JPH1153422A - Device and method for supporting optimum design and electromagnetic measuring instrument - Google Patents

Abstract

PROBLEM TO BE SOLVED: To support the optimization of a distribution of property values of components of electric equipment. SOLUTION: A target electromagnetic field distribution and a design evaluation function are received by an input/output process part 520 and an electromagnetic field distribution calculation part 540 finds an electromagnetic field distribution of a parameter distribution including at least one kind of decision parameter distribution. A parameter distribution optimization part 560 improves the decision parameter distribution so that the difference distribution between the found electromagnetic field distribution and target electromagnetic field distribution becomes minimum and when the value of the design evaluation function meets convergence conditions, the decision parameter distribution is displayed by the input/output part 520, but when not, the improved decision parameter is sent to the electromagnetic field distribution calculation part 540 to repeat the process.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an optimum design support apparatus and method capable of optimizing a determination parameter including physical property values of a part, and an electromagnetic measuring apparatus for measuring physical property values of an object to be measured. In particular, in the optimal design of parts constituting an electric device, design support suitable for determining distribution values such as magnetoresistance, conductivity, and applied current density so that the value of the design evaluation function is minimized. Apparatus and method, and magnetoresistivity, conductivity in the measured object,
The present invention relates to an electromagnetic measurement device capable of measuring a distribution value such as an applied current density.

[0002]

2. Description of the Related Art A conventional electromagnetic field analysis apparatus executes an electromagnetic field analysis in accordance with an electromagnetic field analysis program based on a numerical analysis method such as a finite element method or a boundary element method, and based on input design parameters, an electromagnetic field distribution and a loss. We are doing analysis to find such. In the design using such an electromagnetic field analysis device, the evaluation of the analysis result and the improvement of the design parameters based on the evaluation are left to the designer.

In recent years, in some electromagnetic field analyzers, the flatness of an electromagnetic field distribution and the degree of coincidence with a specified electromagnetic field distribution at a specified site are used as a design evaluation function, and the localization of a component such as a magnetic material or a coil is performed. A function is added to determine the basic shape and dimensions so that the design evaluation function is minimized.

[0004] Regarding the current state of electromagnetic field analysis technology having such a design parameter optimization function, see IEEJ Technical Report No. 611, "Electromagnetic field analysis and its application to inverse and optimization problems" (October 1996). A comprehensive report on recent trends in the problem of optimization of electromagnetic fields has been reported.

[0005]

DISCLOSURE OF THE INVENTION The present inventors are studying to make an optimal design in consideration of miniaturization and weight reduction of components and to promote miniaturization and weight reduction of electric equipment.

On the other hand, if recent advances in material development are applied, the distribution of physical properties in the materials constituting parts,
It is expected that the topology (phase) of the shape of the part can be used as a design target. For example, it is conceivable to control the distribution of the magnetic resistivity by unevenly distributing the composition ratio of the composite material. By optimizing the distribution of such physical property values and the topology, the inventors can make the realized electromagnetic field distribution closer to the target, and further consider the amount other than the electromagnetic field distribution, for example, the weight of parts. We are considering making an optimal design.

However, the conventional electromagnetic field analyzer does not have the function of optimizing the determined parameters, or even if it does, the design evaluation function determines the flatness and the degree of coincidence of the electromagnetic field distribution. Is limited to In addition, the determination parameters that can be determined are limited to the local shape and dimensions of the part, and the topology of the part shape,
It is not considered that the property values of the materials constituting the parts are to be determined.

On the other hand, when performing physical measurement, the measurable amount is limited to the strength of a field, for example, an electric field or a magnetic field in electromagnetic measurement. For this reason, it is difficult to measure the current density distribution inside the object to be measured and to measure the physical properties, for example, the magnetic resistivity and the dielectric constant, without destroying the measured object.

According to the present invention, a design evaluation function including an arbitrary variable is set using physical property values of a material as a determination parameter, and an optimal design that can optimize the determination parameter so as to minimize the design evaluation function. A first object is to provide a support device.

It is a second object of the present invention to provide an electromagnetic measuring device capable of measuring the physical properties of a material.

[0011]

According to a first aspect of the present invention, there is provided an optimum design support apparatus for supporting an optimum design relating to an electromagnetic field, wherein a governing equation representing a phenomenon in the electromagnetic field is provided. An input / output processing means for receiving a design evaluation function representing an objective of optimal design, an initial set value of a decision parameter distribution to be determined, and outputting an optimized decision parameter distribution, and a decision parameter distribution Electromagnetic field distribution calculating means for obtaining the electromagnetic field distribution in the parameter distribution based on the governing equation, and parameter distribution optimizing means for obtaining an optimized parameter distribution so that the design evaluation function is minimized. The parameter distribution optimizing means detects that the design evaluation function fluctuates in accordance with a change in the determined parameter distribution. Parameter sensitivity distribution calculation means for obtaining a determined parameter sensitivity distribution indicating the distribution of the parameter distribution, and parameter distribution calculation for obtaining a determined parameter distribution improved so that the design evaluation function is reduced using the determined parameter sensitivity distribution And an optimal design support apparatus characterized by comprising:

According to a second aspect of the present invention, there is provided an optimal design support apparatus for supporting an optimal design relating to a temperature field, wherein a governing equation representing heat conduction in the temperature field, a design evaluation function representing a target of the optimal design, And an input / output processing means for receiving an initial set value of the determined parameter distribution to be determined, and outputting an optimized determined parameter distribution, and a temperature field distribution in the parameter distribution including the determined parameter distribution as the governing equation. Temperature field distribution calculation means for obtaining a parameter distribution optimization means for obtaining an optimized parameter distribution such that the design evaluation function is minimized, wherein the parameter distribution optimization means comprises: A decision parameter sensitivity distribution indicating a sensitivity distribution in which the design evaluation function fluctuates with a change in the decision parameter distribution is calculated. And a parameter distribution calculating means for obtaining a decision parameter distribution improved so that the design evaluation function is reduced using the determined parameter sensitivity distribution. An optimal design support device is provided.

According to a third aspect of the present invention, there is provided an optimal design support apparatus for supporting an optimal design relating to an electromagnetic field and a temperature field, wherein a governing equation representing a phenomenon relating to the electromagnetic field and the temperature field, and a design representing a target of the optimal design. An evaluation function, input / output processing means for receiving an initial set value of a determined parameter distribution to be determined, and outputting an optimized determined parameter distribution; and an electromagnetic field distribution and a temperature field in the parameter distribution including the determined parameter distribution. Numerical analysis means for performing a numerical analysis for obtaining a distribution based on the governing equation, and a parameter distribution optimizing means for obtaining an optimized parameter distribution so that the design evaluation function is minimized, The parameter distribution optimizing means changes the design evaluation function with a change in the determined parameter distribution. Parameter sensitivity distribution calculating means for determining a determined parameter sensitivity distribution indicating a distribution of sensitivity, and a parameter for obtaining a determined parameter distribution improved so that the design evaluation function is reduced using the determined parameter sensitivity distribution. An optimal design support device characterized by comprising distribution calculation means is provided.

According to a fourth aspect of the present invention, there is provided an optimal design support apparatus for supporting an optimal design using an analysis apparatus for performing a finite element analysis, wherein a governing equation to be analyzed by the analysis apparatus, an optimal design target Accepts a design evaluation function that represents and an initial set value of a decision parameter distribution to be determined,
Input / output processing means for outputting an optimized decision parameter distribution, the accepted governing equation, and a parameter distribution including the decision parameter distribution to the analyzer, and accepting the analyzed field quantity Interface means for obtaining, based on the amount of the field received by the interface means, a parameter distribution optimization means for obtaining a parameter distribution optimized so that the design evaluation function is minimized, The parameter distribution optimizing means uses a parameter sensitivity distribution calculating means for obtaining a determined parameter sensitivity distribution indicating a sensitivity distribution in which the design evaluation function varies with a change in the determined parameter distribution, and the determined parameter sensitivity distribution. The decision parameter distribution improved so that the above-mentioned design evaluation function becomes small Optimal design support apparatus characterized in that it is configured with a parameter distribution calculating means for Mel is provided.

According to a fifth aspect of the present invention, there is provided an optimal design support apparatus for supporting an optimal design relating to an electromagnetic field in an analysis target space divided into a plurality of finite elements,
A parameter distribution memory for storing, in advance, a parameter distribution which is a distribution value of parameters of a magnetoresistance, an applied current density, a charge density, and a dielectric constant in each finite element of the design target space; An electromagnetic field distribution memory for storing an electromagnetic field distribution which is a value of an electromagnetic field in each finite element in space; a decision parameter of at least one of the above parameters; and a decision parameter distribution comprising at least a part of the plurality of finite elements Input means for inputting an area and a parameter distribution stored in the parameter distribution memory, and calculating an electromagnetic field distribution in the analysis target space by solving a potential equation that determines an electromagnetic field; Electromagnetic field distribution calculation means for storing the distribution in the electromagnetic field distribution memory, From the difference distribution in the target electromagnetic field distribution area between the electromagnetic field distribution stored in the electromagnetic field distribution memory and the target electromagnetic field distribution, the variation of the parameter distribution of the decision parameter in the decision parameter distribution area becomes the variation of the difference distribution. Parameter sensitivity distribution calculating means for calculating a parameter sensitivity distribution representing the effected sensitivity distribution, and using the sensitivity distribution calculated by the parameter sensitivity distribution calculating means, the determined parameter distribution area so as to minimize the difference distribution. A parameter distribution calculating means for calculating the parameter distribution of the determined parameter in the parameter distribution memory and storing the parameter distribution in a corresponding part of the parameter distribution memory; and a display means for displaying the distribution of the determined parameter stored in the parameter distribution memory. An optimal design support apparatus characterized by having the above is provided.

According to a sixth aspect of the present invention, there is provided a recording medium storing an optimum design support program for supporting an optimum design using a computer, wherein the optimum design support program executes an optimum design for an electromagnetic field. In an optimal design support device for supporting, a governing equation representing a phenomenon in an electromagnetic field, a design evaluation function representing a goal of optimal design, and an initial set value of a decision parameter distribution to be determined are received, and the optimized decision parameter distribution is determined. An input / output processing procedure for outputting, an electromagnetic field distribution calculation procedure for obtaining an electromagnetic field distribution in a parameter distribution including a determined parameter distribution based on the governing equation, and the design evaluation function are optimized so as to be minimized. And a parameter distribution optimization procedure for obtaining the parameter distribution. The parameterization procedure is a parameter sensitivity distribution calculation procedure for obtaining a decision parameter sensitivity distribution indicating a sensitivity distribution in which the design evaluation function fluctuates with a change in the decision parameter distribution, and using the decision parameter sensitivity distribution, And a parameter distribution calculation procedure for obtaining a decision parameter distribution improved so that the design evaluation function is reduced.

According to a seventh aspect of the present invention, there is provided an optimal design method for optimally designing a parameter distribution of an electromagnetic field so as to minimize a design evaluation function which is a function of the distribution of the electromagnetic field. An electromagnetic field equation established in the analysis target space, an initial set value of a decision parameter distribution to be optimally designed, and a design evaluation function representing a target of the optimal design are received. (2) From the electromagnetic field equation and the design evaluation function, the design Determine a decision parameter sensitivity distribution which is a gradient with respect to the decision parameter distribution of the evaluation function,
(3) determining the distribution of the electromagnetic field in the parameter distribution including the determined parameter; (4) determining the provisional increment of the determined parameter in the obtained distribution of the electromagnetic field; (5) vector potential accompanying the change in the determined parameter distribution The sensitivity vector potential indicating the change of is obtained from the electromagnetic field equation using the obtained provisional increment,
(6) The decision parameter distribution is improved so as to minimize the design objective function. (7) If the amount of improvement in which the decision parameter distribution is improved is smaller than a predetermined threshold, the improved decision parameter is improved. Is the optimal design value,
Otherwise, there is provided an optimal design method characterized by repeating the above steps (3) and after for the parameter distribution including the improved decision parameter.

According to an eighth aspect of the present invention, there is provided an electromagnetic measurement apparatus for measuring a distribution of physical property values on an object to be measured, the object space including the object to be measured. Electromagnetic field measurement means for measuring the electromagnetic field distribution in, the electromagnetic field equation, measurement evaluation function representing the measurement state, and accepts the initial set value of the physical property value to be measured, and outputs the distribution of the measured physical property value Input / output processing means, an electromagnetic field distribution calculating means for calculating an electromagnetic field distribution in a parameter distribution including a distribution of physical property values to be measured based on the electromagnetic field equation, and an electromagnetic field distribution measured by the electromagnetic field measuring means, Physical property value calculating means for obtaining a physical property value distribution in which the difference distribution from the electromagnetic field distribution calculated by the electromagnetic field distribution calculating means is minimized, The calculating means is a property value sensitivity distribution calculating means for obtaining a property value sensitivity distribution indicating a sensitivity distribution in which the difference distribution fluctuates with the change in the property value distribution, and using the property value sensitivity distribution, There is provided an electromagnetic measurement device characterized by comprising physical property value calculation means for obtaining a physical property value distribution improved so as to reduce the difference distribution.

[0019]

Embodiments of the present invention will be described below with reference to the drawings.

In the following description, j is an imaginary unit (√
(-1)). ∇ is a differential operator, the symbol “•” represents an inner product of vectors, and the symbol “x” represents an outer product of vectors. The dot “•” attached to the upper part of the symbol represents the derivative of the amount represented by the symbol with respect to time.

First, a first embodiment of the present invention will be described with reference to FIG. The optimal design support device according to the present embodiment is for supporting optimal design for an electromagnetic field.

The basic processing procedure in the optimal design support apparatus according to the present embodiment is as follows: (a) With the initial set values of the decision parameters as inputs, the vector potential is determined according to the governing equation of the electromagnetic field. Evaluate with a function to improve the decision parameters. Then, (c) an improved decision parameter is substituted into the input for obtaining the vector potential, and the procedure of (a) to (b) is repeated. Here, in improving the above-mentioned decision parameter, a gradient regarding the decision parameter of the design evaluation function is used. This makes it possible to increase the speed and certainty of iterative convergence.

In FIG. 1, an optimal design support apparatus 500 according to the present embodiment accepts a governing equation, a design evaluation function, and an initial set value of a decision parameter distribution, and outputs an optimized decision parameter distribution. An output processing unit 520, an electromagnetic field distribution calculation unit 540 for obtaining an electromagnetic field distribution at an initial set value of the determined parameter distribution based on the governing equation, and a parameter optimized so that the design evaluation function is minimized. A parameter distribution optimizing unit 560 for obtaining a distribution.

The parameter distribution optimizing section 560 includes a parameter sensitivity distribution calculating section 570 for obtaining a determined parameter sensitivity distribution indicating a sensitivity distribution in which the design evaluation function varies with a change in the determined parameter distribution. And a parameter distribution calculation unit 580 for obtaining a decision parameter distribution improved so as to reduce the design evaluation function using the decision parameter sensitivity distribution.

Next, referring to FIG. 1, an outline of the operation of the optimal design support apparatus according to the present embodiment will be described.

First, in the input / output processing unit 520,
A governing equation describing a natural phenomenon to be analyzed, a type of a decision parameter to be optimally designed and its initial set value, and a design evaluation function for evaluating a difference between a state to be a design target and a design evaluation function are accepted.

Next, in the electromagnetic field distribution calculation section 540, the distribution of the electromagnetic field is calculated based on the governing equation, with the initial setting value of the distribution of the decision parameter as an input.

The parameter distribution optimizing unit 56
At 0, the distribution of the decision parameters is improved so that the design evaluation function becomes smaller.

In improving the distribution of the decision parameters, first, the parameter sensitivity distribution calculation unit 570 obtains the distribution of the decision parameter sensitivity using the solution function of the electromagnetic field equation determined from the governing equation and the design evaluation function.
Next, a variation equation of the design evaluation function with respect to the change of the decision parameter is obtained based on the distribution of the decision parameter sensitivity.

Then, the parameter distribution calculation unit 580 obtains a distribution of the determined parameters improved so as to minimize the variation equation of the design evaluation function.

Next, it is determined whether or not a predetermined convergence determination condition is satisfied, and when the convergence determination condition is satisfied, the obtained distribution of the determined parameters is sent to the input / output processing unit 520. When the convergence determination condition is not satisfied, the distribution of the determined decision parameter is provided to the electromagnetic field distribution calculation unit 540, and the above-described processing is repeated.

Next, the operation of the present invention for improving the determination parameter will be described by taking a case of an alternating magnetic field as an example.

In this case, the following equation (a
The electromagnetic field equation represented by 1) holds.

[0034]

(Equation 1)

In the equation (a1), A is the vector potential, λ is the magnetic resistivity, σ is the conductivity, and J is the applied current density. These are functions related to the position in the analysis target space V, that is, the distributions of the respective physical quantities. Ω is the angular frequency of the applied current density J.

The above-mentioned design evaluation function represents a target of the optimal design as a state in which the function is minimized. For example, as a design evaluation function corresponding to the equation (a1), the following equation (a2)
Can be set.

[0037]

(Equation 2)

In the equation (a2), the vector potential A and the magnetic flux density B are determined when the magnetoresistance λ, the conductivity σ, and the applied current density J are given.

Equation (a2) is used as the determination parameter.
, The conductivity σ, the applied current density J
At least one of the following.

As the design evaluation function F in the equation (a2), for example, the flatness of the electromagnetic field in a predetermined area on the analysis target space V, the degree of coincidence indicating the degree of coincidence with the predetermined electromagnetic field, Loss L and the like can be set.

The loss L is determined by the above-mentioned conductivity σ and the vector potential A.

[0042]

(Equation 3)

Can be expressed as follows.

The improvement of the decision parameter in the present invention is as follows.
The determination is performed using a gradient relating to a decision parameter of the design evaluation function (hereinafter, referred to as a decision parameter sensitivity distribution) and a sensitivity vector potential.

Magnetic resistivity λ, conductivity σ, applied current density J
For each of the above decision parameter sensitivity distributions Δλ, Δ
σ, ΔJ are (here, the subscript parameter of Δ (λ,
σ, J, etc.) indicate a sensitivity distribution for the parameter. In the text, a character indicating a parameter is written after Δ to indicate a subscript. ), An electromagnetic field equation defined by the vector potential A and the equations (a1) and (a2),

[0046]

(Equation 4)

The following equations (a4) to (a6) are obtained using the adjoint vector potential Ψ which is the solution function of

[0048]

(Equation 5)

Equations (a4) to (a6) give the determined parameter sensitivity distributions Δλ, Δσ, ΔJ when the magnetoresistance λ, conductivity σ, and applied current density J are the determining parameters, respectively. These decision parameter sensitivity distributions Δλ, Δσ, Δ
J is a function relating to a position in the analysis target space V, that is, a distribution.

Since the decision parameter sensitivity distribution is a gradient of the design evaluation function, the design evaluation function increases when the magnetoresistance, conductivity, and applied current density are changed in the direction of the decision parameter sensitivity distribution.

Next, the parameter (λ, σ, J, A,
B, etc.) to indicate the parameter change (in the text, the letter indicating the parameter is written after δ to represent the suffix), the magnetoresistance λ, the conductivity σ When the applied current density J changes as follows: λ → λ + δλ, σ → σ + δσ, J → J + δJ, and the variation of the vector potential A is A → A + δA, the sensitivity vector potential δA is represented by the electromagnetic field equation

[0052]

(Equation 6)

Is calculated as the solution function of According to equation (a7), when t is an arbitrary positive number and is changed as follows: λ → λ−tδλ, σ → σ−tδσ, J → J−tδJ, the changes in the vector potential A and the magnetic flux density B are A → A−tδA, B → B−t∇ × δA = B−tδB The value of the design evaluation function at this time is

[0054]

(Equation 7)

Changes as follows. Where α and β are λ, σ,
J, A, and B are meant.

More specifically, for example, the magnetic resistivity λ,
When the conductivity σ and the applied current density J are all determined parameters, the convergence repetition by the optimal design support apparatus in the present embodiment is performed according to the following procedure.

<Step S1> An initial set value of the decision parameter is input.

<Step S2> The electromagnetic field equation of the equation (a1) is solved to determine the vector potential A and the magnetic flux density B.

<Step S3> An associated vector potential is obtained by solving the electromagnetic field equation of equation (a3), and using this and the vector potential obtained in step S2,
The determined parameter sensitivity distribution is calculated according to the equations (a4) to (a6).

<Step S4> Next, the sum R of the determined parameter sensitivity distribution is obtained according to the following equation (a9).

[0061]

(Equation 8)

Then, s = R / (R at the previous iteration) is obtained, and a provisional increment of the decision parameter is determined by the following equation (a10).

[0063]

(Equation 9)

Using the provisional increment of this decision parameter,
The sensitivity vector potential is obtained by the electromagnetic field equation (a7), and the decision parameters are improved so as to minimize the variation equation (a8) of the design evaluation function. That is, the following equation (a
11) The decision parameters are improved according to (a12).

[0065]

(Equation 10)

<Step S5> If the improvement amount of the decision parameter is sufficiently small, the repetition ends. If not, the process returns to step S2.

The processing procedure described above is a procedure performed when the magnetoresistance σ, the conductivity λ, and the applied current density J are simultaneously determined parameters. If any of these parameters is not a decision parameter (not a target for optimal design), the processing corresponding to that parameter is omitted in the above-described processing procedure.

The electromagnetic field equations (a1), (a
As a method for solving 3) and (a7), for example, a numerical analysis method such as a finite element method can be used. In the finite element method, the analysis target space is divided by meshes (finite elements), and an approximation formula (section polynomial) introduced for each mesh
Is selected as a basis function (shape function) and is approximately obtained.

Here, in applying the finite element method to the electromagnetic field equation (a3), when the basis function of the finite element method is represented by N _i ,

[0070]

[Equation 11]

The following calculation appears. In the present invention, instead of performing this calculation,

[0072]

(Equation 12)

Is executed. Thereby, calculation accuracy can be ensured.

In the above description, the case where an alternating magnetic field is targeted has been described, but the natural phenomenon that can be targeted by the present invention is not limited to this. For example, other natural phenomena related to an electromagnetic field include a static magnetic field, an unsteady magnetic field, and the like.

In the case of a static magnetic field, the above-mentioned governing equation, the electromagnetic field equation, is given by the following equation (b1).

[0076]

(Equation 13)

In the equation (b1), M is a magnetization vector, and λ ₀ is a magnetic resistivity of air.

The design evaluation function F can be defined as the following equation (b2) as a function including at least one of the above-described magnetoresistance λ, applied current density J, and magnetization vector M.

[0079]

[Equation 14]

And the adjoint equation is

[0081]

(Equation 15)

Is expressed as follows.

Therefore, in the case of a static magnetic field, the magnetic resistivity λ,
When the applied current density J and the magnetization vector M are the decision parameters, the respective decision parameter sensitivities Δλ, ΔJ, and ΔM are:

[0084]

(Equation 16)

Is obtained.

Similarly, when a natural phenomenon of an unsteady magnetic field is targeted, an electromagnetic field equation which is a governing equation is expressed by the following equation (c
Given by 1).

[0087]

[Equation 17]

The design evaluation function is one of the above-described magnetoresistance λ, conductivity σ, applied current density J, magnetization vector M, and time derivative of vector potential A (represented by dots on symbol A). Can be set as in the following equation (c2).

[0089]

(Equation 18)

The adjoint equation is:

[0091]

[Equation 19]

[0092]

Accordingly, when the magnetoresistance λ, conductivity σ, applied current density J, and magnetization vector M are used as decision parameters in the case of an unsteady magnetic field, the respective decision parameter sensitivities Δλ, Δσ, ΔJ , ΔM are

[0094]

(Equation 20)

Is obtained by

Therefore, corresponding to the natural phenomenon of interest,
By substituting the governing equations for the electromagnetic field equation, design evaluation function, adjoint equation, and decision parameter sensitivity, optimal design can be supported in the same manner as the above-described processing procedure.

As described above, as the first embodiment of the present invention,
The case where the optimal design support apparatus is used for optimal design in which an electromagnetic field is analyzed has been described. For a natural phenomenon to which the present invention is applied, a governing equation of the phenomenon is described by a differential process, for example, a diffusion differential equation. Anything can be used. In this case, the electromagnetic field distribution calculation unit 540 (see FIG. 1) only needs to be able to perform an analysis for obtaining a physical quantity (amount of a field) by inputting a parameter group including a decision parameter according to the differential equation. Such an analysis can be performed, for example, by applying the finite element method described above. Also,
Other analysis methods include a difference method and a boundary element method.

The natural phenomena for which the above-mentioned diffusion differential equation is satisfied include, more specifically, for example, heat conduction and material diffusion. The physical quantities in the heat conduction are temperature and heat flux, and in Fourier's law, which is a natural law representing this phenomenon, the temperature and heat flux are related by a heat conduction coefficient. The governing equation for this phenomenon is called the heat conduction equation. The physical quantities in the substance diffusion are a concentration and a substance flux, and the concentration and the substance flux are related by a diffusion coefficient in Fick's law which is a natural law representing this phenomenon. The governing equation for this phenomenon is called the diffusion equation.

The present invention can be applied not only to the above-mentioned optimum design for individual natural laws such as the electromagnetic field, heat conduction, and material diffusion but also to the optimum design for a composite phenomenon involving a plurality of natural laws. Such complex phenomena include, for example, generation of Joule heat due to electric current and its conduction, and / or
Alternatively, there is a composite phenomenon in which a change in conductivity due to temperature occurs.

Next, a second embodiment of the present invention will be described with reference to FIGS.

First, with reference to FIG. 10 and FIGS. 3 to 5, an outline of the optimal design support apparatus according to the present embodiment will be described. The optimal design support apparatus according to the present embodiment targets an analysis target space obtained by dividing a subspace mesh in a specified coordinate space, and in a specified target electromagnetic field distribution area, an electromagnetic field distribution value and a specified target electromagnetic field distribution value. Of the parameters of magnetoresistance, applied current density, dielectric constant and charge density so that the difference
This is for calculating the value of the decision parameter designated by the input in the decision parameter distribution area designated by the input.

In FIG. 3, the optimal design support device
As shown in (1), an analysis is performed by designating an analysis target space 9 obtained by dividing a subspace 90 of a coordinate space including a part or the whole of an electric machine by a mesh (finite element, that is, a space element having a finite area) 99. In the target electromagnetic field distribution area 51 (described later), the magnetic resistance, the applied current density, and the like are set so that the difference between the electromagnetic field distribution value obtained by the calculation described later and the target electromagnetic field distribution value specified by the input is minimized. Among the parameters of the permittivity and the charge density, the value of the determined parameter specified by the input is calculated in a determined parameter distribution area 52 described later specified by the input.

Here, for the mesh 99, a triangle or a quadrangle is used for two-dimensional analysis, and a tetrahedron or hexahedron is used for three-dimensional analysis. This embodiment can be implemented regardless of the number of dimensions of the analysis target space 9 and the shape of the mesh. Hereinafter, the two-dimensional subspace 90
The analysis target space 9 in which the mesh 99 is divided by the mesh 99 will be described. Note that an identifier is assigned to each of the divided meshes. For example, a consistent number can be used as the identifier.

The analysis target space will be described with reference to FIGS.

As the partial space, for example, a space including one or more parts of an electric machine and air can be selected. More specifically, for example, as shown in FIG. 3A, an electric part 91 and a partial space 90 containing air 95 can be selected. For this subspace 90, for example,
As shown in FIG. 3B, the analysis target space 9 can be defined by performing mesh division. In FIG. 3A, a two-dimensional space is selected as the subspace 90, and the two-dimensional analysis is performed. Accordingly, the analysis target space 9 is defined by being divided by a polygonal mesh. In FIG. 3B, a quadrilateral mesh is drawn, and its grid points 98 are drawn. Note that a triangular mesh can also be used.

Also, a subspace 90 of the three-dimensional space is selected,
When performing a three-dimensional analysis, an analysis target space 9 divided by a tetrahedral or hexahedral mesh is defined.

Referring to FIG. 4, the target electromagnetic field distribution area 5
1 will be described.

In FIG. 4, the target electromagnetic field distribution area 51 is
It is composed of a group of points or a group of meshes belonging to the analysis target space 9. FIG. 4A shows a target electromagnetic field distribution area 51 composed of a point group, and FIG. 4B shows a target electromagnetic field distribution area 51 composed of a mesh group.

With reference to FIG. 5, the above-mentioned determined parameter distribution area will be described.

In FIG. 5, the decision parameter distribution area 52
Is further composed of one or more partial areas 521. The sub-region 521 is composed of a single or a plurality of mesh groups, and is operated in one sub-region 521 so as to be specified by an input and to have a constant value of a parameter to be calculated.

Next, the configuration of the optimal design support apparatus according to the present embodiment will be described with reference to FIG.

Referring to FIG. 10, an optimal design support apparatus according to the present embodiment includes an operation unit 1, a storage unit 2, and a display control unit 3.
, A display 4, and reception units 5 and 6.

The storage section 2 stores a program storage section 2 for storing a program read and operated by the operation section 1.
1, a mesh data storage unit 22 for storing mesh data including coordinate values of all grid points 98 in the analysis target space 9 and grid points constituting each mesh;
A parameter distribution memory 23 for storing values such as a magnetic resistivity, an applied current density, a dielectric constant and a charge density in each mesh, and an electromagnetic field distribution memory 24 for storing a calculated electromagnetic field distribution and the like described later are provided. I have.

In the present embodiment, the storage unit 2 has a hard disk device and a semiconductor memory. Further, in the present embodiment, the values of the magnetic resistivity, the applied current density, the permittivity, and the charge density for each mesh in the analysis target space 9 are respectively referred to as a magnetoresistive distribution, an applied current density distribution, and a permittivity. These are called distribution and charge density distribution, and these are collectively called parameter distribution.

The operation unit 1 includes an input / output processing unit 11, an electromagnetic field calculation unit 12, a parameter sensitivity distribution calculation unit 13, and a parameter distribution calculation unit 14. These operations are realized by the operation unit 1 reading a program stored in the program storage unit 21 of the storage unit 2 and executing a process according to a procedure described in the program. As the arithmetic unit 1, a computer that performs processing according to a program describing a processing procedure, for example, a general-purpose computer can be used. In the present embodiment, a description will be given on the assumption that a workstation or a personal computer is used as the arithmetic unit 1.

The receiving section 5 is composed of a keyboard or the like.
The receiving unit 6 includes an input display unit 4 displayed on the display 4.
2 and means for receiving a user's instruction on the result display section 41, and is constituted by a mouse or the like. The data received by the receiving unit 5 from the user includes an instruction from the user by picking an icon, a determination parameter, the number of points when the target electromagnetic field distribution area 51 is a point group, their coordinate values, a target electromagnetic field value, and a target electromagnetic field distribution area. Reference numeral 51 denotes a target electromagnetic field distribution function and a calculation convergence determination condition value when the mesh group is used. The data received by the receiving unit 6 from the user includes designation of a mesh group when the target electromagnetic field distribution region 51 is a mesh group, and designation of a mesh group constituting each subregion 521 of the decision parameter distribution region 52 of the decision parameter. In the present embodiment, a target electromagnetic field value when the target electromagnetic field distribution area 51 is a group of points and a target electromagnetic field distribution function when the target electromagnetic field distribution area 51 is a group of meshes are collectively referred to as a target electromagnetic field distribution.

The result display section 41 of the display 4 also has a function of displaying an electromagnetic field distribution, a parameter distribution, and the like in a manner superimposed on the analysis target space 9 according to a user's specification.

The display control unit 3 controls the display of the display 4 and controls the receiving operation of the receiving unit 6.

Next, the operation of the optimal design support apparatus according to the present embodiment will be outlined first with reference to FIG. 2 and then the details of the processing of each step will be described.

First, the overall operation will be described with reference to FIG.

The input / output processing unit 11 of the arithmetic unit 1 reads the program stored in the program storage unit 21 and executes steps S101 and S105 in FIG. Similarly,
The electromagnetic field distribution calculator 12 executes step S102, the parameter sensitivity distribution calculator 13 executes step S103, and the parameter distribution calculator 14 executes step S104.

Specifically, step S101 is a step of preparing for the operation following step S102. The input / output processing unit 11 reads mesh data of the analysis target space 9 stored in the mesh data storage unit 22 of the storage unit 2 in advance, and displays the mesh data on the input display unit 42 of the display 4. After that, they are sequentially input from the receiving units 5 and 6,
The decision parameter, the decision parameter distribution area 52, the target electromagnetic field distribution area 51, the target electromagnetic field distribution, and the convergence condition value of the operation are received, and the preparation for the operation in step S102 and thereafter is completed.

Step S102 is a step for calculating an electromagnetic field distribution or the like by solving a potential equation described later derived from Maxwell's electromagnetic field equation. The electromagnetic field distribution calculation unit 12 reads the mesh data and the parameter distribution stored in advance in the mesh data storage unit 21 and the parameter distribution memory 22 of the storage unit 2, and performs the above-mentioned calculation using a numerical analysis method such as a difference method or a finite element method. Is solved to calculate the electromagnetic field distribution and the like, and write it to the electromagnetic field distribution memory 24. In the present embodiment, the finite element method is assumed as the numerical analysis method, but the present embodiment does not require any essential change even if other methods are used.

The step S103 is the same as the electromagnetic field distribution memory 2
4 is calculated and the difference distribution between the electromagnetic field distribution stored in step S101 and the target electromagnetic field distribution determined in step S101 is calculated.
This is a step for calculating the sensitivity of a change in the value of the determination parameter similarly determined in step S101 in the determination parameter distribution area 52 determined in step 101 to the variation in the difference distribution. In the present embodiment, a pair of the decision parameter distribution region 52 of the decision parameter and the sensitivity is referred to as a decision parameter sensitivity distribution of the decision parameter.

Step S104 uses the decision parameter sensitivity distribution determined in step S103 to minimize the difference distribution calculated in step S103 in the decision parameter distribution area 52 determined in step S101. Is a step for calculating the value of the determination parameter determined in step S101. The values of the decision parameters are calculated by a numerical calculation method such as a conjugate direction method, which is a sensitivity-based minimization calculation method, a quadratic programming or another nonlinear programming.

In the following description, the conjugate direction method is assumed as a numerical calculation method, but it goes without saying that other methods may be used.

In this embodiment, a pair of the decision parameter distribution area 52 and the value of the decision parameter in the decision parameter distribution area 52 is called a decision parameter distribution. Finally, the content of the corresponding part of the parameter distribution memory 23 is rewritten with the calculated determined parameter distribution, and the process proceeds to step S1.
04 is ended.

The above steps S102 to S104 are repeated until the difference distribution between the calculated electromagnetic field distribution and the target electromagnetic field distribution becomes smaller than the convergence condition value determined in step S101.

In step S105, the parameter distribution of the determined parameter stored in the parameter distribution memory 23 and the electromagnetic field distribution stored in the electromagnetic field distribution memory 24 are sequentially displayed on the result display section 41 of the display 4 according to the designation of the user. It is a step for.

Next, the parameter distribution memory 23 and the electromagnetic field distribution memory 24 will be described with reference to FIGS.

First, the parameter distribution memory will be described with reference to FIG.

In FIG. 6, the parameter distribution memory 23
Are a magnetoresistance distribution memory 231, an applied current density distribution memory 232, a dielectric constant distribution memory 233, and a charge density distribution memory 234;
It comprises an applied current density sensitivity distribution memory 236, a dielectric constant sensitivity distribution memory 237, and a charge density sensitivity distribution memory 238, each of which further comprises a plurality of memory cells 89. The first half 231 to 234 are memories for storing parameter distributions of respective parameters. 235 of the second half
238 are memories for storing the sensitivity of each parameter for each mesh. For example, the magnetoresistive sensitivity distribution memory 235 stores the sensitivity of the magnetic resistivity for each mesh.

Each memory of the parameter distribution memory 23, for example, a specific memory cell 891 of the magnetoresistive distribution memory 231 has a specific mesh 991 of the analysis target space 9.
Have a one-to-one correspondence between the memory cells and the meshes.

Next, the electromagnetic field distribution memory will be described with reference to FIG.

In FIG. 7, the electromagnetic field distribution memory 24 includes:
It comprises a magnetic field distribution memory 241, an electric field distribution memory 242, a vector potential differential coefficient distribution memory 243, and a scalar potential differential coefficient distribution memory 244.
These fields store the magnetic field, electric field, vector potential derivative, and scalar potential derivative for each mesh. Each memory of the electromagnetic field distribution memory 24 is further composed of a plurality of memory cells 89, and the memory cells and the mesh have a one-to-one correspondence relationship like the parameter distribution memory 23.

As described above, each memory cell of the parameter distribution memory 23 and the mesh have a one-to-one correspondence,
Further, since each memory cell of the electromagnetic field distribution memory 24 has a one-to-one correspondence with the mesh, a data structure having the relationship shown in Table 1 below is configured.

[0137]

[Table 1]

Here, the analysis target space is divided into N meshes, and the target electromagnetic field f (A, B; λ, σ,
J), the data structure in the case where the magnetoresistivity λ, the magnetic resistivity σ,... In each mesh are set as the decision parameters to be determined for B = ∇ × A.

As the mesh identifier used for mutually identifying the meshes, for example, coordinate values of predetermined points in the mesh can be used. More specifically, for example, the mesh can be identified by the coordinate value of the center of gravity of the mesh. For example, when three-dimensional orthogonal coordinates are used, the coordinates of the center of gravity are used to determine
Can be expressed as shown in Table 2 below.

[0140]

[Table 2]

Further, the optimal design support apparatus according to the present embodiment can be applied to natural phenomena other than electromagnetic fields, similarly to the above-described optimal support apparatus according to the first embodiment. In this case, for each mesh, the field values,
The decision parameter to be determined and the sensitivity of the change of the field to the decision parameter are stored in a data structure having the following relationship. That is, the field value, the determination parameter, and the determination parameter sensitivity in each mesh are associated with each other using the mesh ID as a pointer. That is, when divided into N meshes, a data structure as shown in the following Table 3 is configured.

[0142]

[Table 3]

Next, steps S101 to S104 (FIG. 2)
) Will be described in detail.

First, referring to FIG. 11, step S10
1 will be described.

In step S 1011, the mesh data of the analysis target space 9 stored in the mesh data storage section is read, and the input display section 42 of the display 4 is read.
And prepares to receive subsequent input. As shown in FIG. 8, the input display unit 42 includes an analysis target space display unit 421 that displays the analysis target space 9, a message box 422 that displays warning information and the like to the user, and various icon groups 42.
3 to 431 are displayed.

The subsequent input accepting step is started when the accepting unit 6 accepts an icon pick operation. If the icon picked up by the reception unit 6 is the icon 423, step S1012 is activated, if the icon is 425, step S1013 is activated, and if it is the icon 428, step S1014 is activated.

In step S1012, first, the receiving unit 5
Receives the input of the determination parameter. Next, the pick of the icon 424 and the subsequent designation of the partial area 521 are repeatedly received from the receiving unit 6, and the icon 4
This step is ended by picking 29. Hereinafter, the number of subregions 521 determined by this procedure is m,
Each of the sub-regions 521 is represented by Ω ₁ , Ω ₂ ,..., Ω _m , and the decision parameter distribution region 52 which is a union of these is represented by Ω.

Step S1013 is a step for receiving input of the target electromagnetic field distribution area 51 and the target electromagnetic field distribution value. First, pick the icon 426 or
By picking the icon 427, the target electromagnetic field distribution area 51
Is a point group or a mesh group.

In the case of a point group, the input of the coordinate value of the point and the target electromagnetic field value at that point from the receiving unit 5 is repeatedly received. Let n be the number of input point groups and p be their coordinate values
_{1, p 2, ..., p} n, a target field distribution values at those points ^{_{(obj F 1, x, obj}} F 1, y), (obj F 2, x, obj F 2, y) ...,
( ^ObjFn _{, x} , ^objFn _{, y} ).

In the case of the mesh group, the input of the constituent mesh group from the receiving unit 6 and, in the case of the mesh group, the constituent mesh group from the receiving unit 6, and then the target electromagnetic field distribution value from the receiving unit 5 is used. a function ^{_{(obj F x, obj F y}} ) accepts an input of.

In any case, the picking of the icon 429 ends this step.

In a succeeding step S1014, the vicinity 56 of the target electromagnetic field distribution area 51 is set. In the case where the target electromagnetic field distribution area 51 is a point group, as shown in FIG. 4A, a neighborhood 56 is formed by a mesh 99 including the target electromagnetic field distribution area 51 and a mesh 99 adjacent to the mesh 99. When the target electromagnetic field distribution area 51 is a mesh group, as shown in FIG. 4B, the target electromagnetic field distribution area 51 is configured by a mesh 99 group constituting the target electromagnetic field distribution area 51 and a mesh 99 group adjacent thereto.

In step S1015, the input of the repetition convergence determination condition value from the receiving unit 5 is received, and the picking of the icon 429 ends this step.

When the above steps are executed and all data input is completed, step S101 ends.

Next, the details of steps S102 to S104 will be described. Since there is no essential difference between the case where the target electromagnetic field distribution area 51 is the point group and the mesh group, the case where the target electromagnetic field distribution area 51 is the point group Will be described.

Step S102 is a step for calculating the electromagnetic field distribution in the analysis target space 9. The electromagnetic field is a generic term for a magnetic field and an electric field, and the determination parameter determines which of the electric field and the magnetic field is to be calculated. Hereinafter, details of step S102 will be described with reference to FIG.
2 will be described.

First, in step S1021, mesh data of the analysis target space 9 is read. Next, if the determination parameter is one of the magnetic resistivity and the applied current density,
The magnetic field calculation in step S1022 is performed. If the decision parameter is not so, that is, if the decision parameter is one of the permittivity and the charge density, step S102
Perform the electric field calculation of 3.

In step S1022, first, the analysis target space 9 is read from each of the magnetoresistivity distribution memory 231 and the applied current density distribution memory 232 of the parameter distribution memory 23.
And the applied current density distribution _Jz are read. Next, according to the procedure of the finite element method, the following equation (d1)
To determine the z component A _z of the vector potential function in the analysis target space 9.

[0159]

(Equation 21)

Subsequently, the magnetic field distributions (F _x , F _y ) for all the meshes 99 in the analysis target space 9 are expressed by the following equation (d)
2)

[0161]

(Equation 22)

Thus, the calculation is performed in accordance with the procedure of the finite element method, and is written in the corresponding memory cells 89 of the magnetic field distribution memory 241. Similarly, all meshes 9 in the analysis target space 9
Against 9 calculates the derivative ∇A _z of the z component A _z of the vector potential function, is written in the corresponding memory cell 89 group vector potential differential coefficient distribution memory 233,
Step S102 ends.

In step S1023, first, the dielectric constant distribution ε and the charge density distribution ρ of the analysis target space 9 are read from each of the dielectric constant distribution memory 234 and the charge density distribution memory 235 of the parameter distribution memory. Next, equation (d3) is calculated according to the procedure of the finite element method, and a scalar potential function φ in the analysis target space 9 is determined.

[0164]

(Equation 23)

Subsequently, the electric field distributions (F _x , F _y ) for all the meshes 99 in the analysis target space 9 are expressed by the following equation (d).
4)

[0166]

(Equation 24)

Thus, calculation is performed in accordance with the procedure of the finite element method, and the result is written in the corresponding memory cell 89 of the electromagnetic field distribution memory 24. Similarly, all meshes 99 in the analysis target space 9
, A differential coefficient ∇φ of the scalar potential function φ is calculated, and a vector potential differential coefficient distribution memory 233 is calculated.
Is written to the corresponding memory cells 89 in the step S10.
2 is ended.

Step S103 is a step for calculating the sensitivity of the decision parameter. Step S102
Similarly to the above, the calculation procedure differs depending on what the decision parameter is. Hereinafter, the details of step S103 will be described with reference to FIG.

In step S1031, the analysis target space 9
Read the mesh data of Next, if the determined parameter is any one of the magnetic resistivity and the applied current density, steps S1032 to S1034 are executed. If the decision parameter is not so, that is, if it is either the decision parameter permittivity or the charge density, step S1035
Execute 1037.

In step S 1032, first, the magnetic field distribution in the analysis target space 9 stored in the magnetic field distribution memory 241, that is, all the meshes 99 in the analysis target space 9.
Then, the magnetic field distribution function (F _x (p), F _y (p)) in the neighborhood 56 is calculated. An appropriate interpolation method is used for the calculation. p is a coordinate value of a point in the analysis target space 9.

In step S1033, first, the magnetic resistivity distribution λ in the analysis target space 9 is read from the magnetic resistivity distribution memory 231. Next, the sensitivity distribution potential function Ψ _z in the analysis target space 9 is calculated by the equation (d5). This calculation is executed in accordance with the procedure of the finite element method, similarly to the calculation of the vector potential function A _{z in} step S1022.

[0172]

(Equation 25)

Here, ( ^obj ) on the right side of equation (d5)
F _{i, x} , ^obj F _{i, y} ) are the target electromagnetic field values determined in step S1014, and δ (p) represents a Dirac delta function. This means that the sensitivity distribution potential function Ψ _z is determined by the difference distribution between the target electromagnetic field distribution and the calculated electromagnetic field distribution.

Subsequently, from the sensitivity distribution potential function Ψ _z determined in the above procedure, the parameter sensitivity distribution Q _Jz of the applied current density in all the meshes of the determined parameter distribution area 52 is calculated.

[0175]

(Equation 26)

Is calculated according to the procedure of the finite element method.

In step S1034, the determined parameter sensitivity distribution Q _{Jz is} calculated from the parameter sensitivity distribution Q _Jz of the applied current density.
Is a step for calculating

When the applied current density is a determining parameter,
_{Let the} parameter sensitivity distribution Q _Jz be the determined parameter sensitivity distribution. That is,

[0179]

[Equation 27]

Is as follows.

When the determined parameter is the magnetic resistivity, the applied current density distribution J and the vector potential differential coefficient distribution ∇A _{z of} the determined parameter distribution area 52 are obtained from the applied current density memory 232 and the vector potential differential coefficient distribution memory 243. Is read and calculated according to the following equation (d9).

[0182]

[Equation 28]

On the other hand, in step S1035, first, the magnetic field distribution of the analysis target space 9 stored in the electric field distribution memory 242, that is, the value of the electric field in all the meshes 99 in the analysis target space 9, is read. The electric field distribution function (F _x (p), F _y (p)) at 56 is calculated. An appropriate interpolation method is used for the calculation. p is a coordinate value of a point in the analysis target space 9.

In step S1036, first, the dielectric constant distribution ε in the analysis target space 9 is read from the dielectric constant distribution memory 233. Next, a sensitivity distribution potential function に お け る in the analysis target space 9 is calculated by the following equation (d10).

[0185]

(Equation 29)

This calculation is executed according to the procedure of the finite element method, similarly to the calculation of the potential function φ in step S1023.

Here, on the right side of equation (d10), (
^obj F _{i, x} , ^obj F _{i, y} ) are the target electromagnetic field values determined in step S1014, and δ (p) is a Dirac delta function. This means that the sensitivity distribution potential function υ is determined by the difference distribution between the target electromagnetic field distribution and the calculated electromagnetic field distribution.

Subsequently, from the potential function υ determined in the above procedure, the charge density parameter sensitivity distribution Qρ in all meshes of the determined parameter distribution area 52 is calculated.

[0189]

[Equation 30]

Is calculated according to the procedure of the finite element method.

Step S1037 is a step for calculating the determined parameter sensitivity distribution Q from the charge density parameter sensitivity distribution Qρ.

When the charge density is the determining parameter, the parameter sensitivity distribution Qρ is set as the determining parameter sensitivity distribution Q. That is,

[0193]

(Equation 31)

Is as follows.

When the determined parameter is the permittivity, the scalar potential derivative distribution ∇φ in the determined parameter distribution region 52 is read from the scalar potential derivative memory 244, and the following equation is obtained.

[0196]

(Equation 32)

Is calculated.

Next, referring to FIG. 14, step S10
4 will be described in detail. This step S104 uses the sensitivity determined in step S103,
This is a step for calculating the value of the decision parameter in the decision parameter distribution area so as to minimize the difference distribution between the target electromagnetic field distribution and the electromagnetic field distribution stored in the electromagnetic field distribution memory 24 based on the conjugate direction method.

First, in step S1041, the mesh data stored in the mesh data storage unit 22 is read, and then in step S1042, the value of the determined parameter in the determined parameter distribution area is read from the parameter distribution memory 23. The value of the determined parameters within each partial region 521 is constant, the value of the decision parameter in the partial region Omega _k represents the D _k.

Next, in step S1043, first, for all the meshes constituting the partial area Ω _k , the sum of the product of the sensitivity and the area of the mesh determined in step S103 is calculated. The sum is referred to as total sensitivity, expressed as T _k. Next, the total sensitivity T _k is divided by the total area of the partial region Ω _k . This is called a partial area sensitivity expressed as ^sens Q _k. The above calculation is performed for all the sub-regions 521.

In step S1044, the sum of the partial area sensitivities is calculated for all the partial areas 521. T
In the repetition until the difference distribution described with reference to FIG. 2 becomes equal to or less than the convergence condition value, the sum of the partial area sensitivities calculated in the previous repetition is expressed as ^old T,

[0202]

[Equation 33]

Thus, α is determined. However, if it is the first repetition (repetition), the calculation of Expression (d15) is not performed, and α is determined to be 0 (zero).

Step S1045 is a step for calculating the conjugate direction of the conjugate direction method.
According to 6), the conjugate direction for each partial area 521 is determined.

[0205]

(Equation 34)

Here, ^old R _k is the conjugate direction calculated in the previous repetition in the repetition until the difference distribution described with reference to FIG. 2 becomes equal to or less than the convergence condition value. In the present embodiment, the conjugate direction method is used. However, even if another nonlinear programming method such as a quadratic programming method is used, a similar calculation method using a linear sum of the sensitivity and the direction determined in the previous iteration is used. Become.

Step S104, the last step of step S104
In 1046, β is calculated by the straight line search method so that the following equation (d17) is minimized, where m is the number of subregions 521.

[0208]

(Equation 35)

Here, ( ^objF _{i, x} , ^objF _{i, y} ) on the right side
Is the target electromagnetic field value determined in step S1014.
(F _x , F _y ) is determined by executing a calculation procedure corresponding to step S1032 or step S1035 in accordance with the change in the value of β changed by the straight line search method.
The electromagnetic field distribution function in the neighborhood 56. Since the calculation procedure of the straight line search method is determined, the description is omitted.

The following equation (d18) calculated by the straight line search method
If the value of beta gives the minimum value of expressed as ^min beta, the value ^{new new} D _k of determining parameters of the partial region Omega _k,

[0211]

[Equation 36]

This is written in the memory cell 89 of the determined parameter distribution memory of the parameter distribution memory corresponding to each mesh forming the partial area Ω _k . This procedure is executed for all the sub-regions 521, and the step S104 ends.

In the case of three-dimensional analysis, the electromagnetic field calculation in step S102, the sensitivity distribution potential calculation in step S103, and the like are all changed to three-dimensional calculations. Accordingly, the memory cell 89 of the electromagnetic field distribution memory 24 and the memory cells of the applied current density distribution memory 231 and the applied current density sensitivity distribution memory 235 have a three-dimensional vector configuration.

The three-dimensional conversion such as electromagnetic field calculation is performed in step S1.
The formulas (d7), (d9) and (d12) for calculating the sensitivity of 03 can be performed by replacing each with the following formula.

[0215]

(37)

[0216]

(38)

With this, additional calculations occur in the related calculations, but the description is omitted because it can be easily estimated. Step S10 when the determination parameter is the current density
The calculation of the decision parameter distribution of No. 4 is executed for each component.

[0218] Step S105, which is the final step of the processing in this embodiment, is a step for displaying the calculation result specified by the user on the result display section 41. This will be specifically described with reference to FIGS. 9 and 15.

FIG. 9 shows an embodiment of the result display section 41. The result display unit 41 performs a screen display including a distribution display unit 411 that displays the distribution 412 specified by the user so as to overlap the analysis target space 9 and various icon groups 413 to 417 and 429.

In step S105, as shown in FIG. 15, first, in step S1051, the mesh data of the analysis target space 9 is read, and the icon group 41 of the result display section 41 is read.
After displaying 3 to 417 and 429, the subsequent steps are started by any one of the icons 413 to 415 picked up by the user from the reception unit 6. For example, icon 41
When 5 is picked, step S1053 is started.

At step S1053, the parameter distribution of the determined parameter is read from the parameter distribution memory. Next, by picking one of the icons 416 to 417, the analysis target is the icon 416 in a bar graph format as shown in FIG. The information is displayed on the distribution display unit 411 so as to overlap the space 9. Other steps S
Also for 1052 and S1054, there is substantially no difference, only the read target is different. Finally, the operation of the optimal design support apparatus according to the present embodiment ends by picking the icon 429.

In the result display section 41, the sensitivity distribution of the parameters and the value of the design target function can be further displayed. This makes it easier to grasp the optimally designed state.

For the purpose of facilitating the understanding of the convergence state of the optimal design, for example, the change rate of the decision parameter associated with the iteration is obtained for each mesh, and the distribution of the obtained change rate associated with the iteration is displayed. In addition, it is possible to display the distribution of the rate of change associated with the repetition of the sensitivity value in each mesh.

By displaying the rate of change associated with the repetition of such a quantity, it is possible to more clearly understand how the decision parameters are improved by the repetition. Therefore, it is easy to determine whether the repetition has been sufficiently performed and whether the convergence point is reasonable.

In displaying the change rate associated with the repetition, the change rate can be made to correspond to a predetermined color scale, and the change rate associated with the repetition in each mesh can be displayed as a color. For example, the display color can be changed from red to blue as the rate of change due to repetition is increased from a large state to a small one.

As a result, it is possible to display the distribution of the change rate due to the repetition in the analysis target space in a state where it is easy to recognize.

Further, the electromagnetic field distribution at the convergence value of the decision parameter can be displayed. Thus, it is possible to assist in confirming whether or not the electromagnetic field realized by the optimally designed decision parameter meets the design goal and does not converge to an irrational solution.

Further, the amount of change of the convergence value of the determined parameter from the initial set value can be displayed. This makes it easier to grasp the relationship between the intention of setting the initial set value and the design goal.

As described above, according to the present embodiment, at least one of the magnetoresistance, applied current density, dielectric constant, and charge density of an electric device is determined by the target electromagnetic field and the target electromagnetic field as the parameters to be optimally designed. Can be determined so as to minimize the difference distribution of.

In addition, in the configuration shown in FIG. 10, a receiving unit 7 directly connected to the arithmetic unit 1 is added, and the receiving unit 7 is connected to an appropriate electromagnetic field measuring device so that the target electromagnetic field distribution area 51 in the case of a point group is a target group. The electromagnetic field value can be a measured value.

By taking the measured values as input and designing optimally so that the difference distribution between the measured electromagnetic field and the electromagnetic field obtained by numerical analysis from the determined parameters is reduced, the magnetoresistivity of the object to be measured is reduced. The distribution of the applied current density, the dielectric constant and the charge density can be known.

In the above description, the optimal design support device including the electromagnetic field analysis unit for performing the electromagnetic field analysis has been described. However, the electromagnetic field analysis may be performed using an existing finite element solver. In this case, as shown in FIG. 16, optimal design can be supported in cooperation.

In FIG. 16, the optimal design support unit includes a gradient calculation module for calculating parameter sensitivity and an optimization module for optimizing a decision parameter using parameter sensitivity.

An electromagnetic field simulator constructed using an existing finite element solver stores an electromagnetic field equation solver for obtaining an electromagnetic field distribution in a given parameter distribution and a plurality of design evaluation function candidates representing a design target. And an evaluation function library.

Further, the electromagnetic field simulator displays a preprocessor for setting a space to be analyzed, for example, a finite element division for performing a finite element analysis, and displays the analyzed electromagnetic field, and supports interpretation of the electromagnetic field. For being connected to a post processor.

The above-mentioned optimal design support unit gives an improved decision parameter distribution by calling a subroutine of the electromagnetic field simulator, and receives the analyzed electromagnetic field distribution.

The optimal design can be supported by configuring the module of the optimal design support unit so as to have such a relationship and mounting the module on a computer realizing the function of the electromagnetic field simulator. Note that the optimal design support unit may be configured as an independent device, and may cooperate with a computer realizing the function of the electromagnetic field simulator by data communication.

The operation of the optimum design support apparatus according to the present embodiment will be described below with reference to some analysis examples.

First, a case where the present invention is applied to the identification of a defect in a conductor will be described with reference to FIGS.

The design evaluation function F in this case is set for the governing equation as shown in FIG. That is, the optimum design is performed so that the magnetic flux density distribution obtained by the electromagnetic field analysis matches the target magnetic flux density distribution.

When the conductivity σ is determined as a parameter, FIG.
The parameter sensitivity distribution shown in (b) is obtained.

Then, the arrangement of coils and conductors in the space to be analyzed is set as shown in FIG.

FIG. 18A shows the state of change in the conductivity when the improvement of the determination parameter is repeated under such conditions. Element 3 in the analysis target space shown in FIG.
The conductivity variations at 5, 36 and 83, 84 are plotted.

In FIG. 18 (a), as the repetition is repeated, the conductivity in element 35 and element 83 approaches the conductivity of the defective conductor, and the element 36 and element 84
Is approaching the conductivity of the normal conductor.

Next, with reference to FIG. 19, a description will be given of a pseudo field current design to which the optimum design support apparatus of the present invention is applied.

In the generator as shown in FIG. 19C, the design is performed so that the generated current becomes the target value. Therefore, the design evaluation function is applied to the governing equation as shown in FIG.
When the parameter sensitivity is set as shown in FIG.
It is obtained as shown in FIG. Therefore, by performing the optimal design using the parameter sensitivity using the optimal design support apparatus of the present invention, the current to be given to the coil, the rotation speed of the rotor, and the like can be optimized.

Next, with reference to FIG. 20, an optimal design for reducing the weight of a magnetic material for a magnetic shield to which the optimal design support device of the present invention is applied will be described.

The purpose of this optimum design is to set the magnetic field generated by the coil in FIG. 20 (b) to be shielded by a magnetic material so that the magnetic field applied to the magnetic field evaluation unit is equal to or less than the target value. Is to reduce the weight.

Conventionally, attempts have been made to optimize the thickness of the magnetic body by trial and error of a designer. On the other hand, by applying the optimal design support device of the present invention, the topology of the magnetic body can be optimized and the weight of the entire magnetic body can be reduced.

That is, in this optimum design, the occupation ratio of the magnetic material in each element is given a degree of freedom by removing the restriction that the magnetic material has a uniform density. For this reason, for each element, the weight W _k of the magnetic element and the occupancy x _k of the magnetic substance in the element are variables, and the design evaluation function is a condition for minimizing the sum of these products, that is, FIG. )
Set as follows.

As a result, the occupancy of the magnetic material in the element effective for the magnetic shield is set to 1, that is, close to the state of complete filling, and the occupancy of the magnetic material in the element having little influence is set to 0, that is, the state of the air gap. It can be designed to be closer.

Based on such an analysis, for example, it is possible to design that a hole should be made in the magnetic member of the element in accordance with the occupancy of the magnetic member.

In the case of using a composite material, that is, a material in which a magnetic material powder is mixed with a resin or the like, it is possible to design such that the mixing ratio of each element is determined.

[0254]

According to the present invention, an optimum design can be performed with the distribution of physical property values in the material constituting the component and the topology (phase) of the shape of the component.

The design evaluation function can be set arbitrarily. For this reason, it is possible to perform an optimum design in consideration of an amount other than the electromagnetic field distribution, for example, the weight of the component.

In addition, the distribution of physical property values in electric machine parts can be measured.

[Brief description of the drawings]

FIG. 1 is a block diagram illustrating a configuration of an optimal design support device according to a first embodiment of the present invention.

FIG. 2 is a flowchart showing an operation of the optimal design support device of FIG.

FIG. 3 is an explanatory diagram showing an operation of the optimal design support device of FIG. 1;

FIG. 4 is an explanatory diagram showing an operation of the optimal design support device of FIG. 1;

FIG. 5 is an explanatory diagram showing an operation of the optimal design support device of FIG. 1;

FIG. 6 is an explanatory diagram showing a correspondence relationship between the configuration of the parameter distribution memory of FIG. 1 and an analysis target space of FIG. 3;

FIG. 7 is an explanatory diagram showing the correspondence between the configuration of the electromagnetic field distribution memory of FIG. 1 and the analysis target space of FIG. 3;

FIG. 8 is an explanatory diagram showing a configuration of an input display unit of the optimal design support device of FIG. 1;

FIG. 9 is an explanatory diagram showing a configuration of a result display unit of the optimal design support device of FIG. 1;

FIG. 10 is a block diagram illustrating a configuration of an optimal design support device according to a second embodiment of the present invention.

FIG. 11 is a flowchart illustrating the flowchart of FIG. 2 in further detail.

FIG. 12 is a flowchart illustrating the flowchart of FIG. 2 in more detail.

FIG. 13 is a flowchart illustrating the flowchart of FIG. 2 in further detail.

FIG. 14 is a flowchart illustrating the flowchart of FIG. 2 in further detail.

FIG. 15 is a flowchart illustrating the flowchart of FIG. 2 in further detail.

FIG. 16 is a block diagram showing an optimal design support device configured to operate in cooperation with an existing electromagnetic field simulator.

FIG. 17 is an explanatory diagram showing defect identification in a conductor to which the optimal design support device of the present invention has been applied.

FIG. 18 is an explanatory diagram showing calculation results of defect identification in a conductor, to which the optimal design support device of the present invention has been applied.

FIG. 19 is an explanatory diagram showing a pseudo field current design to which the optimal design support device of the present invention is applied.

FIG. 20 is an explanatory diagram showing a design for reducing the weight of a magnetic body of a magnetic shield to which the optimum design support device of the present invention is applied.

[Explanation of symbols]

DESCRIPTION OF SYMBOLS 1 ... Operation part, 2 ... Storage part, 3 ... Display control part, 4 ... Display, 5-7 ... Reception part, 9 ... Analysis space, 11 ... Input / output processing part, 12 ... Electromagnetic field distribution calculation part, 13 ... Parameter Sensitivity calculation unit, 14 parameter sensitivity calculation unit, 21 program storage unit, 22 mesh data storage unit, 23
Parameter distribution memory, 24 ... electromagnetic field distribution memory, 41
... Result display part, 42 ... Input display part, 51 ... Target electromagnetic field distribution area, 52 ... Decision parameter distribution area, 56 ... Nearby, 90
... Partial space of coordinate space, 91 ... Parts, 95 ... Air, 89
... memory cells, 98 ... lattice points, 99 ... meshes, 231
... Magnetoresistance distribution memory, 232... Applied current density distribution memory, 233... Charge distribution memory, 234... Dielectric constant distribution memory, 235... Magnetoresistivity sensitivity distribution memory, 236. Distribution memory, 238: dielectric constant distribution memory, 521: partial area, 24
1: magnetic field distribution memory, 242: electric field distribution memory, 243
... Vector potential differential coefficient distribution memory 244 scalar potential differential coefficient distribution memory 411 distribution display unit 412 distribution values 413 to 417 423 to 43
1 ... icon, 421 ... analysis target space display part, 422 ...
Message window, 500 ... Optimal design support device, 5
20: input / output processing unit, 540: electromagnetic field distribution calculation unit, 56
0: parameter distribution optimizing unit, 570: parameter sensitivity distribution calculating unit, 580: parameter distribution calculating unit

 ──────────────────────────────────────────────────の Continuing on the front page (72) Inventor Yasuo Morooka 7-2-1, Omika-cho, Hitachi City, Ibaraki Pref. Hitachi, Ltd.

Claims (21)

[Claims] 1. An optimal design support apparatus for supporting an optimal design related to an electromagnetic field, comprising: a governing equation representing a phenomenon in the electromagnetic field, a design evaluation function representing a target of the optimal design, and an initial setting value of a distribution of decision parameters to be determined. And an input / output processing means for receiving an optimized decision parameter distribution, an electromagnetic field distribution calculating means for obtaining an electromagnetic field distribution in a parameter distribution including the decision parameter distribution based on the governing equation, Parameter distribution optimizing means for obtaining an optimized parameter distribution so that the evaluation function is minimized, wherein the parameter distribution optimizing means includes Decision parameter that shows the distribution of fluctuating sensitivity Parameter sensitivity for obtaining sensitivity distribution Calculating means, comprising: a parameter distribution calculating means for obtaining a decision parameter distribution improved so that the design evaluation function is reduced by using the decision parameter sensitivity distribution. Design support equipment. 2. An optimal design support apparatus for supporting an optimal design for a temperature field, comprising: a governing equation representing heat conduction in the temperature field, a design evaluation function representing a target of the optimal design, and a distribution of a decision parameter to be determined. Input / output processing means for receiving an initial set value and outputting an optimized decision parameter distribution; and a temperature field distribution calculation for obtaining a temperature field distribution in a parameter distribution including the decision parameter distribution based on the governing equation. Means, and parameter distribution optimizing means for obtaining an optimized parameter distribution so that the design evaluation function is minimized, wherein the parameter distribution optimizing means accompanies a change in the determined parameter distribution. Parameter sensitivity for determining the sensitivity distribution that determines the sensitivity distribution in which the above design evaluation function fluctuates Cloth calculation means; and parameter distribution calculation means for obtaining a decision parameter distribution improved so that the design evaluation function is reduced using the decision parameter sensitivity distribution. Optimal design support equipment. 3. An optimum design support apparatus for supporting an optimum design related to an electromagnetic field and a temperature field, wherein a governing equation representing a phenomenon related to the electromagnetic field and the temperature field, a design evaluation function representing a target of the optimal design, and a decision to be determined. An input / output processing means for receiving an initial setting value of the parameter distribution and outputting an optimized decision parameter distribution; and obtaining an electromagnetic field distribution and a temperature field distribution in the parameter distribution including the decision parameter distribution based on the governing equation. Numerical analysis means for performing a numerical analysis, and parameter distribution optimization means for obtaining an optimized parameter distribution so that the design evaluation function is minimized, wherein the parameter distribution optimization means Decision showing the distribution of sensitivity where the above design evaluation function fluctuates with the change of decision parameter distribution Parameter sensitivity distribution calculating means for obtaining a parameter sensitivity distribution; and parameter distribution calculating means for obtaining a determined parameter distribution improved so that the design evaluation function is reduced using the determined parameter sensitivity distribution. An optimal design support device characterized by comprising: 4. An optimum design support apparatus for supporting an optimum design using an analysis apparatus for performing a finite element analysis, comprising: a governing equation to be analyzed by the analysis apparatus; a design evaluation function representing a target of the optimum design; Input / output processing means for receiving an initial setting value of a decision parameter distribution to be output, and outputting an optimized decision parameter distribution; and the accepted governing equation, and a parameter distribution including the decision parameter distribution to the analyzer. Interface means for receiving and analyzing the quantity of the field, and obtaining a parameter distribution optimized based on the quantity of the field received by the interface means so as to minimize the design evaluation function. Parameter distribution optimizing means, wherein the parameter distribution optimizing means comprises: Parameter sensitivity distribution calculation means for determining a determined parameter sensitivity distribution indicating a distribution of sensitivity in which the design evaluation function varies with a change in cloth; and using the determined parameter sensitivity distribution, the design evaluation function is reduced. And a parameter distribution calculation means for obtaining an improved decision parameter distribution. 5. The optimal design support apparatus according to claim 4, further comprising storage means for storing the determined parameter distribution, the field quantity, and the determined parameter sensitivity distribution, wherein the storage means is configured to perform the analysis. For each finite element divided in the finite element analysis in the device, the decision parameter distribution in each finite element, the amount of the field, and the decision parameter sensitivity distribution, is stored in association with each finite element Optimal design support equipment. 6. The optimal design support apparatus according to claim 5, wherein the association between the field quantity, the decision parameter, and the decision parameter sensitivity for each finite element is performed by using an identification code defined for each finite element. An optimal design support device characterized by being used as a pointer. 7. The optimal design support apparatus according to claim 4, wherein the interface means receives a quantity of the analyzed field by calling a subroutine of the analysis apparatus using the governing equation and the parameter distribution as arguments. An optimal design support device characterized by the following. 8. An optimal design support apparatus for supporting an optimal design of an electromagnetic field in an analysis target space divided into a plurality of finite elements, comprising: A parameter distribution memory for storing a parameter distribution that is a distribution value of parameters such as an applied current density, a charge density, and a dielectric constant; and a parameter distribution memory for storing an electromagnetic field distribution that is a value of an electromagnetic field in each finite element of the analysis target space. An input unit for inputting an electromagnetic field distribution memory, at least one type of decision parameter among the above parameters, and a decision parameter distribution area including at least a part of the plurality of finite elements; stored in the parameter distribution memory Reading the parameter distribution and solving the potential equation that determines the electromagnetic field Calculate the electromagnetic field distribution in the analysis target space from the above, electromagnetic field distribution calculation means for storing the calculated electromagnetic field distribution in the electromagnetic field distribution memory, and the electromagnetic field distribution and the target electromagnetic field distribution stored in the electromagnetic field distribution memory A parameter sensitivity distribution calculation for calculating a parameter sensitivity distribution representing a sensitivity distribution in which the variation of the parameter distribution of the decision parameter in the decision parameter distribution area affects the variation of the difference distribution from the difference distribution in the target electromagnetic field distribution area. Means, using the sensitivity distribution calculated by the parameter sensitivity distribution calculating means, to calculate a parameter distribution of a decision parameter in the decision parameter distribution area so as to minimize the difference distribution, and a corresponding part of the parameter distribution memory. Parameter distribution calculating means for storing in the Display means for displaying the distribution of the decision parameters stored in the distribution memory. 9. The optimal design support apparatus according to claim 8, wherein the determined parameter distribution area is determined for each type of the determined parameter. 10. The optimal design support apparatus according to claim 8, wherein the display means displays the distribution of the determined parameter in a manner superimposed on the analysis target space. 11. The optimal design support device according to claim 8, wherein the display means displays the sensitivity distribution and the value of the design target function together when displaying the distribution of the determined parameters. An optimal design support device characterized by the following. 12. The optimal design support device according to claim 8, wherein the parameter distribution including the parameter distribution of the determined parameter calculated by the parameter distribution calculating means is set as a new parameter distribution, and The calculation, the calculation of the parameter sensitivity distribution in the parameter sensitivity distribution calculation means, and the calculation of the parameter distribution of the decision parameter in the parameter distribution calculation means are repeated, and the display means displays the distribution of the decision parameter, An optimal design support device, wherein a change rate at which the decision parameter changes with the repetition is obtained for each finite element, and the obtained change rate is displayed for each finite element. 13. The optimal design support device according to claim 8, wherein the parameter distribution including the parameter distribution of the determined parameter calculated by the parameter distribution calculating means is set as a new parameter distribution, and the electromagnetic field distribution in the electromagnetic field distribution calculating means is calculated. The calculation, the calculation of the parameter sensitivity distribution in the parameter sensitivity distribution calculation means, and the calculation of the parameter distribution of the decision parameter in the parameter distribution calculation means are repeated, and the display means displays the distribution of the decision parameter, An optimal design support apparatus, wherein a change rate at which the parameter sensitivity distribution changes with the repetition is obtained for each finite element, and the obtained change rate is displayed for each finite element. 14. The optimal design support device according to claim 12, wherein the display unit associates the change rate with a predetermined color scale and associates a display color of each finite element with the corresponding color. An optimal design support device characterized by the color of the attached color scale. 15. The optimal design support device according to claim 8, wherein the display means displays the electromagnetic field distribution when displaying the determined parameter. 16. The optimal design support apparatus according to claim 8, wherein the display means sets the determined parameters of the determined parameters stored in the parameter distribution memory when displaying the distribution of the determined parameters. An optimal design support device characterized by displaying a change with respect to a value. 17. The optimal design support device according to claim 8, wherein the determined parameter is determined as a function of a packing density of a substance in a corresponding finite element, and the display means is stored in the parameter distribution memory. An optimal design support apparatus characterized in that when the packing density of a substance indicated by a decision parameter is smaller than a predetermined threshold, the decision parameter indicates that no material exists in the corresponding finite element. 18. The optimal design support device according to claim 17, wherein the display means draws a contour at a boundary between a finite element whose filling density is smaller than a predetermined threshold and a finite element that is not. Characteristic optimal design support device. 19. A recording medium recording an optimum design support program for supporting an optimum design using a computer, wherein the optimum design support program is an optimum design support apparatus for supporting an optimum design related to an electromagnetic field. An input / output processing procedure for accepting a governing equation representing a phenomenon in an electromagnetic field, a design evaluation function representing an optimal design goal, and an initial set value of a decision parameter distribution to be determined, and outputting an optimized decision parameter distribution. An electromagnetic field distribution calculation procedure for obtaining an electromagnetic field distribution in a parameter distribution including a determined parameter distribution based on the governing equation; and a parameter distribution for obtaining an optimized parameter distribution so that the design evaluation function is minimized. And an optimization procedure, wherein the parameter distribution optimization procedure includes the above-described determination. A parameter sensitivity distribution calculation procedure for obtaining a decision parameter sensitivity distribution indicating a sensitivity distribution in which the design evaluation function fluctuates with a change in the parameter distribution, and the design evaluation function is reduced using the decision parameter sensitivity distribution. And a parameter distribution calculation procedure for obtaining an improved determined parameter distribution. 20. An optimal design method for optimally designing a parameter distribution of an electromagnetic field so as to minimize a design evaluation function that is a function of a distribution of the electromagnetic field, comprising: (1) an electromagnetic field equation established in the analysis target space; , The initial setting value of the decision parameter distribution to be optimized,
And (2) obtaining a decision parameter sensitivity distribution, which is a gradient of the design evaluation function with respect to the decision parameter distribution, from the electromagnetic field equation and the design evaluation function; Determining the distribution of the electromagnetic field in the parameter distribution including the determining parameter; (4) determining the provisional increment of the determining parameter in the obtained electromagnetic field distribution; and (5) indicating the change in the vector potential accompanying the change in the determining parameter distribution. The sensitivity vector potential is obtained from the electromagnetic field equation using the obtained provisional increment. (6) The decision parameter distribution is improved so as to minimize the design target function. (7) The decision parameter distribution is improved. If the amount of improvement to be made is smaller than a predetermined threshold, The optimum design value data, otherwise, the parameter distribution comprising determining the abovementioned parameters improved, optimum design method characterized by repeating the procedure of (3) or later. 21. An electromagnetic measuring apparatus for measuring the distribution of physical property values in a measured object, an electromagnetic field measuring means for measuring an electromagnetic field distribution in a target space including the measured object, an electromagnetic field equation, and a measurement state. Measurement evaluation function, and
An input / output processing means for receiving an initial set value of a physical property value to be measured, and outputting a distribution of the measured physical property value; and an electromagnetic field distribution in a parameter distribution including the physical property value distribution to be measured based on the electromagnetic field equation. Electromagnetic field distribution calculating means for calculating the electromagnetic field distribution measured by the electromagnetic field measuring means,
Physical property value calculating means for obtaining a physical property value distribution in which a difference distribution from the electromagnetic field distribution calculated by the electromagnetic field distribution calculating means is minimized, wherein the physical property value calculating means changes the physical property value distribution The physical property value sensitivity distribution calculating means for obtaining a physical property value sensitivity distribution indicating the distribution of the sensitivity in which the difference distribution fluctuates with the physical property value sensitivity distribution is improved so that the difference distribution is reduced. An electromagnetic measurement device comprising: a physical property value calculation unit for obtaining a physical property value distribution.