
Next, the approximate predicted value obtained in step S30 is compared with the actual calculated value, and a determination is made based on a predetermined determination condition (step S32).
If the determination condition is satisfied in step S32, multi-objective optimization calculation is performed using the approximate model created in step S18 (step S34). Next, a Pareto solution is extracted from the multi-objective optimization calculation result to obtain a Pareto solution (step S36). Step S34 is the same process as step S20 described above, and step S36 is the same process as step S22 described above, and therefore detailed description thereof is omitted.

On the other hand, if the determination condition is not satisfied in step S32, that is, if the accuracy of the approximate model at the sampling point does not fall within the predetermined allowable range, the process returns to step S16, and an additional output value is obtained again to obtain the approximate model. Is created (step S18). That is, the approximate model is updated.
Then, using the updated approximate model, an approximate prediction value is calculated by the calculation unit 24. That is, verification calculation is performed (step S30). The result of the verification calculation is determined based on the determination condition in step S32. Until the determination condition of step S32 is satisfied, acquisition of additional output values (step S16) and creation of an approximate model (step S18) are repeated.

In step S32, the acquisition of the additional output value when the determination condition is not satisfied may be performed by changing the output value 42 to be set, or by changing the acquisition method of the additional output value by setting the output value 42 to be the same. The setting method 42 is not particularly limited.
As the determination condition in step S32, for example, the slope of the approximate straight line between the actual calculated value and the approximate predicted value, the correlation coefficient, the determination coefficient, and the like can be used. Further, a threshold value may be given to the error at each sampling point, and this may be used as the determination condition.
More specifically, when comparing the approximate predicted value and the actual calculation value, one-point exclusion cross validation and K-division cross validation can be used. For example, when one-point exclusion cross validation is used, FIG. The result shown in is obtained.

Next, a third example of the structure approximate model creation method of the present embodiment will be described.
FIG. 8 is a flowchart showing a third example of the approximate structure creation method for a structure according to the embodiment of the present invention in the order of steps.
In the third example of the approximate model creation method, detailed description of the same steps as those in the first example of the approximate model creation method is omitted.

Compared with the first example of the approximate model creation method, the third example of the approximate model creation method includes a step (Step S42) of performing actual calculation on the extracted Pareto solution (Step S40). If the result of the above does not satisfy the predetermined determination condition (step S44), that is, if the accuracy of the approximate model in the characteristic value space other than the sampling point does not fall within the predetermined allowable range, the approximate model is again used. The points to be created are different, and the other steps are the same as those in the first example, and thus detailed description thereof is omitted. In the third example of the approximate model creation method, by providing a process for confirming the accuracy of the Pareto solution, it is confirmed that the accuracy of the approximate model in the characteristic value space other than the sampling points is within a predetermined allowable range. A process is provided, and the accuracy of the optimization calculation result can be improved.
In addition, since the process of extracting the Pareto solution of step S40 is the same process as the process of obtaining the Pareto solution of step S22 of the first example, detailed description thereof is omitted.

In the third example of the approximate model creation method, actual calculation is performed as confirmation calculation for confirming the accuracy of the Pareto solution using the Pareto solution obtained in step S40 (step S42). The actual calculation in step S42 is, for example, to calculate by putting the design variable value of the Pareto solution obtained in step S40 into a calculation model for calculating characteristic value 1 and characteristic value 2 using the finite element method.
Next, the actual calculation value obtained in step S42 is compared with the actual calculation value calculated using the finite element method (hereinafter referred to as FEM actual calculation value), and the determination is made based on a predetermined determination condition. (Step S44). When the determination condition is satisfied in step S44, the Pareto solution obtained in step S40 is output as the final Pareto solution (step S46).

On the other hand, if the determination condition is not satisfied in step S44, the process returns to step S16, an additional output value is acquired again, and an approximate model is created (step S18). That is, the approximate model is updated.
Then, multi-objective optimization calculation is performed using the updated approximate model (step S20), and a Pareto solution is obtained (step S40). Actual calculation using the obtained Pareto solution is performed (step S42), and the result of the actual calculation is determined based on the determination condition in step S44. Until the determination condition of step S44 is satisfied, acquisition of additional output values (step S16), creation of an approximate model (step S18), calculation of multi-objective optimization (step S20), extraction of Pareto solution from the result of multi-objective optimization calculation (step S20) Step S40) and actual calculation using the Pareto solution (step S42) are repeated.

The Pareto solution used for the actual calculation in step S42 may be all the Pareto solutions obtained in step S40. However, from the viewpoint of efficiency, it is preferable to select discretely such as an end Pareto solution or a central Pareto solution among a plurality of Pareto solutions.
For example, an error is used as the determination condition in step S44. This error may be a relative error or an actual error. When a plurality of Pareto solutions are used, their standard deviation or variance value may be set.
As shown in FIG. 9, for example, three Pareto solutions P ₁ , P ₂ , and P ₃ are set for the Pareto solution P. FEM actual calculation values G ₁ , G ₂ , and G ₃ are calculated by inputting design variable values corresponding to the Pareto solutions P ₁ , P ₂ , and P ₃ . Differences d ₁ , d ₂ , and d ₃ between the Pareto solutions P ₁ , P ₂ , and P ₃ and the FEM actual calculation values G ₁ , G ₂ , and G ₃ are obtained, respectively. In this case, the determination is made by comparing the differences d ₁ , d ₂ , and d ₃ with an error set as a determination condition.

  The present invention is basically configured as described above. The structure approximate model creation method, the structure approximate model creation apparatus, and the program according to the present invention have been described in detail above. However, the present invention is not limited to the above-described embodiment and does not depart from the spirit of the present invention. Of course, various improvements or modifications may be made.

Examples of the approximate model creation method of the present invention will be specifically described below.
In this example, the effect of the approximate model creation method of the present invention was confirmed using the following Example 1, Comparative Examples 1 and 2, and Reference Example.

In this embodiment, the tire cross-sectional shape is used as a design variable, and two characteristic values (objective functions) that are physical characteristics of the tire are set. Here, as the desired characteristic of the objective function, the characteristic value 1 is set to be large and the characteristic value 2 is set to be small, and the Pareto solution is extracted from the optimization calculation result using the multi-objective genetic algorithm. The effect of the approximate model creation method was confirmed.
With reference to a tire model of tire size 215 / 55R17, input values represented by design variables φ1 to φ6 were set for the cross-sectional shape of the tire. Note that 100 cases of input values represented by design variables φ1 to φ6 were set by the Latin hypercube method (LHC).
In addition, in order to verify the accuracy of the approximate model, the design variables and their domain of definition, and the calculation conditions such as the number of individuals, the number of generations, and the mutation rate of the genetic algorithm are the same in both Example 1 and Comparative Examples 1 and 2. Values were used.
Hereinafter, Example 1, Comparative Examples 1 and 2, and a reference example will be described.

In Example 1, in addition to the result of the sampling calculation in the 100 cases described above, four points were extracted from the output values obtained from the sampling calculation result. With respect to the extracted output values 50 of the four points, as shown in FIG. 10A, medians were obtained for the design variables φ1 to φ6. By using the Monte Carlo method, the fluctuation range is set as ± 20% of the design variable domain by the median value of the design variables φ1 to φ6. By changing the combination of values within the fluctuation range, additional sampling points can be obtained. 50 cases of output value 52 were set. The result is shown in FIG.
In Comparative Example 1, only 100 cases set by the Latin hypercube method were used. The result is shown in FIG.
In Comparative Example 2, four output values were extracted in the same manner as in Example 1. For the four extracted points, as shown in FIG. 10 (b), the range of the upper limit value and the lower limit value among the four extracted points for the design variables φ1 to φ6 is set as the fluctuation range. 50, the output value 52 was set to 50 cases as additional sampling points by changing the combination of design variable values. The result is shown in FIG.
For the four output values used in Example 1 and Comparative Example 2, the solution having the largest characteristic value 1 and the smallest characteristic value 2 is defined as the desired characteristic among the output values, and the improvement range is the largest. These are the four points that will be closest to the Pareto solution calculated in the subsequent optimization calculation.

  In the reference examples, the characteristic values are all calculated using the finite element method without using an approximate model. The actual calculation result of this reference example is shown in FIG. Since the actual calculation result 60 shown in FIG. 12 has no calculation error, it was set as a reference for confirming the calculation accuracy of the approximate model.

For Example 1 and Comparative Examples 1 and 2, an approximation model using a polynomial is created, optimization calculation is performed, a Pareto solution is extracted, and the result is shown in FIG.
As shown in FIG. 12, the actual calculation result 60 and the result 62 of Example 1 are close. On the other hand, the result 64 of Comparative Example 1 is farthest from the actual calculation result 60. Comparative Example 2 has the same number of cases as Example 1, but the result 66 of Comparative Example 2 is farther from the actual calculation result 60 than the result 62 of Example 1.
In Example 1, the accuracy close to the actual calculation result 60 was obtained as compared with Comparative Examples 1 and 2. In Example 1, the number of cases is substantially the same as that in Comparative Example 3, but higher accuracy was obtained in Example 1. Further, the actual calculation result 60 does not use an approximate model, and the calculation amount is much larger than that of the first embodiment, and the calculation time is also long. Thus, according to the present invention, the accuracy of the approximate model is high, and the calculation amount and the calculation time can be reduced.

Approximate model creation device for structure 10 (approximate model creation device)
DESCRIPTION OF SYMBOLS 12 Processing part 14 Input part 16 Display part 20 Condition setting part 22 Model preparation part 24 Calculation part 26 Pareto solution search part 28 Memory 30 Display control part 32 Control part 40, 50, 52 Output value 42 Selected output value 44 Output value (Additional sampling points)
46a-46f points

Claims (13)

A plurality of input parameters defined as design variables among the parameters defining the structure and the material constituting the structure, and a plurality of parameters defined as characteristic values among the parameters defining the structure and the material constituting the structure A method of creating an approximate model of a structure for two types of data with output parameters,
A first step of setting the plurality of types of design variables and domains of the design variables, and the plurality of types of characteristic values;
A second step of defining a nonlinear response relationship between the plurality of types of design variables and the plurality of types of characteristic values;
A third step of calculating an output value in a characteristic value space composed of the values of the plurality of types of design variables and the characteristic values, using the nonlinear response relationship determined in the second step;
A fourth step of setting at least one output value of the characteristic value space, perturbing an input parameter value in the set output value, setting a plurality of input parameter values, and acquiring an additional output value;
A fifth step of creating an approximate model using the additional output value and the output value obtained in the third step as a characteristic value as an objective function;
And a sixth step of performing multi-objective optimization calculation using the approximate model. A method for creating an approximate model of a structure.   The step of obtaining the additional output value in the fourth step is to obtain a sparse region of the output value in the characteristic value space, select an output value from the sparse region, and input the selected output value The method for creating an approximate model of a structure according to claim 1, wherein the parameter values are perturbed to set a plurality of input parameter values and acquire additional output values.   The output value set in the fourth step sets a reference value in the characteristic value space in the first step, and the output value is in a region larger or smaller than the reference value, or the reference value The method of creating an approximate model of a structure according to claim 1 or 2, wherein setting is made from an output value in a predetermined distance region. Between the fifth step and the sixth step, the approximation model created in the fifth step is subjected to verification calculation using the additional output value and the output value of the characteristic value space, When the result of the verification calculation satisfies a predetermined determination condition, the multi-objective optimization calculation is performed in the sixth step,
If the verification result does not satisfy the predetermined determination condition, another additional output value is acquired in the fourth step, and the approximate model is updated using the other additional output value in the fifth step. A method for creating an approximate model of a structure according to any one of claims 1 to 3. After the sixth step, there is a step of performing an actual calculation for verifying an error of the approximate model using a Pareto solution obtained by performing the multi-objective optimization calculation of the sixth step,
When the result of the actual calculation satisfies a predetermined determination condition, the Pareto solution obtained by performing the multi-objective optimization calculation obtained in the sixth step is set as a final Pareto solution,
When the result of the actual calculation does not satisfy a predetermined determination condition, another additional output value is obtained in the fourth step, and the approximate model is obtained using the other additional output value in the fifth step. The method for creating an approximate model of a structure according to any one of claims 1 to 3. The design variable is at least one parameter that changes the shape or structure of the tire, and the characteristic value is at least one of the physical characteristic values of the tire;
The method for creating an approximate model of a structure according to any one of claims 1 to 5, wherein a physical quantity of a tire is calculated by the multi-objective optimization calculation. A plurality of input parameters defined as design variables among the parameters defining the structure and the material constituting the structure, and a plurality of parameters defined as characteristic values among the parameters defining the structure and the material constituting the structure An apparatus for creating an approximate model of a structure targeting two types of data with output parameters,
Setting of the plurality of types of design variables and the domain of each design variable, and the plurality of types of characteristic values, and setting conditions for determining a nonlinear response relationship between the types of design variables and the types of characteristic values And
Using the nonlinear response relationship, calculating an output value in a characteristic value space composed of the values of the plurality of types of design variables and the characteristic value, setting at least one output value in the characteristic value space, Perturbing the input parameter value at the set output value, setting a plurality of input parameter values, obtaining an additional output value, and using the additional output value and the output value in the characteristic value space to determine the characteristic value As an objective function, create an approximate model, and use the created approximate model to perform a multi-objective optimization calculation,
An apparatus for creating an approximate model of a structure, comprising: a Pareto solution search unit that extracts a Pareto solution.   The calculation unit obtains a sparse region of the output value in the characteristic value space, selects an output value from the sparse region, and perturbs the input parameter value in the selected output value, thereby obtaining a plurality of input parameters. The apparatus for creating an approximate model of a structure according to claim 7, wherein a value is set and an additional output value is acquired.   A reference value is set in the characteristic value space in the condition setting unit, and the set output value is set to the characteristic value space in the first step and is larger than the reference value. The apparatus for creating an approximate model of a structure according to claim 7 or 8, set from an output value in a small area or an output value in an area of a predetermined distance with respect to the reference value. When the calculation unit causes the approximation model to perform a verification calculation using the additional output value and the output value of the characteristic value space, and the result of the verification calculation satisfies a predetermined determination condition, the calculation unit In the multi-objective optimization calculation, the Pareto solution search unit extracts the Pareto solution,
A control unit that, when the result of the verification does not satisfy a predetermined determination condition, causes the arithmetic unit to acquire another additional output value and updates the approximate model using the other additional output value. An apparatus for creating an approximate model of a structure according to any one of 7 to 9. Causing the arithmetic unit to perform an actual calculation for verifying an error of the approximate model using a Pareto solution obtained by performing the multi-objective optimization calculation;
When the result of the actual calculation satisfies a predetermined determination condition, the Pareto solution obtained by performing the multi-objective optimization calculation is a final Pareto solution,
A control unit that, when the result of the actual calculation does not satisfy a predetermined determination condition, causes the arithmetic unit to acquire another additional output value and updates the approximate model using the other additional output value. An apparatus for creating an approximate model of a structure according to any one of 7 to 9. The design variable is at least one parameter that changes the shape or structure of the tire, and the characteristic value is at least one of the physical characteristic values of the tire;
The apparatus for creating an approximate model of a structure according to any one of claims 7 to 11, wherein a physical quantity of a tire is calculated by the multi-objective optimization calculation.   The program for making a computer perform as a procedure each process of the creation method of the approximate model of the structure of any one of Claims 1-6.