JP6544005B2 - 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 , And a second step of determining a non-linear response relation between the plurality of design variables and the plurality of characteristic values, and a second step of setting the plurality of characteristic values. The third step of calculating the output value in the characteristic value space configured of the values of the plurality of design variables and the characteristic value using the determined non-linear response relationship, and at least one output value of the characteristic value space are set And set out Perturbs the input parameter value in the value, sets a plurality of input parameter values, and obtains the additional output value, and the characteristic using the additional output value and the output value obtained in the third process. A method of creating an approximate model of a structure, comprising: a fifth step of creating an approximate model using values as an objective function; and a sixth step of performing multi-objective optimization calculation using the approximate model. To provide

The step of obtaining the additional output value of the fourth step determines an area having a sparse output value in the characteristic value space, selects an output value from the sparse area, and perturbs an input parameter value at the selected output value. Preferably, a plurality of input parameter values are set to obtain additional output values.
Also, for the output value set in the fourth step, a reference value is set 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 is previously set. It is preferable to set to be set from the output value in the area of the defined distance.

In addition, between the fifth and sixth steps, 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, and if the verification result does not satisfy the predetermined determination condition, another additional output value is calculated in the fourth step. Preferably, in the fifth step, the approximation model is updated with another additional output value.
In addition, after the sixth step, there is a step of performing 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, and performing the actual calculation If the result of the condition satisfies the predetermined judgment condition, the Pareto solution obtained by carrying out the multi-objective optimization calculation obtained in the sixth step is regarded as the final Pareto solution, and the actual calculation result is the predetermined judgment If the condition is not satisfied, it is preferable to acquire another additional output value in the fourth step and update the approximate model with 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 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 A condition setting unit that sets characteristic values and determines a non-linear response relation between multiple design variables and multiple property values, and is composed of values and characteristic values of multiple design variables using the non-linear response relation Calculating output values in the characteristic value space to be set, setting at least one output value in the characteristic value space, perturbing input parameter values at the set output values, and setting a plurality of input parameter values An operation of acquiring an additional output value, creating an approximate model using the additional output value and the output value of the characteristic value space as an objective function, and using the created approximate model, performing multi-objective optimization calculation And an Pareto solution search unit for extracting a Pareto solution.

The operation unit obtains an area having a sparse output value in the characteristic value space, selects an output value from the sparse area, perturbs an input parameter value at the selected output value, and sets a plurality of input parameter values. And preferably obtain additional output values.
Set the reference value in the characteristic value space in the condition setting unit, set the reference value in the characteristic value space in the first step, and set the output value in a region larger or smaller than the reference value Alternatively, it is preferable to set from an output value in an area of a predetermined distance with respect to the reference value.

Make the operation unit perform the verification calculation using the additional model and the output value of the characteristic value space in the approximate model, and if the result of the verification calculation satisfies the predetermined judgment condition, perform the multi-objective optimization calculation in the operation unit Preferably, the Pareto solution search unit extracts the Pareto solution. On the other hand, when the verification result does not satisfy the predetermined determination condition, it is preferable to have a control unit that causes the operation unit to acquire another additional output value and update the approximate model using another additional output value. .
When the operation unit performs actual calculation for verifying the error of the 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, The Pareto solution obtained by carrying out multi-objective optimization calculation is taken as the final Pareto solution, and if the result of the actual calculation does not satisfy the predetermined judgment condition, the operation unit is made to acquire another additional output value. It is preferable to have a control unit that updates the approximate model using the additional output value of.

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 showing an example of a design variable, (b) is a graph showing the relationship between characteristic value 1 and characteristic value 2, (c) schematically shows how to change the design variable value FIG. (A) is a graph which shows the 1st example of acquisition method of additional output value, (b) is a graph which shows the 2nd example of acquisition method of additional output value, (c) is 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 setting method of reference point, (b) is a graph showing a second example of setting method of reference point, (c) is a graph of reference point It is a graph which shows the 3rd example of a setting method. 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. (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 Comparative example 2 typically. (A) is a graph showing a set point of Example 1, (b) is a graph showing a design point of Comparative Example 1, and (c) is a graph showing a design point of Comparative Example 2. . It is a graph which shows the characteristic value of Example 1, comparative examples 1 and 2, 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 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.
Since there are multiple types of design variables, discrete level values are set for some of the design variables, and the Pareto solution to be described later is extracted using the domain of the remaining design variables as a constant. May be
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.
In addition, the calculation unit 24 calculates an output value (characteristic value) in a characteristic value space configured by values of a plurality of kinds of design variables and a characteristic value using a non-linear response relation. Then, at least one output value is set in the characteristic value space configured by the characteristic values, the input parameter value at the set output value is perturbed to set a plurality of input parameter values, and the additional output value ( An additional model is obtained by obtaining the additional sampling point) and using the additional output value and the output value in the characteristic value space, with the characteristic value being the output value as the objective function. Furthermore, the calculation unit 24 performs multi-objective optimization calculation using the created approximate model.
The above-mentioned approximate model (meta-model) is a mathematical model that approximates the input / output relationship, and various input / output relationships can be approximated by adjusting the parameters. For example, polynomial models, kriging, neural networks, radial basis functions, and the like can be used as the above-described approximate models.

The calculation unit 24 also performs verification calculation such as cross verification using the additional output value and the output value of the characteristic value space in the approximate model.
Moreover, the calculating part 24 performs real calculation using a finite element method using the Pareto solution obtained by implementing multi-objective optimization calculation. Besides this, the calculation unit 24 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.
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 searches for a Pareto solution from the multi-objective optimization calculation result using the approximate model obtained by the operation unit 24 according to the conditions of the Pareto solution search set by the condition setting unit 20, and Pareto It is to extract the 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 the relationship of the characteristic value 1 and the characteristic value 2, and (c) is a model of the change method of a design variable value. It is a graph shown.

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, six design variables φ1 to φ6 that change the cross-sectional shape or structure of the tire are set. The setting method of the design variable 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, design values of design variables are uniformly set in the design variable space.
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, the output value in the characteristic value space configured by the values of the plurality of design variables and the characteristic value 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. The result obtained using the design values of the design variables shown in FIG. 3A is shown in FIG. 3B as the relationship between the characteristic value 1 and the characteristic value 2.
The code | symbol 40 shown to FIG. 3B shows the output value (sampling point) represented by the combination of the characteristic value 1 and the characteristic value 2 obtained by the set non-linear relationship. Reference numeral 42 denotes one characteristic value selected from among the plurality of output values 40 (sampling points). Reference numeral 44 denotes a plurality of output values (sampling points) set by setting a plurality of input parameter values by perturbing the input parameter values (the values of design variables φ1 to φ6) in the selected output value 42. .

Next, one output value 42 is set out of the output values 40 shown in FIG. Note that at least one output value 42 may be selected from the output values 40, a plurality of output values 42 may be selected, and all the output values 40 may be selected as the output value 42.
In addition, the setting method of the output value 42 is not specifically limited, It can set from the output values 40 at random.

  In this embodiment, the input parameter value in the output value 42 is perturbed to set a plurality of input parameter values, and a plurality of output values 44 are obtained (step S16). The output value 44 is, for example, a value represented by a combination of design variables φ1 to φ6 (input parameter values). With the values of the design variables φ1 to φ6 at the output value 44 of FIG. 3C as the central value, variation is given to the design variables φ1 to φ6. 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, variation of a predetermined width δ is allowed for the point 46b. In the design variable φ3, variation of a predetermined width δ is allowed for the point 46c. In the design variable φ4, variation of a predetermined width δ is allowed for the point 46d. In the design variable φ5, variation of a predetermined width δ is allowed for the point 46e. In the design variable φ6, fluctuation of a predetermined width δ is permitted for the point 46 f.

  At each point 46 a to 46 f of the design variables φ 1 to φ 6 of the output value 42, a combination in which the design variable is varied by a predetermined width δ is set. For example, using the Monte Carlo method, combinations of a plurality of, for example, 10 cases of design variables φ1 to φ6 are created for the combination of design variables in the output value 42, and the output value 44 is set. The number of output values to be added is not limited to 10 cases, and may be, for example, 50 cases.

Further, each value of design variables φ1 to φ6 at a predetermined width δ may use equally divided values of the value intervals, and the distribution of each design variable value is set based on a probability distribution such as a Gaussian distribution. You may For example, the output value 44 output by the combination of design variables using a Gaussian distribution has a high probability that the output value 44 having a value close to the output value 42 is added. Also, it is preferable to combine these design variable values using a random sampling method such as Monte Carlo method.
In the present invention, the term "perturbation" means that, in the characteristic values represented by a plurality of design variables, the value of each design variable as the median value is dispersed within a predetermined range of δ. . By using a combination of these values, it is possible to obtain a combination of design variables similar to the combination of design variables selected as the median, and therefore obtain an output value near the output value indicated by the combination of the selected design variables. 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 represented by an approximate model or an approximate expression.
Next, multi-objective optimization calculation using an approximation model is performed in the operation unit 24 (step S20). Next, the Pareto solution is extracted by the Pareto solution search unit 26 from the multi-objective optimization calculation result, and the Pareto solution is obtained (Step S22). Thus, a Pareto solution can be obtained using an approximate model. Note that the Pareto solution obtained using the approximate model as described above is an approximate prediction value.

The method of acquiring the additional output value (additional sampling point) in step S16 will be described.
The additional output value is obtained by the operation unit 24. In the characteristic value space, an area having a sparse output value is obtained, an output value is selected from the sparse area, and the input parameter value at the selected output value is perturbed. Preferably, a plurality of input parameter values are set to obtain additional output values. The following more specifically describes.
FIG. 4 (a) is a graph showing a first example of a method of acquiring an additional output value, (b) is a graph showing a second example of a method of acquiring an additional output value, and (c) is a graph 10 is a graph showing a third example of a method of obtaining an additional output value.

In step S16, the characteristic value space shown in FIG. 3B in step S14 is, for example, an average value Pb of all output values (hereinafter referred to as an average value Pb of all output values). Is simply set as the average value Pb) and divided into _four regions D _{1 to} D ₄ . Each of the regions D _{1 to} D ₄ is a square. Examining the distribution of the output values of the characteristic value space, determine the density of an output value in each region D ₁ to D _4. In the regions D _{1 to} D ₄ , at least one output value is set for the region with the lowest density of output values to perturb the input parameter values at the output values as described above, and a plurality of input parameters By setting the value, you get an additional output value.
In the region _D 1 to D _4, the density of regions _{D 1} and most output value is low, one of the output value 40 of the region _{D 1,} to set at least one output value 42. The input parameter values at the set output value 42 are perturbed to set a plurality of input parameter values and add output values.
Note that if the areas D _{1 to} D ₄ have the same area, it is possible to easily identify areas having sparse output values by comparing the number of output values in each of the areas D _{1 to} D ₄ . Therefore, it is preferable that the average value Pb be 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 above-described output value as long as the areas D _{1 to} D ₄ are known.

Other than 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 concentrically around the average value Pb. In this case, the distribution of the output value in the characteristic value space is examined, and the density of the output value in each of the regions D ₁₁ , D ₂₁ and D ₃₁ is examined. In the regions D ₁₁ , D ₂₁ and D ₃₁ , characteristic values are added to the region where the density of the output value is the lowest. The density of the output value of the area D ₃₁ is the lowest among the areas D ₁₁ , D ₂₁ , and D ₃₁ , and at least one output value 42 of the output values 40 of the area D ₃₁ is set. The output value is added as described above using the set output value 42, and the additional output value is acquired.
When the regions D ₁₁ , D ₂₁ and D ₃₁ are concentrically divided, they may be combined with the regions D _{1 to} D ₄ shown in FIG. This makes it possible to specify an area having a sparse output value with higher accuracy in the characteristic value space. 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 areas D having the same area, and areas having sparse output values may be determined. In this case, when there is no output value in the region D, the output value is excluded from the target of sparse and dense output values. In the region D, the region D ₄₀ has the lowest density of output values. Although there is only one output value ₄₀ in the area D ₄₀ , the output value 40 is set as the output value 42. The output value is added as described above using the set output value 42, and the additional output value is acquired.

In step S16, at least one output value for acquiring the 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 preferable directions according to the required specification and the like, and the preferable directions include increasing the value, decreasing the value, or approaching a predetermined value.
When selecting an output value, it is preferable to increase the density of the output value in a region in which two characteristic values 1 and 2 are in a preferable direction. Thus, 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. An area in the direction in which two characteristic values 1 and 2 are preferable can be set in step S10, and is set in the condition setting unit 20.
FIG. 5 (a) is a graph showing a first example of the setting method of reference points, (b) is a graph showing a second example of the setting method of reference points, and (c) is a reference It is a graph which shows the 3rd example of the setting method of a point.

For example, as shown in FIG. 5 (a), the average value Pb is set to an output value calculated by the combination of the respective medians in the design variable space, or as shown in FIG. 5 (b), step S10. When setting optimization conditions such as design variables, characteristic values (objective functions), and constraints for a structure to be a target, 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 preferable directions according to the required specification etc. For example, the characteristic value 1 is a characteristic whose larger value is better, and the characteristic value 2 is better whose value is smaller. 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 direction in which good characteristics can be obtained and bad characteristics can be obtained. The direction and the direction in which the predetermined characteristic converges can be set by the combination of the magnitudes 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 in which a larger value is better for characteristic value 1, but setting it to a smaller value results in a characteristic value 2 having a smaller value being a better characteristic. However, it is to set to a larger value. Further, the direction in which the predetermined characteristic converges is a direction from the reference point toward a predetermined value for the characteristic value 1, and is a direction from the reference point to a predetermined value for the characteristic value 2.

Next, a second example of the method for creating an approximate model of a structure according to this embodiment will be described.
FIG. 6 is a flowchart showing the second 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. 7 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 S30) of performing verification calculation using the created approximate model, as compared with the first example of the approximate model creating method. When the result does not satisfy the predetermined judgment condition (step S32), 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 will be I omit it. 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 creation method, in step S30, the computation unit 24 calculates an approximate prediction value using the approximate model created in step S18. Further, the calculation unit 24 carries out an actual calculation for calculating the characteristic value in order to verify the error of the approximate model by the combination of the design variable and the characteristic value using the non-linear relationship defined without using the approximate model.
Next, the approximate predicted value obtained in step S30 and the actual calculated value are compared, 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 thus the 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 to acquire additional output values again and approximate model Are created (step S18). That is, the approximate model is updated.
Then, using the updated approximate model, the calculating unit 24 calculates an approximate prediction value. That is, verification calculation is performed (step S30). The result of the verification calculation is determined based on the determination condition in step S32. Acquisition of an additional output value (step S16) and creation of an approximate model (step S18) are repeated until the determination condition of step S32 is satisfied.

In step S32, acquisition of the additional output value in the case where the determination condition is not satisfied, even if the output value 42 to be set is changed, the output value 42 to be set may be the same and the method of acquiring the additional output value may be changed The setting method of 42 is not particularly limited.
As the determination condition of step S32, 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 verification and K-division cross verification can be used when comparing the approximate prediction value and the actual calculation value, for example, when one point exclusion cross verification 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. 8 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 S42) of performing actual calculation on the extracted Pareto solution (step S40) as compared to the first example of the approximate model creating method, and the actual calculation is performed. If the result of 結果 does not satisfy the predetermined judgment 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 The difference is in the point of creation, and the other steps are the same as those in the first example, so the detailed description thereof will be omitted. In the third example of the approximation model generation method, by providing a step of confirming the accuracy of the Pareto solution, it is confirmed that the accuracy of the approximation model in the characteristic value space other than the sampling point is within a predetermined allowable range. A process is provided to improve the accuracy of the optimization calculation result.
The process of extracting the Pareto solution in step S40 is the same process as the process of obtaining the Pareto solution in step S22 of the first example, and thus the detailed description thereof is omitted.

In the third example of the approximate model creating 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 S40 (Step S42). The actual calculation in step S42 is, for example, calculation 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 (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 S44). If 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, when the determination condition is not satisfied in step S44, the process returns to step S16, acquires additional output values again, and creates an approximate model (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). An actual calculation is performed using the obtained Pareto solution (step S42), and the result of the actual calculation is determined in step S44 based on the determination condition. Acquisition of additional output value (step S16), creation of approximate model (step S18), calculation of multi-objective optimization (step S20), extraction of Pareto solution from multi-objective optimization calculation results (step S16) until the determination condition of step S44 is satisfied Step S40) and the actual calculation (Step S42) using the Pareto solution 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 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 S44. 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. 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 . 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 creation method of the present invention were confirmed using Example 1 and Comparative Examples 1 and 2 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 φ6 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 the design variables φ1 to φ6 were set to 100 cases by 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 and 2, respectively. The value was used.
Hereinafter, Example 1 and Comparative Examples 1 and 2 and a reference example will be described.

In Example 1, in addition to the result of performing the sampling calculation in the above 100 cases, four points were extracted from the output values obtained from the sampling calculation result. About the extracted output value 50 of four points | pieces, as shown to Fig.10 (a), the median was calculated | required about design variable (phi) 1- (phi) 6. As the additional sampling point by setting the fluctuation range as ± 20% of the domain of the design variable by the median of design variables φ1 to φ6 using Monte Carlo method, and changing the combination of values in the fluctuation range The output value 52 was set to 50 cases. The result is shown in FIG.
In Comparative Example 1, only 100 cases were set by the Latin hypercube method. 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 points extracted for the design variables φ1 to φ6 is set as the fluctuation range, and among the fluctuation ranges By changing the combination of design variable values in, 50 cases of output values 52 were set as additional sampling points. The result is shown in FIG.
The output values of the four points used in Example 1 and Comparative Example 2 are determined as the desired characteristics having a characteristic value 1 larger and a characteristic value 2 smaller among the output values, and the improvement range is largest, ie, The four points that will be the closest to the Pareto solution calculated in the optimization calculation below.

  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. 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, 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. 12, 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. 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.
Example 1 was able to obtain accuracy close to the actual calculation result 60 as compared with Comparative Examples 1 and 2. Example 1 has substantially the same number of cases as Comparative Example 3, but higher precision was obtained in Example 1. Further, 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, according to the present invention, the accuracy of the approximate model is high, and the amount of calculation and the calculation time can be reduced.

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, 50, 52 output value 42 selected output value 44 output value (Additional sampling point)
46a to 46f points

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,
The computer is
A first step of setting the plurality of design variables and the domain of each design variable, and the plurality of characteristic values;
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 an output value in a characteristic value space configured by the values of the plurality of design variables and the characteristic value using the non-linear response relation determined in the second step;
A fourth step of setting at least one output value in 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 by using the additional output value and the output value obtained in the third step as an objective function for the characteristic value;
And a sixth step of performing multi-objective optimization calculation using the approximate model, and a method of creating an approximate model of a structure. In the step of acquiring the additional output value of the fourth step, the computer determines an area having a sparse output value in the characteristic value space, selects an output value from the sparse area, and is selected. The method according to claim 1, wherein the input parameter value at the output value is perturbed to set a plurality of input parameter values, and an additional output value is acquired. The output value set in the fourth step by the computer is an output for which the computer sets a reference value in the characteristic value space in the first step, and is in a region larger or smaller than the reference value. The method for creating an approximate model of a structure according to claim 1 or 2, wherein the value or the output value in an area of a predetermined distance with respect to the reference value is set. The computer verifies the approximate model created in the fifth step between the fifth step and the sixth step using the additional output value and the output value of the characteristic value space. If the calculation is performed and the result of the verification calculation satisfies a predetermined judgment condition, the computer executes the multi-objective optimization calculation in the sixth step,
If the result of the verification does not satisfy the predetermined judgment condition, another additional output value is obtained in the fourth step, and the approximate model is updated using the other additional output value in the fifth step. The creation method of the approximation model of the structure of any one of Claims 1-3. The computer, after said sixth step, the step of performing a real computer for verifying the error of the approximate model using Pareto solutions obtained by executing the multi-objective optimization calculation of said sixth step Have
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 sixth step as a final Pareto solution. ,
If the result of the actual calculation does not satisfy the predetermined determination condition, another additional output value is obtained in the fourth step, and an approximation model is performed using the other additional output value in the fifth step. The method of creating an approximate model of a structure according to any one of claims 1 to 3, which updates. 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,
Condition setting for setting the non-linear response relationship between the plurality of design variables and the plurality of characteristic values by setting the plurality of design variables and the domain of the design variables and the plurality of characteristic values. Department,
An output value in a characteristic value space composed of the values of the plurality of design variables and the characteristic value is calculated using the non-linear response relation, and at least one output value of the characteristic value space is set, The input parameter value at the set output value is perturbed to set a plurality of input parameter values, the additional output value is obtained, and the characteristic value is calculated using the additional output value and the output value of the characteristic value space. An operation unit that creates an approximation model as an objective function and performs multi-objective optimization calculation using the created approximation model;
An apparatus for creating an approximate model of a structure, comprising: a Pareto solution search unit for extracting a Pareto solution.   The operation unit obtains an area having a sparse output value in the characteristic value space, selects an output value from the sparse area, and perturbs an input parameter value in the selected output value to obtain a plurality of input parameters. The apparatus for creating an approximate model of a structure according to claim 7, wherein values are set and additional output values are obtained. Sets the reference value to the characteristic value space to the condition setting unit, the setting the output value, the output value is a large or small area with respect to the reference value, or predetermined for the reference value The apparatus for creating an approximate model of a structure according to claim 7 or 8, which is set from an output value in a range of distance. The calculation unit causes the approximate model to perform verification calculation using the additional output value and the output value in the characteristic value space, and when the result of the verification calculation satisfies a predetermined determination condition, the calculation unit Perform multi-objective optimization calculations in step S. and extract the Pareto solution in the Pareto solution search unit,
When the result of the verification does not satisfy a predetermined determination condition, the control unit is configured to cause the operation unit to acquire another additional output value and to update the approximate model using the other additional output value. The creation apparatus of the approximation model of the structure of any one of 7-9. Causing the calculation unit to perform actual calculation for verifying the error of the approximate model using the Pareto solution obtained by performing the multi-objective optimization calculation;
If the result of the actual calculation satisfies a predetermined judgment condition, the Pareto solution obtained by performing the multi-objective optimization calculation is taken as a final Pareto solution,
When the result of the actual calculation does not satisfy a predetermined determination condition, the control unit is configured to cause the operation unit to acquire another additional output value, and to update the approximate model using the other additional output value. The creation apparatus of the approximation model of the structure of any one of 7-9. 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 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.