WO2018042968A1

WO2018042968A1 - Sound oscillation simulation program

Info

Publication number: WO2018042968A1
Application number: PCT/JP2017/027367
Authority: WO
Inventors: 洋祐田部; 和人大山; 吉田　毅
Original assignee: 日立オートモティブシステムズ株式会社
Priority date: 2016-08-31
Filing date: 2017-07-28
Publication date: 2018-03-08
Also published as: DE112017003671T5; JP6663825B2; JP2018036863A

Abstract

The purpose of the present invention is to provide a sound oscillation simulation model which is incorporated into a product operation simulator which simulates an operation of a product overall and with which it is possible to examine the energy balance of said product overall. This sound oscillation simulation program causes a computer to function as either: a first computation unit 8 which, in accordance with an inputted first parameter P1, outputs a second parameter P2 which has a dimension which results when a dimension of power or work is divided by a dimension of the first parameter P1; or a second computation unit 9 which outputs the first parameter P1 in accordance with the inputted second parameter P2. The first computation unit 8 is represented as a function which includes the first parameter P1 and a first characteristic C1. The second computation unit 9 is represented as a function which includes the second parameter P2 and a second characteristic C2. The first characteristic C1 and the second characteristic C2 are characteristics which characterize a shape of a structure. The first characteristic C1 is a ratio of the dimension of the second parameter P2 and the second characteristic C2 is a ratio of the dimension of the first parameter P1.

Description

Sound vibration simulation program

The present invention relates to a sound vibration simulation program.

For the purpose of shortening and optimizing product development, model-based development, in which performance and function evaluations that have been performed in tests using prototypes in the past, is performed upstream by simulation, has become widespread. In model-based development, in order to model products composed of parts from different fields such as electricity, machinery, and fluid, the energy flow between parts is defined by the amount that defines energy (potential difference amount) and strength ( There is known a method of expressing by exchanging a two-dimensional quantity (flow quantity) (for example, Patent Document 1).

However, in the technique described in Patent Document 1, since the physical characteristics of parts are expressed as lumped constants, the energy balance during product operation can be calculated, but the sound vibration performance of products that depend on the three-dimensional part shape is directly measured. Cannot be evaluated. Therefore, in order to evaluate the sound vibration performance of a product, for example, it is necessary to use a sound vibration characteristic analysis method as described in Patent Document 2. In this analysis method, a three-dimensional shape of a product is modeled by a finite element method or the like, and an excitation force separately calculated outside the model is input and evaluated.

JP 2002-175338 A

However, in the method of analyzing sound vibration characteristics by applying the analysis method described in Patent Document 2 to the technique described in Patent Document 1, the excitation force output from the product operation simulator described in Patent Document 1 is used as the patent document. The sound vibration is reproduced by inputting into the sound vibration simulator described in 2 above. In this case, since the energy balance at the time of product operation and the energy balance of sound vibration are calculated independently by different simulators, there is a problem that the overall energy balance is not established.

According to the first aspect of the present invention, the sound and vibration simulation program causes the computer to generate sound of the structure attached to the part based on the first parameter and / or the second parameter input as an action from the part. A sound / vibration simulation program for functioning as a sound / vibration simulator for performing vibration simulation, wherein a second parameter having a dimension obtained by dividing a work rate or a work dimension by a dimension of the first parameter is input. Causing the computer to function as a first calculation unit that outputs corresponding to a parameter, or a second calculation unit that outputs corresponding to the second parameter to which the first parameter is input, , Expressed as a function including the first parameter and the first characteristic, the second calculation unit, It is expressed as a function including two parameters and a second characteristic, and the first characteristic and the second characteristic are characteristics that characterize the shape of the structure in the sound vibration simulation, and the first characteristic is the second characteristic. It is a ratio of the dimension of the parameter, and the second characteristic is a ratio of the dimension of the first parameter.

According to the present invention, it is possible to provide a sound vibration simulation model that can be incorporated into a product operation simulator for simulating the operation of the entire product and can examine the energy balance of the entire product.

FIG. 1 is a diagram showing an example of a whole product simulator in which a sound vibration simulation model is incorporated. FIG. 2 is a diagram illustrating an example of a part shape represented by a finite element model. FIG. 3 is a diagram for explaining hardware on which the sound and vibration simulation program according to the present embodiment is executed. FIG. 4 is a diagram illustrating a processing procedure in the overall product simulator. FIG. 5 is a diagram illustrating a comparative example. FIG. 6 shows an example of a functional block diagram.

Hereinafter, embodiments for carrying out the present invention will be described with reference to the drawings.
-First embodiment-
FIG. 1 is a diagram for explaining a first embodiment of the present invention, and is a diagram showing an overall product simulator 13. FIG. 1 is a diagram showing an example of an overall product simulator 13 constructed by incorporating the sound vibration simulation model 10 of the present embodiment into a product operation model. The overall product simulator 13 includes a product operation simulator 3 and two sound vibration simulation models 10.

The product operation simulator 3 has a plurality of part models 4 which are functional models of parts constituting the product. In the part model 4, the physical characteristics of the parts are expressed as lumped constants. The product operation simulator 3 reproduces the energy balance between components during product operation by exchanging the first parameter P1 and the second parameter P2 between the plurality of component models 4. The first parameter P1 and the second parameter P2 express the energy exchanged between the component models 4, and the dimension of the first parameter P1 is the power [J / s] or the work [J]. The dimension is divided by the dimension of the two parameters P2. That is, the product of the dimension of the first parameter P1 and the dimension of the second parameter P2 is the dimension of work [J / s] or work [J]. One of the first parameter P1 and the second parameter P2 corresponds to the above-described difference amount, and the other corresponds to the flow amount.

For example, when the product operation simulator 3 is related to an electric power train of an electric vehicle, the plurality of component models 4 are composed of component models such as an inverter, a motor, a gear box, and a vehicle. In the case of the first parameter P1 and the second parameter P2 exchanged between the inverter and the motor, one is a voltage and the other is a current. In the case of the first parameter P1 and the second parameter P2 exchanged between the motor and the gear box, one is the rotational speed and the other is the torque.

In the example shown in FIG. 1, two sound vibration simulation models 10 </ b> A and 10 </ b> B are provided as the sound vibration simulation model 10. Here, the case where the second component is further attached to the first component attached to the component model 4 is shown as an example. Here, the sound vibration simulation model 10A simulates the vibration of the first part, and the sound vibration simulation model 10B simulates the vibration of the second part.

The sound vibration simulation model 10 receives the first parameter P1 and receives the second parameter P2, the first calculation unit 8 (8A to 8C) that transmits the second parameter P2, the second parameter P2, and the first parameter P1. And the second arithmetic unit 9 (9A to 9C) for transmitting. The first calculation unit 8 is expressed as a function F1 including a first parameter P1 and a first characteristic C1 related to the shape of the component, and the second calculation unit 9 calculates a second characteristic C2 related to the second parameter P2 and the shape of the component. It is represented as a function F2 containing.

That is, the first calculation unit 8 converts the first parameter P1 into the second parameter P2 by the first characteristic C1 as P2 = F1 (C1, P1). Similarly, the 2nd calculating part 9 converts the 2nd parameter P2 into the 1st parameter P1 by the 2nd characteristic C2 like P1 = F2 (C2, P2).

The first characteristic C1 is a dimension ratio of the second parameter P2, and the second characteristic C2 is a dimension ratio of the first parameter P1.

In the case of the part model 4 of the product operation simulator 3, as described above, each part model 4 represents the physical characteristics of the part as a lumped constant. On the other hand, in the sound vibration simulation model 10 of the present embodiment, the characteristics related to the shape of the part are configured by vibration characteristics and stress characteristics at each point obtained by discretizing the shape of the part by modeling using the finite element method. I did it.

FIG. 2 is a diagram illustrating an example of a part shape (part model 20) represented by a finite element model. The part model 20 is represented by a tetrahedron shape having four discrete nodes 200a to 200d. When vibration occurs in the structure of the part represented by the tetrahedral shape in FIG. 2, energy is exchanged between adjacent nodes. That is, each node can be considered to correspond to a part model in the energy model, and the first and second parameters are exchanged between the nodes.

In addition, when connected to another component at a position corresponding to any node, the first parameter P1 and the second parameter P2 are exchanged between the node and the other component connected. The exchange of the first parameter P1 and the second parameter P2 is defined by the first calculation unit 8 (8A to 8C) and the second calculation unit 9 (9A to 9C) shown in FIG. As described above, the first calculation unit 8 and the second calculation unit 9 are expressed as functions including parameters and characteristics, but the shape of the function is determined according to the characteristics to be simulated. For example, here, a function corresponding to the simulation of the vibration of the structure is applied. Although a detailed description of the function determination method is omitted, the same concept as in the case of the energy model in Patent Document 1 can be applied. For example, the component model 4 is configured in the same manner as the functional block when the first parameter P1 and the second parameter P2 are vibration system parameters.

FIG. 6 shows an example of a functional block diagram. The sound vibration simulation model 10 described above is given as a program for executing the processing represented by such a functional block diagram. In the example shown here, in the part model 20 in which the first parameter is expressed as a vibration system of velocity [m / s] and the second parameter is force [N], the second calculation unit 9 is set at the node 200a and the second calculation unit 9 is set at the node 200b. It is a functional block diagram at the time of setting 1 calculating part 8. FIG.

Specifically, the calculation function of the second calculation unit 9 will be described in detail. The second calculation unit 9 receives the second parameter P2A output from the component model 4 and the second parameter P2C transmitted from the first calculation unit 8, and receives the first parameter P1D and the first calculation unit 8 in the component model 4. To the first parameter P1C. Among these, for the second parameter P2A, first, the second characteristic C2 of vibration related to the shape at the node 200a is integrated, and the second parameter P2B is output. Here, the second characteristic is a dimensional ratio of velocity [m / s], and is obtained from eigenvalue analysis of the part model 20 expressed by the finite element method.

Next, the second parameter P2B and the second parameter P2C are input to the first conversion characteristic 201, and the first parameter P1A is output. The function of the first conversion characteristic 201 can be expressed as the following expression (1) using an expression.
First parameter P1A = first conversion characteristic 201
× (second parameter P2B-second parameter P2C)
... (1)

Here, the first conversion characteristic 201 has a function of converting the dimension of the second parameter P2 into the dimension of the first parameter P1, such as the mass characteristic and plastic deformation of the part model 20, and can be obtained by a finite element method or the like. Can do. The output first parameter P1A is branched by a branch 202 into a first parameter P1B directed to the part model 4 and a first parameter P1C directed to the first calculation unit 8. For the first parameter P1B, the second characteristic C2 of vibration relating to the shape at the node 200a is integrated, and the first parameter P1D is output.

Although the detailed description of the first calculation unit 8 is the same as that of the second calculation unit 9, the second conversion characteristic 203 is the dimension of the first parameter P1, such as the rigidity characteristic and viscous friction of the component model 20. It has a function of converting to the dimension of the second parameter P2.

On the other hand, the vibration characteristic of the structure, that is, the vibration characteristic related to the shape at each node is expressed by the first characteristic C1 and the second characteristic C2. A first characteristic C1 and a second characteristic C2 as shown in FIG. 2B are respectively set at the nodes 200a to 200d of the component model 20 shown in FIG. FIG. 2B shows both the case where the product of the dimension of the first parameter P1 and the dimension of the second parameter P2 is the work rate [J / s] and the case of the work [J].

Since the vibration simulation is performed in the sound vibration simulation model 10A, when the product of dimensions is the power [J / s], the first characteristic C1 is represented by the ratio of force [N], and the second characteristic C2 is Expressed as a ratio of velocity [m / s]. This indicates that when a force is applied to a node, a speed that is a constant multiple of the second characteristic C2 is generated at the node. In the vibration simulation, the first parameter P1 is a velocity [m / s] or a displacement [m], and the second parameter P2 is a force [N]. That is, the first computing unit 8 outputs the second parameter P2 of the force dimension from the first parameter P1 of the speed dimension and the first characteristic C1 of the force ratio. The second calculator 9 outputs the second parameter of the speed dimension from the second parameter P2 of the force dimension and the second characteristic C2 of the speed ratio.

Also, when the product of dimensions is work [J], the first characteristic C1 is represented by the ratio of force [N], and the second characteristic C2 is represented by the ratio of displacement [m]. This indicates that when a force is applied to a node, a displacement that is a constant multiple of the second characteristic C2 occurs at that node. Since the part model 20 is a solid element, each node has a three-dimensional motion (displacement), and the velocity, displacement, and force are composed of components in three directions of X, Y, and Z.

2 has four nodes 200a to 200d, any of the nodes can be applied to connection points connected to the component model 4. For example, when the

nodes

200b and 200c are selected as connection points with the component model 4, the first calculation unit 8 or the second calculation unit 9 between the component model 4 and the first characteristic C1 or the second characteristic of the

nodes

200b and 200c It is expressed as a function including two characteristics C2. Since the displacement of one node affects other nodes, for example, the second parameter P2 output from the first calculation unit 8A shown in FIG. 1 is not only the component model 4 but also the second calculation unit 9A. , 9B.

Note that which of the first calculation unit 8 and the second calculation unit 9 is applied to a node that is a connection point with the component model 4 is performed as follows, for example. That is, when the rigidity of the connection point of the component model 4 is sufficiently higher than the rigidity of the connection point of the component model 20, the component model 4 is considered to output a speed [m / s] or a displacement [m]. The first calculation unit 8 that receives them and transmits the force to the component model 4 is applied. Conversely, if the rigidity of the connection point of the part model 4 is sufficiently lower than the rigidity of the connection point of the part model 20, the part model 4 is considered to output a force [N]. A second calculation unit 9 that transmits [m / s] or displacement [m] to the component model 4 is applied.

The database 16A stores a first characteristic C1 and a second characteristic C2 related to the nodes 200a to 200d. The database 16B is a database provided for the sound vibration simulation model 10B and is configured in the same manner as the database 16A.

As shown in FIG. 2B, in the case of a solid element, since one node has six characteristics including the first characteristic C1 and the second characteristic C2, as shown in FIG. In the case of the part model 20 having four nodes, it has 24 characteristics in total. The

first calculation units

8A and 8B and the second calculation units 9A and 9B of the sound vibration simulation model 10A shown in FIG. 1 are configured by adopting some of these 24 characteristics. That is, the total number of degrees of freedom f1 of the database of the first characteristic C1 and the degree of freedom f2 of the database of the second characteristic C2 is determined by the

first calculation units

8A and 8B and the second calculation units 9A and 9B of the sound vibration simulation model 10A. More than the total number.

Thereby, the change of the mounting position can be reproduced by changing the characteristics adopted in the

first calculation units

8A and 8B and the second calculation units 9A and 9B of the sound vibration simulation model 10A. For example, in FIG. 1, when the attachment positions of the component model 4 and the component model 20 are the

nodes

200a and 200b in FIG. 2A, the characteristic of the first calculation unit 8A and the second calculation unit 9A is the node 200a. 200b is used, but by changing the characteristic of the second arithmetic unit 9A to the characteristic of the node 200c, the difference in energy balance when the mounting position is changed can be estimated.

In addition, for example, by rewriting the first characteristic C1 and the second characteristic C2 of the database 16A from the tetrahedral part model 20 to the characteristics of other shape parts, the energy balance of the entire product when the shape is changed is examined. There is an effect that can be done.

When a sound field model is used as the sound vibration simulation model 10, when the product of dimensions is the power [J / s], the dimension of the first parameter P1 is the volume velocity [m ³ / s] The dimension of the second parameter P2 is the sound pressure [Pa]. When the product of dimensions is the dimension of work [J], the dimension of the first parameter P1 is volume [m ³ ], and the dimension of the second parameter P2 is sound pressure [Pa]. Thereby, the energy balance of the whole product can be examined as a work rate or work.

For example, when simulating the noise generated by the vibration of the structure represented by the component model 20, the sound vibration simulation of the sound field model is compared to the sound vibration simulation model 10A that simulates the vibration of the structure. Connect the model 10B. The sound vibration simulation model 10B simulates noise based on the simulation result of the sound vibration simulation model 10A.

FIG. 3 is a diagram showing a schematic configuration of a computer 100 constituting hardware for executing a program (sound vibration simulation program) related to the sound vibration simulation model 10. The computer 100 includes a CPU 101, a memory 102, an input device 103, a hard disk 104, and a display 105. These are connected via a system bus 106. The CPU 101 functions as a control / arithmetic unit of the computer 100 and executes the sound vibration simulation model 10 program. Further, the CPU 101 executes the program of the product operation simulator 3. That is, the entire product simulator 13 includes a program for the product operation simulator 3 and a program for the sound vibration simulation model 10.

The memory 102 is, for example, a RAM (Random Access Memory), functions as a work area of the CPU 101, and stores data being processed. The hard disk 104 stores programs, data, and the like that make up the entire product simulator 13. These programs and data are loaded into the memory 102 by the CPU 101. The input device 103 is a keyboard or a mouse, for example, and functions as an input unit for an operator to input an instruction.

FIG. 4 is a diagram for explaining a processing procedure in the overall product simulator 13. When the process of the whole product simulator 13 is started, first, in step S1, an input / output process of a connection point of a structure which is a sound vibration simulation target is performed. The operator uses the input device 103 to specify a node corresponding to the connection point of the structure. Then, based on the connection point setting information, the node parameters applied to the connection points are read from the database 16 and the computing units corresponding to the connection points are set. For example, the first calculation unit 8 that receives the first parameter P1 and transmits the second parameter P2 is set for the connection point.

In step S2, the input from the connection point to the product operation simulator 3 and the sound vibration simulation model 10 is set. For example, when the connection point of the sound vibration simulation model 10 has the first calculation unit 8, the input to the product operation simulator 3 is the second parameter P 2 transmitted by the first calculation unit 8, and the sound vibration simulation model 10 Is the first parameter P1 received by the first calculation unit 8.

In step S3, numerical integration is performed, the current state of the product motion simulator 3 and sound vibration simulation model 10A corresponding to the input set in step S2 is obtained, and the output from the connection point is calculated. For example, when the connection point of the sound vibration simulation model 10 </ b> A has the first calculation unit 8, the output from the product operation simulator 3 is the first parameter P <b> 1 received by the first calculation unit 8. Is the second parameter P2 transmitted by the first calculation unit 8.

It should be noted that the numerical integration step does not have to be the same between the product motion simulator 3 and the sound vibration simulation model 10. That is, the product motion simulator 3 and the sound vibration simulation model 10 may independently perform numerical integration according to their respective time scales.

In step S4, the continuation of calculation is confirmed. When continuing, it progresses to step S2, and complete | finishes calculation, when complete | finishing.

As described above, the sound vibration simulation model 10 receives the first parameter P1 from the part model and determines the second parameter P2 as the part when the product dimension is the power factor or the work dimension and the first parameter P1 and the second parameter P2. A first calculation unit 8 that transmits to the model, and a first calculation unit 9 that receives the second parameter P2 from the component model and transmits the first parameter P1 to the component model are provided. Therefore, by incorporating such a sound vibration simulation model 10 into the product operation simulator 3, it becomes possible to examine the energy balance of the entire product operation.

As described above, the CPU 101 executes the program (sound and vibration simulation program) of the sound and vibration simulation model 10 according to the present embodiment, so that the computer 100 has the structure attached to the part to be simulated by the part model 4. It functions as a sound vibration simulator that performs sound vibration simulation.

The sound vibration simulation program corresponds to the input first parameter P1 with the second parameter P2 having a dimension obtained by dividing the CPU 101 of the computer 100 by the power or the dimension of the work by the dimension of the first parameter P1. The first computing unit 8 to output or the second parameter P1 having a dimension obtained by dividing the work rate or the work dimension by the dimension of the second parameter P2 and corresponding to the input second parameter P2 It functions as the calculation unit 9. The first calculation unit 8 is expressed as a function including the first parameter P1 and the first characteristic C1, and the second calculation unit 9 is expressed as a function including the second parameter P2 and the second characteristic C2. The first characteristic C1 and the second characteristic C2 are characteristics that characterize the shape of the structure in the sound vibration simulation. The first characteristic C1 is a dimensional ratio of the second parameter P2, and the second characteristic C2 is the second characteristic C2. The ratio of the dimension of one parameter P1.

In this way, the simulation including the exchange of energy between the component model 4 and the sound and vibration simulation model 10 is provided by providing the sound and vibration simulation model 10 with the first calculation unit 8 and the second calculation unit 9 as described above. It can be performed. As a result, the entire product simulator 13 capable of examining the energy balance of the entire product operation can be configured. Moreover, since the 1st calculating part 8 and the 2nd calculating part 9 are functions containing the 1st characteristic C1 and the 2nd characteristic C2 regarding the shape of the components (structure) which are simulation objects, they are three-dimensional part shapes. It is possible to reproduce the sound and vibration characteristics of dependent products more accurately.

FIG. 5 is a diagram showing a comparative example. As described above, the method described in Patent Document 1 cannot directly evaluate the sound vibration performance of a product that depends on the three-dimensional part shape. On the other hand, regarding the evaluation of the sound vibration performance of a product, a method has been proposed in which a three-dimensional shape of a product is modeled by a finite element method or the like, and an excitation force calculated separately outside the model is input and evaluated (for example, JP, 2015-11567, A).

Therefore, when trying to simulate the sound vibration, as shown in FIG. 5, the excitation force is output from the product operation simulator 3 to which Patent Literature 1 is applied, and the excitation force is modeled as described in Patent Literature 2. A method of simulating sound vibration by giving it to the converted sound vibration simulator 6 can be considered.

The product operation simulator 3 reproduces the energy balance between components during product operation by exchanging the first parameter P1 and the second parameter P2 in the plurality of component models 4. Regarding the sound vibration of the corresponding product, the vibration force 5 output from the product operation simulator 3 is applied to the sound vibration simulator 6 to reproduce the sound vibration. Therefore, the energy balance during product operation and the energy balance of sound and vibration are calculated independently by different simulators, and there is a problem that the overall energy balance is not established.

On the other hand, in the present embodiment, since the first calculation unit 8 and the second calculation unit 9 described above are provided and the exchange of energy between the component model 4 and the structure is reproduced, the energy balance of the entire product operation is reduced. The entire product simulator 13 that can be considered can be configured.

Note that the program of the sound and vibration simulation model 10 of the present embodiment can be operated as a single unit, and is not necessarily incorporated into the product operation simulator 3 and operated as the entire product simulator 13.

Further, the hard disk 104 of the computer 100 having the first characteristic C1 and the second characteristic C2 associated with the nodes 200a to 200d, the first characteristic C1 and the second characteristic C2 associated with the nodes 200a to 200d, That is, it functions as a data storage unit that stores the database 16A. Thereby, the change of the mounting position can be reproduced by changing the characteristics adopted in the first calculation unit 8 and the second calculation unit 9 of the sound vibration simulation model 10, and the energy balance when the mounting position is changed. It is possible to estimate the difference. In addition, by rewriting each characteristic of the database 16A to a characteristic when the shape of the structure is changed, it is possible to easily cope with a change in the shape of the structure.

Although various embodiments and modifications have been described above, the present invention is not limited to these contents. Other embodiments conceivable within the scope of the technical idea of the present invention are also included in the scope of the present invention.

3 ... Product operation simulator, 4, 20 ... Parts model, 8, 8A to 8C ... First calculation unit, 9, 9A-9C ... Second calculation unit, 10, 10A, 10B ... Sound vibration simulation model, 13 ... Entire product Simulator, 16A, 16B ... database, 100 ... computer, 101 ... CPU, P1 ... first parameter, P2 ... second parameter

Claims

A sound and vibration simulation program for causing a computer to function as a sound and vibration simulator for performing sound and vibration simulation of a structure attached to a part based on the first parameter and / or the second parameter input as an action from the part Because
A first computing unit that outputs a second parameter having a dimension obtained by dividing a work rate or a work dimension by the dimension of the first parameter, corresponding to the input first parameter, or input the first parameter The computer is caused to function as a second calculation unit that outputs in response to the second parameter,
The first calculation unit is expressed as a function including the first parameter and a first characteristic,
The second calculation unit is represented as a function including the second parameter and a second characteristic,
The first characteristic and the second characteristic are characteristics that characterize the shape of the structure in the sound vibration simulation,
The sound vibration simulation program, wherein the first characteristic is a dimensional ratio of the second parameter, and the second characteristic is a dimensional ratio of the first parameter.
In the sound and vibration simulation program according to claim 1,
The sound vibration simulator is a sound vibration simulation program for performing sound vibration simulation by discretizing the shape of the structure attached to the component into a plurality of nodes.
In the sound vibration simulation program according to claim 2,
Having the first characteristic and the second characteristic associated with the node;
A sound and vibration simulation program that causes the computer to function as a data storage unit that stores the first characteristic and the second characteristic associated with the node.
In the sound and vibration simulation program according to claim 3,
Causing the computer to function so as to have one or more of the first calculation unit or the second calculation unit;
The sound vibration simulation program, wherein the total number of the first characteristics and the second characteristics stored in the data storage unit is equal to or greater than the total number of the first calculation unit and the second calculation unit.