JP6248402B2 - How to display data - Google Patents

Description

  The present invention relates to a method for displaying data consisting of predetermined design factors (design variables) and their characteristic values, and in particular, displays a Pareto solution in a scatter diagram in an objective function space, and designs on a scatter diagram according to the value of the design variable. The present invention relates to a data display method for displaying a symbol represented as a variable value by changing at least one of its color, type, and size.

In the simulation, a response to a predetermined design factor, that is, a design variable, that is, a characteristic value can be calculated. In the optimization, the value of a design variable for obtaining a desired characteristic value can be calculated.
On the other hand, a technique called design exploration is a technique for trying to find a causal relationship between a design variable and a characteristic value by using optimization and data mining. In design exploration, it is often the case that a plurality of characteristic values, that is, objective functions, are targeted and a trade-off relationship exists between them. Therefore, optimal solutions called Pareto solutions form a set. Therefore, a method called a self-organizing map is used to analyze Pareto solution data from both the characteristic value side and the design variable side (see Patent Document 1 and Non-Patent Document 1).

  Patent Document 1 uses a numerical simulation of a structure such as a tire to generate a self-organizing map to which information on a Pareto solution for an objective function is added, and also generates a self-organizing map to which information on a design variable is added. It is described that. For this reason, the designer can determine the optimal design plan by determining the position on the self-organizing map while considering the performance balance in a trade-off relationship while looking at the whole image of the Pareto solution on the surface of these maps. It is described in Patent Document 1 that it can be determined.

  Further, in Non-Patent Document 1, a self-organizing map is used, and an objective function and design variables can be displayed on the self-organizing map. It is described that not only the relationship can be grasped, but also the causal relationship between the objective function and the design variable can be understood.

Japanese Patent No. 4339808

Masataka Koishi, Journal of Japan Rubber Association, Vol.85, 2012, 289-295.

  However, the self-organizing maps disclosed in Patent Document 1 and Non-Patent Document 1 have a problem that they are not suitable for analysis along the Pareto front between objective functions and analysis focusing on the vicinity of the Pareto front. On the other hand, the scatter plot display of the Pareto solution in the objective function space is easy to focus on the Pareto front and its vicinity, but it is difficult to find the causal relationship with the design variable, and there are many data overlapping and poor visibility There is.

  An object of the present invention is to provide a data display method capable of solving a problem based on the above-described conventional technology and displaying a scatter diagram in which a causal relationship between a design variable and a characteristic value (objective function) can be easily understood. There is to do.

  In order to achieve the above object, at least one parameter defined as a design variable among parameters defining a structure and a material constituting the structure, and a parameter defining a material constituting the structure and the structure A method for displaying data for two types of data with at least one parameter defined as a characteristic value, the first step for defining a nonlinear response relationship between the design variable and the characteristic value, and the design variable The second step of calculating the Pareto solution by performing optimization with the characteristic value as the objective function using the nonlinear response relationship determined in the first step, and the Pareto solution in the objective function space When displaying as a scatter diagram, depending on the value of the design variable, display a symbol representing the value of the design variable in the scatter diagram by changing at least one of its color, type and size. There is provided a method for displaying data, characterized in that it comprises a third step.

Between the second step and the third step, there is a step of setting at least one discrete value within the domain of the design variable, and reducing the Pareto solution calculated based on the discrete value. The symbol representing the reduced Pareto solution value is preferably displayed as a scatter diagram by changing at least one of the color, type and size of the symbol.
In the second step, it is preferable to set at least one discrete value within the domain of the design variable and calculate a Pareto solution using the nonlinear response relationship determined in the first step based on the discrete value.
In calculating the Pareto solution in the second step, the characteristic value obtained in the Pareto solution search process is held as objective function data, and in the third step, the objective function data is stored together with the Pareto solution and the objective function space. It is preferable to display as a scatter diagram.

Furthermore, a parameter defined as a characteristic value is added, a nonlinear response relationship between the design variable and the characteristic value to which the parameter is added is determined, a domain of the design variable is defined, and the nonlinear response relationship is used to determine the characteristic value. It is preferable to include a step of calculating an extended Pareto solution by performing optimization with the objective function as a scatter function, and displaying the extended Pareto solution as a scatter diagram in the objective function space together with the Pareto solution in the third step.
It is preferable that the third step further includes a step of displaying a line passing through the Pareto solution at the Pareto front for each value of the design variable.
For example, the design variable is at least one parameter among the tire material behavior, the tire shape, and the tire structure, and the characteristic value is the tire characteristic value.

  According to the present invention, it is possible to display a scatter diagram in which a causal relationship between a design variable and a characteristic value (objective function) can be easily understood.

It is a schematic diagram which shows the display processing apparatus utilized for the display method of embodiment of this invention. It is a flowchart which shows the 1st example of the display method of embodiment of this invention in process order. (A) is a scatter diagram showing an example of a Pareto solution obtained for a tire design variable and a tire characteristic value, and (b) is a Pareto obtained for a tire design variable and a tire characteristic value. It is a scatter diagram which shows the other example of a solution. (A) is a scatter diagram showing an example in which the display of only a part of the design variables is changed for the Pareto solution obtained for the tire design variables and the tire characteristic values, and (b) is a tire design variable. It is a scatter diagram which shows the other example which changed only a part of design variable about the Pareto solution obtained about the characteristic value of the tire. It is a flowchart which shows the 2nd example of the display method of embodiment of this invention in process order. (A) is a schematic diagram explaining the definition area of a design variable, (b) is a schematic diagram explaining an example of the discrete value of the definition area of a design variable, (c) is a definition of a design variable. It is a schematic diagram explaining the other example of the discrete value of a range. (A) is a scatter diagram showing Pareto solutions obtained with respect to tire design variables and tire characteristic values, and (b) is a scatter diagram showing the Pareto solution shown in FIG. It is a scatter diagram which shows the example contracted according to the value. (A) is a scatter diagram showing Pareto solutions obtained with respect to tire design variables and tire characteristic values, and (b) is a scatter diagram showing the Pareto solution shown in FIG. It is a scatter diagram which shows the example contracted according to the value. (A) is a scatter diagram showing the Pareto solution obtained for the tire design variables and the tire characteristic values, and (b) is an example in which the Pareto front is clarified in the Pareto solution shown in FIG. FIG. It is a flowchart which shows the 3rd example of the display method of embodiment of this invention in process order. (A) is a scatter diagram showing Pareto solutions obtained for tire design variables and tire characteristic values, and (b) is a Pareto solution shown in FIG. It is a scatter diagram which shows the example which added data. It is a flowchart which shows the 4th example of the display method of embodiment of this invention in process order. (A) is a scatter diagram showing Pareto solutions obtained for tire design variables and tire characteristic values, and (b) shows other characteristic values in the Pareto solution shown in FIG. 13 (a). It is a scatter diagram which shows the example which added the Pareto solution which was made.

Hereinafter, a data display method of the present invention will be described in detail based on a preferred embodiment shown in the accompanying drawings.
FIG. 1 is a schematic diagram showing a display processing apparatus used in a display method according to an embodiment of the present invention. FIG. 2 is a flowchart showing a first example of the display method according to the embodiment of the present invention in the order of steps.

A display processing apparatus 10 shown in FIG. 1 is an example of an apparatus that is used to implement the display method according to the embodiment of the present invention. The display processing device 10 is configured using hardware such as a computer.
The display processing device 10 includes a processing unit 12, an input unit 14, and a display unit 16. The processing unit 12 includes a condition setting unit 20, a model generation 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 generation unit 22, the calculation unit 24, and the Pareto solution search unit 26 are connected to the memory 28, and the condition setting unit 20, the model generation unit 22, the calculation unit 24, and the Pareto solution Data of the search unit 26 is stored in the memory 28.

  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, a figure obtained by the display method of the present invention, 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 display processing device 10 executes a program (computer software) stored in a ROM or the like by the control unit 26 so that the condition setting unit 20, the model generation unit 22, the calculation unit 24, and the Pareto solution search unit 26 are configured. Form functionally. As described above, the display processing device 10 may be configured by a computer in which each part functions by executing a program, or may be a dedicated device 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 a scatter diagram in the objective function space by the display method of the present embodiment. Various conditions and information are input via the input unit 12. 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 at least one parameter determined as a design variable among parameters defining the structure and the material constituting the structure. Note that variation factors such as loads and boundary conditions may be set in the parameters of the design variables.
In addition, at least one parameter determined as a characteristic value (objective function) is set from among parameters defining the structure and the material constituting the structure. 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 characteristic value set in the condition setting unit 20 is a physical quantity to be evaluated. The objective function is a function for obtaining a physical quantity to be evaluated.
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 at a slip angle of 1 degree, which is an index of steering stability, and an index 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, and wear energy of a tire tread member as an index of wear resistance. The objective function is a function for obtaining them. The objective function has a preferable direction in terms of performance, and the value increases, decreases, or approaches a predetermined 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, the design variable is at least one parameter of the tire material behavior, the tire shape, and the 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 the design variable parameter and the characteristic value parameter is set in the condition setting unit 20. This nonlinear response relationship includes, for example, a numerical simulation such as FEM, a theoretical expression, an approximate expression, 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 can be used as a method for searching for a Pareto solution. In general, it is known that the exploration ability of a genetic algorithm decreases as the objective function increases. One way to solve this is to increase the number of individuals. On the other hand, when the number of individuals is increased and Pareto solutions are searched, many Pareto solutions are calculated. Therefore, a method for displaying the causal relationship between a large amount of characteristic value data and design parameters with high visibility is one of the problems in design exploration, but the present invention can solve this.
In addition to this, the condition setting unit 20 sets the definition area of the design variable. In addition, the condition setting unit 20 sets discrete values used when contracting the Pareto solution as will be described later.

  The model generation unit 22 creates various calculation models based on the set nonlinear response relationship. As described above, the non-linear response relationship includes a numerical simulation such as FEM. In this case, the model generation unit 22 generates a mesh model corresponding to the design parameter representing the design variable and the characteristic value parameter representing the characteristic value. Is done. Also in the case of theoretical formulas and approximate formulas, theoretical formulas and approximate formulas corresponding to design parameters and characteristic value parameters are 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 generation 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.

  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 using, for example, a tire design plan that optimizes tire performance including tire wet performance. Generate a model. For example, various models that reproduce water, snow, mud, sand, gravel, ice, and the like on the road surface may be generated as discretization models 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 25 calculates characteristic values using various models created by the model generation unit 22. Thereby, a characteristic value for the setting variable is obtained. Among these characteristic values, there is a Pareto solution. The obtained characteristic value is stored in the memory 28.
In the calculation unit 25, for example, the behavior of the tire model when a simulation condition for reproducing the rolling of the tire rolling on the road surface is given to the tire model generated by the model generation unit 22, the road surface model, or the like, or Obtain physical quantities such as force acting on the tire model in time series. The calculation unit 25 functions, for example, by executing a subroutine using a known finite element solver.
Further, when the model generation unit 22 creates a theoretical formula, an approximate formula, and the like, the calculation unit 25 solves the theoretical formula, the approximate formula, and the like, and calculates a characteristic value.

  The Pareto solution search unit 26 searches for the Pareto solution from the characteristic values obtained by the calculation unit 25 in accordance with the Pareto solution search conditions set by the condition setting unit 20, and calculates a Pareto solution. is there. The obtained Pareto solution is stored in the memory 28.

Here, the Pareto solution is a solution in which a plurality of objective functions that are in a trade-off relationship are not superior to any other arbitrary solution, but no other superior solution exists. 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 genetic algorithm.
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. At that time, it is necessary to obtain a set of Pareto solutions with high accuracy because the solution sets are widely distributed in the solution space. For this reason, the Pareto solution search unit 26 performs selection using, for example, a vector evaluation genetic algorithm (VEGA), a Pareto ranking method, or a tournament 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. It is also possible to use theoretical formulas, approximate formulas, and the like. For example, the value of the objective function may be calculated using a simulation approximation formula instead of the calculation using the simulation model. In this case, a Pareto solution can be obtained from an experimental result obtained based on the experimental design using an approximate expression between the design variable and the objective function, for example, a simulation approximate expression. As this simulation approximate expression, a known nonlinear function obtained by a polynomial or a neural network can be used.

  The display control unit 30 changes at least one of the color, type, and size of the symbol that represents the parameter value of the design variable in accordance with the parameter value of the design variable for the obtained Pareto solution. . Information of the Pareto solution whose display form has been changed is stored in the memory 28. The obtained Pareto solution is displayed on the display unit 16 with the display form changed by the display control unit 30. The display control unit 30 also has a function of displaying a line connecting the Pareto solutions for each design variable parameter value.

Next, the display method of this embodiment will be described.
Although the display processing apparatus 10 shown in FIG. 1 is used for the display method of the present embodiment, the display processing apparatus 10 is not limited to the display processing apparatus 10 as long as the display method can be executed using hardware such as a computer and software. Absent.
First, design variables and characteristic values are set for the target structure. In the present embodiment, the structure is, for example, a tire. The tire size is 195 / 65R15.
A tire shape parameter is set as a design variable for the tire. Then, two of the rolling resistance and the lateral spring constant are set as characteristic values. In the present embodiment, the input is a tire shape parameter, and the output is a rolling resistance and a lateral spring constant. Displays how the rolling resistance and the lateral spring constant change depending on the value of the tire shape parameter. The tire shape parameters, rolling resistance and lateral spring constant are set in the condition setting unit 20.

  Next, as shown in FIG. 2, a non-linear response used when obtaining a characteristic value from a design variable is determined (step S10). 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 shape parameter, the rolling resistance and the lateral spring constant is set. When the tire shape parameter is input and the rolling resistance or the lateral spring constant is output, the relationship to be set is expressed by using a nonlinear function such as a quadratic polynomial in which the rolling resistance is a variable of the tire shape parameter. Is. Further, the lateral spring constant is expressed using a nonlinear function such as a second-order polynomial with the tire shape parameter as a variable.

  Next, a design variable definition area is set (step S12). In this case, an upper limit value and a lower limit value are set for the parameters of the design variable, and it is assumed that the interval between the lower limit value and the upper limit value is continuous. For example, if it is a tire shape parameter, the upper limit and the lower limit of the size are set as the domain of the design variable, assuming that the interval between the lower limit value and the upper limit value is continuous. Moreover, if it is a rubber composition of a tire, the upper limit and the lower limit of the elastic modulus are set as the definition area of the design variable. The definition area of the design variable is set by the condition setting unit 20 and stored in the memory 28, for example. In this embodiment, an upper limit value and a lower limit value are set for the tire shape parameters.

  Next, model creation is performed by the model creation unit 22 based on the nonlinear response relationship, and a characteristic value is calculated based on the nonlinear response relationship set in step S10 by the calculation unit 24 (step S14). At this time, the definition area of the set design variable is read from the memory 28 and the characteristic value is calculated. The calculation result of the characteristic value is stored in the memory 28, for example. In the case of a simulation such as FEM, a mesh model is created by the model creation unit 22, and a response to an input is simulated by the calculation unit 24 by FEM or the like. Specifically, the rolling resistance and the lateral spring constant for the tire shape parameter are calculated.

  Next, the parade solution search unit 26 performs optimization using the characteristic value as an objective function for the calculation result of the characteristic value to obtain a Pareto solution (step S16). For example, a genetic algorithm is used to calculate the Pareto solution. The obtained Pareto solution is stored in the memory 28.

Next, the display control unit 30 changes at least one of the color, type, and size of the symbol that represents the value of the design variable in accordance with the value of the design variable. Specifically, for the design variables X1 and X2, for example, the symbol types are ◇, +, Δ, ×, □, and ○. Note that the color, type, and size of the symbol are not particularly limited.
Then, as shown in FIG. 3A, the type of symbol representing the value of the design variable X1 (◇) with the objective function (characteristic value) Y1 on the vertical axis and the objective function (characteristic value) Y2 on the horizontal axis. , +, Δ, ×, □, ○) and the color are changed to show the Pareto solution on the display unit 16 as a scatter diagram in the objective function space (step S18). For example, in FIG. 3A, the Pareto solution in the region D is preferable.
In FIG. 3A, an objective function (characteristic value) Y1 is a tire lateral spring constant, an objective function (characteristic value) Y2 is a tire rolling resistance, and a design variable X1 is a tire shape parameter.

  In the present embodiment, as shown in FIG. 3A, the Pareto solution can be stratified with respect to the design variable. This makes it easy to recognize the relationship between the design variable and the characteristic value. It can be seen that the position of the Pareto solution on the scatter diagram changes for each value of the design variable X1. In this way, the change in the characteristic value due to the change in the tire shape parameter can be easily recognized, and thus the design policy index can be obtained.

In addition to FIG. 3A, instead of the tire shape parameter of the design variable X1, the design variable X2 which is another tire shape parameter and the rolling resistance as a characteristic value (objective function (characteristic value) Y2) And the lateral spring constant (objective function (characteristic value) Y1), the Pareto solution can be displayed as shown in FIG.
The Pareto solution shown in FIG. 3B is also displayed on the display unit 16 as a scatter diagram in the objective function space by changing the symbol type (◇, +, Δ, ×, □, ○) and color representing the value of the design variable X2. It can also be shown.

In the present invention, the display method is not limited to that shown in FIGS. 3 (a) and 3 (b). For example, only certain values among design variable values may be displayed by changing at least one of the color, type and size of the symbol. In this case, a scatter diagram shown in FIGS. 4A and 4B is displayed on the display unit 16. As a display method, the color and size of a specific value among design variable values are changed with respect to the obtained Pareto solution. Then, it is displayed on the display unit 16. Thereby, it can be made to recognize clearly where the value of a specific value among the values of a design variable exists on a scatter diagram.
4A, the symbol ○ in FIG. 3A has a specific value and the display form is changed to ●, and in FIG. 4B, the symbol ◇ in FIG. The display form is changed to ●.

Next, a second example of the display method of the present invention will be described.
FIG. 5 is a flowchart showing a second example of the display method according to the embodiment of the present invention in the order of steps. 6A is a schematic diagram for explaining the domain of the design variable, FIG. 6B is a schematic diagram for explaining an example of the discrete values of the domain of the design variable, and FIG. It is a schematic diagram explaining the other example of the discrete value of the definition area of a design variable.
7A is a scatter diagram showing Pareto solutions obtained for the tire design variables and the tire characteristic values, and FIG. 7B is a scatter diagram showing the Pareto solutions shown in FIG. It is a scatter diagram which shows the example contracted according to the discrete value of the domain. FIG. 7A is the same as FIG.
FIG. 8A is a scatter diagram showing Pareto solutions obtained for the tire design variables and the tire characteristic values, and FIG. 8B is a scatter diagram showing the Pareto solutions shown in FIG. It is a scatter diagram which shows the example contracted according to the discrete value of the domain. FIG. 8A is the same as FIG.

  The second example of the display method is the same as the first example except that the Pareto solution is displayed after the Pareto solution is reduced as compared to the first example of the display method shown in FIG. Therefore, detailed description thereof is omitted.

In the display method of the second example, after the Pareto solution is calculated by the Pareto solution search unit 26 in the display processing apparatus 10, the Pareto solution is calculated by the calculation unit 24 based on the discrete values of the design variables described later. Is discretely reduced. As a result, the Pareto solution is thinned out. The thinned Pareto solution is displayed on the display unit 16 in the same manner as in the first example. The display form of the reduced Pareto solution is changed by the display control unit 30, stored in the memory 28, and displayed on the display unit 16.
Steps S20 to S26 shown in FIG. 5 are the same steps as steps S10 to S16 shown in FIG. In the second example, the Pareto solution reduction process in step S28 will be described.

Here, in the case of setting the design variable domain, in the first example, the range from the lower limit value α to the upper limit value β is continuous with respect to the design variable domain Xi as shown in FIG. Set. That is, the domain of the design variable is continuous with α ≦ Xi ≦ β.
On the other hand, as shown in FIG. 6B, for example, five discrete values are set at equal intervals in the definition regions α to β. Among the Pareto solutions, those corresponding to the discrete values are extracted by the calculation unit 24 to reduce the Pareto solution, and the reduced Pareto solution is stored in the memory 28.

Next, the display form of the reduced Pareto solution is changed by the display control unit 30 and the Pareto solution is displayed on the display unit 16. The Pareto solution display method can be displayed as shown in FIGS. 3 and 4 as described above. FIG. 7A is a scatter diagram showing the Pareto solution obtained in step S26. By reducing the Pareto solution, a scatter diagram of the Pareto solution as shown in FIG. 7B is obtained.
In addition to this, FIG. 8A is a scatter diagram showing the Pareto solution obtained in step S26. By reducing the Pareto solution, the scatter showing the distribution of the Pareto solution shown in FIG. 8B. A figure is obtained.

As described above, since the number of data of the Pareto solution can be effectively reduced by discretely reducing the Pareto solution, it is easy to find the causal relationship between the objective function and the design variable in the scatter diagram. Discrete values are more preferable if they are equally spaced because the rate of change can be easily estimated.
Note that the discrete values are not limited to the discrete values shown in FIG. 6B, but as shown in FIG. 6C, each discrete value is not a single value, and each discrete value is a predetermined value. It may have a range t.

  In the second example of the display method, the Pareto solution is reduced after being calculated. However, the present invention is not limited to this, and the reduced Pareto solution may be calculated. For example, in the first example of the display method, when the domain of the design variable is set (step S12), the characteristic value is calculated (step S14) as a discrete value shown in FIGS. It is possible to calculate a solution (step S16) and display a Pareto solution (step S18). In this case, the same Pareto solution scatter diagram as shown in FIG. 7B of the second example can be obtained.

Furthermore, as a display method, the symbols of the Pareto solution having the best characteristics among the Pareto solutions in the area where the characteristics are good can be displayed for each design variable by connecting them with lines.
FIG. 9A is a scatter diagram showing the Pareto solution obtained for the tire design variables and the tire characteristic values, and FIG. 9B clearly shows the Pareto front in the Pareto solution shown in FIG. It is a scatter diagram showing an example. FIG. 9A is the same as FIG. 8B, and a region having good characteristics is a region D.
9A, lines E _{1 to} E ₄ are obtained as shown in FIG. 9B by connecting the symbols closest to the region D among the Pareto solutions for each design variable. These lines E _{1 to} E ₄ indicate the Pareto front for each value of the design variable. Thereby, the change of the Pareto front by the change of the value of a design variable can be clarified.

A Pareto front is obtained for the Pareto solution obtained by the Pareto solution search unit 26. A known method for obtaining the Pareto front can be used. The Pareto front information is stored in the memory 28.
Next, the display control unit 30 reads Pareto front information from the memory 28, and creates line information connecting symbols representing Pareto solutions on the Pareto front for each design variable value based on this information. The line information is stored in the memory 28.
The display control unit 30 causes the display unit 16 to display lines E _{1 to} E ₄ based on the line information together with the Pareto solution.

For the Pareto solution obtained by the Pareto solution search unit 26, for each value of the design variable, as shown in FIG. 9A, the objective function (characteristic value) Y1 is equal to each value of the objective function (characteristic value) Y2. Extract the Pareto solution with the largest value. Information of the extracted Pareto solution is stored in the memory 28.
Then, the display control unit 30 creates information on lines connecting the symbols representing the extracted Pareto solutions. The line information is stored in the memory 28.
Then, the display control unit 30 causes the display unit 16 to display the lines E _{1 to} E ₄ based on the line information together with the Pareto solution. Even in this way, as shown in FIG. 9B, lines E _{1 to} E ₄ indicating the Pareto front can be obtained.

Next, a third example of the display method will be described.
FIG. 10 is a flowchart showing a third example of the display method according to the embodiment of the present invention in the order of steps. FIG. 11A is a scatter diagram showing Pareto solutions obtained for tire design variables and tire characteristic values, and FIG. 11B is a Pareto solution shown in FIG. It is a scatter diagram which shows the example which added characteristic value data.

  As compared with the first example of the display method shown in FIG. 2, when the number of display data is less than a predetermined number, the third example of the display method uses the characteristic value obtained in the Pareto solution search process as the objective function data. The objective function data is the same as that of the first example except that the objective function data is displayed together with the Pareto solution, and detailed description thereof is omitted.

In the display method of the third example, steps S30 to S36 shown in FIG. 10 are the same steps as steps S10 to S16 shown in FIG. In the third example, the process of determining the number of Pareto solutions in step S38 will be described.
The characteristic value is calculated by the calculation unit 24 and then stored in the memory 28. Thereafter, after the Pareto solution search unit 26 calculates the Pareto solution, the Pareto solution search unit 26 moves the Pareto solution and stores it in the memory 28, and the Pareto solution search unit 26 counts the number of Pareto solutions. The number of Pareto solutions is output to the control unit 32. If the number of display data exceeds the predetermined number in the control unit 32 (step S38), the Pareto solution is displayed on the display unit 16 (step S40). In this case, for example, it is displayed as shown in FIG. Note that the display method described above can be used as the display method.

On the other hand, when the number of display data is less than the predetermined number in step S38, among the characteristic values calculated from the memory 28 in step S34, a characteristic value that is not a Pareto solution is called as objective function data together with the Pareto solution, Objective function data is added to the Pareto solution (step S42).
Then, the characteristic value is displayed as objective function data together with the Pareto solution on the display unit 16. In this case, for example, it is displayed as shown in FIG. Note that the display method described above can be used as the display method.
In this way, the Pareto solution and other than the Pareto solution, for example, by displaying characteristic values that were not Pareto solutions in the Pareto solution search process as objective function data at the same time, the relationship between the Pareto solution and the data near the Pareto solution Can be visualized. The display method shown in FIG. 11B is particularly effective when there are two characteristic values.

Next, a fourth example of the display method will be described.
FIG. 12 is a flowchart showing a fourth example of the display method according to the embodiment of the present invention in the order of steps. FIG. 13A is a scatter diagram showing the Pareto solution obtained for the tire design variables and the tire characteristic values, and FIG. 13B shows other characteristic values for the Pareto solution shown in FIG. It is a scatter diagram which shows the example which added the Pareto solution in consideration of.
Compared to the first example of the display method shown in FIG. 2, the fourth example of the display method separately calculates a Pareto solution to which the type of characteristic value is added when the number of display data is less than a predetermined number. Since the separately calculated Pareto solution (hereinafter referred to as an extended Pareto solution) and the already calculated Pareto solution are displayed together, the process is the same as in the first example, and detailed description thereof is omitted. To do.

In the display method of the fourth example, steps S30 to S36 shown in FIG. 12 are the same steps as steps S10 to S16 shown in FIG. In the third example, the process of determining the number of Pareto solutions in step S38 will be described.
The characteristic value is calculated by the calculation unit 24 and then stored in the memory 28. Thereafter, after the Pareto solution search unit 26 calculates the Pareto solution, the Pareto solution search unit 26 moves the Pareto solution and stores it in the memory 28, and the Pareto solution search unit 26 counts the number of Pareto solutions. The number of Pareto solutions is output to the control unit 32. If the number of display data exceeds the predetermined number in the control unit 32 (step S38), the Pareto solution is displayed on the display unit 16 (step S40). In this case, for example, it is displayed as shown in FIG. Note that the display method described above can be used as the display method.

  On the other hand, in step S38, when the number of display data is less than the predetermined number, a parameter defined as a characteristic value set in the condition setting unit 20 is added, and a nonlinear response between the design variable and the added characteristic value. Define domain of relations and design variables. The model generation unit 22 generates a model, and the calculation unit 24 calculates characteristic values having different numbers of parameters. The expanded pareto solution is calculated by the pareto solution search unit 26 and stored in the memory 28. Specifically, the tire shape parameters (design variables) are obtained by adding further characteristic values such as tread wear and road noise to the currently set characteristic values such as rolling resistance and lateral spring constant. And the domain of these four characteristic values and the definition area of the tire shape parameter. Then, the model generation unit 22 generates a model, and the calculation unit 24 calculates four characteristic values. Then, the Pareto solution search unit 26 performs optimization using the four characteristic values as objective functions, and calculates an extended Pareto solution (step S44). The expanded Pareto solution is stored in the memory 28. In step S38, the extended Pareto solution is repeatedly calculated until the number of display data exceeds a predetermined number (step S44). The parameter value defined as the characteristic value to be added is not particularly limited.

In step S38, when the number of display data exceeds a predetermined number, the extended Pareto solution is called from the memory 28 together with the Pareto solution, and the extended Pareto solution is displayed on the display unit 16 together with the Pareto solution. In this case, for example, it is displayed as shown in FIG. Note that the display method described above can be used as the display method.
Thus, by simultaneously displaying the Pareto solution and the extended Pareto solution having a different number of characteristic values, the relationship between the Pareto solution and data in the vicinity of the Pareto solution can be visualized. This is particularly effective when there are two characteristic values.

As described above, by visualizing the relationship between the tire characteristic value and the tire shape parameter (design variable), the causal relationship can be understood, and the obtained design information can be utilized for the design. In particular, by using this information when determining the direction of the initial stage of design, it is possible to proceed with product development that is not greatly revised even in the detailed design at the end of the design. This can reduce development costs and product lead time.
In the present embodiment, the tire has been described as an example, but the display method of the present invention is not limited to this. For example, the present invention can be applied to structural designs of rubber products, home appliances, automobiles, airplanes, and the like. Even in this case, the causal relationship between the design variable and the characteristic value (objective function) can be understood, and the obtained design information can be utilized for the design. Furthermore, as described above, product development can be promoted, development costs can be reduced and development lead time can be shortened.

  The present invention is basically configured as described above. The data display method of the present invention has been described in detail above. However, the present invention is not limited to the above embodiment, and various improvements or modifications may be made without departing from the spirit of the present invention. It is.

DESCRIPTION OF SYMBOLS 10 Display processing apparatus 12 Processing part 14 Input part 16 Display part 20 Condition setting part 22 Model production | generation part 24 Calculation part 26 Pareto solution search part 28 Memory 30 Display control part 32 Control part

Claims (6)

At least one parameter defined as a design variable among the parameters defining the structure and the material constituting the structure, and at least one defined as a characteristic value among the parameters defining the structure and the material constituting the structure A method for displaying data targeting two types of data with two parameters,
A first step of defining a non-linear response relationship between the design variable and the characteristic value;
A second step of determining a domain of the design variable and performing optimization with a characteristic value as an objective function using the nonlinear response relationship determined in the first step to calculate a Pareto solution;
When displaying the Pareto solution as a scatter diagram in the objective function space, according to the value of the design variable, the symbol representing the value of the design variable in the scatter diagram is at least one of its color, type and size. Execute the third step of changing the display ,
The computer further adds a parameter defined as a characteristic value, defines a nonlinear response relationship between the design variable and the characteristic value to which the parameter is added, defines a domain of the design variable, and determines its nonlinear response Use the relationship to perform optimization with the characteristic value as the objective function to calculate the extended Pareto solution ,
In the third step, the computer displays the extended Pareto solution together with the Pareto solution as a scatter diagram in the objective function space . The computer between the second step and the third step,
Setting at least one discrete value within the domain of the design variable, and executing the step of reducing the Pareto solution calculated based on the discrete value,
In the third step, the computer displays a symbol representing the reduced Pareto solution value as the scatter diagram by changing at least one of the color, type and size of the symbol. The data display method according to 1. In the second step, the computer sets at least one discrete value within the domain of the design variable, and uses the nonlinear response relationship determined in the first step based on the discrete value, The data display method according to claim 1, wherein a solution is calculated. In the second step, when the computer calculates the Pareto solution, the characteristic value obtained in the Pareto solution search process is held as objective function data,
The data display method according to claim 1, wherein in the third step, the computer displays the objective function data as a scatter diagram in the objective function space together with the Pareto solution. The data according to any one of claims 1 to 4 , wherein in the third step, the computer further executes a step of displaying a line passing through a Pareto solution at a Pareto front for each value of the design variable. How to display. The design variables, material behavior of the tire, of the structure of the shape and tires, at least one parameter, said characteristic value, according to any one of claims 1 to 5, which is a characteristic value of the tire How to display your data.