JP6544006B2 - Method for creating approximate model of structure, device for creating approximate model for structure, and program - Google Patents

Description

  The present invention relates to a method of creating an approximate model of a structure that creates an approximate model representing the relationship between a plurality of input values and a plurality of output values relating to a structure, an approximation model creating apparatus of the structure, and a program. The present invention relates to a method for creating an approximate model of a structure with high accuracy and capable of reducing the amount of calculation and calculation time, an approximate model generating device for a structure, and a program.

In the simulation, predetermined design factors, responses to design variables, and characteristic values (objective functions) for design variables can be calculated. In optimization, values of design variables for obtaining desired characteristic values can be calculated.
In the simulation, the design variable of the structure and the material constituting the structure is used as an input value (input parameter), and a plurality of characteristic values (objective functions) of the material constituting the structure and the structure are output values (output parameter) An approximate model that represents the relationship between design variables and an objective function has been created. It is also possible to create a response surface instead of an approximate model.
In multi-objective optimization that targets multiple characteristic values (objective functions), a trade-off relationship often exists between the characteristic values, so depending on the accuracy of the approximation model, an approximate predicted value may be calculated with respect to the actual calculated value. There may be a large gap between the two. Therefore, various methods have been proposed for simulation methods (see Patent Documents 1 and 2).

  In Patent Document 1, the response surface is divided based on an objective function (output value), and the accuracy of the response surface is improved and optimized by sequentially updating the response surface while adding a sampling calculation in each. It describes how to do the calculation.

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

JP, 2011-103036, A Unexamined-Japanese-Patent No. 2013-242662

In patent document 1, since sampling calculation is repeated until convergence conditions are satisfied, when convergence conditions are made severe, there exists a problem that very time is required.
In Patent Document 2, even if implemented at a sufficiently wide level, random sampling may cause a bias in combination when viewed in a design variable space. In addition, in the case of using a sampling method uniformly distributed on the design variable space as in the Latin hypercube, if the sampling number is small, the distance between the points on the design variable space becomes large, and the characteristic value space There is a high possibility that the characteristic peaks are hidden between the points, that is, the multimodality of the solution can not be expressed. Therefore, the response surface function can not accurately represent the tendency of the entire design variable space, and there is a possibility that the design variable and the value thereof for improving the target characteristic can not be accurately derived. 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 amount of calculation becomes enormous. As described above, in any of Patent Document 1 and Patent Document 2, if it is attempted to accurately determine an important region in the characteristic value space from the entire design variable space and try to improve the approximation accuracy of the calculated optimal solution It was a problem to have computational complexity.

  SUMMARY OF THE INVENTION The object of the present invention is to solve the above-mentioned problems based on the prior art, and to create an approximate model of a structure, which has high accuracy of the approximate model and can reduce the calculation amount and time. An apparatus and a program are provided.

  In order to achieve the above object, according to a first aspect of the present invention, a structure and a plurality of input parameters defined as design variables out of parameters defining a material constituting the structure, a structure and a structure A method of creating an approximate model of a structure targeting two types of data of a plurality of output parameters defined as characteristic values among parameters defining a material to be configured, the plurality of design variables and each design variable The first step of setting the values of design variables, and the second step of defining the non-linear response relation between the plurality of design variables and the plurality of property values. A third step of calculating a first output value in a characteristic value space configured of characteristic values of design variable values using the step and the nonlinear response relation defined in the second step; It is the first output value obtained in the process A fourth step of creating a first approximate model using a characteristic value as an objective function, and a fifth step of performing multi-objective optimization calculation using the first approximate model and extracting a first Pareto solution And at least one of the upper limit value and the lower limit value among the values of the plurality of design variables in the first Pareto solution, and at least one value of the extracted upper limit value and the lower limit value is fixed and extracted. There is a sixth step of setting the new value of the design variable by not varying the value of the design variable, and the characteristic value of the second design variable in which the new value of the design variable is included in the value of the design variable. A seventh step of calculating a second output value in the characteristic value space, and a second approximate model is created using the characteristic value which is the second output value obtained in the seventh step as an objective function Multi-objective optimization calculation using 8 processes and the second approximation model Implemented, there is provided a method of creating an approximate model of the structure and having a ninth step of extracting the second Pareto solutions.

  In the sixth step, at least one design variable showing a constant value is extracted from the combination of values of a plurality of design variables in the first Pareto solution, the value of the constant value of the extracted design variable is fixed, and the extraction is performed It is preferable to have the step of changing the values of the design variables not being set to set new values of the design variables. The values of the design variables are preferably set using the Latin hypercube method.

A verification calculation is performed on the second approximate model created in the seventh step using the second output value between the eighth step and the ninth step, and the result of the verification calculation is a predetermined determination condition If the condition is satisfied, multi-objective optimization calculation is performed in the ninth step, and if the verification result does not satisfy the predetermined judgment condition, the value of the design variable is added and added in the sixth step. Preferably, the second approximate model is updated using the second design variable including the value of the design variable and the second output value.
After the ninth step, there is a step of performing an actual calculation for verifying the error of the second approximate model using the Pareto solution obtained by performing the multi-objective optimization calculation of the ninth step. If the result of the calculation satisfies the predetermined judgment condition, the Pareto solution obtained by performing the multi-objective optimization calculation obtained in the ninth step is taken as the final Pareto solution, and the result of the actual calculation is the predetermined. If the determination condition is not satisfied, in the sixth step, the value of the design variable is added, and the second approximation is performed using the second design variable and the second output value including the value of the added design variable. It is preferable to update the model.

  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 property values of the tire, and the physical quantity of the tire is calculated by multipurpose optimization calculation. Ru.

  According to a second aspect of the present invention, a plurality of input parameters defined as design variables among the parameters defining the structure and the material constituting the structure, and the parameters defining the material constituting the structure and the structure are described. An apparatus for creating an approximate model of a structure for two types of data with a plurality of output parameters defined as characteristic values, comprising a plurality of design variables and domains of each design variable, and a plurality of types The characteristic value is set, the value of design variable is set, and the condition setting unit that determines the non-linear response relationship between the plurality of design variables and the plurality of characteristic values, and the non-linear response relationship Calculating a first output value in the characteristic value space configured by the characteristic values calculated by the combination of the above, and creating a first approximate model with the characteristic value being the first output value as an objective function; The approximate model of 1 And the Pareto solution search unit for obtaining the first Pareto solution, and the condition setting unit further selects the values of the plurality of design variables in the first Pareto solution. Extract at least one of the upper limit value and the lower limit value, fix at least one of the extracted upper limit value and lower limit value, and change the value of the design variable not extracted to set a new value of the design variable The operation unit further calculates a second output value in the characteristic value space configured by the characteristic values of the second design variable whose value of the design variable includes the new value of the design variable, The second approximate model is created using the characteristic value which is the second output value as the objective function, and the multipurpose optimization calculation is performed using the second approximate model, and the Pareto solution search unit Extract the Pareto solution of 2 There is provided a producing apparatus of the approximate model of the structure and features.

The condition setting unit extracts at least one design variable indicating a constant value from the combination of values of a plurality of design variables in the first Pareto solution, fixes the value of the constant value of the extracted design variable, and extracts It is preferable to set the new value of the design variable by changing the value of the non-design variable.
The values of the design variables are preferably set using the Latin hypercube method.

In the calculation unit, verification calculation is performed on the second approximate model using the second output value, and if the result of the verification calculation satisfies a predetermined determination condition, multipurpose optimization calculation is performed. If the result of the verification does not satisfy the predetermined determination condition, the condition setting unit adds the value of the design variable, and the second design variable and the second output value including the value of the design variable added to the operation unit It is preferable to have a control unit that updates the second approximate model using
When the operation unit performs actual calculation for verifying the error of the second approximate model using the Pareto solution obtained by performing multi-objective optimization calculation, and the result of the actual calculation satisfies a predetermined determination condition In the above, the Pareto solution obtained by performing multi-objective optimization calculation is used as the final Pareto solution, and when the result of the actual calculation does not satisfy the predetermined judgment condition, the value of the design variable is added to the condition setting unit It is preferable to have a control unit that causes the second approximate model to be updated using the second design variable including the value of the design variable added to the calculation unit and the second 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 property values of the tire, and the physical quantity of the tire is calculated by multipurpose optimization calculation. Ru.

  A third aspect of the present invention provides a program for causing a computer to execute each step of the method for creating an approximate model of a structure of the first aspect of the present invention as a procedure.

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

It is a schematic diagram which shows the approximate model production apparatus of the structure utilized for the approximate model production method of the structure of embodiment of this invention. It is a flowchart which shows the 1st example of the approximation model creation method of the structure of embodiment of this invention to process order. (A) is a graph which shows an example of a design variable, (b) is a graph which shows an example of the design variable in a Pareto solution, (c) is a graph which shows an example of a design variable. It is a flowchart which shows the 2nd example of the approximation model creation method of the structure of embodiment of this invention to 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 approximation model creation method of the structure of embodiment of this invention in order of a process. It is a graph for demonstrating an error. It is a graph which shows the Pareto solution of Example 1, Comparative Examples 1-3, and a reference example.

In the following, based on the preferred embodiments shown in the attached drawings, a computer or the like for executing the method of creating an approximate model of a structure, an approximate model creating device of a structure, and a method of creating an approximate model of a structure according to the present invention. Explain the program in detail.
FIG. 1 is a schematic view showing an apparatus for creating an approximate model of a structure used in the method for creating an approximate model of a structure according to an embodiment of the present invention.
The approximate model creation device 10 of the structure shown in FIG. 1 is used as the approximate model creation method of the structure of the present embodiment. Hereinafter, the approximate model creating apparatus 10 for a structure is referred to as an approximate model creating apparatus 10.
The approximate model creating device 10 is configured using hardware such as a computer. As described above, although the approximate model creating apparatus 10 shown in FIG. 1 is used in the approximate model creating method of the present invention, the approximate model creating method can be executed using hardware and software such as a computer. It is not limited to the creation device 10.

  In this embodiment, a plurality of input parameters defined as design variables among the parameters defining the structure and the material constituting the structure, and the characteristic values among the parameters defining the structure and the material constituting the structure The target is a data set which is a set of two types of data of a plurality of defined output parameters. For example, the design variable is displayed as visualization information such as a scatter chart in a characteristic value space (objective function space).

The approximate model creating device 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, an operation unit 24, a Pareto solution search unit 26, a memory 28, a display control unit 30, and a control unit 32. 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 creating unit 22, the calculating unit 24, and the Pareto solution searching unit 26 are connected to the memory 28, and the condition setting unit 20, the model creating unit 22, the calculating unit 24, and the Pareto The data of the solution search unit 26 is stored in the memory 28.
In the method of creating an approximate model of a structure to be described below, various processes are performed in each part of the processing unit 12. Although in the following description, the control unit 32 omits the description that the various processes are performed in the respective units of the processing unit 12, a series of processes of the respective units are 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 a variety of input devices for inputting various information such as a mouse and a keyboard according to an instruction of the operator. The display unit 16 displays, for example, results obtained by the approximate model creating method, and various known displays may be used. The display unit 16 also includes a device such as a printer for displaying various information on an output medium.

  The approximate model creation device 10 executes a program (computer software) stored in the ROM or the like by the control unit 32 to obtain the condition setting unit 20, the model creation unit 22, the calculation unit 24, and the Pareto solution search unit 26. Functionally form each part. As described above, the approximate model creating device 10 may be configured by a computer in which each portion functions by executing a program, or may be a dedicated device in which each portion is configured by a dedicated circuit.

  The condition setting unit 20 receives 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 approximation model creating method of a structure according to the present embodiment. . Various conditions and information are input through the input unit 14. Various conditions and information set by the condition setting unit 20 are stored in the memory 28.

In the condition setting unit 20, a plurality of parameters defined as design variables among the parameters defining the structure and the material constituting the structure are set. As parameters of design variables, variation factors such as load and boundary conditions, and in the case of a product, constraint conditions such as size and mass may be set.
Further, among the parameters defining the structure and the material constituting the structure, a plurality of parameters defined as characteristic values (objective functions) are set. As the characteristic value, an index for evaluating a structure and materials constituting the structure may be used other than physical and chemical characteristic values such as cost.
The structural body and the material constituting the structural body may be a whole system including the structural body such as a part constituting the structural body, an assembly form of the structural body, or a part thereof instead of a single structural body.

The plurality of types of characteristic values set in the condition setting unit 20 are physical quantities to be evaluated, that is, an objective function. The objective function has a desirable direction for performance, and the value may increase, decrease, or approach a predetermined value. Also, with regard to the objective function, there is also an undesirable direction opposite to the preferred direction other than the preferred direction described above.
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 serving as an indicator of steering stability, and an indicator of riding comfort. The primary natural frequency of the tire, the rolling resistance as an index of rolling resistance, the lateral spring constant as an index of steering stability, the wear energy of the tire tread member as an index of wear resistance, the fuel efficiency and the like can be mentioned. Besides these, there are shapes and dimensional values as examples of the physical quantity of the tire. The shape is, for example, a cross-sectional shape. The dimension value is, for example, the width of the tire, the outer diameter of the tire, or the like. As an example of the physical quantity of the tire, in addition to the shape or the dimension value, there are a deflection amount, a contact pressure distribution, a rolling resistance, a cornering characteristic and the like.

The design variables define the shape of the structure, the internal structure of the structure, material characteristics, and the like. In the case of a tire, the design variables are parameters of the material behavior of the tire, the shape of the tire, the cross-sectional shape of the tire, the natural vibration mode of the tire and the structure of the tire. Examples of design variables include a radius of curvature that defines a crown shape in a tread portion of a tire, and a belt width dimension of a tire that defines an internal structure of the tire. In addition to this, for example, a filler dispersion shape, a filler volume ratio, and the like which define material characteristics in the tread portion may be mentioned.
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.
When the structure is a tire, load load of the tire, traveling conditions including the rolling speed of the tire, road surface conditions on which the tire travels, for example, uneven shape, coefficient of friction, etc. Information on vehicle specifications of the vehicle is set.

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

The conditions for the Pareto solution search are a method for searching 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. Generally, it is known that the search capability of the genetic algorithm decreases as the characteristic value (objective function) increases. One way to solve it is to increase the number of individuals.
In addition to this, the domain of design variables 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 for the remaining design variables, the computer changes the combination of design variables with the domain as a constant. The characteristic value may be calculated while extracting the Pareto solution described later.

For example, the design variable is set by the condition setting unit 20 using, for example, the Latin hypercube method (Latin hypersquare method). The Latin hypercube method is a sample method that covers design variable space discretely and evenly. Therefore, design values can be set uniformly in the design variable space. In this case, for example, as shown in FIG. 3C, the design value 50 is set uniformly in the design variable space. Values of multiple design variables are set.
In addition to the Latin hypercube method, for example, an orthogonal array, a Monte Carlo method, or the like can be used to set the values of design variables.

In addition, the condition setting unit 20 sets the upper limit value and the lower limit value of a plurality of types of design variables in the Pareto solution (first Pareto solution), for example, values of design variables φ1 to φ7 (see FIG. 3B). At least one is extracted, and at least one of the extracted upper limit value and lower limit value is fixed. For example, the upper limit 40 (see FIG. 3 (b)) of the design variable φ7 (see FIG. 3 (b)) is fixed. Then, values of design variables not extracted, for example, values of design variables φ1 to 6 (see FIG. 3B) are changed to set new values of a plurality of design variables.
In addition, at least one design variable showing a constant value is extracted from combinations of values of multiple design variables in the Pareto solution, for example, combinations of design variables φ1 to φ7 (see FIG. 3B), for example, At least one design variable φ1 (see FIG. 3B) is extracted. Fix the value of the extracted constant value 44 (see FIG. 3B), and change the value of the design variable not extracted, for example, the values of design variables φ2 to φ7 (see FIG. 3B), It is intended to set new values of a plurality of design variables. The value of the design variable set by the condition setting unit 20 is stored in the memory 28.

Here, the upper limit value is the maximum value of the values of the design variables, but is not limited to the maximum value. For example, the upper limit value may be 90% or more of the maximum value. The lower limit is the minimum of the design variable, but is not limited to the minimum. For example, a value obtained by adding 10% or less of the minimum to the minimum may be the lower limit. For example, when the maximum value is 100 as the upper limit value, 90 is also set as the upper limit value. When the minimum value is 1 as the lower limit value, 1.1 is also the lower limit value.
The constant value indicates that the values of design variables in all Pareto solutions fall within a predetermined allowable range, and for example, indicates that all values are within ± 5% of the average value of the values of setting variables. . The definition of the tolerance of the value can be set in advance by the operator via the input unit 14 in the problem setting.

  With regard to multi-objective optimization calculation, whichever of the method of sequentially searching using non-linear relation (response surface) of input variables and output variables, and the method of calculating and searching output values while changing input variables according to optimization algorithm May be used.

  The model creating unit 22 creates various calculation models based on the set non-linear response relation. The non-linear response relationship includes the numerical simulation such as FEM as described above. In this case, the model creating unit 22 generates a mesh model according to design parameters representing design variables and characteristic value parameters representing characteristic values. Be done. Further, also in the case of a theoretical formula etc., a theoretical formula etc. corresponding to the design parameter and the characteristic value parameter is created. When the structure is a tire, a tire model is created. The computing unit 24 performs a simulation operation using the tire model.

Although the tire model created by the model creating unit 22 is created using the design parameters of each type set by the condition setting unit 20, a known creation method can be used to create the tire model. . The tire model also generates at least a road surface model to be rolled on the tire model. Also, a tire model may be used to reproduce the rim on which the tire is mounted, the wheel, and the tire rotation axis. In addition, if necessary, a model that reproduces a vehicle on which the tire is mounted may be incorporated into the tire model. At this time, it is also possible to create a model in which a tire model, a rim model, a wheel model, and a tire rotation axis model are integrated based on preset boundary conditions.
Further, 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 a pattern.

Although the tire model created by the model creating unit 22 is created using the design parameters of each type set by the condition setting unit 20, a known creation method can be used to create 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. Analysis modeling may be performed as a viscoelastic body, and further analysis modeling may be performed as a rigid body.
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, a hexahedral solid element in a three-dimensional body, a shell such as a triangular shell element or a square shell element It is a computer-analyzable element such as an element or a plane element. Elements divided in this manner are identified one by one in the process of analysis using three-dimensional coordinates in the three-dimensional model and two-dimensional coordinates in the two-dimensional model.

  Each of these models may be a discrete model capable of numerical calculation, for example, a finite element model for use in a known finite element method (FEM) or the like. In addition to the road surface model and the tire model, inclusions present on the road surface are reproduced, for example, when obtaining a tire design plan that optimizes tire performance such as tire wet performance using a tire model. You just have to generate a model. For example, various models that reproduce water, snow, mud, sand, gravel, ice and the like on the road surface may be generated as an inclusion model using a discrete model that can be numerically calculated. Note that the road surface model is not limited to a model that reproduces a road surface having a flat surface, but may be a model that reproduces a road surface shape having irregularities on the surface as needed.

The calculation unit 24 calculates the characteristic value using the various models created by the model creation unit 22. Thereby, characteristic values (output values) for design variables can be obtained. The obtained characteristic value (output value) is stored in the memory 28. The operation unit 24 functions by executing a subroutine based on, for example, a known finite element solver.
The calculation unit 24 calculates the first output value (characteristic value) in the characteristic value space configured by the values of the plurality of design variables and the characteristic value using the non-linear response relation. The calculation unit 24 also uses the design variable and the first output value to create a first approximate model using the characteristic value that is the output value as an objective function.
In addition, using the non-linear response relationship, operation unit 24 outputs a second output value in the characteristic value space configured by the characteristic value of the second design variable including the value of the design variable and the new value of the design variable. Is calculated again, and a second approximate model is created using the characteristic value which is the second output value as the objective function. Furthermore, the operation unit 24 performs multi-objective optimization calculation using the created first approximate model and second approximate model.
The first approximation model (metamodel) and the second approximation model (metamodel) described above are mathematical models that approximate the input / output relationship, and various input / output relationships can be obtained by adjusting the parameters. Can be approximated. For example, a polynomial model, a kriging, a neural network, and a radial basis function can be used for the first approximate model and the second approximate model described above.

  The operation unit 24 also performs verification calculation such as cross verification of the approximate model. The operation unit 24 also performs multi-objective optimization calculation using an approximate model, and uses the non-linear relationship defined using the Pareto solution extracted by the Pareto solution search unit 26 from the multi-object optimization calculation result. It is also the one that executes the actual calculation. In addition to this, the calculation unit 24 also calculates the characteristic value by the combination of the design variable and the characteristic value using the finite element method without using the approximate model. As the multi-objective optimization calculation method, for example, a genetic algorithm (GA) which is one of evolution calculation methods is used. As a genetic algorithm, for example, a solution set is divided into a plurality of regions along an objective function, and a multi-objective GA is performed for each divided solution set, and a DRMOGA (Divided Range Multi-Objective GA), NCGA (Neighborhood Culture GA) Using known methods such as distributed operation model of MOGA and SOGA (DCMGA), non-dominated sorting (NSGA), non-dominated sorting (NSGA2), and SPEA II (Strength Pareto Evolutionary Algorithm-II). Can.

The Pareto solution search unit 26 calculates multi-objective optimization calculation results using the first approximate model and the second approximate model obtained by the operation unit 24 according to the conditions of the Pareto solution search set by the condition setting unit 20. The Pareto solution is searched for to extract the Pareto solution. The obtained Pareto solution is stored in the memory 28.
Here, the Pareto solution is not superior to any other solution in a plurality of characteristic values (objective functions) in a trade-off relationship, but a solution with no other superior solution Say. In general, there are a plurality of Pareto solutions as a set.
The Pareto solution search unit 26 searches for a Pareto solution, for example, using a Pareto ranking method.

  The Pareto solution search unit 26 performs selection using, for example, Vector Evaluated Generic Algorithm (VEGA), Pareto ranking method, or tournament method. Other than the genetic algorithm (GA), for example, annealing (SA) or particle swarm optimization (PSO) may be used as the same evolution 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 obtaining the characteristic value using the design variable is not limited to the simulation of FEM etc. A theoretical formula etc. can also be used like this.

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, an output value obtained by the calculation unit 24, and a Pareto solution. For example, the value of 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 the axis. That is, the design variable is displayed in the characteristic value space. Besides the scatter plot, 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 input via the input unit 14, a tire model, results of numerical calculation, and an optimal solution. 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 generation method described below on the model generation unit 22 of the processing unit 12, the operation unit 24, and the Pareto solution. It is made to be performed by the search unit 26.
In the approximate model creation device 10, in the input file for changing the shape or structure, the common part such as boundary conditions and analysis step and the coordinate values of nodal point, the part different depending on the individual shape such as the placement angle of reinforcement and initial tension By dividing the file and using file formats such as incorporating in common parts, that is, by making individual information into an include file, it is easy to use tire shapes, even when examining a large number of tire shapes. An examination is possible.

Next, a first example of the method for creating an approximate model of a structure according to the present embodiment will be described.
FIG. 2 is a flowchart showing the first example of the method for creating an approximate model of a structure of the embodiment of the present invention in the order of steps. Fig.3 (a) is a graph which shows an example of a design variable, (b) is a graph which shows an example of the design variable in a Pareto solution.

First, as shown in FIG. 2, optimization conditions such as design variables, characteristic values (objective functions), and constraints are set for a target structure (step S10). For example, the structure includes a tire of 195 / 65R15 in size.
As design variables, for example, seven design variables φ1 to φ7 (input parameters) for changing the cross-sectional shape or structure of the tire are set. For example, a Latin hypercube method is used as a method of setting design variables.
Examples of the characteristic value include tire rigidity, rolling resistance, air resistance, cornering performance, friction energy, and the like as physical characteristics of the tire. For example, two tire physical characteristics of characteristic value 1 and characteristic value 2 are set as an objective function. Note that two or more characteristic values may be set.

The design variable (input parameter) is a parameter of the cross-sectional shape of the tire, and the characteristic value (output parameter) is two characteristic values which are tire physical characteristics. The parameters of the cross-sectional shape of the tire and the two characteristic values are set in the condition setting unit 20. For example, the characteristic value 1 is a characteristic requiring a large value, and the characteristic value 2 is a characteristic requiring a small value.
In the present embodiment, an approximate model is created by the approximate model creating method under such setting conditions. Change of the characteristic value 1 and the characteristic value 2 according to the value of the parameter of the sectional shape of the tire is determined.

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

  Next, using the non-linear response relationship set in step S12, an output value in a characteristic value space configured of characteristic values of values of a plurality of design variables is calculated. That is, sampling calculation is performed to calculate a characteristic value which 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 configured by the characteristic value 1 and the characteristic value 2 can be known.

Next, a first approximate model is created using the output value obtained in step S14 (step S16). That is, to create the first approximate model is to represent the relationship between the design variable and the characteristic value using an approximate model.
Next, the first multi-objective optimization calculation using the first approximate model is performed in the operation unit 24 (step S18). Then, the first Pareto solution is extracted by the Pareto solution search unit 26 from the first multi-objective optimization calculation result, and the first Pareto solution is obtained. In this manner, the first Pareto solution can be obtained using the approximate model. The first Pareto solution obtained using the first approximate model as described above is an approximate prediction value.

In step S18, for example, the Pareto solution P (first Pareto solution) shown in FIG. 3A is obtained. The reference point Pb is also shown in FIG. 3 (a). The value of the design variable of the Pareto solution shown in FIG.3 (b) is shown.
As shown in FIG. 3B, it is known that when the value of the design variable of the Pareto solution includes the upper limit 40 or the lower limit 42 of the design variable, the accuracy of the approximate model is low.
Therefore, at least one of the upper limit value and the lower limit value is extracted from the values of the plurality of design variables in the first Pareto solution, and at least one value of the extracted upper limit value and the lower limit value is fixed and extracted. Change the value of no design variable and set multiple new values of the design variable. Specifically, any one of the upper limit value 40 and the lower limit value 42 shown in FIG. 3B is fixed. For example, the lower limit value 42 of the design variable φ3 is fixed, and the values of the remaining design variables φ1, φ2, and φ4 to φ7 are varied to set a plurality of new values of the design variable. Thereby, the approximation accuracy of the approximation model in the vicinity of the Pareto solution can be improved.
A design variable, to which new values of a plurality of design variables are added, is referred to as a second design variable. In this case, the design variable is set as shown in FIG. 3C, for example, in a two-variable design variable space. In FIG. 3C, reference numeral 52 is set as a new design variable.

In addition, at least one design variable indicating a constant value is extracted from a combination of values of a plurality of design variables in the first Pareto solution, the value of the extracted constant value is fixed, and the values of design variables not extracted are extracted. May be varied to set a plurality of new values of design variables. In this case, in the design variables φ1 to φ7 shown in FIG. 3B, the value of the design variable φ1 indicates a constant value 46. The design variable φ4 also exhibits a constant value. At least one fixed value of the design variables φ1 and φ4 is fixed, and the values of the other design variables are varied to set a plurality of new values of the design variables. In this way, by setting the values of design variables, by fixing those with optimum values within the given design variable domain, additional values can be generated that fluctuate other than design variables with high sensitivity to characteristic values. It is possible to obtain the values of design variables. Thereby, since the actual calculation result in the vicinity of the first Pareto solution can be acquired, the accuracy of the Pareto solution in the second optimization calculation, that is, the approximate prediction value can be improved.
Note that the constant value indicates that the values of design variables in all Pareto solutions fall within a predetermined allowable range, and, for example, all values are within ± 5% of the average value of the values of setting variables as described above. It says that there is a value.

In addition, although the upper limit or lower limit of the design value variable is fixed for multiple types of design variables that constitute the Pareto solution, the characteristic value is fixed when the upper limit or lower limit of the design value variable is fixed. There is no limitation to selecting one that exhibits good characteristics. For example, when the upper limit value is selected, the opposite lower limit value may be selected when the characteristic value exhibits a good characteristic. In the case where the characteristic value exhibits a characteristic that converges to a preset range, the upper limit value or the lower limit value may be selected so as to indicate the characteristic to converge. The accuracy of the Pareto solution can be improved by selecting one that exhibits good characteristics.
When the upper limit value or the lower limit value is fixed and the values of other design variables are varied, the value of the design variable may be randomly varied using the Monte Carlo method, for example, between the upper limit value and the lower limit value. The values of the design variables may be varied according to a Gaussian distribution, or the values of the design variables may be varied using an orthogonal array. Also, even if the design variable has a large contribution in the input / output relationship in the approximate model, the result of actual calculation according to it may occur due to a problem for which a design variable with little or little contribution is a target . In order to improve the difference between the sensitivity of each design variable in such approximate predicted value and the sensitivity of each design variable in the actual calculation value, an approximate model in which characteristic value 1 and characteristic value 2 are calculated using the prescribed non-linear relationship The values of the design variables may be changed using actual calculation results calculated by putting the values of the design variables in the first Pareto solution.

A combination of a plurality of design variables in the first Pareto solution is output (step S20), and the design variable including the upper limit value or the lower limit value of the plurality of design variables is output as shown in FIG. Extract and classify a plurality of design variables (step S22).
Next, fix at least one value of the upper limit value or the lower limit value of the design variable values extracted as described above, change the value of the design variables not extracted, and change the new value of the design variables. Are set to obtain the second design variable described above. Then, the second output value in the characteristic value space configured by the characteristic values of the second design variable is calculated again. That is, the second sampling calculation is performed (step S24).
Next, a second approximate model is created with the characteristic value as an objective function using the second design variable and the second output value obtained by the second sampling calculation (step S26). Then, the second multi-objective optimization calculation is performed using the second approximate model (step S28), and the second Pareto solution is extracted by the Pareto solution search unit 26 from the multi-objective optimization calculation result, and the Pareto solution is obtained. Obtained (step S30). As a result, the approximation accuracy in the good characteristic region for the characteristic value 1 and the characteristic value 2 can be improved, and the reliability of the optimization calculation result can be improved.

Next, a second example of the method for creating an approximate model of a structure according to this embodiment will be described.
FIG. 4 is a flowchart showing a second example of the method for creating an approximate model of a structure according to the embodiment of the present invention in the order of steps. FIG. 5 is a graph showing an example of the verification result.
In the second example of the approximate model creating method, detailed description of steps similar to those of the first example of the approximate model creating method will be omitted.

  The second example of the approximate model creating method has a step (step S40) of performing verification calculation using the created approximate model, as compared with the first example of the approximate model creating method, and the result of the verification calculation However, when not satisfying the predetermined determination condition (step S42), the difference is that the approximate model is created again, and the other steps are the same as the first example, so the detailed description thereof is omitted. Do. In the second example of the approximation model creation method, the approximation model accuracy in the output value (sampling point) of 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 creating method, in step S40, the computing unit 24 calculates an approximate predicted value using the second approximate model created in step S16. In addition, in the calculation unit 24, the characteristic value is calculated to verify the error of the second approximate model by the combination of the design variable and the characteristic value using the nonlinear relationship defined without using the second approximate model. Carry out the calculation.
Next, the approximate predicted value obtained in step S40 and the actual calculated value are compared, and a determination is made based on a predetermined determination condition (step S42).
If the determination condition is satisfied in step S42, multi-objective optimization calculation is performed using the first approximate model created in step S16 (step S44). Next, a Pareto solution is extracted from the multi-objective optimization calculation result to obtain a Pareto solution (step S46). Step S44 is the same process as step S20 described above, and step S46 is the same process as step S30 described above, and thus the detailed description thereof is omitted.

On the other hand, if the determination condition is not satisfied in step S42, the process returns to step S24, a plurality of design variable values are added as described above, and a second sampling calculation is performed (step S24). Are created (step S26). That is, the second approximate model is updated. The addition of values of design variables includes, for example, changing design variables to be fixed, increasing the number of design variables to be fixed, and the like.
Then, using the updated second approximation model, the calculation unit 24 calculates an approximation prediction value. That is, verification calculation is performed (step S40). The result of the verification calculation is determined in step S42 based on the determination condition. The addition of design variables (step S24), the second sampling calculation (step S24), and the creation of a second approximate model (step S26) are repeated until the determination condition of step S42 is satisfied.

As the determination condition of step S42, for example, a slope in an approximate straight line between the actual calculation value and the approximate prediction value, a correlation coefficient, a determination coefficient, or the like can be used. Also, a threshold may be given to the error at each sampling point, and this may be used as the determination condition.
More specifically, one-point exclusion cross validation and K-division cross validation can be used when comparing the approximate prediction value and the actual calculation value, and for example, when one point exclusion cross validation is used, FIG. The results shown in are obtained.

Next, a third example of the method for creating an approximate model of a structure according to the present embodiment will be described.
FIG. 6 is a flowchart showing, in the order of steps, a third example of the method for creating an approximate model of a structure according to an embodiment of the present invention.
In the third example of the approximate model creating method, detailed description of steps similar to those of the first example of the approximate model creating method will be omitted.

The third example of the approximate model creating method has a step (step S52) of performing actual computation on the calculated Pareto solution (step S50) as compared to the first example of the approximate model creating method, and the actual computation is performed. In the case where the result of does not satisfy the predetermined determination condition (step S54), the point of creating the approximate model again is different, and the other steps are the same as those in the first example, and therefore the detailed description thereof Is omitted. In the third example of the approximate model creating method, the accuracy of the optimization calculation result can be improved by providing the step of confirming the accuracy of the Pareto solution.
The process of extracting the Pareto solution in step S50 is the same process as the process of obtaining the second Pareto solution in step S28 of the first example, and thus the detailed description thereof is omitted.

In the third example of the approximate model creation method, an actual calculation is performed as a confirmation calculation for confirming the accuracy of the Pareto solution using the Pareto solution obtained in Step S50 (Step S52). The actual calculation in step S52 is, for example, calculation by putting the design variable value of the Pareto solution obtained in step S50 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 S52 is compared with the actual calculation value (hereinafter referred to as FEM actual calculation value) calculated using the finite element method, and determination is made based on a predetermined determination condition. (Step S54). If the determination condition is satisfied in step S54, the Pareto solution obtained in step S50 is output as the final Pareto solution (step S66).

On the other hand, if the determination condition is not satisfied in step S54, the process returns to step S24, a plurality of design variable values are added as described above, and a second sampling calculation is performed (step S24). Are created (step S26). That is, the second approximate model is updated. The addition of values of design variables includes, for example, changing design variables to be fixed, increasing the number of design variables to be fixed, and the like.
Then, a second multi-objective optimization calculation is performed using the updated second approximation model (step S28), and a second Pareto solution is extracted from the second multi-objective optimization calculation result, and the second Pareto solution Are obtained (step S50). An actual calculation is performed using the obtained second Pareto solution (step S52), and the result of the actual calculation is determined in step S54 based on the determination condition. Addition of design variables (step S24), second sampling calculation (step S24), creation of second approximate model (step S26), second multi-objective optimization calculation (step S28) until the determination condition of step S54 is satisfied. Repeat).

The Pareto solution used for the actual calculation in step S52 may be all the Pareto solutions obtained in step S50. However, from the viewpoint of efficiency, it is preferable to select discretely the Pareto solution at the end, the Pareto solution at the center, and the like among the plurality of Pareto solutions.
For example, an error is used as the determination condition of step S54. This error may be a relative error or an actual error. Also, when using a plurality of Pareto solutions, their standard deviation or variance may be set.
As shown in FIG. 7, 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 . Obtaining a Pareto solution _{P 1, P 2, P 3} , the difference _d 1 between the FEM actual calculated value _{G 1, G 2, G 3} , d 2, d 3 , respectively. In this case, the determination is made by comparing the differences d ₁ , d ₂ and d ₃ with the errors set as the determination conditions.

  The present invention is basically configured as described above. As mentioned above, although the approximation model creation method of the structure of the present invention, the approximation model creation device of a structure, and the program were explained in detail, the present invention is not limited to the above-mentioned embodiment, In the range which does not deviate from the main point of the present invention Of course, various improvements or modifications may be made.

Hereinafter, an embodiment of the approximate model creating method of the present invention will be specifically described.
In the present example, the effects of the approximate model creating method of the present invention were confirmed using Example 1 and Comparative Examples 1 to 3 shown below and a reference example.

In this embodiment, the cross-sectional shape of the tire is used as a design variable, and two characteristic values (objective functions) which are physical characteristics of the tire are set. Here, the characteristic value 1 is set to be large and the characteristic value 2 is set to be small as the expected characteristic of the objective function, and the Pareto solution is extracted from the optimization calculation result using the multipurpose genetic algorithm. We confirmed about the effect of approximate model creation method.
Input values represented by design variables φ1 to φ7 were set with respect to the cross-sectional shape of the tire based on the tire model of the tire size 215 / 55R17. The input values represented by design variables φ1 to φ7 were set using the Latin hypercube method (LHC).
In addition, in order to verify the accuracy of the approximate model, calculation conditions such as design variables and their domains, number of individuals of genetic algorithm, number of generations, and mutation rate are the same in Example 1 and Comparative Examples 1 to 3, respectively. The value was used.
Hereinafter, Example 1 and Comparative Examples 1 to 3 and a reference example will be described.

In Example 1, in addition to 100 cases set by the Latin hypercube method, 50 cases of design variable values were added using the approximate model creation method of the present invention. Example 1 is 150 cases in all.
In Comparative Example 1, only 100 cases were set by the Latin hypercube method. The comparative example 1 is 100 cases in total.
In Comparative Example 2, only 150 cases were set by the Latin hypercube method. The comparative example 2 is 150 cases in total.
In Comparative Example 3, only 300 cases were set by the Latin hypercube method. The comparative example 3 is 300 cases in all.

  In the reference example, 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. 8 has no calculation error, it is set as a reference for confirming the calculation accuracy of the approximate model.

For Example 1 and Comparative Examples 1 to 3, approximate models using polynomials are created, optimization calculations are performed, Pareto solutions are extracted, and the results are shown in FIG.
As shown in FIG. 8, the actual calculation result 60 is close to the result 62 of the first embodiment. On the other hand, the result 64 of Comparative Example 1 is farthest from the actual calculation result 60. The comparative example 2 has the same number of cases as the example 1, but the result 66 of the comparative example 2 is farther from the actual calculation result 60 than the result 62 of the example 1, and is substantially the same result as the comparative example 1. The comparative example 3 has more cases than the example 1, but the result 68 of the comparative example 3 is further from the actual calculation result 60 than the result 62 of the example 1, and the shape is different from the actual calculation result 60.

As in Comparative Examples 1 to 3 shown in FIG. 8, even if the number of samplings is simply increased by the same Latin hypercube method, the calculation time is only increased, which hardly contributes to the improvement of the approximation accuracy. This is a sample method in which the Latin hypercube covers the design variable space discretely and evenly, and is excellent for uniformly approximating the entire design variable space, but a design variable whose optimal solution group shows an upper limit value or a lower limit value It can be seen that the effect is low even if the sampling density within the domain is increased, if it is configured in a combination including.
On the other hand, as shown in Example 1, in addition to the Latin hypercube method, a combination of design variables indicating the upper limit value, the lower limit value, or a constant value, which is the approximation model creation method of the present invention, is added to the design variable values. While approximating the entire design space uniformly and grasping the whole tendency, the approximation accuracy of the characteristic value region in which the accurate solution is required can be improved. Furthermore, even if the number of design variables to be added is small, the approximation accuracy can be efficiently improved.
The actual calculation result 60 does not use an approximate model, and the amount of calculation is much larger than in the first embodiment, and the calculation time is also long. As described above, in the present invention, although the number of cases is small, the accuracy of the approximate model is high. Moreover, the present invention can reduce the amount of calculation and calculation time.

10 Approximate model creation device for structure (approximate model creation device)
12 processing unit 14 input unit 16 display unit 20 condition setting unit 22 model creation unit 24 arithmetic unit 26 pareto solution search unit 28 memory 30 display control unit 32 control unit 40 upper limit value 42 lower limit value 44 fixed value 50 design variable 52 new design variable

Claims (13)

Among the parameters defining the structure and the material constituting the structure, a plurality of input parameters defined as design variables among the parameters defining the material constituting the structure and a plurality of parameters defined as the characteristic value among the parameters defining the structure and the material forming 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 a plurality of design variables, a domain of each design variable, and the plurality of characteristic values, and setting the values of the design variables;
A second step of determining a non-linear response relationship between the plurality of design variables and the plurality of characteristic values;
A third step of calculating a first output value in a characteristic value space constituted by the characteristic value of the value of the design variable using the non-linear response relation defined in the second step;
A fourth step of creating a first approximate model using the characteristic value which is the first output value obtained in the third step as an objective function;
Performing a multi-objective optimization calculation using the first approximate model to extract a first Pareto solution;
At least one of the upper limit value and the lower limit value is extracted from the values of the plurality of design variables in the first Pareto solution, and at least one of the extracted upper limit value and the lower limit value is fixed and extracted. A sixth step of changing values of undesigned design variables to set new values of the design variables;
A seventh step of calculating a second output value in a characteristic value space constituted by the characteristic values of a second design variable whose value of the design variable includes a new value of the design variable;
An eighth step of creating a second approximate model using the characteristic value which is the second output value obtained in the seventh step as an objective function;
The second using an approximate model, implement multi-objective optimization calculation, the method of creating an approximate model of the structure and executes a ninth step of extracting the second Pareto solutions. In the sixth step, the computer extracts at least one design variable indicating a constant value from a combination of values of the plurality of design variables in the first Pareto solution, and the constant of the extracted design variable The method for creating an approximate model of a structure according to claim 1, comprising the steps of fixing the value of the value and changing the value of the design variable not extracted to set a new value of the design variable.   The method according to claim 1 or 2, wherein the value of the design variable is set using a Latin hypercube method. Between the eighth step and the ninth step, the computer performs verification calculation on the second approximate model created in the eighth step using the second output value, If the result of the verification calculation satisfies the predetermined judgment condition, the multi-objective optimization calculation is executed in the ninth step,
If the result of the verification does not satisfy a predetermined judgment condition, in the sixth step, the value of the design variable is added, and the second design variable including the value of the added design variable and the second design variable The method for creating an approximate model of a structure according to any one of claims 1 to 3, wherein the second approximate model is updated using an output value of 2. The computer, after said ninth step, the actual calculations for verifying the error of the second approximation model using Pareto solutions obtained by executing the multi-objective optimization calculation of said ninth step run the step of performing,
If the result of the actual calculation satisfies a predetermined judgment condition, the computer determines the Pareto solution obtained by executing the multi-objective optimization calculation obtained in the ninth step as a final Pareto solution. ,
If the result of the actual calculation does not satisfy a predetermined determination condition, the computer adds the value of the design variable in the sixth step, and the second including the value of the added design variable. The method of creating an approximate model of a structure according to any one of claims 2 to 4, wherein the second approximate model is updated using the design variable of and the second output value. 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 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 multipurpose optimization calculation. Among the parameters defining the structure and the material constituting the structure, a plurality of input parameters defined as design variables among the parameters defining the material constituting the structure and a plurality of parameters defined as the characteristic value among the parameters defining the structure and the material forming the structure An apparatus for creating an approximate model of a structure for two types of data with output parameters,
The plurality of design variables, the domain of each design variable, and the plurality of characteristic values are set, the value of the design variable is set, and the plurality of design variables and the plurality of characteristic values are set. A condition setting unit that determines the non-linear response relationship between
A first output value in a characteristic value space constituted of characteristic values calculated by a combination of the design variable values is calculated using the non-linear response relation, and the characteristic value which is the first output value is calculated. An operation unit that creates a first approximate model as an objective function and performs multi-objective optimization calculation using the first approximate model;
And a Pareto solution search unit for obtaining a first Pareto solution,
The condition setting unit further extracts at least one of the upper limit value and the lower limit value among the values of the plurality of design variables in the first Pareto solution, and at least one of the extracted upper limit value and the lower limit value. Fix one value and change the value of the unextracted design variable to set a new value of the design variable,
The calculation unit further calculates a second output value in the characteristic value space configured by the characteristic value of the second design variable whose new value of the design variable is included in the value of the design variable, The second approximate model is created using the characteristic value which is the output value of 2 as the objective function, and the multi-objective optimization calculation is performed using the second approximate model, and the Pareto solution search unit An apparatus for creating an approximate model of a structure characterized by extracting a Pareto solution of   The condition setting unit extracts at least one design variable indicating a constant value from combinations of values of the plurality of design variables in the first Pareto solution, and fixes the value of the constant value of the extracted design variable. 8. The apparatus according to claim 7, wherein a new value of the design variable is set by changing the value of the design variable not extracted.   9. The apparatus according to claim 7, wherein the value of the design variable is set using a Latin hypercube method. In the calculation unit, verification calculation is performed on the second approximate model using the second output value, and multi-objective optimization calculation is performed when the result of the verification calculation satisfies a predetermined determination condition. Let it go
If the result of the verification does not satisfy a predetermined judgment condition, the condition setting unit is made to add the value of the design variable, and the calculation unit is made to include the second design variable including the value of the added design variable. The creation apparatus of the approximation model of the structure of any one of Claims 7-9 which have a control part which updates a said 2nd approximation model using a said 2nd output value. The operation unit is caused to perform actual calculation for verifying the error of the second approximate model using the Pareto solution obtained by performing the multi-objective optimization calculation, and the result of the actual calculation is determined to be predetermined If the condition is satisfied, the Pareto solution obtained by performing the multi-objective optimization calculation is taken as the final Pareto solution,
If the result of the actual calculation does not satisfy a predetermined determination condition, the condition setting unit is caused to add the value of the design variable, and the calculation unit is caused to include the value of the added design variable. 10. The apparatus for creating an approximate model of a structure according to any one of claims 7 to 9, further comprising a control unit that updates the second approximate model using the variable and the second output value. 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 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 multipurpose optimization calculation.   A program for causing a computer to execute each step of the method for creating an approximate model of a structure according to any one of claims 1 to 6 as a procedure.

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