JP6565285B2 - Structure approximate model creation method, structure approximate model creation apparatus, and program - Google Patents

Description

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

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

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

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

JP 2011-103036 A JP2013-242662A

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

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

  In order to achieve the above object, according to a first aspect of the present invention, there are provided a plurality of input parameters defined as design variables among parameters defining a structure and a material constituting the structure, and the structure and the structure. A method for creating an approximate model of a structure for two types of data with a plurality of output parameters defined as characteristic values among parameters defining a constituent material, the plurality of types of design variables and each design variable A first step of setting a design variable value using a Latin hypercube method and an orthogonal table, and a plurality of design variables and a plurality of characteristic values; And calculating the output value in the characteristic value space composed of the characteristic values of the values of the design variables using the second step of determining the non-linear response relationship between and the non-linear response relationship determined in the second step, Design change And an output value, and using a characteristic value as an objective function, a third step of creating an approximate model, and a fourth step of performing multi-objective optimization calculation using the approximate model A method for creating an approximate model of a structure is provided.

  According to a second aspect of the present invention, there are a plurality of input parameters defined as design variables among parameters defining a structure and a material constituting the structure, and parameters defining a material constituting the structure and the structure. A method for creating an approximate model of a structure for two types of data with multiple output parameters defined as characteristic values, including multiple types of design variables, domains of each design variable, and multiple types of data A first step of setting characteristic values and setting values of design variables; a second step of determining a non-linear response relationship between a plurality of types of design variables and a plurality of types of characteristic values; and a second step. The first output value in the characteristic value space composed of the characteristic values of the design variable values is calculated using the determined non-linear response relationship, and the characteristic value is obtained using the design variable and the first output value. Create a first approximation model as a function A third step of performing the first multi-objective optimization calculation using the first approximation model, and a first approximation model after creating the first approximation model. A fifth step of extracting a Pareto solution, a sixth step of setting a design variable that becomes an upper limit value or a lower limit value from the values of the design variables in the Pareto solution, and an orthogonal table that includes the upper limit value or the lower limit value in the level value A characteristic value space composed of characteristic values of the second design variable in which the new value of the design variable set in the orthogonal table is included in the value of the design variable using the seventh step to be set and the nonlinear response relationship An eighth step of calculating a second output value at, using the second design variable and the second output value, and creating a second approximate model using the characteristic value as an objective function; And a ninth step of performing a second multi-objective optimization calculation using the approximate model. Creating a approximate model of the structure, characterized in there is provided a.

In the orthogonal table, it is preferable that the upper limit value or the lower limit value of the design variable be a level value.
When the verification calculation is performed using the output value on the approximate model created in the third step between the third step and the fourth step, and the result of the verification calculation satisfies a predetermined determination condition, When the multi-objective optimization calculation is performed in step 4, and the verification result does not satisfy the predetermined determination condition, the value of the design variable is added in the first step, and the value of the added design variable is included. It is preferable to update the approximate model using the design variable and the output value.
A verification calculation is performed on the second approximate model created in the eighth 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, the multi-objective optimization calculation is performed in the eighth step. If the verification result does not satisfy the predetermined determination condition, the value of the design variable is added and added in the first step. It is preferable to update the second approximate model using the second design variable including the design variable value and the second output value.

After the fourth step, there is a step of performing an actual calculation for verifying the error of the approximate model using the Pareto solution obtained by performing the multi-objective optimization calculation of the fourth step, and the result of the actual calculation Is the final Pareto solution obtained by performing the multi-objective optimization calculation obtained in the fourth step, and the result of the actual calculation satisfies the predetermined determination condition If not, it is preferable to add the value of the design variable in the first step and update the approximate model using the design variable and the output value including the value of the added design variable.
After the ninth step, there is a step of performing an actual calculation for verifying the error of the approximate model using the Pareto solution obtained by performing the multi-objective optimization calculation of the ninth step, and the result of the actual calculation Is the final Pareto solution obtained by performing the multi-objective optimization calculation obtained in the ninth step, and the result of the actual calculation satisfies the predetermined determination condition If not, in the first step, the value of the design variable is added, and the second approximate model is updated using the second design variable and the second output value including the value of the added design variable. It is preferable to do.

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

  According to a third aspect of the present invention, there are a plurality of input parameters defined as design variables among parameters defining the structure and the material constituting the structure, and parameters defining the material constituting the structure and the structure. A device for creating an approximate model of a structure for two types of data with multiple output parameters defined as characteristic values, including multiple types of design variables, domain of each design variable, and multiple types of data A condition setting unit that sets characteristic values, sets values of design variables using at least a Latin hypercube method and an orthogonal table, and determines a nonlinear response relationship between a plurality of types of design variables and a plurality of types of characteristic values; Using nonlinear response relations, calculate the output value in the characteristic value space consisting of the characteristic values of the design variable values, use the design variables and output values, use the characteristic values as objective functions, and create an approximate model. And providing an apparatus for creating an approximate model of a structure, characterized by having an arithmetic unit that performs a first multi-objective optimization calculation using an approximate model and a Pareto solution search unit that extracts a Pareto solution To do.

  According to a fourth aspect of the present invention, there are a plurality of input parameters defined as design variables among parameters defining a structure and a material constituting the structure, and parameters defining a material constituting the structure and the structure. A device for creating an approximate model of a structure for two types of data with multiple output parameters defined as characteristic values, including multiple types of design variables, domain of each design variable, and multiple types of data A condition setting unit that sets characteristic values, sets values of design variables using at least a Latin hypercube method and an orthogonal table, and determines a nonlinear response relationship between a plurality of types of design variables and a plurality of types of characteristic values; A first output value in a characteristic value space composed of characteristic values of design variable values is calculated using a non-linear response relationship, and the characteristic value is used as an objective function using the design variable and the first output value. , A first approximation model, a first approximation model is used to perform a first multi-objective optimization calculation, and a Pareto solution search unit that extracts a Pareto solution from the result of the first multi-objective optimization calculation And a condition setting unit to set a design variable that becomes an upper limit value or a lower limit value from a design variable value in the Pareto solution, and to set an orthogonal table that includes the upper limit value or the lower limit value as a level value, In addition, using the non-linear response relationship, the first value in the characteristic value space configured by the characteristic value of the second design variable, in which the design variable value includes the new value of the design variable set in the second orthogonal table. 2 is calculated, the second design variable and the second output value are used, the second approximation model is created using the characteristic value as the objective function, and the second approximation model is used. Characterized by having a control unit that performs multi-objective optimization calculation of There is provided a producing apparatus of the approximate model of the concrete body.

In the orthogonal table, it is preferable that the upper limit value or the lower limit value of the design variable be a level value.
When the calculation unit performs verification calculation using the output value for the approximate model, and the verification calculation result satisfies a predetermined determination condition, the Pareto solution search unit performs multi-objective optimization calculation, and the verification result If the specified condition is not satisfied, the condition setting unit adds the value of the design variable, and the arithmetic unit updates the approximate model using the design variable and the output value including the added design variable value. It is preferable to have a control unit.
Let the calculation unit perform verification calculation using the second output value for the second approximate model, and if the result of the verification calculation satisfies a predetermined determination condition, cause the calculation unit to perform multi-objective optimization calculation. ,
If the result of the verification does not satisfy the predetermined determination condition, the value of the design variable is added to the condition setting unit, and the second design variable and the second output value including the value of the design variable added to the calculation unit It is preferable to have a control unit that updates the second approximate model using.

When the arithmetic unit performs actual calculation for verifying the error of the approximate model using the Pareto solution obtained by performing the multi-objective optimization calculation, and the result of the actual calculation satisfies a predetermined determination condition, If the Pareto solution obtained by performing multi-objective optimization calculation is the final Pareto solution, and the actual calculation result does not satisfy the predetermined judgment condition, the value of the design variable is added to the condition setting unit, and the calculation is performed. It is preferable to have a control unit that updates the approximate model using the design variable including the value of the design variable added to the unit and the output value.
When the arithmetic unit performs actual calculation for verifying the error of the approximate model using the Pareto solution obtained by performing the multi-objective optimization calculation, and the result of the actual calculation satisfies a predetermined determination condition, If the Pareto solution obtained by performing multi-objective optimization calculation is the final Pareto solution, and the actual calculation result does not satisfy the predetermined judgment condition, the value of the design variable is added to the condition setting unit, and the calculation is performed. It is preferable to have a control unit that updates the second approximate model using the second design variable including the value of the design variable added to the 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 characteristic values of the tire, and the physical quantity of the tire is calculated by multi-objective optimization calculation. The

According to a fifth aspect of the present invention, there is provided a program for causing a computer to execute each step of the method for creating an approximate model of a structure according to the first aspect of the present invention as a procedure.
According to a sixth aspect of the present invention, there is provided a program for causing a computer to execute each step of the method for creating an approximate model of a structure according to the second aspect of the present invention as a procedure.

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

It is a schematic diagram showing an approximate model creation apparatus for a structure used in the approximate model creation method for a structure according to an embodiment of the present invention. It is a flowchart which shows the 1st example of the approximate model creation method of the structure of embodiment of this invention in process order. (A) is a graph which shows an example of a design variable, (b) is a graph which shows an example of the design variable in a Pareto solution. It is a flowchart which shows the 2nd example of the approximate model creation method of the structure of embodiment of this invention in process order. (A) is a graph which shows an example of a Pareto solution, (b) is a graph which shows an example of the setting method of a design variable. It is a flowchart which shows the 3rd example of the approximate model creation method of the structure of embodiment of this invention in process order. It is a graph which shows an example of a verification result. It is a flowchart which shows the 4th example of the approximate model creation method of the structure of embodiment of this invention in process order. It is a graph for demonstrating an error. (A) is a graph which shows typically the change method of the design variable value of Example 1, (b) is a graph which shows the change method of the design variable value of Example 2 typically. It is a graph which shows the Pareto solution of Example 1, Example 2, Comparative Examples 1-3, and a reference example.

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

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

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

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

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

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

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

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

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

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

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

The design variable is set by the condition setting unit 20 using a Latin hypercube method (Latin hypersquare method) and an orthogonal table, for example, a design value. The Latin hypercube method is a sample method that covers the design variable space discretely and uniformly. For this reason, design values can be set evenly in the design variable space. In addition to the Latin hypercube method, the value of the design variable can be set by the condition setting unit 20 using, for example, an orthogonal table, a Monte Carlo method, or the like. For example, in the first example of the method for creating an approximate model of a structure, the condition setting unit 20 sets design values using the Latin hypercube method (Latin hypersquare method) and an orthogonal table. In the second example of the method of creating an approximate model of a structure, a design value is set by the condition setting unit 20 using a Latin hypercube method, a Monte Carlo method, or the like.
In addition, the condition setting unit 20 sets a design variable that becomes an upper limit value or a lower limit value from among a plurality of design variables in the Pareto solution (first Pareto solution), and includes a second value that includes the upper limit value or the lower limit value in the level value. The orthogonal table is also set.
In the first orthogonal table and the second orthogonal table, the type is not particularly limited. A two-level system, a three-level system, a mixed system, or the like can be used. The level value preferably includes at least one of an upper limit value and a lower limit value in each design variable. 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 design variable, 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 value is the minimum value of the design variable, but is not limited to the minimum value. For example, a value obtained by adding a value of 10% or less of the minimum value to the minimum value may be used as the lower limit value. 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 set as the lower limit value. The definition regarding the tolerance of the value can be set in advance by the operator via the input unit 14 in problem setting.

  For multi-objective optimization calculations, either a method of searching sequentially using a nonlinear relationship (response surface) between input variables and output variables, or a method of searching by calculating output values while changing input variables according to an optimization algorithm May be used.

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

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

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

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

The calculation unit 24 calculates characteristic values using various models created by the model creation unit 22. Thereby, a characteristic value (output value) for the design variable is obtained. The obtained output value (output value) is stored in the memory 28. The calculation unit 24 functions, for example, by executing a subroutine using a known finite element solver.
The computing unit 24 calculates an output value (sampling point) in a characteristic value space composed of a plurality of types of design variable values and characteristic values using a non-linear response relationship. The computing unit 24 uses the design variable and the output value (sampling point), and creates an approximate model using the characteristic value that is the output value as an objective function.
In addition, the calculation unit 24 calculates a first output value (sampling point) in a characteristic value space composed of a plurality of types of design variable values and characteristic values using a non-linear response relationship. In addition, the calculation unit 24 uses the design variable and the first output value (sampling point) to create a first approximate model using the characteristic value that is the output value as an objective function.
In addition, the calculation unit 24 uses a non-linear response relationship, and a characteristic value space including a characteristic value of the second design variable in which the design variable includes a new value of the design variable set in the second orthogonal table. The second output value (additional sampling point) is calculated using the second design variable and the second output value (additional sampling point), and the characteristic value that is the second output value is used as an objective function. It also creates a second approximate model.
Further, the calculation unit 24 performs multi-objective optimization calculation using the created approximate model, the first approximate model, and the second approximate model.
The approximate model (meta model), the first approximate model (meta model), and the second approximate model (meta model) described above are mathematical models that approximate the input / output relationship, and parameters are adjusted. Thus, various input / output relationships can be approximated. For example, a polynomial model, kriging, a neural network, a radial basis function, or the like can be used for the above-described approximate model, first approximate model, and second approximate model.

The calculation unit 24 also performs verification calculation such as cross verification of the approximate model and the second approximate model.
The calculation unit 24 also performs multi-objective optimization calculation using the approximate model, the first approximate model, and the second approximate model, and the Pareto solution search unit 26 extracts the multi-objective optimization calculation result. The Pareto solution is also used to execute the actual calculation using the specified nonlinear relationship. In addition to this, the calculation unit 24 calculates a characteristic value using a combination of a design variable and a characteristic value by using a finite element method without using an approximate model. As the multi-objective optimization calculation method, for example, a genetic algorithm (GA) which is one of evolutionary calculation methods is used. Genetic algorithms include, for example, DRMOGA (Divided Range Multi-Objective GA) or NCGA (Neighborhood Cultivation GA), which divides a solution set into a plurality of regions along an objective function and performs multi-objective GA for each divided solution set. , Using known methods such as DCMOGA (Distributed Cooperation model of MOGA and SOGA), NSGA (Non-dominated Sorting GA), NSGA2 (Non-dominated Sorting GA-II), and SPEAII (Strength Pareto Evolutionary Algorithm-II) Can do.

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

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

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

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

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

Next, a first example of a method for creating an approximate model of a structure according to the present embodiment will be described.
FIG. 2 is a flowchart showing a first example of the approximate structure creation method for a structure according to the embodiment of the present invention in the order of steps. FIG. 3A is a graph showing an example of the design variable, and FIG. 3B is a graph showing an example of the design variable in the Pareto solution.

First, as shown in FIG. 2, optimization conditions such as design variables, characteristic values (objective functions), and constraint conditions are set for the target structure (step S10). For example, as the structure, a tire having a size of 195 / 65R15 can be given.
As design variables, for example, seven design variables φ1 to φ7 that change the cross-sectional shape or structure of the tire are set. As a design variable setting method, for example, a Latin hypercube method and an orthogonal table are used, and the design values of the design variables shown in FIG. In FIG. 3A, reference numeral 40 indicates a design value set by the Latin hypercube method, and reference numeral 42 indicates a design value set by the first orthogonal table. Symbol Pb indicates a reference value, which is a median value in FIG. As shown in FIG. 3A, the design value 40 is set uniformly in the design variable space.
The first orthogonal table is, for example, a two-level system, in which a lower limit value of a design variable domain is assigned to level 1 and an upper limit value of a design variable domain is assigned to level 2.
The characteristic values include, for example, tire rigidity, rolling resistance, air resistance, cornering performance, friction energy, and the like as tire physical characteristics. For example, two tire physical characteristics of characteristic value 1 and characteristic value 2 are set as objective functions. Two or more characteristic values may be set.

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

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

  Next, using the nonlinear response relationship set in step S12, an output value in a characteristic value space composed of a plurality of types of design variable values and characteristic values is calculated. That is, sampling calculation is performed to calculate a characteristic value that is an output when a design variable is input (step S14). Thereby, the position of the design value of the design variable in the characteristic value space composed of the characteristic value 1 and the characteristic value 2 can be known.

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

Here, for example, as shown in FIG. 3B, when the value of the design variable of the Pareto solution includes the upper limit value 44 or the lower limit value 46 of the design variable, the approximate model or the approximate expression formed in step S16. It is known that the accuracy of is low. For this reason, approximation accuracy improves by adding the combination in which a design variable contains an upper limit or a lower limit as a design value. However, if there are seven design variables, calculating all combinations, 2 ⁷ case, i.e., it requires 128 cases additional calculations, calculation volume increases consuming and computation time. Therefore, by using the orthogonal tables (the first orthogonal table and the second orthogonal table described above) for setting the design variable values, the upper limit value and the lower limit value of the design variables are included as shown in FIG. In addition, an increase in the number of design variable values can be suppressed, and an increase in calculation time can also be suppressed.

Next, a second example of the approximate model creation method of the structure according to the present embodiment will be described.
FIG. 4 is a flowchart showing a second example of the approximate structure creation method for a structure according to the embodiment of the present invention in the order of steps. FIG. 5A is a graph showing an example of a Pareto solution, and FIG. 5B is a graph showing an example of a design variable setting method.
In the second example of the approximate model creation method, detailed description of the same steps as those in the first example of the approximate model creation method is omitted.

As compared with the first example of the approximate model creation method, the second example of the approximate model creation method performs the first sampling calculation, creates the first approximate model, and performs the first multi-objective optimization calculation. To obtain the first Pareto solution, but the orthogonal table is created using the design variables in the first Pareto solution, and it is not necessary to use the orthogonal table in the first sampling calculation. Further, steps S30 to S42 described later are different.
In the second example, the second multi-objective optimization calculation is performed in step S44. Since this step is the same as step S18 in the first example, detailed description thereof is omitted. Step S46 outputs a Pareto solution. Since this step is the same as step S20 in the first example, detailed description thereof is omitted.

In this example, as in the first example, as shown in FIG. 4, optimization conditions such as design variables, characteristic values (objective functions), and constraint conditions are set for the target structure (step S10). For example, as the structure, a tire having a size of 195 / 65R15 can be given. In step S10 of this example, the process is the same as that of step S10 of the first example, except that, for example, the Latin hypercube method or the Monte Carlo method is used as the design variable setting method compared to the first example. Therefore, detailed description thereof is omitted.
The next step, which is a step (step S12) for setting the nonlinear response used when obtaining the characteristic value from the design variable in the condition setting unit 20 (step S12) is the same as step S10 in the first example, and therefore its details Detailed explanation is omitted.

In this example, using the linear response relationship set in step S12, an output value in a characteristic value space composed of characteristic values of a plurality of types of design variables is calculated. That is, a first sampling calculation for calculating a characteristic value that is an output when a design variable is input is performed (step S30). Next, a first approximate model is created using the output value obtained in step S30 (step S32). Then, the first multi-objective optimization calculation using the first approximate model is performed by the arithmetic unit 24 (step S34), and the Pareto solution search unit 26 extracts the Pareto solution from the first multi-objective optimization calculation result. To obtain a first Pareto solution.
Since the first approximate model created in step S32 is the same as the approximate model created in step S16 of the first example, detailed description thereof is omitted. Since the first multi-objective optimization calculation in step S34 is the same as the multi-objective optimization calculation in step S18 of the first example, detailed description thereof is omitted.

In step S34, for example, a Pareto solution P (first Pareto solution) shown in FIG. 5A is obtained. FIG. 5A also shows a reference point Pb. The value of the design variable of the Pareto solution shown in FIG.
As shown in FIG. 5B, the upper limit value 50 is set if the upper limit value 50 is located on the side of the upper limit value 50 with respect to the median value of the design variable values. If the orthogonal table is a two-level system, a median value is assigned to level 1 and an upper limit value 50 is assigned to level 2. Further, the lower limit value 52 is set if the lower limit value 52 side of the median value is based on the median value of the design variable. If the orthogonal table is a two-level system, a median value is assigned to level 1 and a lower limit value 52 is assigned to level 2. In this way, by comparing the magnitudes of the design variable values with the median as a reference, the condition setting unit 20 easily forms an orthogonal table including the upper limit value 50 or the lower limit value 52 of the design variable value in the level value. be able to. The orthogonal table created by the condition setting unit 20 based on the first Pareto solution and including the upper limit value 50 or the lower limit value 52 of the design variable value in the level value is referred to as a second orthogonal table.

  The design variables in the first Pareto solution are output (step S36), and the design variables that are the upper limit value or the lower limit value are extracted as shown in FIG. 5B (step S38). A second orthogonal table including the upper limit value or lower limit value of the design variable value is set in the above-described level value. As a result, a second design variable is obtained in which the design variable includes a new value of the design variable set in the second orthogonal table. Then, the second output value in the characteristic value space composed of the characteristic values of the second design variable is calculated again. That is, the second sampling calculation is performed (step S40).

Next, a second approximate model is created using the second design variable and the second output value obtained by the second sampling calculation as a characteristic value as an objective function (step S42). Then, the second multi-objective optimization calculation is performed by the arithmetic unit 24 using the second approximate model (step S44), and the Pareto solution search unit 26 extracts the Pareto solution from the second multi-objective optimization calculation result. Then, a Pareto solution is obtained (step S46). As a result, the approximation accuracy with good characteristics can be improved for the characteristic value 1 and the characteristic value 2, and the reliability of the optimization calculation result can be improved.
In the setting of the second orthogonal table, even if the design variable does not become the upper limit value or the lower limit value, when a constant value is indicated in the Pareto solution, a value indicating the constant value may be used as the level value.

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

  Compared to the first example of the approximate model creation method, the third example of the approximate model creation method has a step of performing verification calculation using the created approximate model (step S50). However, when the predetermined determination condition is not satisfied (step S52), the approximation model is created again, and the other steps are the same as those in the first example, and thus detailed description thereof is omitted. To do. In the third example of the approximate model creation method, the approximate model accuracy at the output value (sampling point) in the characteristic value space can be improved, and thereby the accuracy of the optimization calculation result can be improved.

In the third example of the approximate model creation method, in step S50, the approximate predicted value is calculated by the calculation unit 24 using the approximate model created in step S16. In addition, the calculation unit 24 performs an actual calculation for calculating the characteristic value using a combination of the design variable and the characteristic value using a nonlinear relationship defined without using an approximate model.
Next, the approximate predicted value obtained in step S50 is compared with the actual calculated value, and a determination is made based on a predetermined determination condition (step S52).
If the determination condition is satisfied in step S52, multi-objective optimization calculation is performed using the approximate model created in step S16 (step S54). Next, a Pareto solution is extracted by the Pareto solution search unit 26 from the multi-objective optimization calculation result to obtain a Pareto solution (step S56). Step S54 is the same process as step S20 described above, and step S56 is the same process as step S20 described above, and thus detailed description thereof is omitted.

On the other hand, if the determination condition is not satisfied in step S52, the process returns to step S10, the value of the design variable is added, and sampling calculation is performed using the approximate model created in step S12 (step S14). Create (step S16). That is, the approximate model is updated. The addition of the design variable value includes, for example, increasing the number of design variables by the Latin hypercube method and changing the value of the design variable by changing the setting of the orthogonal table.
Then, using the updated approximate model, an approximate prediction value is calculated by the calculation unit 24. That is, verification calculation is performed (step S50). The result of the verification calculation is determined based on the determination condition in step S52. Until the determination condition of step S52 is satisfied, the addition of design variables (step S10) and the creation of an approximate model (step S16) are repeated.

As the determination condition in step S52, for example, the slope of the approximate straight line between the actual calculated value and the approximate predicted value, the correlation coefficient, the determination coefficient, and the like can be used. Further, a threshold value may be given to the error at each sampling point, and this may be used as the determination condition.
More specifically, when comparing the approximate predicted value and the actual calculation value, one-point exclusion cross validation and K-division cross validation can be used. For example, when one-point exclusion cross validation is used, FIG. The result shown in is obtained.

The third example of the approximate model creation method can also be applied to the second example of the approximate model creation method shown in FIG. In this case, after the verification calculation step (step S50), if the verification calculation result satisfies a predetermined determination condition (step S52), the second approximation model created in step S42 is used for multipurpose purposes. Optimization calculation is performed (step S54).
On the other hand, after the verification calculation step (step S50), if the verification calculation result does not satisfy the predetermined determination condition (step S52), the process returns to step S10 to add the value of the design variable. The first sampling calculation is performed (step S30), the first approximate model is created (step S32), the first multi-objective optimization calculation is performed (step S34), and the Pareto is calculated from the first multi-objective optimization calculation result. A Pareto solution is extracted by the solution search unit 26 to obtain a first Pareto solution. And the design variable in a 1st Pareto solution is output (step S36), and the design variable used as an upper limit or a lower limit is extracted (step S38). Then, a second design variable including a new value of the design variable set in the second orthogonal table is obtained as the design variable (step S40), and the second design variable including the value of the added design variable is obtained. The second approximate model may be updated using the second output value (step S42).
Alternatively, the process returns to step S38, the value of the design variable is added, and the second approximate model may be updated using the second design variable including the value of the added design variable and the second output value ( Step S42).

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

Compared to the first example of the approximate model creation method, the fourth example of the approximate model creation method includes a step (step S62) of performing actual calculation on the extracted Pareto solution (step S60). If the result does not satisfy the predetermined determination condition (step S64), the approximate model is created again, and the other steps are the same as those in the first example. Is omitted. In the fourth example of the approximate model creation method, the accuracy of the optimization calculation result can be improved by providing a step of confirming the accuracy of the Pareto solution.
In addition, since the process of obtaining the Pareto solution in step S60 is the same process as the process of obtaining the Pareto solution in step S20 of the first example, detailed description thereof is omitted.

In the fourth example of the approximate model creation method, actual calculation is performed as confirmation calculation for confirming the accuracy of the Pareto solution using the Pareto solution obtained in step S60 (step S62). The actual calculation in step S62 is, for example, to calculate by putting the value of the Pareto solution obtained in step S60 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 S62 is compared with the actual calculation value calculated using the finite element method (hereinafter referred to as FEM actual calculation value), and the determination is made based on a predetermined determination condition. (Step S64). If the determination condition is satisfied in step S64, the Pareto solution obtained in step S60 is output as the final Pareto solution (step S66).

On the other hand, if the determination condition is not satisfied in step S64, the process returns to step S10, the value of the design variable is added, sampling calculation is performed using the approximate model created in step S12 (step S14), and the approximate model is calculated. Create (step S16). That is, the approximate model is updated. The addition of the design variable value includes, for example, increasing the number of design variables by the Latin hypercube method and changing the value of the design variable by changing the setting of the orthogonal table.
Then, using the updated approximate model, multi-objective optimization calculation is performed (step S18), a Pareto solution is extracted from the multi-objective optimization calculation result, and a Pareto solution is obtained (step S60). The actual calculation using the obtained Pareto solution is performed (step S62), and the result of the actual calculation is determined based on the determination condition in step S64. The design variable addition (step S10) and the approximation model creation (step S16) are repeated until the determination condition of step S64 is satisfied.

The Pareto solution used for the actual calculation in step S62 may be all the Pareto solutions obtained in step S60. However, from the viewpoint of efficiency, it is preferable to select discretely such as an end Pareto solution or a central Pareto solution among a plurality of Pareto solutions.
For example, an error is used as the determination condition in step S64. This error may be a relative error or an actual error. When a plurality of Pareto solutions are used, their standard deviation or variance value may be set.
As shown in FIG. 9, for example, three Pareto solutions P ₁ , P ₂ , and P ₃ are set for the Pareto solution P. FEM actual calculation values G ₁ , G ₂ , and G ₃ are calculated by inputting design variable values corresponding to the Pareto solutions P ₁ , P ₂ , and P ₃ . Differences d ₁ , d ₂ , and d ₃ between the Pareto solutions P ₁ , P ₂ , and P ₃ and the FEM actual calculation values G ₁ , G ₂ , and G ₃ are obtained, respectively. In this case, the determination is made by comparing the differences d ₁ , d ₂ , and d ₃ with an error set as a determination condition.

The fourth example of the approximate model creation method can also be applied to the second example of the approximate model creation method shown in FIG. In this case, using the Pareto solution obtained in step S60, actual calculation is performed as a confirmation calculation for confirming the accuracy of the Pareto solution (step S62), and determination is made based on a predetermined determination condition (step S62). S64). If the determination condition is satisfied in step S64, the Pareto solution obtained in step S60 is output as the final Pareto solution (step S66).
On the other hand, if the determination condition is not satisfied in step S64, the process returns to step S10, the value of the design variable is added, the first sampling calculation is performed (step S30), and the first approximate model is created (step S32). ), The first multi-objective optimization calculation is performed (step S34), the first Pareto solution is extracted from the first multi-objective optimization calculation result, and the first Pareto solution is obtained. And the design variable in a 1st Pareto solution is output (step S36), and the design variable used as an upper limit or a lower limit is extracted (step S38). Then, a second design variable including a new value of the design variable set in the second orthogonal table is obtained as the design variable (step S40), and the second design variable including the value of the added design variable is obtained. The second approximate model is updated using the second output value (step S42). Then, the second multi-objective optimization calculation is performed using the second approximate model (step S44), the second Pareto solution is extracted from the second multi-objective optimization calculation result, and the second Pareto solution is obtained. (Step S60). The actual calculation using the obtained second Pareto solution is performed (step S62), and the result of the actual calculation is determined based on the determination condition in step S64. The above-described series of steps S10 and S30 to S60 are repeated until the determination condition of step S64 is satisfied.

  Returning to step S38, the value of the design variable is added, and the second approximate model is updated using the second design variable and the second output value including the value of the added design variable (step S42). Then, the second multi-objective optimization calculation is performed using the second approximate model (step S44), and the second Pareto solution is extracted from the second multi-objective optimization calculation result to obtain the second Pareto solution ( Step S60). An actual calculation using the obtained second Pareto solution may be performed (step S62), and the result of the actual calculation may be determined based on the determination condition in step S64. Also in this case, the above-described series of steps S42, S44, and S60 is repeated until the determination condition of step S64 is satisfied.

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

Examples of the approximate model creation method of the present invention will be specifically described below.
In this example, the effects of the approximate model creation method of the present invention were confirmed using Examples 1 and 2 and Comparative Examples 1 to 3 shown below and a reference example.

In this embodiment, the tire cross-sectional shape is used as a design variable, and two characteristic values (objective functions) that are physical characteristics of the tire are set. Here, as the desired characteristic of the objective function, the characteristic value 1 is set to be large and the characteristic value 2 is set to be small, and the Pareto solution is extracted from the optimization calculation result using the multi-objective genetic algorithm. The effect of the approximate model creation method was confirmed.
With reference to a tire model of tire size 215 / 55R17, input values represented by design variables φ1 to φ7 were set for the cross-sectional shape of the tire. The input values represented by the 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, the design variables and their domain, and the calculation conditions such as the number of individuals, the number of generations, and the mutation rate of the genetic algorithm are the same in each of Examples 1, 2 and Comparative Examples 1-3. The same value was used.
Hereinafter, Example 1, Comparative Examples 1 to 3, and a reference example will be described.

Example 1, in addition to the 100 cases that set Latin hypercube method, the value of the design variable by using the orthogonal table L ₁₈ was added 18 cases. The orthogonal table L ₁₈ is represented by 3 ⁷ × 2 ¹ , with 3 levels being 7 factors and dummy and 2 levels being 1 factor. Example 1 has 118 cases in total. In the first embodiment, before the optimization calculation, the upper limit value 60, the lower limit value 61, and the median value 62 are set as reference points for the design variables in advance as shown in FIG.
Example 2, in addition to the 100 cases that set Latin hypercube method, the value of the design variable by using the orthogonal table L ₁₈ was added 18 cases. The orthogonal table L ₁₈ is represented by 3 ⁷ × 2 ¹ , with 3 levels being 7 factors and dummy and 2 levels being 1 factor. Example 2 has 118 cases in total. In Example 2, the optimization calculation using the first approximate model was performed once, then the Pareto solution was extracted, the preferred direction of the design variable was determined, and the benchmark was set. Specifically, as shown in FIG. 10B, the maximum value 63 (including the minimum value) in the absolute value in the preferred direction of the design variable, the median value 64 of the definition area, and the intermediate value 65 are set as levels. Set as a point. The intermediate value 65 is an intermediate value between the absolute maximum value 63 (including the minimum value) and the median value 64.

In Comparative Example 1, only 100 cases set by the Latin hypercube method were used. Comparative example 1 is 100 cases in total.
In Comparative Example 2, only 120 cases set by the Latin hypercube method were used. The comparative example 2 is 120 cases in total.
In Comparative Example 3, only 300 cases set by the Latin hypercube method were used. In Comparative Example 3, there are 300 cases in total.

  In the reference examples, the characteristic values are all calculated using the finite element method without using an approximate model. The actual calculation results of this reference example are shown in FIG. The actual calculation result 70 shown in FIG. 11 serves as a reference for confirming the calculation accuracy of the approximate model.

For Examples 1 and 2 and Comparative Examples 1 to 3, an approximation model using a polynomial is created, optimization calculation is performed, a Pareto solution is extracted, and the result is shown in FIG.
As shown in FIG. 11, the actual calculation result 70 is close to the result 72 of the first embodiment and the result 74 of the second embodiment. On the other hand, the result 76 of Comparative Example 1 is farthest from the actual calculation result 70. Comparative Example 2 has approximately the same number of cases as Example 1, but the result 78 of Comparative Example 2 is farther from the actual calculation result 70 than the result 72 of Example 1, and is substantially the same result as Comparative Example 1. . Comparative Example 3 has more cases than Example 1, but the result 80 of Comparative Example 3 is farther from the actual calculation result 70 than the result 72 of Example 1, and the shape is different from the actual calculation result 70.

As in Comparative Examples 1 to 3 shown in FIG. 11, even if the number of samplings is simply increased by the same Latin hypercube method, the calculation time is increased and it 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 when the optimal solution group is composed of combinations including design variables that indicate the upper limit value or the lower limit value, It can be seen that the effect is low even if the sampling density is increased.
On the other hand, as shown in Example 1, in addition to the Latin hypercube method, a design variable to be added by adding a combination of design variables indicating an upper limit value, a lower limit value, and a constant value to the design variable value using an orthogonal table The approximation accuracy can be improved efficiently even when there is a small number of.
Example 2 in which the orthogonal table is set based on the Pareto solution after performing the optimization calculation once without using the orthogonal table is set only using the Latin hypercube method and the orthogonal table before the optimization calculation. Compared to the first embodiment, the number of cases is the same, but closer to the actual calculation result 70, and the approximation accuracy can be improved more efficiently.
It should be noted that the actual calculation result 70 does not use an approximate model, and the calculation amount is very large and the calculation time is long as compared with the first and second embodiments. Thus, in the present invention, the number of cases is small, but the accuracy of the approximate model is high. Moreover, the present invention can reduce the calculation amount and the calculation time.

Approximate model creation device for structure 10 (approximate model creation device)
DESCRIPTION OF SYMBOLS 12 Processing part 14 Input part 16 Display part 20 Condition setting part 22 Model preparation part 24 Calculation part 26 Pareto solution search part 28 Memory 30 Display control part 32 Control part 40 Design value 42 Design value 44 set by 1st orthogonal table 44 Upper limit 46 Lower limit

Claims (17)

A plurality of input parameters defined as design variables among the parameters defining the structure and the material constituting the structure, and a plurality of parameters defined as characteristic values among the parameters defining the structure and the material constituting the structure A method of creating an approximate model of a structure for two types of data with output parameters,
The computer sets the plurality of types of design variables, the domains of the design variables, and the plurality of types of characteristic values, and sets the values of the design variables using at least a Latin hypercube method and an orthogonal table. And the process of
A second step of defining a nonlinear response relationship between the plurality of types of design variables and the plurality of types of characteristic values;
Using the nonlinear response relationship defined in the second step, calculating an output value in a characteristic value space constituted by the characteristic value of the design variable value, using the design variable and the output value, A third step of creating an approximate model using the characteristic value as an objective function;
A method for creating an approximate model of a structure, wherein a fourth step of performing multi-objective optimization calculation is executed using the approximate model. A plurality of input parameters defined as design variables among the parameters defining the structure and the material constituting the structure, and a plurality of parameters defined as characteristic values among the parameters defining the structure and the material constituting the structure A method of creating an approximate model of a structure for two types of data with output parameters,
A first step in which a computer sets the plurality of types of design variables and domain of each design variable, and sets the plurality of types of characteristic values, and sets the values of the design variables;
A second step of defining a nonlinear response relationship between the plurality of types of design variables and the plurality of types of characteristic values;
Using the nonlinear response relationship determined in the second step, a first output value in a characteristic value space constituted by the characteristic values of the design variable values is calculated, and the design variable and the first A third step of creating a first approximate model using the output value and using the characteristic value as an objective function;
A fourth step of performing a first multi-objective optimization calculation using the first approximate model;
A fifth step of extracting a Pareto solution using the first approximate model after creating the first approximate model;
A sixth step of setting a design variable that becomes an upper limit value or a lower limit value from the value of the design variable in the Pareto solution;
A seventh step of setting an orthogonal table including the upper limit value or the lower limit value as a level value;
Using the nonlinear response relationship, a second value in a characteristic value space configured by the characteristic value of the second design variable in which the value of the design variable includes a new value of the design variable set in the orthogonal table. An eighth step of calculating an output value, using the second design variable and the second output value, and creating a second approximate model using the characteristic value as an objective function;
And a ninth step of performing a second multi-objective optimization calculation using the second approximate model. A method for creating an approximate model of a structure.   The method for creating an approximate model of a structure according to claim 1 or 2, wherein the orthogonal table uses an upper limit value or a lower limit value of a design variable as a level value. The computer, between the third step and the fourth step, the approximation model created in the third step, to validate calculated by using the output value of the verification calculation result is given If the determination condition is satisfied, the multi-objective optimization calculation is executed in the fourth step,
When the verification result does not satisfy a predetermined determination condition, the computer adds the value of the design variable in the first step, and the design variable including the value of the added design variable and the output The method for creating an approximate model of a structure according to claim 1 , wherein the approximate model is updated using a value. The computer performs a verification calculation using the second output value on the second approximate model created in the eighth step between the eighth step and the ninth step, If the result of the verification calculation satisfies a predetermined determination condition, the second multi-objective optimization calculation is executed in the ninth step,
If the result of verification does not satisfy a predetermined determination condition, the computer adds the value of the design variable in the first step, and includes the value of the added design variable. the method of creating an approximate model of a structure according to claim 2 configured to update the second approximation model using the variable second output value. The computer performs an actual calculation for verifying an error of the approximate model using the Pareto solution obtained by executing the multi-objective optimization calculation of the fourth step after the fourth step. Run
When the result of the actual calculation satisfies a predetermined determination condition, the computer uses the Pareto solution obtained by executing the multi-objective optimization calculation obtained in the fourth step as a final Pareto solution. ,
When the result of the actual calculation does not satisfy a predetermined determination condition, the computer adds a value of the design variable in the first step, and a design variable including the value of the added design variable The method for creating an approximate model of a structure according to claim 1 , wherein the approximate model is updated using the output value. Actual calculation for the computer to verify the error of the approximate model using the Pareto solution obtained by executing the second multi-objective optimization calculation of the ninth step after the ninth step Execute the process of
When the result of the actual calculation satisfies a predetermined determination condition, the computer finally calculates the Pareto solution obtained by executing the second multi-objective optimization calculation obtained in the ninth step. 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 first step, and includes the value of the added design variable. the method of creating an approximate model of a structure according to claim 2 which design variables and using said second output value to update the second approximation model. The design variable is at least one parameter that changes the shape or structure of the tire, and the characteristic value is at least one of the physical characteristic values of the tire;
The method for creating an approximate model of a structure according to any one of claims 1 to 7, wherein a physical quantity of a tire is calculated by the multi-objective optimization calculation. A plurality of input parameters defined as design variables among the parameters defining the structure and the material constituting the structure, and a plurality of parameters defined as characteristic values among the parameters defining the structure and the material constituting the structure An apparatus for creating an approximate model of a structure targeting two types of data with output parameters,
The plurality of types of design variables and the domain of each design variable, and the plurality of types of characteristic values are set, and the values of the design variables are set using at least a Latin hypercube method and an orthogonal table. A condition setting unit for defining a nonlinear response relationship between a design variable and the plurality of characteristic values;
Using the nonlinear response relationship, calculate an output value in a characteristic value space composed of the characteristic values of the design variable value, and use the design variable and the output value to approximate the characteristic value as an objective function. A calculation unit that creates a model and performs the first multi-objective optimization calculation using the approximate model;
An apparatus for creating an approximate model of a structure, comprising: a Pareto solution search unit that extracts a Pareto solution. A plurality of input parameters defined as design variables among the parameters defining the structure and the material constituting the structure, and a plurality of parameters defined as characteristic values among the parameters defining the structure and the material constituting the structure An apparatus for creating an approximate model of a structure targeting two types of data with output parameters,
The plurality of types of design variables and the domain of each design variable, and the plurality of types of characteristic values are set, and the values of the design variables are set using at least a Latin hypercube method and an orthogonal table. A condition setting unit for defining a nonlinear response relationship between a design variable and the plurality of characteristic values;
A first output value in a characteristic value space constituted by the characteristic values of the design variable values is calculated using the nonlinear response relationship, and the characteristic values are calculated using the design variables and the first output values. Using the first approximate model as an objective function and performing a first multi-objective optimization calculation using the first approximate model;
A Pareto solution search unit that extracts a Pareto solution from the result of the first multi-objective optimization calculation;
The condition setting unit is allowed to set a design variable that is an upper limit value or a lower limit value from a design variable value in the Pareto solution, and a level value is set to an orthogonal table that includes the upper limit value or the lower limit value,
The calculation unit is configured with the characteristic value of the second design variable including the new value of the design variable set in the second orthogonal table in the value of the design variable using the nonlinear response relationship. A second output value in the characteristic value space is calculated, and a second approximate model is created using the second design variable and the second output value, using the characteristic value as an objective function, and the second An apparatus for creating an approximate model of a structure, comprising: a control unit that executes a second multi-objective optimization calculation using the approximate model.   The apparatus for creating an approximate model of a structure according to claim 9 or 10, wherein the orthogonal table uses an upper limit value or a lower limit value of a design variable as a level value. When the calculation unit causes the approximation model to perform verification calculation using the output value, and the result of the verification calculation satisfies a predetermined determination condition, the calculation unit performs multi-objective optimization calculation,
When the verification result does not satisfy a predetermined determination condition, the condition setting unit adds the value of the design variable, and the calculation unit includes the design variable including the added design variable value and the output value. The apparatus for creating an approximate model of a structure according to claim 9 , further comprising: a control unit that updates the approximate model using a computer. When the calculation unit causes the second approximate model to perform verification calculation using the second output value, and the result of the verification calculation satisfies a predetermined determination condition, the calculation unit performs multi-objective optimization. Let the calculations be performed,
When the verification result does not satisfy a predetermined determination condition, the condition setting unit adds the value of the design variable, and the calculation unit includes the second design variable including the added design variable value; The apparatus for creating an approximate model of a structure according to claim 10 , further comprising a control unit that updates the second approximate model using the second output value. Causing the arithmetic unit to perform an actual calculation for verifying an error of the approximate model using a Pareto solution obtained by performing the first multi-objective optimization calculation;
When the result of the actual calculation satisfies a predetermined determination condition, the Pareto solution obtained by performing the first multi-objective optimization calculation is a final Pareto solution,
When the result of the actual calculation does not satisfy a predetermined determination condition, the condition setting unit adds the value of the design variable, and the calculation unit includes the design variable including the added design variable value and the output The apparatus for creating an approximate model of a structure according to claim 9 , further comprising a control unit that updates the approximate model using a value. The arithmetic unit is caused to perform an actual calculation for verifying an error of the approximate model using a Pareto solution obtained by performing the first multi-objective optimization calculation, and the result of the actual calculation is a predetermined determination If the condition is satisfied, the Pareto solution obtained by performing the first multi-objective optimization calculation is set as the final Pareto solution,
If the result of the actual calculation does not satisfy a predetermined determination condition, the condition setting unit adds the value of the design variable, and the calculation unit includes the value of the added design variable. The apparatus for creating an approximate model of a structure according to claim 10 , further comprising a control unit that updates the second approximate model using a 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 the physical characteristic values of the tire;
The apparatus for creating an approximate model of a structure according to any one of claims 9 to 15, wherein a physical quantity of a tire is calculated by the multi-objective 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 8 as a procedure.

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