Optimization apparatus, optimization method, and computer-readable medium storing optimization program

Abstract

The present invention relates to an optimization device, an optimization method, and a computer-readable medium storing an optimization program. An optimization device that optimizes a shape of an object, the optimization device configured to execute an optimization process including: obtaining a target function equation based on a contribution of each element of a plurality of elements to a predetermined characteristic of the object, each element of the plurality of elements being an element obtained by dividing the object arranged in a design region; and optimizing the shape of the object by determining, for each element of the object, whether to arrange each element of the object based on the obtained target function equation.

Description

TECHNICAL FIELD

[0001] The case discussed herein relates to an optimization device, an optimization method, and a non-transitory computer-readable storage medium storing an optimization program. BACKGROUND

[0002] In recent years, computer-aided engineering (CAE) analysis has been applied to the design of various products (devices, equipment, etc.). CAE analysis is a general term for modeling techniques that virtually experiment by performing numerical calculations that apply various conditions to a product modeled on a computer using computer-aided design (CAD) or the like.

[0003] By performing CAE analysis, it is possible to optimize the shape of a product or the like without actually manufacturing the product, and it is possible to efficiently design the product.

[0004] An example of a prior art technique that optimizes the shape of a product using CAE analysis includes a technique called parameter optimization in which, for example, a person who designs the product sets parameters (design variables) that can uniquely determine the shape of the product and uses these parameters for optimization. In parameter optimization, which is an example of a prior art technique, due to the nature of the parameters set (the radius of a circle, the length of each side of a polygon, etc.), the shape of the product can be limited and can not be sufficiently optimized. Furthermore, in parameter optimization, which is an example of a prior art technique, CAE analysis is performed for each set value of the parameters set, and thus a large number of CAE analyses need to be performed, and there is a problem of high computational cost.

[0005] Furthermore, an example of a technique that performs optimization without using the above-described parameters (design variables) that can uniquely determine the shape of the product includes, for example, a technique called topology optimization. In topology optimization, the shape of the product is not limited by the nature of the parameters (design variables), and thus the shape of the product can be optimized with a higher degree of freedom compared to parameter optimization.

[0006] Here, topology optimization can be classified according to techniques that represent the shape of a product, and for example, topology optimization can be classified into continuous topology optimization and discrete topology optimization.

[0007] Continuous topology optimization (density method or level set method) is a technique that optimizes the shape of a product by representing the shape of the product or the like with continuous values and performing a differential search.

[0008] For continuous topology optimization, a technique has been proposed in which a design domain of an object is repeatedly divided by elements, a physical quantity of a field shape is derived by a finite element method, a target function and its sensitivity are derived, and a reaction diffusion equation is solved until the target function converges.

[0009] In such a continuous topology optimization, the searched shape of the product can be limited to a local solution, and there is a problem that the range of searchable shapes is narrow. Further, the continuous topology optimization as an example of the related art requires a large number of CAE analyses in the optimization process, and there is a problem that the computational cost is high.

[0010] Discrete topology optimization (ON-OFF method) is a technique of optimizing the shape of a product by expressing the shape of the product as discrete values (for example, "1" or "0") and searching for whether to arrange material in the divided regions of the product for all combinations of these discrete values. The range of searchable shapes of the discrete topology optimization as an example of the related art is wider than that of the continuous topology optimization, but since CAE analysis is performed for each combination of a large number of discrete values, a large number of CAE analyses are required to be performed, and there is a problem that the computational cost is very high.

[0011] As described above, in the related art, when optimizing and designing the shape of a product (an object to be designed, such as a device or equipment) using CAE analysis, the searchable shape is limited, and the shape can not be sufficiently optimized. Further, in the related art, since a large number of CAE analyses need to be repeatedly performed, the computational cost becomes high, and it is sometimes difficult to optimize the shape of the product within a realistic time.

[0012] Examples of the related art include Japanese Laid-Open Patent Publication No. 2010-108451. SUMMARY

[0013] TECHNICAL PROBLEM

[0014] In one aspect, an object of the present application is to provide an optimization device or the like capable of optimizing the shape of an object sufficiently within a short time.

[0015] SOLUTION TO PROBLEM

[0016] According to an aspect of the embodiments, there is provided an optimization device that optimizes the shape of an object. In an example, the optimization device includes a memory, and a processor coupled to the memory, the processor configured to perform an optimization process including obtaining a target function equation based on a contribution of each element of a plurality of elements to a predetermined characteristic of the object, the each element of the plurality of elements being an element obtained by dividing the object arranged in a design region, and optimizing the shape of the object by determining whether to arrange each element of the object based on the obtained target function equation for each element of the object.

[0017] The objects and advantages of the present application will be realized and attained by means of the elements and combinations particularly pointed out in the claims.

[0018] It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the application.

[0019] Advantages of the Invention

[0020] In one aspect, the present application can provide an optimization device or the like capable of optimizing the shape of an object in a short time and sufficiently. BRIEF DESCRIPTION OF DRAWINGS

[0021] FIG. 1A is a diagram showing an example of the length of each side of a triangle in a case where the length of each side of the triangle is designated as a parameter in parameter optimization;

[0022] FIG. 1B is a diagram showing another example of the length of each side of a triangle in a case where the length of each side of the triangle is designated as a parameter in parameter optimization;

[0023] FIG. 2 is a diagram showing an example of a bitmap representing the shape of an object in discrete topology optimization;

[0024] FIG. 3 is a diagram showing an example of a state in searching for a combination of bits that gives a minimum value to an Ising model equation in a Quadratic Unconstrained Binary Optimization (QUBO) format;

[0025] FIG. 4 is a diagram showing an example of a hardware configuration of an optimization device disclosed in the present application;

[0026] FIG. 5 is a diagram showing another example of a hardware configuration of an optimization device disclosed in the present application;

[0027] FIG. 6 is a diagram showing an example of a functional configuration of an optimization device disclosed in the present application;

[0028] FIG. 7 is a flowchart showing an example of a flow when the shape of an example optimization object is optimized using the technology disclosed in the present application;

[0029] FIG. 8 is a diagram showing an example of a functional configuration of an annealing machine for an annealing method;

[0030] FIG. 9 is a diagram showing an example of an operation flow of a transition control unit;

[0031] FIG. 10 is a diagram showing an example of a calculation model when the shape of a magnetic shield is optimized in Example 1;

[0032] FIG. 11FIG. 1 is a graph showing an example of a BH curve (hysteresis curve) of a magnetic material that forms a magnetic shield set in Example 1;

[0033] FIG. 12A FIG. 2 is a graph showing an example of a flow for describing a procedure when a magnetic flux density in each element is obtained by dividing the calculation model in Example 1 and performing analysis using a finite element method;

[0034] FIG. 12B FIG. 3 is a graph showing an example of a flow for describing a procedure when a magnetic flux density in each element is obtained by dividing the calculation model in Example 1 and performing analysis using a finite element method;

[0035] FIG. 12C FIG. 4 is a graph showing an example of a flow for describing a procedure when a magnetic flux density in each element is obtained by dividing the calculation model in Example 1 and performing analysis using a finite element method;

[0036] FIG. 13 FIG. 5 is a graph showing an example of a magnetic flux density distribution in a design region when a magnetic material as a material of a magnetic shield is arranged throughout the design region in Example 1;

[0037] FIG. 14 FIG. 6 is a graph showing an example of each element obtained by dividing the magnetic shield in the design region when a magnetic material as a material of a magnetic shield is arranged throughout the design region in Example 1;

[0038] FIG. 15 FIG. 7 is a graph showing an example of a shape of a magnetic shield as an initial shape at the time of optimization in Example 1 as an example of a shape of a magnetic shield when a condition that a magnetic material as a material of a magnetic shield is arranged throughout a design region is set;

[0039] FIG. 16A FIG. 8 is a graph showing an example of a shape of a magnetic shield before filtering is performed in the first optimization of Example 1;

[0040] FIG. 16B FIG. 9 is a graph showing an example of a shape of a magnetic shield after filtering is performed in the first optimization of Example 1;

[0041] FIG. 17A FIG. 10 is a graph showing an example of a shape of a magnetic shield before filtering is performed in the second optimization of Example 1;

[0042] FIG. 17B FIG. 11 is a graph showing an example of a shape of a magnetic shield after filtering is performed in the second optimization of Example 1;

[0043] FIG. 18A FIG. 12 is a graph showing an example of a shape of a magnetic shield before filtering is performed in the third optimization of Example 1;

[0044] FIG. 18B is a diagram showing an example of the shape of the magnetic shield after filtering in the third optimization of Example 1;

[0045] FIG. 19A is a diagram showing an example of the shape of the magnetic shield before filtering in the fourth optimization of Example 1;

[0046] FIG. 19B is a diagram showing an example of the shape of the magnetic shield after filtering in the fourth optimization of Example 1;

[0047] FIG. 20A is a diagram showing an example of the shape of the magnetic shield before filtering in the fifth optimization of Example 1;

[0048] FIG. 20B is a diagram showing an example of the shape of the magnetic shield after filtering in the fifth optimization of Example 1;

[0049] FIG. 21A is a diagram showing an example of the shape of the magnetic shield before filtering in the sixth optimization of Example 1;

[0050] FIG. 21B is a diagram showing an example of the shape of the magnetic shield after filtering in the sixth optimization of Example 1;

[0051] FIG. 22A is a diagram showing an example of the shape of the magnetic shield before filtering in the seventh optimization of Example 1;

[0052] FIG. 22B is a diagram showing an example of the shape of the magnetic shield after filtering in the seventh optimization of Example 1;

[0053] FIG. 23A is a diagram showing an example of the shape of the magnetic shield before filtering in the eighth optimization of Example 1;

[0054] FIG. 23B is a diagram showing an example of the shape of the magnetic shield after filtering in the eighth optimization of Example 1;

[0055] FIG. 24A is a diagram showing an example of the shape of the magnetic shield before filtering in the ninth optimization of Example 1;

[0056] FIG. 24B is a diagram showing an example of the shape of the magnetic shield after filtering in the ninth optimization of Example 1;

[0057] FIG. 25AFIG. 1 is a diagram showing an example of a shape of a magnetic shield before filtering is performed in the tenth optimization of Example 1;

[0058] FIG. 25B FIG. 2 is a diagram showing an example of a shape of a magnetic shield after filtering is performed in the tenth optimization of Example 1;

[0059] FIG. 26A FIG. 3 is a diagram showing an example of a shape of a magnetic shield before filtering is performed in the eleventh optimization of Example 1;

[0060] FIG. 26B FIG. 4 is a diagram showing an example of a shape of a magnetic shield after filtering is performed in the eleventh optimization of Example 1;

[0061] FIG. 27A FIG. 5 is a diagram showing an example of a shape of a magnetic shield before filtering is performed in the twelfth optimization of Example 1;

[0062] FIG. 27B FIG. 6 is a diagram showing an example of a shape of a magnetic shield after filtering is performed in the twelfth optimization of Example 1;

[0063] FIG. 28A FIG. 7 is a diagram showing an example of a shape of a magnetic shield before filtering is performed in the thirteenth optimization of Example 1;

[0064] FIG. 28B FIG. 8 is a diagram showing an example of a shape of a magnetic shield after filtering is performed in the thirteenth optimization of Example 1;

[0065] FIG. 29A FIG. 9 is a diagram showing an example of a shape of a magnetic shield before filtering is performed in the fourteenth optimization of Example 1;

[0066] FIG. 29B FIG. 10 is a diagram showing an example of a shape of a magnetic shield after filtering is performed in the fourteenth optimization of Example 1;

[0067] FIG. 30A FIG. 11 is a diagram showing an example of a shape of a magnetic shield in a case where a magnetic material that will be a material of the magnetic shield is arranged throughout the design region in Example 1;

[0068] FIG. 30B FIG. 12 is a diagram showing an example of magnetic force lines of a magnetic force generated by the coil in the shape of the magnetic shield in a case where a magnetic material that will be a material of the magnetic shield is arranged throughout the design region in Example 1;

[0069] FIG. 31A FIG. 13 is a diagram showing an example of an optimization result of a shape of a magnetic shield in a case where a = 0.95 and β = 0.05 in Example 1;

[0070] FIG. 31B FIG. 6 is a diagram showing an example of magnetic field lines generated by the magnetic force of the coil in the shape of the optimization result of the magnetic shield in the case where a = 0.95 and β = 0.05 in Example 1;

[0071] FIG. 32A FIG. 7 is a diagram showing an example of the optimization result of the shape of the magnetic shield in the case where a = 0.5 and β = 0.5 in Example 2;

[0072] FIG. 32B FIG. 8 is a diagram showing an example of magnetic field lines generated by the magnetic force of the coil in the shape of the optimization result of the magnetic shield in the case where a = 0.5 and β = 0.5 in Example 2;

[0073] FIG. 33A FIG. 9 is a diagram showing an example of the optimization result of the shape of the magnetic shield in the case where a = 0.7 and β = 0.3 in Example 3;

[0074] FIG. 33B FIG. 10 is a diagram showing an example of magnetic field lines generated by the magnetic force of the coil in the shape of the optimization result of the magnetic shield in the case where a = 0.7 and β = 0.3 in Example 3;

[0075] FIG. 34A FIG. 11 is a diagram showing an example of the optimization result of the shape of the magnetic shield in the case where a = 0.8 and β = 0.2 in Example 4;

[0076] FIG. 34B FIG. 12 is a diagram showing an example of magnetic field lines generated by the magnetic force of the coil in the shape of the optimization result of the magnetic shield in the case where a = 0.8 and β = 0.2 in Example 4;

[0077] FIG. 35A FIG. 13 is a diagram showing an example of the optimization result of the shape of the magnetic shield in the case where a = 0.99 and β = 0.01 in Example 5;

[0078] FIG. 35B FIG. 14 is a diagram showing an example of magnetic field lines generated by the magnetic force of the coil in the shape of the optimization result of the magnetic shield in the case where a = 0.99 and β = 0.01 in Example 5;

[0079] FIG. 36 FIG. 15 is a diagram showing an example of the relationship between the mean square of the magnetic flux density in the object region and the area of the magnetic material (magnetic material area) in Examples 1 to 5; and

[0080] FIG. 37 FIG. 16 is a diagram showing an example of the processing flow in one embodiment of the technology disclosed in the present case. DETAILED DESCRIPTION

[0081] (Optimized device)

[0082] The technology disclosed in this case is based on the inventor's discovery that the prior art cannot sufficiently optimize the shape of an object in a short time. Therefore, before describing the details of the technology disclosed in this case, the problems of the prior art will be described in detail.

[0083] First, as described above, in parameter optimization, for example, when optimizing the shape of an object (device, equipment, etc.), the person who designed the object sets parameters (design variables) that uniquely determine the shape of the object, and optimization is performed based on these parameters. Examples of parameters to be set in parameter optimization include the radius of a circle, the length of each side of a polygon, the angle between the sides, and the like.

[0084] Here, in parameter optimization, when the shape of an object is represented by a parameter, if the radius of a circle is specified as a parameter, the shape of the object to be optimized is limited to a circle. Similarly, in parameter optimization, when the length of each side of a triangle is specified as a parameter, the shape of the object to be optimized is limited to a triangle.

[0085] More specifically, when the length of each side of the triangle is specified as a parameter in parameter optimization, consider that the length of each side of the triangle before optimization is FIG. 1A In this case, assuming the result of parameter optimization is as follows FIG. 1B The lengths of the sides of the triangle shown are a1, a2, and a3.

[0086] exist FIG. 1A and FIG. 1B In the example shown in , the lengths a1, a2, and a3 of the sides of the triangle can be optimized by performing parameter optimization, but the shape of the object is limited to a triangle, and it is impossible to search for shapes other than triangles. In this way, in parameter optimization, the shape of the object is limited due to the nature of setting parameters, and sufficient optimization may not be performed.

[0087] Furthermore, when parameter optimization is used to optimize the shape of an object, a CAE analysis (e.g., analyzing the performance of the object) needs to be performed using the set parameter values ​​each time the parameter values ​​are changed. Therefore, when parameter optimization is used to optimize the shape of an object, a CAE analysis needs to be performed for each set parameter value, resulting in a large number of CAE analyses and a high computational cost.

[0088] Further, as described above, in continuous topology optimization (density method or level set method), the shape of an object is represented by a function using continuous values, and the shape of the object is optimized by performing a differential search without using parameters (design variables) that uniquely determine the shape of the object. In this way, since the continuous topology optimization is an optimization technique using a differential search, the optimization result depends on an initial setting value (initial value of the function using continuous values). Therefore, in the continuous topology optimization, the shape of the object by which the optimization search is performed can be limited to (fall into) a local solution, and there is a problem that the range of searchable shapes is narrow.

[0089] When the shape of an object is optimized by the continuous topology optimization, a CAE analysis is performed for each shape obtained in the optimization process, and thus a large number of CAE analyses are required, and there is a problem that the computational cost is high.

[0090] Further, as described above, in discrete topology optimization (ON-OFF method), the shape of an object is represented by discrete values, and whether material is arranged in each divided region of the object is searched for all combinations of these discrete values. When the shape of an object is represented by discrete values in the discrete topology optimization, for example, "1 (arranged)" or "0 (not arranged)" is used to represent whether material is arranged in each divided region of the object.

[0091] More specifically, in the discrete topology optimization, "x i = 1" is a case where material (substance) is arranged in the i-th region (ON), and "x i = 0" is a case where material is not arranged in the i-th region (OFF). In this case, in the discrete topology optimization, as shown in FIG. 2 , the shape of an object can be represented by a figure (bitmap) of bits "1" and "0".

[0092] In this way, in the discrete topology optimization, the shape of an object is represented by combinations of discrete values, and the shape is searched for all combinations of these discrete values (solving a combinatorial optimization problem), so that the shape can be searched in a wider range than the continuous topology optimization.

[0093] However, in the discrete topology optimization, when the shape is searched for all combinations of discrete values representing the shape of an object, it is necessary to perform a CAE analysis, for example, for each combination of a large number of discrete values (for example, for each shape that the object can assume). Therefore, in the discrete topology optimization, a large number of CAE analyses are required for various combinations of a large number of discrete values, and there is a problem that the computational cost is extremely high.

[0094] As described above, in the related art, when the shape of an object is optimized, the search range of the shape of the object is limited and the search becomes insufficient, or the optimization takes time due to high computational cost, and it is sometimes difficult to optimize the shape of the object within real time.

[0095] Therefore, the present inventors have earnestly studied a device or the like that can optimize the shape of an object in a short time and sufficiently, and have obtained the following findings.

[0096] That is, the present inventors have found that the shape of an object can be optimized in a short time and sufficiently by an optimization device or the like that:

[0097] An example of the technology disclosed in the present case is an optimization device that optimizes the shape of an object, the optimization device including:

[0098] an optimization processing unit configured to specify the shape of the object as follows:

[0099] using an objective function equation based on a contribution of each of a plurality of elements to a predetermined characteristic of the object, each of the plurality of elements being obtained by dividing the object to be arranged in a design region; and

[0100] whether to arrange each of the elements of the object is specified for each of the elements of the object.

[0101] Here, in an example of the technology disclosed in the present case, the shape of an object is optimized by specifying the shape of the object using an objective function equation based on a contribution of each of a plurality of elements to a predetermined characteristic of the object, each of the plurality of elements being obtained by dividing the object arranged (to be arranged) in a design region.

[0102] In an example of the technology disclosed in the present case, for an object for which the shape is to be optimized, the object is divided into a plurality of elements by arranging the object in a design region and dividing the object. In other words, in an example of the technology disclosed in the present case, a plurality of elements that are divided objects to be arranged in a design region are obtained by dividing the design region into a plurality of elements, the design region being a region in which an object can be arranged. That is, in an example of the technology disclosed in the present case, the design region of the object is divided into a plurality of elements, and the plurality of elements represent the design region of the object as a set.

[0103] Then, in the example of the technology disclosed in the present case, the shape of the object is specified by using a target function equation based on the contribution of each of the plurality of elements obtained by dividing the object to the predetermined property of the object to optimize the shape of the object. In other words, in the example of the technology disclosed in the present case, a target function equation based on the contribution of each element to the predetermined property of the object is constructed for the elements obtained by dividing the object, and the shape of the object is specified and optimized based on the constructed target function equation.

[0104] The predetermined property of the object can be, for example, a property related to the performance of the object. As the property related to the performance of the object, for example, a property whose performance varies depending on the shape of the object can be appropriately selected in accordance with the use of the object, or the like.

[0105] More specifically, in the case where the object is a magnetic shield, as will be described in examples and the like below, the predetermined property of the object can be, for example, a shielding performance with respect to the magnetic flux of a region (object region) in which it is desired that a magnetic force be shielded in the magnetic shield. In this example, for example, in order to optimize the shape of the magnetic shield (in order to determine an element of a material (magnetic material) in which the magnetic shield is disposed), a target function equation capable of taking into account the shielding performance (example of the predetermined property) with respect to the magnetic flux of the region in which it is desired that the magnetic force be shielded and other conditions is used.

[0106] Note that the target function equation (objective function) can be, for example, a function that takes a minimum value when the variables in the target function equation are in an optimal combination in a combinatorial optimization problem. Thus, by searching for a combination of variables that minimizes the target function equation (minimizes the target function equation), a solution to the combinatorial optimization problem can be searched for and the shape of the object can be optimized.

[0107] Further, in the example of the technology disclosed in the present case, the contribution to the predetermined property of the object can be, for example, a physical quantity that represents the degree of influence (degree of influence) on the predetermined property as described above. That is, in the example of the technology disclosed in the present case, for example, a physical quantity in the object that influences the performance of the object can be used as the contribution.

[0108] More specifically, in the case where the object is a magnetic shield and the predetermined property is a shielding performance of the magnetic flux, the contribution to the predetermined property of the object can be a magnetization vector of each element in the magnetic shield. In this example, for example, a shape having an optimized shielding performance of the magnetic flux can be specified by using a target function equation based on the magnetization vector in each element obtained by dividing the magnetic shield to optimize the shape of the magnetic shield.

[0109] Further, in the example of the technology disclosed in the present case, the shape of the object can be optimized by adding another condition (constraint) to the objective function equation in addition to the contribution as described above to take the other condition into consideration.

[0110] Then, in the example of the technology disclosed in the present case, the shape of the object is optimized by specifying whether to arrange each element of the object for each element of the object using the objective function equation based on the contribution as described above. In other words, in the example of the technology disclosed in the present case, optimization can be performed by specifying the shape of the object to improve a predetermined characteristic by specifying whether to arrange each element of the object for the design region based on the contribution to the predetermined characteristic of the object.

[0111] Here, in the example of the technology disclosed in the present case, since whether to arrange each element of the object is specified based on the objective function equation, the shape of the object can be searched in a wide range while taking into consideration all combinations in which each element can be arranged in the design region. That is, in the example of the technology disclosed in the present case, since the arrangement of each element of the object can be discretely expressed and the shape can be searched, the shape of the object can be sufficiently searched in a wide range without being affected by the nature of the parameter representing the shape or the initial value of the function.

[0112] Further, in the example of the technology disclosed in the present case, as described above, since the shape of the object is optimized using the objective function equation based on the contribution to the predetermined characteristic of the object, the shape of the object can be effectively optimized taking into consideration the contribution, thereby improving the predetermined characteristic. That is, in the example of the technology disclosed in the present case, for example, the optimization direction (optimization guide) of the shape of the object can be determined to improve the predetermined characteristic, for example, taking into consideration the contribution as a physical quantity representing the degree of influence on the predetermined characteristic (performance of the object) of the object.

[0113] Further, in the example of the technology disclosed in the present case, a previously specified contribution or a newly specified contribution can be used as the contribution used in the objective function equation. In the case of using a newly specified contribution, an example of the technology of specifying the contribution includes a technology of specifying the contribution by performing CAE analysis capable of obtaining a physical quantity that affects the performance of the object in the object.

[0114] In the example of the technology disclosed in this case, as described above, since the optimization direction of the object's shape can be determined to improve a predetermined characteristic, even when CAE analysis is performed when specifying a contribution, the number of CAE analyses performed for specifying the contribution can be reduced. In other words, in the example of the technology disclosed in this case, for example, since a shape that improves a predetermined characteristic can be efficiently searched based on the contribution, the number of CAE analyses performed can be reduced even when the contribution is updated through CAE analysis.

[0115] As described above, in the example of the technology disclosed in the present case, even in the case of obtaining a contribution to predetermined characteristics of an object by performing CAE analysis, etc., the number of CAE analyses required when optimizing the shape of the object can be reduced and the optimization can be performed in a short time.

[0116] As described above, in the example of the technology disclosed in this case, for example, when optimizing the shape of an object (device, equipment, etc.), an objective function equation based on its contribution to a predetermined characteristic of the object is used to specify whether to arrange each of the multiple elements obtained by dividing the object. Therefore, the technology disclosed in this case can optimize the shape of the object in a short time and in a sufficient manner.

[0117] In the following description, an example of the technology disclosed in this case will be described with reference to the accompanying drawings. Note that, for example, processing (operation) in the optimization device as an example of the technology disclosed in this case, such as optimizing the shape of an object, can be performed by an optimization processing unit included in the optimization device.

[0118] Here, the optimization device disclosed in this case advantageously has a contribution designation unit and may also have another unit (device) if necessary. Note that, for example, the optimization processing unit can be implemented by a combination of a processor such as a central processing unit (CPU) and a memory such as a random access memory (RAM), or as part of an annealing machine.

[0119] First, an optimization device as an example of the technology disclosed in this case may be an optimization device that optimizes the shape of an object.

[0120] The object whose shape is to be optimized using the examples of the technology disclosed herein is not particularly limited, as long as the predetermined characteristic varies depending on the shape and the contribution to the predetermined characteristic can be specified. The object can be appropriately selected depending on the intended use. For example, an object having a shape that can be optimized using known topology optimization methods can be appropriately selected and applied as the object.

[0121] For example, specific examples of the object include a magnetic shield, a mechanical part, a heat insulating material, a light shielding member, a soundproofing material, a vibration damping material, a wave proofing material, and the like to be described in the following examples.

[0122] Further, in examples of the technology disclosed in the present case, the shape of the object to be optimized can be a two-dimensional shape or a three-dimensional shape. In examples of the technology disclosed in the present case, for example, it is advantageous to optimize (search) the two-dimensional shape of the object because the shape can be optimized in a shorter time. Further, when optimizing the two-dimensional shape of the object, optimization can be performed under a condition that each element obtained by dividing the object to be arranged in the design region is thickened.

[0123] <Optimization processing unit>

[0124] As described above, the optimization device, which is an example of the technology disclosed in the present case, has an optimization processing unit that specifies the shape of the object using a target function equation based on a contribution of each element of a plurality of elements to a predetermined characteristic of the object, the each element being obtained by dividing the object to be arranged in the design region. Further, the optimization processing unit optimizes the shape of the object by specifying whether to arrange each element of the object for each element of the object.

[0125] In examples of the technology disclosed in the present case, the optimization processing unit specifies and optimizes the shape of the object using the target function equation. Here, the target function equation can be, for example, a function that takes a minimum value when variables in the target function equation are in an optimal combination based on conditions or constraints in a combinatorial optimization problem in the combinatorial optimization problem. Therefore, by searching for a combination of variables that minimizes (minimizes the target function equation), a solution to the combinatorial optimization problem can be searched for and the shape of the object can be optimized. Note that the target function can also be referred to as an energy function, a cost function, a Hamiltonian, or the like.

[0126] In examples of the technology disclosed in the present case, the target function equation based on a contribution of each element of a plurality of elements obtained by dividing the object to be arranged in the design region to a predetermined characteristic of the object is used.

[0127] Further, "dividing the object to be arranged in the design region" means virtually dividing a region (design region) in which the object can be arranged when designing the object having the optimized shape.

[0128] The division method at the time of division of the object is not particularly limited and can be appropriately selected according to the purpose. As the division method at the time of division of the object, for example, it is advantageous to divide the object into shapes such that each element is formed into a shape suitable for analysis by numerical calculation (for example, a finite element method) to be described below.

[0129] For example, the number of divisions (the number of elements) at the time of division of the object can be appropriately selected according to the number of bits that can be used by a computer (for example, an annealing machine) for optimization of the objective function equation, the required calculation accuracy, the size of the object that can be actually manufactured, and the like.

[0130] Here, the contribution specified in advance or the contribution specified anew can be used as the contribution of each element of the plurality of elements obtained by dividing the object to be arranged in the design region to the predetermined characteristic of the object. However, it is advantageous to use the contribution specified anew.

[0131] <Contribution specifying unit>

[0132] The technique of specifying the contribution is not particularly limited as long as the contribution to the predetermined characteristic can be specified for each element of the object, and can be appropriately selected according to the purpose, but it is advantageous to specify the contribution by the contribution specifying unit to be described below.

[0133] The contribution specifying unit can be a unit (device) for specifying the distribution of the physical quantity related to the predetermined characteristic by performing analysis using numerical calculation with respect to the object to be arranged in the design region. That is, in the example of the technology disclosed in the present case, it is advantageous to additionally include a contribution specifying unit that specifies the contribution of each element of the object by specifying the distribution of the physical quantity related to the predetermined characteristic by performing analysis using numerical calculation with respect to the object to be arranged in the design region. Note that the contribution specifying unit can be realized, for example, by a combination of a processor such as a CPU and a memory such as a RAM.

[0134] For example, the CAE analysis described above can be used as the analysis using numerical calculation that the contribution specifying unit performs with respect to the object to be arranged in the design region. The analysis using numerical calculation (CAE analysis) is not particularly limited as long as the contribution can be specified, and can be appropriately selected according to the purpose, but it is advantageous to use analysis of the finite element method. In other words, in the example of the technology disclosed in the present case, it is advantageous that the contribution specifying unit specifies the contribution of each element of the object by performing analysis using the finite element method.

[0135] In the finite element method (FEM), for example, a region to be analyzed is divided into a large number of small regions called elements (meshes), and potentials defined at nodes and edges of each small region are approximated by simple equations to create simultaneous linear equations, and a potential distribution and the like are obtained by solving the simultaneous linear equations. Thus, by using the finite element method, it is possible to solve differential equations that are difficult to solve with an analytical method, it is possible to perform simulation of various objects with high precision, and it is possible to specify a contribution more accurately.

[0136] Note that analysis using the finite element method can be performed using known analysis simulation software.

[0137] The contribution specifying unit specifies a distribution of a physical quantity related to a predetermined characteristic of an object by performing analysis using numerical calculation (for example, analysis by the finite element method).

[0138] Here, the physical quantity related to the predetermined characteristic of the object (for example, a characteristic related to the performance of the object) is not particularly limited as long as the physical quantity has an influence on the predetermined characteristic, and can be appropriately selected according to the purpose. Examples of the physical quantity related to the predetermined characteristic of the object include, for example, a magnetic flux density distribution in electromagnetic field analysis, a stress distribution in structural analysis, a temperature distribution in thermal analysis, an optical intensity distribution in optical analysis, a sound magnitude distribution in sound analysis (acoustic analysis), a vibration distribution in vibration analysis, a wave distribution in fluid wave analysis, and the like. Note that hereinafter, the distribution of the physical quantity specified by the contribution specifying unit can be referred to as a "field distribution".

[0139] In addition, the contribution of each element of the object specified by the contribution specifying unit that specifies the distribution of the physical quantity is not particularly limited as long as the contribution is a physical quantity that influences the predetermined characteristic of the object specified based on the distribution of the physical quantity, and can be appropriately selected according to the purpose. Specific examples of the contribution specified by the contribution specifying unit include a magnetization vector in electromagnetic field analysis, a load vector in structural analysis, a heat generation value in thermal analysis, an optical intensity of each element in optical analysis, a magnitude of sound of each element in sound analysis (acoustic analysis), a vibration amplitude of each element in vibration analysis, a wave amplitude of each element in fluid wave analysis, and the like.

[0140] Further, in an example of the technology disclosed in this case, it is advantageous to repeatedly perform optimization of the shape of the object and update the contribution based on the result of the optimization. By doing so, it is possible to optimize the shape of the object using an objective function equation based on a more appropriate contribution, and it is possible to obtain a more appropriate shape of the object.

[0141] More specifically, it is advantageous that the contribution specifying unit updates the contribution of each element of the object based on the specific result regarding whether to arrange each element of the object, and the optimization processing unit specifies the shape of the object using the objective function equation based on the updated contribution. As described above, in the example of the technology disclosed in the present case, by repeatedly performing the processing of the contribution specifying unit and the optimization processing unit, a more suitable shape can be gradually searched for, and a more fully optimized shape of the object can be finally specified.

[0142] In the example of the technology disclosed in the present case, in a case where the processing of the contribution specifying unit and the optimization processing unit is repeatedly performed, the condition (the number of repetitions) of repeating the processing is not particularly limited and can be appropriately selected according to the purpose. In a case where the processing of the contribution specifying unit and the optimization processing unit is repeatedly performed, the condition of repeating the processing is advantageously repeating the processing until, for example, the change in the minimum value of the objective function equation for optimization becomes equal to or smaller than a predetermined value.

[0143] In other words, in the example of the technology disclosed in the present case, it is advantageous that the updating of the contribution in the contribution specifying unit and the optimization in the optimization processing unit using the objective function equation based on the updated contribution are repeatedly performed until the change in the minimum value of the objective function equation becomes equal to or smaller than a predetermined value. By doing so, the contribution of the objective function equation can be more fully optimized, and a more fully optimized shape of the object can be specified. Note that the change in the minimum value of the objective function equation can be determined to be equal to or smaller than a predetermined value by, for example, comparing with the immediately preceding calculation result (comparing between the (n+1)th calculation result and the nth calculation result).

[0144] Further, the maximum number of calculations (the number of loops) is determined as the condition of the repeated processing, and the shape specified based on the objective function equation having the lowest minimum value among the multiple calculations can be specified as the final optimization result.

[0145] Here, in the example of the technology disclosed in the present case, the optimization processing unit specifies the shape of the object by specifying whether to arrange each element of the object for each element of the object using the objective function equation. In other words, in the example of the technology disclosed in the present case, since whether to arrange each element of the object is specified by solving the combinatorial optimization problem based on the objective function equation, it is possible to search for the shape of the object in a wide range considering all combinations in which each element can be arranged in the design region.

[0146] Further, an example of the technology capable of solving the combinatorial optimization problem at high speed based on the objective function equation includes a technology that performs the calculation by, for example, an annealing method (annealing).

[0147] In order to minimize the objective function at high speed and efficiently by an annealing method (annealing), there are cases where it is necessary to express the objective function in a quadratic unconstrained binary optimization (QUBO) format. Here, the QUBO format means a format in which an objective function with respect to a variable that can be only two values (for example, 0 or 1) to be maximized or minimized can be expressed to a second-order term and the range of the variable space is not explicitly limited.

[0148] In the annealing method, for example, the objective function expressed in the QUBO format is converted into a format called an Ising model, and the value of the objective function converted into the Ising model is minimized to solve a combinatorial optimization problem.

[0149] For example, an equation (Ising model equation) obtained by converting the objective function in the QUBO format into the Ising model can be an Ising model equation in the QUBO format represented by the following formula.

[0150]

[0151] However, in the above equation, E(s) is an objective function that means to minimize the solution of the combinatorial optimization problem.

[0152] w ij is a coefficient (weight) for weighting between the i-th element (bit) and the j-th element (bit).

[0153] s i is a binary variable that represents that the i-th element (bit) is 0 or 1, and s j is a binary variable that represents that the j-th element (bit) is 0 or 1.

[0154] b i is a numerical value that represents a bias with respect to the i-th element (bit).

[0155] const. is a constant.

[0156] In the annealing method, for example, in a case where various changes are made to each bit (element) in the above Ising model equation in the QUBO format, the minimum value of the Ising model equation can be efficiently searched in a short time.

[0157] For example, as illustrated in FIG. 1, by searching for a combination of bits (s: 0 or 1) that gives the minimum value to the above Ising model equation in the QUBO format (searching for a portion surrounded by a circle), it is possible to specify a state of bits that can optimize the Ising model equation. Note that in FIG. 1, the vertical axis represents the magnitude of the value of the energy calculated by the Ising model equation (E(s)), and the horizontal axis represents the combination of bits (s). FIG. 3 FIG. 3

[0158] ​​Then, in the annealing method, since the parameters of the objective function can be obtained based on the designated state of the bits, the objective function can be efficiently optimized in a short time. If the objective function can be expressed in the QUBO format in this way, the objective function can be converted into an Ising model equation in the QUBO format, and the energy value in the Ising model equation can be efficiently optimized (minimized) in a short time by the annealing method.

[0159] In this way, in the example of the technology disclosed in the present case, as the technology of optimizing the objective function equation based on the contribution to the predetermined characteristics, the technology of converting the objective function equation into an Ising model equation in the QUBO format and minimizing the value of the objective function equation converted into the Ising model equation is advantageous.

[0160] In addition, examples of the process of converting the objective function equation into the Ising model equation include, for example, a technology of expanding and converting the objective function equation using a "for loop" using a self-made program, a technology of converting the objective function equation using a program that can handle mathematical expressions themselves, and the like.

[0161] For example, it is advantageous to use an equation represented by the following formula (2) as the objective function equation converted into the Ising model equation. In other words, in the example of the technology disclosed in the present case, it is advantageous that the optimization processing unit preferably specifies (optimizes) the shape of the object based on the objective function equation converted into the Ising model equation represented by the following formula (2).

[0162]

[0163] Note that, in the above formula (2),

[0164] E is the objective function equation converted into the Ising model equation,

[0165] w ij is a numerical value representing the interaction between the i-th bit and the j-th bit,

[0166] b i is a numerical value representing the bias with respect to the i-th bit,

[0167] x i is a binary variable representing that the i-th bit is 0 or 1, and

[0168] x j is a binary variable representing that the j-th bit is 0 or 1.

[0169] Here, x i and x jw in the above equation (2) is obtained, for example, by extracting the numerical value of each parameter in the objective function equation before the objective function equation is converted into the Ising model equation ij and w ij is generally a matrix.

[0170] The first term on the right side in the above equation (2) is obtained by merging the product of the state (state) and the weight value (weight) of the two circuits with respect to all combinations of two states that can be selected from all states of each bit without omission or duplication.

[0171] Further, the second term on the right side in the above equation (2) is obtained by merging the product of the offset value and the state of each state of all states of each bit.

[0172] That is, by extracting the parameters of the objective function equation before the objective function equation is converted into the Ising model equation and obtaining w ij and b i , the objective function equation can be converted into the Ising model equation represented by the above equation (2).

[0173] Further, in an example of the technology disclosed in the present case, the objective function equation converted into the Ising model equation as described above can be optimized (minimized) in a short time by performing an annealing method (annealing) using, for example, an annealing machine or the like. That is, in an example of the technology disclosed in the present case, it is advantageous that the optimization processing unit specifies (optimizes) the shape of the object by minimizing the objective function equation converted into the Ising model equation using the annealing method.

[0174] Examples of the annealing machine for optimizing the objective function equation include, for example, a quantum annealing machine, a semiconductor annealing machine using semiconductor technology, a machine that performs simulated annealing performed by software by using a central processing unit (CPU) or a graphics processing unit (GPU), or the like. Further, for example, Digital Annealer (registered trademark) can be used as the annealing machine.

[0175] Note that details of the annealing method using the annealing machine will be described below.

[0176] In addition, in an example of the technology disclosed in the present case, it is advantageous to filter the shape of the object optimized using the objective function equation based on the contribution. It is advantageous to correct a "scattered shape (mottled shape)" that is actually difficult to manufacture to a slightly continuous shape (remove small scattered parts, etc.) by filtering the optimized shape of the object.

[0177] Here, regarding the shape of the object optimized using the contribution-based objective function equation, depending on the optimization conditions and the like, there are some cases in which the shape in which the objective function equation takes the lowest value becomes a shape in which the material (substance) of the object is spread in the design region. In this case, the spread shape is considered to be a shape having high predetermined characteristics and high computational performance, but it can be difficult to actually manufacture the object. Therefore, it is advantageous to correct the object to have a continuous shape by filtering the shape of the object optimized using the contribution-based objective function equation. In other words, in the example of the technology disclosed in this case, it is advantageous that the optimization processing unit corrects the specified shape of the object to a continuous shape.

[0178] Further, in a case in which the update of the contribution and the optimization of the shape based on the contribution are repeatedly performed, it is advantageous to perform the correction to a continuous shape at each repetition.

[0179] Here, a specific example of the filtering (correction of the shape) will be described.

[0180] For example, in performing the filtering, the average density of each element in the design region is obtained in consideration of the elements around the each element, and the filtering can be performed based on the obtained average density.

[0181] In the technology of performing the filtering based on the average density, for example, the following equation using a distance (r) is used to specify the elements present within a radius (r min ) specified for the e-th element.

[0182] If

[0183] Note that, in the above equation, g denotes the barycentric coordinates of the element.

[0184] Next, in the technology of performing the filtering based on the average density, the average density (p e ) of the material weighted by the distance is specified by using the following two equations.

[0185]

[0186]

[0187] Then, in the technology of performing the filtering based on the average density, the filtering is performed by updating the distribution (x e ) of the material in the e-th element according to the magnitude of the average density using the following formula.

[0188]

[0189] Note that, regarding the filtering method based on the above-described average density, the method proposed by Almeida et al. in "A simple and effective inverse projection scheme for void distribution control in topology optimization." Struct Multidisc Optim, 39, 359-371 2009 can be used.

[0190] Hereinafter, examples of the technology disclosed in the present case will be described in more detail using configuration examples of the apparatus, flowcharts, and the like.

[0191] FIG. 4 A hardware configuration example of the optimization apparatus disclosed in the present case is shown.

[0192] In the optimization apparatus 100, for example, the control unit 101, the main storage apparatus 102, the auxiliary storage apparatus 103, the I / O interface 104, the communication interface 105, the input apparatus 106, the output apparatus 107, and the display apparatus 108 are connected to each other via a system bus 109.

[0193] The control unit 101 performs arithmetic operations (for example, four arithmetic operations, comparison operations, and arithmetic operations regarding the annealing method), hardware and software operation control, and the like. The control unit 101 can be, for example, a central processing unit (CPU), a part of an annealing machine for the annealing method, or a combination thereof.

[0194] The control unit 101 realizes various functions, for example, by executing a program (for example, an optimization program disclosed in the present case or the like) read in the main storage apparatus 102 or the like.

[0195] The processing performed by the optimization processing unit and the contribution designation unit in the optimization apparatus disclosed in the present case can be performed, for example, by the control unit 101.

[0196] The main storage apparatus 102 stores various programs and data required for execution of various programs, and the like. For example, an apparatus having at least one of a read only memory (ROM) and a random access memory (RAM) can be used as the main storage apparatus 102.

[0197] The ROM stores various programs, for example, a basic input / output system (BIOS) or the like. Furthermore, the ROM is not particularly limited, and can be appropriately selected according to the purpose. For example, a mask ROM, a programmable ROM (PROM), or the like can be exemplified.

[0198] For example, the RAM is used as a work range that is expanded when the control unit 101 executes various programs stored in the ROM, the auxiliary storage device 103, or the like. The RAM is not particularly limited, and can be appropriately selected depending on the purpose. For example, a dynamic random access memory (DRAM), a static random access memory (SRAM), or the like can be exemplified.

[0199] The auxiliary storage device 103 is not particularly limited as long as the device can store various information, and can be appropriately selected depending on the purpose. For example, a solid state drive (SSD), a hard disk drive (HDD), or the like can be exemplified. Furthermore, the auxiliary storage device 103 can be a portable storage device such as a CD drive, a DVD drive, or a Blu-ray (registered trademark) disc (BD) drive.

[0200] Furthermore, the optimization device program disclosed in the present case is stored in the auxiliary storage device 103, for example, loaded into the RAM (main memory) of the main storage device 102, and executed by the control unit 101.

[0201] The I / O interface 104 is an interface for connecting various external devices. The I / O interface 104 can input data to or output data from a device such as a compact disc ROM (CD-ROM), a digital versatile disc ROM (DVD-ROM), a magneto-optical disc (MO disc), a universal serial bus (USB) memory (USB flash drive), or the like.

[0202] The communication interface 105 is not particularly limited, and a known communication interface can be appropriately used. For example, a communication device using wireless communication or wired communication, or the like can be exemplified.

[0203] The input device 106 is not particularly limited as long as the device can receive input of various requests and information regarding the optimization device 100, and a known device can be appropriately used. For example, a keyboard, a mouse, a touch panel, a microphone, or the like can be exemplified. Furthermore, in a case where the input device 106 is a touch panel (touch display), the input device 106 can also function as the display device 108.

[0204] The output device 107 is not particularly limited, and a known device can be appropriately used. For example, a printer or the like can be exemplified.

[0205] The display device 108 is not particularly limited, and a known device can be appropriately used. For example, a liquid crystal display, an organic EL display, or the like can be exemplified.

[0206] FIG. 5 Another hardware configuration example of the optimization device disclosed in the present case is shown.

[0207] In FIG. 5 the example shown, the optimization device 100 is divided into a computer 200 that performs processing of specifying a contribution, processing of defining an objective function equation, processing of converting the objective function equation into an Ising model equation, and the like, and an annealing machine 300 that optimizes the Ising model equation. Further, in the example shown in FIG. 5, the computer 200 and the annealing machine 300 in the optimization device 100 are connected via a network 400.

[0208] In FIG. 5 the example shown, for example, a CPU or the like can be used as the control unit 101a of the computer 200, and a device dedicated to an annealing method (annealing) can be used as the control unit 101b of the annealing machine 300.

[0209] In FIG. 5 the example shown, for example, the computer 200 performs analysis by a finite element method and specifies a contribution as a function of the contribution specifying unit, sets various settings for defining an objective function equation to define the objective function equation, and converts the defined objective function equation into an Ising model equation. Then, information about values of a weight (w ij ) and a bias (b i ) in the Ising model equation is transmitted from the computer 200 to the annealing machine 300 via the network 400.

[0210] Next, the annealing machine 300 optimizes (minimizes) the Ising model equation based on the received information about the values of the weight (w ij ) and the bias (b i ), and obtains a minimum value of the Ising model equation and a state (state) of bits that give the minimum value. Then, the obtained minimum value of the Ising model equation and the obtained state (state) of bits that give the minimum value are transmitted from the annealing machine 300 to the computer 200 via the network 400.

[0211] Next, the computer 200 obtains an optimized shape or the like of the object based on the received state (state) of bits that give the minimum value for the Ising model equation.

[0212] FIG. 6 An example of a functional configuration of the optimization device disclosed in the present case is shown.

[0213] As FIG. 6 shown, the optimization device 100 includes a communication function unit 120, an input function unit 130, an output function unit 140, a display function unit 150, a storage function unit 160, and a control function unit 170.

[0214] The communication function unit 120, for example, transmits and receives various data to and from an external device. For example, the communication function unit 120 can receive data on the bias and weight in the objective function equation converted into the Ising model equation from the external device.

[0215] The input function unit 130, for example, receives various instructions for the optimization device 100. Furthermore, the input function unit 130 can receive, for example, an input of data on the bias and weight in the objective function equation converted into the Ising model equation.

[0216] The output function unit 140 prints and outputs, for example, information on the optimized shape of the object and the like.

[0217] The display function unit 150 displays, for example, information on the optimized shape of the object and the like on a display.

[0218] The storage function unit 160 stores, for example, various programs, information on the optimized shape of the object, and the like.

[0219] The control function unit 170 has an optimization processing unit 171 and a contribution specifying unit 172. The control function unit 170 executes, for example, various programs stored in the storage function unit 160 and controls the operation of the entire optimization device 100.

[0220] The optimization processing unit 171 executes, for example, a process of specifying (optimizing) the shape of the object using the objective function equation based on the contribution of the predetermined characteristics of the object.

[0221] The contribution specifying unit 172 executes, for example, a process of specifying the distribution of the physical quantity related to the predetermined characteristics by performing an analysis using numerical calculation with respect to the object to be arranged in the design region, thereby executing the specification of the contribution of each element of the object.

[0222] Here, an example of a flow when the shape of an example optimization object is described using the technology disclosed in the present case will be described with reference to FIG. 7

[0223] First, the optimization processing unit 171 divides the object to be arranged in the design region into a plurality of elements (S101). In other words, in S101, the optimization processing unit 171 prepares the elements obtained by dividing the object to be arranged in the design region.

[0224] ​Next, the optimization processing unit 171 sets a condition for arranging the elements in the divided object in the entire design region (S102). In other words, in S102, the optimization processing unit 171 sets the variable representing the distribution of the material for each element of the object in the design region to satisfy a condition that the material of the object is arranged in all the elements (for example, sets all the variables x indicating the presence or absence of the material to "1").

[0225] Next, the optimization processing unit 171 specifies a predetermined property of the object and a type of contribution to the predetermined property (S103). In other words, in S103, the optimization processing unit 171 specifies, for example, a performance to be considered when optimizing the object as the predetermined property and a physical quantity that affects the performance as the contribution, with respect to the object for which the shape is to be optimized.

[0226] Next, the contribution determination unit 172 performs analysis using numerical calculation by the finite element method and specifies the distribution of the physical quantity related to the predetermined property (S104). In other words, in S104, the contribution determination unit 172 specifies the physical quantity related to the predetermined property for each element by performing numerical calculation (simulation) of the finite element method with respect to the object in the design region divided into elements.

[0227] Then, the contribution specifying unit 172 specifies the contribution of each element of the object in the design region to the predetermined property of the object (S105). In other words, in S105, the contribution specifying unit 172 specifies the contribution of each element of the object on the basis of the distribution of the physical quantity specified in S104.

[0228] Next, the optimization processing unit 171 constructs an objective function equation on the basis of the contribution (S106). In other words, in S106, the optimization processing unit 171 defines an objective function equation based on the contribution of each element of the object to the predetermined property of the object on the basis of the contribution specified in S105.

[0229] Next, the optimization processing unit 171 converts the objective function equation into an Ising model equation represented by the following formula (2) (S107). In other words, in S107, the optimization processing unit 171 converts the objective function equation defined by extracting the parameters in the objective function equation and obtaining b i (deviation) and w ij (weight) in the following formula (2) into an Ising model equation represented by the following formula (2).

[0230]

[0231] Note that, in the above formula (2),

[0232] E is an objective function equation to be converted into an Ising model equation,

[0233] w ij is a value indicating an interaction between the i-th bit and the j-th bit,

[0234] b i is a value indicating a bias with respect to the i-th bit,

[0235] x i is a binary variable indicating that the i-th bit is 0 or 1, and

[0236] x j is a binary variable indicating that the j-th bit is 0 or 1.

[0237] Next, the optimization processing unit 171 minimizes the above-described equation (2) by using a simulated annealing machine (S108). In other words, in S108, the optimization processing unit 171 calculates the minimum value of the above-described equation (2) by performing a ground state search (optimization calculation) using a simulated annealing method with respect to the above-described equation (2) to specify the state of the bit that gives the minimum value to the objective function equation.

[0238] Then, the optimization processing unit 171 specifies the shape of the object based on the result of minimizing the above-described equation (2) (S109). In other words, in S109, the optimization processing unit 171 specifies the shape of the object at the time when the objective function equation becomes the minimum value based on the state of the bit that gives the minimum value to the above-described equation (2).

[0239] Next, the optimization processing unit 171 filters the specified shape of the object to correct the shape to a continuous shape (S110). More specifically, in S110, the optimization processing unit 171 performs processing of correcting the shape of the object specified in S109 to a continuous shape.

[0240] Next, the optimization processing unit 171 determines whether or not the change in the minimum value of the objective function equation is equal to or smaller than a predetermined value, and moves the processing to S112 in the case where it is determined that the change is equal to or smaller than the predetermined value, or returns the processing to S104 in the case where it is determined that the change is not equal to or smaller than the predetermined value (determination of equal to or larger than the predetermined value) (S111). More specifically, in S111, the optimization processing unit 171 determines whether or not the difference (ΔΕ) between the minimum value of the objective function equation in the n-th calculation and the minimum value of the objective function equation in the (n+1)-th calculation is smaller than a predetermined residual (ε). Then, in the case where it is determined that ΔE is smaller than ε (ΔΕ<ε), the processing is moved to S112, or in the case where it is determined that ΔE is equal to or larger than ε (ΔΕ≥ε), the processing is returned to S104.

[0241] Then, the optimization processing unit 171 outputs the optimization result of the shape of the object and terminates the processing (S112). In other words, in S112, the optimization processing unit 171 performs the filtering in S110, outputs the shape of the object when the change in the minimum value of the objective function equation is equal to or smaller than a predetermined value as the optimization result, and terminates the processing.

[0242] Further, in FIG. 7 In the present case, the flow of the processing in the example of the technology disclosed in the present case has been described in accordance with a specific order. However, in the technology disclosed in the present case, the order of the respective steps can be switched as appropriate within a technically feasible range. Further, in the technology disclosed in the present case, a plurality of steps can be executed in common within a technically feasible range.

[0243] An example of an annealing method and an annealing machine will be described below.

[0244] The annealing method is a method for finding a solution using random numbers and superposition probabilities of qubits. An example will be described below with a problem of minimizing the value of an evaluation function to be optimized. The value of the evaluation function is referred to as energy. Further, in a case where the value of the evaluation function is maximized, only the sign of the evaluation function needs to be changed.

[0245] First, the processing is started from an initial state in which one discrete value is assigned to each variable. For the current state (combination of variable values), a state close to the current state (for example, a state in which only one variable is changed) is selected, and a state transition between these two states is considered. An energy change related to the state transition is calculated. According to the value, it is probabilistically determined whether to adopt the state transition to change the state or not to adopt the state transition to keep the original state. In a case where the adoption probability at the time of energy decrease is selected to be greater than the adoption probability at the time of energy increase, it is expected that the state change will occur in the direction of energy average decrease, and state transitions to a more appropriate state will occur over time. Thus, there is a possibility that an optimal solution or an approximate solution giving an energy close to an optimal value can be obtained eventually.

[0246] If the state transition is adopted at the time of energy deterministic decrease and the state transition is not adopted at the time of energy increase, the energy change monotonically decreases with respect to time in a broad sense, but no further change occurs when a local solution is reached. As described above, since there are a very large number of local solutions in a discrete optimization problem, the state almost certainly falls into a local solution that is not close to an optimal value. Therefore, it is important to probabilistically determine whether to adopt a certain state when solving a discrete optimization problem.

[0247] In the annealing method, it has been proven that the state reaches an optimal solution under the constraint of infinite time (iteration count) by determining the adoption (allowance) probability of the state transition as follows.

[0248] Hereinafter, a method for finding an optimal solution using an annealing method will be described step by step.

[0249] (1) For the energy change value (-ΔΕ) due to state transition (energy decrease), the allowed probability p of state transition is determined by any one of the following functions f().

[0250] p(ΔΕ, T) = f(-ΔΕ / T) (Equation 1-1)

[0251] f metro (x) = min(l, e x ) (METROPOLIS method) (Equation 1-2)

[0252]

[0253] Here, the mark T is a parameter called a temperature value, and can be varied, for example, as follows.

[0254] (2) The temperature value T is logarithmically reduced with respect to the iteration count t as represented by the following equation.

[0255]

[0256] Here, T0 is an initial temperature value, and T0 is a value large enough depending on the problem.

[0257] In the case where the allowed probability represented by the equation in (1) is used, if a steady state is reached after a sufficient number of iterations, the occupation probability of each state follows the Boltzmann distribution for a thermal equilibrium state in thermodynamics.

[0258] Then, as the temperature gradually decreases from a high temperature, the occupation probability of a low-energy state increases. Therefore, it is considered that a low-energy state is obtained when the temperature is sufficiently reduced. Since this state is very similar to the state change caused when a material is annealed, this method is called an annealing method (or a pseudo annealing method). Note that the probabilistic occurrence of state transition that increases energy corresponds to thermal excitation in physics.

[0259] FIG. 8 An example of a functional configuration of an annealing machine that performs the annealing method is shown. However, in the following description, a case where a plurality of state transition candidates are generated is also described. However, the basic annealing method generates one transition candidate at a time.

[0260] The annealer 300 includes a state holding unit 111 that holds a current state S (a plurality of state variable values). Further, the annealer 300 includes an energy calculation unit 112 that calculates an energy change value {-ΔEi} of each state transition that occurs when a state transition with respect to the current state S occurs due to a change in any one of the plurality of state variable values. In addition, the annealer 300 includes a temperature control unit 113 that controls a temperature value T and a transition control unit 114 that controls a state change. Note that the annealer 300 can be part of the optimization device 100 described above.

[0261] The transition control unit 114 probabilistically determines whether to accept any one of the plurality of state transitions on the basis of the temperature value T, the energy change value {-ΔEi}, and a random number value according to a relative relationship between the energy change value {-ΔEi} and a thermal excitation energy.

[0262] Here, the transition control unit 114 includes a candidate generation unit 114a that generates state transition candidates and an availability determination unit 114b that probabilistically determines whether to allow a state transition for each candidate on the basis of the energy change value {-ΔEi} and the temperature value T. Further, the transition control unit 114 includes a transition determination unit 114c that determines a candidate to be adopted from among the allowed candidates and a random number generation unit 114d that generates a random variable.

[0263] The operation of the annealer 300 in one iteration is as follows.

[0264] First, the candidate generation unit 114a generates one or more state transition candidates (candidate numbers {Ni}) from the current state S held in the state holding unit 111 to a next state. Next, the energy calculation unit 112 calculates the energy change value {-ΔEi} of each state transition listed as a candidate using the current state S and the state transition candidates. The availability determination unit 114b allows the state transition according to the above-described allowable probability of formula (1) from the energy change value {-ΔEi} of each state transition using the temperature value T generated by the temperature control unit 113 and the random variable (random number value) generated by the random number generation unit 114d.

[0265] Then, the availability determination unit 114b outputs the availability {fi} of each state transition. In the case where a plurality of allowed state transitions exist, the transition determination unit 114c randomly selects one of the allowed state transitions using the random number value. Then, the transition determination unit 114c outputs the transition number N and the transition availability f of the selected state transition. In the case where one allowed state transition exists, the state variable values stored in the state holding unit 111 are updated according to the adopted state transition.

[0266] From the initial state, the above iteration is repeated while the temperature value is decreased by the temperature control unit 113. When a completion determination condition such as reaching a certain iteration count or the energy falling below a certain value is satisfied, the operation is completed. The answer output by the annealer 300 is the state at the time of completion of the operation.

[0267] FIG. 8 The illustrated annealer 300 can be implemented by using, for example, a semiconductor integrated circuit. For example, the transition control unit 114 can include a random number generation circuit functioning as the random number generation unit 114d, a comparison circuit functioning as at least a part of the availability determination unit 114b, a noise table to be described later, and the like.

[0268] Regarding FIG. 8 Details of the mechanism of allowing a state transition at the allowed probability represented in Expression (1) will be further described with respect to the illustrated transition control unit 114.

[0269] By inputting the allowed probability p with respect to input A and a uniform random number taking a value in the interval [0, 1) with respect to input B in a comparator having two inputs A and B, outputting 1 when A > B and outputting 0 when A < B, a circuit outputting 1 at the allowed probability p and outputting 0 at the allowed probability (1 - p) can be implemented. Therefore, if the value of the allowed probability p calculated based on the energy change value and the temperature value T using Expression (1) is input to input A of this comparator, the above function can be implemented.

[0270] This means that, with a circuit outputting 1 when f(ΔE / T) is greater than u, the above function can be implemented, in which f(ΔE / T), f is a function used in Expression (1), and u is a uniform random number taking a value in the interval [0, 1).

[0271] Further, the same function as the above function can also be implemented by making the following modification.

[0272] Applying the same monotonically increasing function to two numbers does not change the size relationship. Therefore, even if the same monotonically increasing function is applied to both inputs of the comparator, the output does not change. If the inverse function f -1 As this monotonically increasing function, it can be seen that a circuit outputting 1 when -ΔE / T is greater than f -1 (u) can be given. Further, since the temperature value T is positive, it can be seen that a circuit outputting 1 when -ΔE is greater than Tf -1 (u) can be sufficient.

[0273] FIG. 8 The transition control unit 114 in Expression (1) is implemented as f -1The conversion table of (u) and can include a noise table that outputs a value of a next function for an input of a discretized interval [0, -1).

[0274]

[0275]

[0276] FIG. 9 is a diagram showing an example of an operation flow of the transition control unit 114. FIG. 9 The illustrated operation flow includes a step of selecting one state transition as a candidate (S0001), a step of determining availability of the state transition by comparing a product of a temperature value and a random number value with an energy change value for the state transition (S0002), and a step of adopting the state transition in a case where the state transition is allowed and not adopting the state transition in a case where the state transition is not allowed (S0003).

[0277] (Optimization method)

[0278] The optimization method disclosed in the present case is an optimization method of optimizing a shape of an object, the optimization method including:

[0279] The optimization processing of the shape of the object is specified by using an objective function equation based on a contribution of each of a plurality of elements to a predetermined characteristic of the object, each of the plurality of elements being obtained by dividing the object to be arranged in a design region, and specifying whether to arrange each of the elements of the object for each of the elements of the object.

[0280] The optimization method disclosed in the present case can be executed by, for example, the optimization device disclosed in the present case. Further, for example, appropriate modes in the optimization method disclosed in the present case can be made similar to appropriate modes in the optimization device disclosed in the present case.

[0281] (Optimization program)

[0282] The optimization program disclosed in the present case is an optimization program for optimizing a shape of an object, the optimization program for causing a computer to execute processing of specifying the shape of the object by using an objective function equation based on a contribution of each of a plurality of elements to a predetermined characteristic of the object and specifying whether to arrange each of the elements of the object for each of the elements of the object, each of the plurality of elements being obtained by dividing the object to be arranged in a design region.

[0283] The optimization program disclosed in the present case can be, for example, a program for causing a computer to execute the optimization method disclosed in the present case. Further, for example, appropriate modes in the optimization program disclosed in the present case can be made similar to appropriate modes in the optimization device disclosed in the present case.

[0284] The optimization program disclosed in the present case can be created using various known programming languages according to the configuration of the computer system to be used, the type and version of the operating system, and the like.

[0285] The optimization program disclosed in the present case can be recorded in a recording medium such as a built-in hard disk or an external hard disk, or can also be recorded in a recording medium such as a CD-ROM, a DVD-ROM, an MO disk, or a USB memory.

[0286] Further, in a case where the optimization program disclosed in the present case is recorded in a recording medium as described above, the program can be used directly or can be installed in a hard disk and then used as needed by a recording medium reader included in a computer system. Further, the optimization program disclosed in the present case can be recorded in an external storage area (another computer or the like) accessible from a computer system through an information communication network. In the present case, the optimization program disclosed in the present case recorded in the external storage area can be used directly or can be installed in a hard disk and then used as needed from the external storage area through the information communication network.

[0287] Note that the optimization program disclosed in the present case can be divided for each of any processes, and recorded in a plurality of recording media.

[0288] (Computer-readable recording medium)

[0289] The computer-readable recording medium disclosed in the present case records the optimization program disclosed in the present case.

[0290] The computer-readable recording medium disclosed in the present case is not limited to any particular medium, and can be appropriately selected according to the purpose. Examples of the computer-readable recording medium include a built-in hard disk, an external hard disk, a CD-ROM, a DVD-ROM, an MO disk, a USB memory, and the like.

[0291] Further, the computer-readable recording medium disclosed in the present case can be a plurality of recording media in which the optimization program disclosed in the present case is divided for each of any processes and recorded.

[0292] Examples

[0293] Examples of the technology disclosed in the present case will be described. However, the technology disclosed in the present case is not limited to these examples.

[0294] Further, in the following examples, as a preferred example in the technology disclosed in the present case, an example in which the object is a magnetic shield, the predetermined characteristic is a shielding performance of a magnetic flux, and the contribution is a magnetization vector will be described.

[0295] (Example 1)

[0296] As Example 1, the shape of a magnetic shield is optimized using an example of the optimization device disclosed in this case. In Example 1, the shape of a magnetic shield is optimized using a magnetic shield having FIG. 5 The optimization device having the hardware configuration illustrated in FIG. 1 performs optimization of the shape of a magnetic shield according to the flow illustrated in the flowchart of FIG. 2. In addition, in order to minimize the objective function equation (make the Ising model equation in Expression (2) minimum), a Digital Annealer (registered trademark) is used. FIG. 7

[0297] <Contribution (magnetization vector) designation>

[0298] First, in Example 1, optimization is performed in which the shape of a magnetic shield is optimized while considering not only the shielding performance of magnetic flux as a predetermined characteristic of a magnetic shield (performance of a magnetic shield) but also the area of a magnetic material that forms a magnetic shield. More specifically, in Example 1, a search is performed for the shape of a magnetic shield that can minimize the magnetic flux density in a target region in which it is desired that a magnetic force be shielded by a magnetic shield and that the area of a magnetic material be as small as possible (the amount of material be as little as possible).

[0299] FIG. 10 is a diagram illustrating an example of a calculation model when the shape of a magnetic shield in Example 1 is optimized. As illustrated in FIG. 10 In Example 1, a target region 20 in which it is desired that a magnetic force be shielded by a magnetic shield is located inside a design region 10, which is a region in which a magnetic material that forms a magnetic shield can be arranged. In addition, in Example 1, a coil 30 (10 kAT (Ampere-Tesla)) that generates magnetic flux is located above the design region 10, as illustrated in FIG. 10 In Example 1, the boundary on the left side of the design region 10 and the target region 20 is a symmetric boundary 40A, and the boundary on the lower side of the design region 10 and the target region 20 is a natural boundary 40B, as illustrated in FIG. 10

[0300] FIG. 11 is a diagram illustrating an example of a BH curve (hysteresis curve) regarding a magnetic material that forms a magnetic shield, which is set in Example 1. In Example 1, the shape of a magnetic shield is optimized with respect to an example in which a magnetic shield is formed using a magnetic material in which the relationship between the magnetic flux density B (T) and the magnetic field (magnetic field) H (A / m) becomes a graph as illustrated in FIG. 11 when a magnetic field H is applied to the magnetic material.

[0301] Then, in Example 1, analysis using the finite element method (FEM) is performed as analysis using numerical calculation (CAE analysis) with respect to the calculation model illustrated in FIG. 10 ​​​

[0302] Specifically, in Example 1, a calculation model shown in FIG. 1 is divided into a plurality of elements, and a distribution of magnetic flux density is obtained by numerically solving a control equation with respect to a two-dimensional static magnetic field through analysis using a finite element method. That is, in Example 1, the magnetic flux density in each element is obtained by performing analysis using a finite element method with respect to the calculation model divided into a plurality of elements. FIG. 10

[0303] FIG. 12A to FIG. 12C is a diagram for describing an example of a flow when the magnetic flux density in each element is obtained by dividing the calculation model and performing analysis through a finite element method in Example 1.

[0304] First, as shown in S101 of FIG. 1, a calculation model similar to the calculation model shown in FIG. 1 is divided to obtain a set of a plurality of elements. Then, as shown in S102 of FIG. 1, the magnetic flux density (B) in each element is obtained by performing analysis through a finite element method with respect to the divided calculation model, and as shown in S103 of FIG. 1, a distribution of the magnetic flux density in the calculation model is specified. FIG. 12B FIG. 12A FIG. 10 FIG. 12B FIG. 12C

[0305] Note that, in Example 1, as described in S102 of FIG. 1, the condition that the magnetic material as the material of the magnetic shield is arranged in the entire design region 10 is set as an initial calculation model for optimizing the shape of the magnetic shield. Further, in Example 1, for each element in the design region 10 divided as shown in S101 of FIG. 1, the condition that the magnetic material is arranged in the ith element is expressed as "x i = 1", and the condition that the magnetic material is not arranged in the ith element is expressed as "x i = 0". FIG. 7 FIG. 12A Here, in Example 1, when numerically solving the control equation of the two-dimensional static magnetic field through analysis using a finite element method, the following equation is used as the control equation of the two-dimensional static magnetic field. FIG. 12B

[0306]

[0307]

[0308] In the above equation, μ denotes magnetic permeability, J0 denotes the current density in the coil 30, and A denotes the vector potential.

[0309] Note that, in a region in which the magnetic material is not present (a region in which air is present), the magnetic permeability μ is μ0 = 4π x 10 -7 (H / m). Further, according to the above equation, the magnetic permeability μ is μ = μ0 x (1 + χ), where χ is the magnetic susceptibility. FIG. 11 ​​​​​​​​​The nonlinear characteristic of the BH curve shown in the middle, in the region where the magnetic material exists (elements in which the magnetic material is disposed are arranged in the design region), the magnetic permeability μ can be represented by the following equation:

[0310]

[0311] Then, in Example 1, the vector potential A is obtained by numerically solving the above control equation with respect to the two-dimensional static magnetic field by analysis using the finite element method (simulation by the finite element method). Next, in Example 1, the magnetic flux density (B) in each element is obtained based on the obtained vector potential A by the following mathematical equation, and the distribution of the magnetic flux density (distribution of the field related to the shielding performance of the magnetic flux) in the calculation model is specified.

[0312] B = rot A

[0313] Next, in Example 1, the magnetization vector M (contribution example) in each element that is a partition of the design region is specified based on the specified distribution of the magnetic flux density (B).

[0314] Regarding the magnetization vector M in each element, in the design region, the elements are classified into elements in which the magnetic material is disposed (cells) and elements in which the magnetic material is not disposed (cells in which air is disposed), the magnetization vector M is calculated and specified.

[0315] For the elements in which the magnetic material is disposed, the magnetization vector M is specified based on the following equation.

[0316]

[0317] Here, in the above equation, M i represents the magnetization vector in the i-th element, H i represents the magnetic field strength in the i-th element, χ represents the coefficient of the magnetic field strength H, μ r represents the relative permeability of the magnetic material, μ0 represents the permeability of air, and B i represents the magnetic flux density of the i-th element.

[0318] In this way, in Example 1, the magnetization vector M that is the contribution of each element is obtained using the relative permeability μ r of the magnetic material, the permeability μ0 of air, and the magnetic flux density B obtained using the finite element method.

[0319] Further, for the elements in which the magnetic material is not disposed (elements in which air is disposed), the calculated value of the magnetization vector M becomes zero because, in the above equation for the magnetization vector M in the i-th element, iThe relative permeability is 1 when the above equation is used. Therefore, in Example 1, as the magnetization vector M of the element in which the magnetic material is not arranged, the magnetization vector M of the previous step when the magnetization vector is repeatedly updated and optimization is performed using the objective function equation will be used. That is, in Example 1, in the case where the magnetic material is arranged in the i-th element in the n-th calculation and the magnetic material is not arranged in the i-th element in the (n+1)-th calculation, the magnetization vector M in the i-th element in the (n+1)-th calculation is used as the magnetization vector M in the i-th element in the n-th calculation.

[0320] FIG. 13 is a graph showing an example of the magnetic flux density distribution in the design region in Example 1 in the case where the magnetic material as the material of the magnetic shield is arranged in the entire design region. FIG. 13 It is shown that the magnetic flux density is large in the region marked with a circle.

[0321] FIG. 14 is a graph showing an example of each element obtained by dividing the magnetic shield of the design region in Example 1 in the case where the magnetic material as the material of the magnetic shield is arranged in the entire design region.

[0322] As FIG. 14 shown in Example 1, the magnetic shield in the design region is divided so that the shape of each element of the magnetic shield in the design region 10 is a triangle. Note that in Example 1, the elements (meshes) used for specifying the distribution of the magnetic flux density when performing analysis using the finite element method are used as they are when specifying whether to arrange each element of the magnetic shield using the objective function equation.

[0323] <Construction of Objective Function Equation>

[0324] Here, in Example 1, the objective function equation is constructed (defined) as follows to perform a search for the shape of the magnetic shield, which can minimize the magnetic flux density in the region (target region) in which it is desired that the magnetic force be shielded by the shield and make the area of the magnetic material as small as possible (the amount of the material as small as possible).

[0325] As the objective function equation capable of obtaining the shape of the magnetic shield having as high a magnetic flux shielding performance as possible and as small an area of the magnetic material as possible, it is advantageous to include a term representing the magnitude of the magnetic flux density in the target region 20 and a term representing the area of the magnetic material in the design region 10. That is, in the example of the technology disclosed in the present case, it is advantageous that the optimization processing unit performs optimization based on an objective function equation including a term representing the magnitude of the magnetic flux density in the region in which the magnetic flux is shielded by the magnetic shield and a term representing the area of the magnetic material in the magnetic shield.

[0326] Specifically, in Example 1, the following equation (1) is defined as an objective function equation including a term representing the magnitude of the magnetic flux density in the region in which the magnetic flux is shielded by the magnetic shield and a term representing the area of the magnetic material in the magnetic shield, based on the magnetization vector M in each element.

[0327]

[0328] Note that, in equation (1),

[0329] E is the objective function equation,

[0330] α is a positive number,

[0331] E1 is a numerical value representing the square of the magnetic flux density in the region (target region) in which the magnetic flux is shielded in the case where the design region is filled with air,

[0332] N T is an integer representing the number of elements into which the region in which the magnetic flux is shielded is divided,

[0333] B k is a vector representing the magnetic flux density in the kth element of the region in which the magnetic flux is shielded,

[0334] ΔS k is a numerical value representing the area of the kth element of the region in which the magnetic flux is shielded,

[0335] β is a positive number,

[0336] E2 is a numerical value representing the area of the magnetic material in the case where the design region is filled with the magnetic material,

[0337] N D is an integer representing the number of elements into which the design region is divided,

[0338] ΔS i is a numerical value representing the area of the ith element of the design region, and

[0339] X i is a binary variable that becomes 1 in the case where the magnetic material is arranged for the ith element of the design region, and becomes 0 in the case where the magnetic material is not arranged and air is arranged.

[0340] In equation (1) described above, the first term on the right side (term with the coefficient α) represents the square of the magnetic flux density in the target region 20 inside the magnetic shield, and the second term on the right side (term with the coefficient β) represents the area of the magnetic material forming the magnetic shield. Note that the magnetic flux density B in the target region in the first term on the right side (term with the coefficient α) is represented by the sum of the magnetic flux density B0 in the case where the design region is filled with air and the magnetic flux density B1 in the case where the design region is filled with the magnetic material. kis obtained by calculation based on the Biot-Savart law using the following equation.

[0341] By specifying the shape of the magnetic shield that minimizes the value of the above equation (1), the shape that minimizes the magnetic flux density in the object region 20 existing inside the magnetic shield and makes the area of the magnetic material as small as possible can be specified.

[0342] Further, in the right side first term (term with the coefficient a), the magnetic flux density B k is a vector, so the equation of the objective function is converted into the QUBO format by converting the vector into a scalar by squaring.

[0343] Note that in Example 1, a = 0.95 and β = 0.05 are set.

[0344] Here, in the above equation (1), the magnetic flux density B k is obtained by calculation based on the Biot-Savart law using the following equation.

[0345]

[0346] Note that in the above equation,

[0347] B k is a vector that represents the magnetic flux density in the kth element of the region in which the magnetic flux is shielded (object region),

[0348] μ0 is the magnetic permeability of air,

[0349] N D is an integer that represents the number of elements into which the design region is divided,

[0350] x i is a binary variable that becomes 1 when a magnetic material is arranged for the ith element in the design region, and becomes 0 when air is used without arranging a magnetic material,

[0351] M i is the magnetization vector in the ith element of the design region,

[0352] R i,k is the position vector between the kth element in the region in which the magnetic flux is shielded and the ith element in the design region,

[0353] ΔS i is a numerical value that represents the area of the ith element in the design region,

[0354] N Cis an integer indicating the number of elements into which the region in which the coil is arranged (coil region) is divided,

[0355] J j is a vector indicating the current density in the jth element of the region in which the coil is arranged, and

[0356] ΔS j is a value indicating the area of the jth element in the region in which the coil is arranged.

[0357] Then, in Example 1, the above objective function equation (equation (1)) is converted into an Ising model equation represented by the following equation (2), and the converted Ising model equation is minimized by using a Digital Annealer (registered trademark) using an annealing method (annealing).

[0358]

[0359] Note that, in the above equation (2),

[0360] E is an objective function equation converted into an Ising model equation,

[0361] w ij is a value indicating the interaction between the ith bit and the jth bit,

[0362] b i is a value indicating the bias with respect to the ith bit,

[0363] x i is a binary variable indicating that the ith bit is 0 or 1, and

[0364] x j is a binary variable indicating that the jth bit is 0 or 1.

[0365] <Filtering>

[0366] In Example 1, a process of filtering and correcting the shape of the magnetic shield to a continuous shape by minimizing the objective function equation converted into the Ising model equation using the above equation (2) is performed.

[0367] Note that, in Example 1, the above technique of obtaining an average density taking into account the elements around each element and performing filtering based on the obtained average density is used.

[0368] Then, in Example 1, the magnetization vector (contribution) is repeatedly updated and optimized using the objective function equation based on the updated magnetization vector until the change in the minimum value of the objective function equation becomes equal to or smaller than a predetermined value, to optimize the shape of the magnetic shield. Note that, in Example 1, the process of performing filtering at each repetition to correct the shape of the magnetic shield to a continuous shape is performed.

[0369] <Results of optimization>

[0370] The shape of the magnetic shield in the process of repeatedly updating the magnetization vector (contribution) and optimizing using the objective function equation based on the updated magnetization vector in Example 1 will be described below.

[0371] First, FIG. 15 is a graph showing an example of the shape of the magnetic shield when the condition of arranging a magnetic material, which is a material to be the magnetic shield, in the entire design region is set, as an initial shape at the time of performing optimization in Example 1.

[0372] FIG. 16A is a graph showing an example of the shape of the magnetic shield before filtering is performed in the first optimization of Example 1. FIG. 16B is a graph showing an example of the shape of the magnetic shield after filtering is performed in the first optimization of Example 1.

[0373] Similarly, in FIG. 17A to FIG. 29B , examples of the shape of the magnetic shield before filtering and the shape of the magnetic shield after filtering from the second optimization to the fourteenth optimization are shown. Note that, in Example 1, since the change in the minimum value of the objective function equation at the time of performing the thirteenth optimization and the change in the minimum value of the objective function equation at the time of performing the fourteenth optimization become equal to or smaller than a predetermined value, optimization of the shape of the magnetic shield is terminated at the time of the fourteenth optimization.

[0374] As FIG. 16A to FIG. 29B shown, in the course of fifteen repetitions including the initial shape setting, the shape gradually changes from a continuous shape having a relatively large area of the magnetic material to a shape having a small area of the magnetic material, and finally, it is possible to obtain FIG. 29B the shape shown in . Note that, as described above, in the course of fifteen repetitions, the specification of the magnetization vector (contribution) using the finite element method is performed again with respect to the shape obtained by performing filtering after optimization, and the value of the magnetization vector is updated.

[0375] Further, as FIG. 16A to FIG. 29B shown, when the shape before filtering and the shape after filtering are compared, it is found that a "scattered shape" that is difficult to manufacture by performing filtering is corrected to a continuous shape.

[0376] FIG. 30A is a drawing illustrating an example of a shape of a magnetic shield when, in Example 1, a magnetic material that is a material of the magnetic shield is arranged in the entire design region. FIG. 30B is a drawing illustrating an example of magnetic force lines of a magnetic force generated by the coil in the shape of the magnetic shield when, in Example 1, a magnetic material that is a material of the magnetic shield is arranged in the entire design region. Note that, in FIG. 30A and FIG. 30B , the magnetic material is illustrated in a light color region, and the magnetic force lines are illustrated in dark color lines.

[0377] As illustrated in FIG. 30A and FIG. 30B , when a magnetic material that is a material of the magnetic shield is arranged in the entire design region, in the shape of the magnetic shield, the area of the magnetic material is large but the magnetic force lines do not intrude into the target region 20, and the shielding performance of the magnetic flux is high.

[0378] Further, the area of the magnetic material having the shape illustrated in FIG. 30A and FIG. 30B is 0.75 cm 2 .

[0379] FIG. 31A is a drawing illustrating an example of an optimization result of a shape of a magnetic shield when, in Example 1, a = 0.95 and β = 0.05. FIG. 31B is a drawing illustrating an example of magnetic force lines of a magnetic force generated by the coil in the shape of the optimization result of the magnetic shield when, in Example 1, a = 0.95 and β = 0.05.

[0380] As illustrated in FIG. 31A and FIG. 31B , when a = 0.95 and β = 0.05 are set in Equation (1), the area of the magnetic material is significantly smaller than the area of the magnetic material in the example illustrated in FIG. 31A and FIG. 31B , and the area of the magnetic material is 0.19 cm 2 . Further, as illustrated in FIG. 31A and FIG. 31B , in the optimization result of Example 1, although the area of the magnetic material is small as described above, the magnetic force lines hardly intrude into the target region 20, and the shielding performance of the magnetic flux can be sufficiently maintained.

[0381] As described above, in Example 1, by optimizing the shape of the magnetic shield using the objective function equation illustrated in Equation (1) above, the shielding performance of the magnetic flux with respect to the target region is sufficient and a shape in which the area of the magnetic material can be suppressed can be specified.

[0382] (Example 2)

[0383] In Example 2, the shape of the magnetic shield is optimized in a similar manner to Example 1, except that in Example 1, a and β of Equation (1) are set to a = 0.5 and β = 0.5, respectively.

[0384] FIG. 32A is a graph showing an example of the optimization result of the shape of the magnetic shield in the case where a = 0.5 and β = 0.5 in Example 2. FIG. 32B is a graph showing an example of the magnetic force lines of the magnetic force generated by the coil in the shape of the optimization result of the magnetic shield in the case where a = 0.5 and β = 0.5 in Example 2.

[0385] (Example 3)

[0386] In Example 3, the shape of the magnetic shield is optimized in a similar manner to Example 1, except that in Example 1, a and β of Equation (1) are set to a = 0.7 and β = 0.3, respectively.

[0387] FIG. 33A is a graph showing an example of the optimization result of the shape of the magnetic shield in the case where a = 0.7 and β = 0.3 in Example 3. FIG. 33B is a graph showing an example of the magnetic force lines of the magnetic force generated by the coil in the shape of the optimization result of the magnetic shield in the case where a = 0.7 and β = 0.3 in Example 3.

[0388] (Example 4)

[0389] In Example 4, the shape of the magnetic shield is optimized in a similar manner to Example 1, except that in Example 1, a and β of Equation (1) are set to a = 0.8 and β = 0.2, respectively.

[0390] FIG. 34A is a graph showing an example of the optimization result of the shape of the magnetic shield in the case where a = 0.8 and β = 0.2 in Example 4. FIG. 34B is a graph showing an example of the magnetic force lines of the magnetic force generated by the coil in the shape of the optimization result of the magnetic shield in the case where a = 0.8 and β = 0.2 in Example 4.

[0391] (Example 5)

[0392] In Example 5, the shape of the magnetic shield is optimized in a similar manner to Example 1, except that in Example 1, a and β of Equation (1) are set to a = 0.99 and β = 0.01, respectively.

[0393] FIG. 35A is a graph showing an example of the optimization result of the shape of the magnetic shield in the case where a = 0.99 and β = 0.01 in Example 5. FIG. 35B: is a diagram showing an example of magnetic lines of force of the magnetic force generated by the coil in the shape of the optimized result of the magnetic shield in the case of α=0.99 and β=0.01 in Example 5.

[0394] FIG. 36 : is a graph showing an example of the relationship between the mean square of the magnetic flux density in the target area and the area of ​​the magnetic material (magnetic material area) in Examples 1 to 5.

[0395] like FIG. 36 As shown, in the example of the technology disclosed in the present case, the shape of the magnetic shield can be obtained according to the purpose of optimization by changing the values ​​of α and β in the formula (1).

[0396] That is, as shown in Examples 1 to 5, by changing the values ​​of α and β in equation (1), it is possible to adjust the balance between the performance of minimizing the magnetic flux density in the target area and the size of the area of ​​the magnetic material to be used, with respect to the shape of the magnetic shield to be searched. More specifically, for example, by increasing α and decreasing β in equation (1), it is possible to search for a shape that is beneficial for minimizing the magnetic flux density in the target area. Furthermore, for example, by decreasing α and increasing β in equation (1), it is possible to search for a shape that is beneficial for suppressing the size of the area of ​​the magnetic material.

[0397] Here, in the example of the technology disclosed in this case, as described above, a fully optimized shape of the magnetic shield can be obtained by repeating the calculation fifteen times. In other words, in the example of the technology disclosed in this case, the shape of the magnetic shield can be optimized by repeating the numerical calculation (simulation) fifteen times using the finite element method.

[0398] Here, when using continuous topology optimization, which is described as prior art, to optimize the shape of a magnetic shield using a computing system with a design region similar to the example of the technology disclosed in this application, it is known that 200 calculations using the finite element method are required. Details of this prior art example are described, for example, in SATO, Takahiro, WATANABE, Kota, and IGARASHI, Hajime, “ON LEVELSET AND EVOLUTIONARY ON / OFF METHODS FOR TOPOLOGY OPTIMIZATION IN MAGNETOSTATIC PROBLEMS,” Proceedings of Computational Methods in Engineering, Vol. 14, pp. 13-18, 2014.

[0399] Further, for example, in a case where a discrete topology optimization as described in the related art is used and the number of elements (the number of meshes) in the finite element method is n, 2 n sub-calculations by the finite element method are required, and the calculation cost increases exponentially with respect to the number of elements in the finite element method.

[0400] As described above, in an example of the technology disclosed in the present case, the number of times of performing a process with a large calculation cost by the finite element method (an example of a numerical calculation method) can be significantly reduced compared to the related art. Thus, the calculation time can be shortened and the shape can be optimized in a short time.

[0401] FIG. 37 FIG. 1 is a diagram illustrating an example of a flow of a process in one embodiment of the technology disclosed in the present case.

[0402] As illustrated in FIG. 37 , in one embodiment of the technology disclosed in the present case, first, an object to be arranged in a design region is divided into a plurality of sets of elements ("1. Element division of design region"). Next, in one embodiment of the technology disclosed in the present case, a distribution of a physical quantity for specifying a contribution to a predetermined characteristic of the object is analyzed by performing a CAE analysis on a calculation model including the design region divided into elements ("2. Analysis of distribution of physical quantity by CAE analysis").

[0403] Next, as illustrated in FIG. 37 , in one embodiment of the technology disclosed in the present case, a contribution of each element is specified based on the analyzed distribution of the physical quantity ("3. Specification of contribution of element"). Then, in one embodiment of the technology disclosed in the present case, an objective function equation based on the specified contribution is constructed ("4. Construction of objective function equation").

[0404] Next, as illustrated in FIG. 37 , in one embodiment of the technology disclosed in the present case, the objective function equation is optimized by an annealing method ("5. Optimization of objective function equation by annealing method"). Next, in one embodiment of the technology disclosed in the present case, a shape of the object obtained by optimizing the objective function equation is filtered to be a continuous shape ("6. Filtering of obtained shape").

[0405] Then, as illustrated in FIG. 37As shown, in one embodiment of the technology disclosed in the present case, in a case where the change in the minimum value of the objective function equation is equal to or greater than a predetermined value, the process in "2. Analyzing the distribution of physical quantities by CAE analysis" is executed, and an iterative process is executed to obtain a more suitable shape ("7. Iterative process when there is a change in the value of the objective function equation").

[0406] Further, in one embodiment of the technology disclosed in the present case, in a case where the change in the minimum value of the objective function equation is equal to or less than a predetermined value, it is considered that sufficient optimization has been completed and the optimized result (the shape of the object) is output ("8. Outputting the final shape when the value of the objective function equation is not changed").

[0407] In one embodiment of the technology disclosed in the present case, for example, by executing the process as shown in FIG. 37 the shape of the object can be optimized in a short time and sufficiently.

[0408] All examples and conditional language recited herein are intended for pedagogical purposes to aid the reader in understanding the present application and the concepts contributed by the inventor to furthering the art, and are to be construed as being without limitation to such specifically recited examples and conditions. Although specific examples of the present application have been described above, various modifications, alterations, and permutations of the described examples can be made and will be suggested to those skilled in the art by the instant disclosure.

Claims

1. An optimization device for optimizing the shape of a magnetic shield, the optimization device comprising: Memory; as well as a processor coupled to the memory, the processor configured to perform an optimization process, the optimization process comprising: An objective function equation is obtained based on a contribution of each of a plurality of elements to a predetermined characteristic of the magnetic shield, each of the plurality of elements being an element obtained by dividing the magnetic shield arranged in a design area, wherein the predetermined characteristic is shielding performance of magnetic flux and the contribution is a magnetization vector, and wherein the objective function equation is represented by the following equation (1): In the above formula (1), E is the objective function equation, α is a positive number, E1 is a value representing the square of the magnetic flux density in the area where the magnetic flux is shielded when the design area is filled with air. N T is an integer representing the number of elements into which the area shielded from magnetic flux is divided, B k is a vector representing the magnetic flux density in the kth element of the region where the magnetic flux is shielded, ΔS k is the numerical value representing the area of ​​the kth element of the region where the magnetic flux is shielded, β is a positive number, E2 is a numerical value representing the area of ​​the magnetic material when the design area is filled with the magnetic material. N D is an integer representing the number of elements into which the design area is divided, ΔS i is a numerical value representing the area of ​​the i-th element of the design region, and x i is a binary variable that becomes 1 when a magnetic material is arranged for the i-th element of the design area and becomes 0 when no magnetic material is arranged and air is used; and The shape of the magnetic shield is optimized by determining whether to arrange each element of the magnetic shield based on the obtained objective function equation for each element of the magnetic shield.

2. The optimization device according to claim 1, wherein: The processor is configured to perform a contribution designation process comprising: obtaining a distribution of a physical quantity related to the predetermined characteristic by performing analysis using numerical calculation on the magnetic shield arranged in the design area; and The contribution of each element of the magnetic shield is obtained by using the obtained distribution of the physical quantity.

3. The optimization device according to claim 2, wherein: The contribution specifying process is configured to obtain a contribution of each element of the magnetic shield by performing an analysis using a finite element method.

4. The optimization device according to claim 2, wherein: The contribution designation process is configured to update the contribution of each element of the magnetic shield based on a specific result as to whether each element of the magnetic shield is arranged, and The optimization process is configured to optimize the shape of the magnetic shield by using an objective function equation obtained based on the updated contribution.

5. The optimization device according to claim 4, wherein: Updating the contribution in the contribution specifying process and performing optimization using the objective function equation based on the updated contribution in the optimization process are repeated until a change in the minimum value of the objective function equation becomes equal to or smaller than a predetermined value.

6. The optimization device according to claim 1, wherein: The optimization process is configured to convert the optimized shape of the magnetic shield into a continuous shape.

7. The optimization device according to claim 1, wherein: Of the two terms included on the right side of the objective function equation, the first term represents the magnitude of the magnetic flux density in the region where magnetic flux is shielded by the magnetic shield, and the second term represents the area of ​​the magnetic material in the magnetic shield.

8. The optimization device according to claim 1, wherein: The optimization process is configured to optimize the shape of the magnetic shield based on an objective function equation converted into an Ising model equation represented by the following equation (2): In the above formula (2), E is the objective function equation converted into the Ising model equation, w ij is a numerical value representing the interaction between the i-th bit corresponding to the i-th element of the design region and the j-th bit corresponding to the j-th element of the design region, b i is a numerical value indicating the deviation about the i-th position, x i means that the i-th bit is 0 or 1, and x j is a binary variable indicating whether the j-th bit is 0 or 1, which becomes 1 when a magnetic material is arranged for the j-th element of the design area and becomes 0 when no magnetic material is arranged and air is used.

9. The optimization device according to claim 8, wherein: The optimization process is configured to optimize the shape of the magnetic shield by minimizing an objective function equation converted into an Ising model equation by means of an annealing method.

10. A computer-based optimization method for optimizing the shape of a magnetic shield, the optimization method comprising: An objective function equation is obtained based on a contribution of each of a plurality of elements to a predetermined characteristic of the magnetic shield, each of the plurality of elements being an element obtained by dividing the magnetic shield arranged in a design area, wherein the predetermined characteristic is shielding performance of magnetic flux and the contribution is a magnetization vector, and wherein the objective function equation is represented by the following equation (1): In the above formula (1), E is the objective function equation, α is a positive number, E1 is a value representing the square of the magnetic flux density in the area where the magnetic flux is shielded when the design area is filled with air. N T is an integer representing the number of elements into which the area shielded from magnetic flux is divided, B k is a vector representing the magnetic flux density in the kth element of the region where the magnetic flux is shielded, ΔS k is the numerical value representing the area of ​​the kth element of the region where the magnetic flux is shielded, β is a positive number, E2 is a numerical value representing the area of ​​the magnetic material when the design area is filled with the magnetic material. N D is an integer representing the number of elements into which the design area is divided, ΔS i is a numerical value representing the area of ​​the i-th element of the design region, and x i is a binary variable that becomes 1 when a magnetic material is arranged for the i-th element of the design area and becomes 0 when no magnetic material is arranged and air is used; and The shape of the magnetic shield is optimized by determining whether to arrange each element of the magnetic shield based on the obtained objective function equation for each element of the magnetic shield.

11. A non-transitory computer-readable storage medium storing an optimization program for optimizing the shape of a magnetic shield, the program comprising instructions that, when executed by a computer, cause the computer to perform a process comprising: An objective function equation is obtained based on a contribution of each of a plurality of elements to a predetermined characteristic of the magnetic shield, each of the plurality of elements being an element obtained by dividing the magnetic shield arranged in a design area, wherein the predetermined characteristic is shielding performance of magnetic flux and the contribution is a magnetization vector, and wherein the objective function equation is represented by the following equation (1): In the above formula (1), E is the objective function equation, α is a positive number, E1 is a value representing the square of the magnetic flux density in the area where the magnetic flux is shielded when the design area is filled with air. N T is an integer representing the number of elements into which the area shielded from magnetic flux is divided, B k is a vector representing the magnetic flux density in the kth element of the region where the magnetic flux is shielded, ΔS k is the numerical value representing the area of ​​the kth element of the region where the magnetic flux is shielded, β is a positive number, E2 is a numerical value representing the area of ​​the magnetic material when the design area is filled with the magnetic material. N D is an integer representing the number of elements into which the design area is divided, ΔS i is a numerical value representing the area of ​​the i-th element of the design region, and x i is a binary variable that becomes 1 when a magnetic material is arranged for the i-th element of the design area and becomes 0 when no magnetic material is arranged and air is used; and The shape of the magnetic shield is optimized by determining whether to arrange each element of the magnetic shield based on the obtained objective function equation for each element of the magnetic shield.

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