Method for designing porous body and method for manufacturing porous body

Abstract

This method for designing a porous body comprises: a learning step for performing learning by means of a conditional generative adversarial network using a plurality of true data items that associate three-dimensional image data of the porous body with a label including one or more kinds of indexes representing the shape and / or performance of the porous body, to obtain a trained generator that generates three-dimensional image data based on the label (S110); and a porous structure identifying step in which the value of the label is varied and input to the trained generator (S120), one or more kinds of parameters are calculated (S130), the parameters representing the shape and / or performance of the porous body represented by the three-dimensional image data with respect to each of the plurality of three-dimensional image data items that the trained generator has generated on the basis of the inputs, and, on the basis of the one or more kinds of parameters that have been calculated, three-dimensional image data of which one or more kinds of parameters are suitable is identified from the plurality of three-dimensional image data items that have been generated (S160).

Description

[Technical Field]

[0001] The present invention relates to a method for designing a porous body and a method for manufacturing a porous body. [Background technology]

[0002] It has been known that porous bodies are used in devices for purifying exhaust gases, such as honeycomb filters. For example, Patent Document 1 describes a porous body in which the porosity and permeability satisfy predetermined numerical ranges and relational expressions, thereby achieving a sufficiently small porosity and a sufficiently large permeability. Furthermore, Patent Document 2 describes a porous body in which the porosity and permeability satisfy predetermined numerical ranges and relational expressions, thereby achieving a sufficiently small porosity and a sufficiently large permeability. 2 It is described that the number of communicating holes per septum is preferably between 3800 and 6000. It is described that the number of communicating holes is calculated by taking continuous cross-sectional images of the septum using an X-ray CT scanner and using a three-dimensional model created from the continuous cross-sectional images using GeoDict, a microstructure simulation software developed by Math2Market GmbH. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Application Laid-Open No. 2015-189666 [Patent Document 2] Patent No. 6940786 Summary of the Invention [Problem to be solved by the invention]

[0004] There are many types of parameters required for porous bodies, including parameters related to shape such as porosity and the number of interconnected pores, and parameters related to performance such as pressure drop characteristics, collection characteristics, mechanical strength characteristics, etc. There has been a demand for efficiently identifying porous bodies having suitable parameters for one or more of these parameters.

[0005] The present invention has been made to solve such problems, and a main object of the present invention is to efficiently identify a porous body having suitable parameters. [Means for solving the problem]

[0006] In order to achieve the above-mentioned main object, the present invention employs the following means.

[0007] The method for designing a porous body of the present invention comprises the steps of: a learning step of performing training using a conditional generative adversarial network using a plurality of true data in which three-dimensional image data of a porous body is associated with labels including one or more types of indicators representing the shape and / or performance of the porous body, to obtain a trained generator that generates three-dimensional image data based on the labels; a porous structure identification step of changing the label values ​​in various ways and inputting them into the trained generator, calculating one or more parameters representing the shape and / or performance of the porous body represented by the three-dimensional image data for each of the multiple three-dimensional image data generated by the trained generator based on the input, and identifying three-dimensional image data for which the one or more parameters are suitable from the multiple three-dimensional image data generated based on the calculated one or more parameters; It includes:

[0008] The method for producing a porous body of the present invention comprises the steps of: A design process for executing the porous body design method described above; a forming step of producing a porous body based on three-dimensional image data in which the one or more parameters specified in the design step are suitable; It includes: [Effects of the Invention]

[0009] In this porous body design method, a conditional generative adversarial network (CGAN) is used to train a plurality of true data sets that associate 3D image data of a porous body with labels containing one or more indicators that represent the shape and / or performance of the porous body, thereby obtaining a trained generator that generates 3D image data based on the labels. The values ​​of the labels are then varied and input into the trained generator. For each of the plurality of 3D image data sets generated by the trained generator based on the input, one or more parameters that represent the shape and / or performance of the porous body represented by the 3D image data are calculated. Based on the calculated one or more parameters, 3D image data with one or more suitable parameters is identified from the plurality of generated 3D image data sets. In this porous body design method, by using a trained generator prepared by training using a CGAN, labels containing one or more indicators are used as input, and multiple 3D image data sets representing various porous bodies corresponding to the labels can be efficiently generated. Therefore, porous bodies with suitable parameters can be efficiently identified using the plurality of generated 3D image data sets. Furthermore, in this method for manufacturing a porous body, the porous body is produced based on the preferred three-dimensional image data identified by the above-mentioned porous body design method, and therefore a porous body having preferred parameters can be obtained. [Brief explanation of the drawings]

[0010] [Figure 1] FIG. 2 is a diagram showing an outline of the configuration of a design device 20. [Figure 2] FIG. 3 is an explanatory diagram schematically showing how a generator 31 generates three-dimensional image data. [Figure 3] FIG. 10 is an explanatory diagram schematically showing how the classifier 32 generates a true image likelihood score that takes label reproducibility into consideration. [Figure 4] 1 is a flowchart showing an example of a porous body design routine. [Figure 5] An illustration of true data. [Figure 6] FIG. 1 is an explanatory diagram showing how three-dimensional image data is generated using the GRF method. [Figure 7] A conceptual diagram showing how 3D image data of a sphere-packed structure is generated. [Figure 8] FIG. 3 is an explanatory diagram of the machine learning unit 30. [Figure 9] FIG. 1 is an explanatory diagram of the labels input to the trained generator 31 and the generated 3D image data and parameters. [Figure 10] FIG. 10 is an explanatory diagram showing a plurality of Pareto optimal solutions finally obtained by the search process and a state in which suitable three-dimensional image data is identified from the plurality of Pareto optimal solutions. [Figure 11] An explanatory diagram showing how 3D image data is generated from an actual porous body using CT scanning. DETAILED DESCRIPTION OF THE INVENTION

[0011] Next, an embodiment of the present invention will be described with reference to the drawings. FIG. 1 is a schematic diagram showing a design device 20, which is one embodiment of a porous body design device that executes the porous body design method of the present invention. In this embodiment, the porous body is used as a diesel particulate filter (DPF) that has the function of capturing particulate matter (PM) in the exhaust gas of a diesel engine. However, the use of the porous body is not limited to this. Furthermore, the porous body may have a porosity of, for example, 1% or more and 99% or less.

[0012] The design device 20 comprises a computer (hardware) including a device main body 21, an input unit 22 such as a keyboard and a mouse, and an output unit 23 such as a display. The device main body 21 comprises a CPU, ROM, RAM, a storage device, a GPU (Graphics Processing Unit), an input / output interface, and a communication port, all of which are not shown. The design device 20 also comprises a program (software) stored in the storage device of the device main body 21. As shown in FIG. 1, the design device 20 comprises a true data generation unit 25, a machine learning unit 30, and a porous structure identification unit 35 as functional blocks constructed by the cooperation of these hardware and software components.

[0013] The true data generation unit 25 generates multiple pieces of true data to be used when the machine learning unit 30 performs learning processing. The true data is data that associates three-dimensional image data of a porous body with labels including one or more types of indices that represent the shape and / or performance of the porous body. The three-dimensional image data included in the true data may be a three-dimensional image of the structure of an actual porous body imaged with an X-ray CT scanner, or a three-dimensional image of the structure of a numerically created virtual porous body.

[0014] The three-dimensional image data is data that associates, for example, position information (e.g., XYZ coordinates) that indicates the three-dimensional position of a pixel (voxel) with color information of the voxel. In this embodiment, each of the multiple voxels included in the three-dimensional image data has binarized color information that indicates whether the voxel is a space (pore) inside the porous body or a substance that constitutes the porous body. The color information may be binarized, for example, into values ​​0 and 1, or may be binarized into values ​​0 and 255 as grayscale brightness values. However, the color information is not limited to this and may be ternary information, or may include brightness values ​​from 0 to 255, or may include RGB values.

[0015] Examples of indicators included in the label that represent the shape (structural characteristics) of the porous body include the porosity, solid fraction, specific surface area, pore diameter, particle diameter, structural uniformity of the pores or solid, the pore chord length, which is the continuous length of the pores in a predetermined direction in the porous body, and the solid chord length, which is the continuous length of the solid in a predetermined direction in the porous body. The label may include one or more of these indicators. Examples of indicators included in the label that represent the performance of the porous body include the pressure drop characteristics, collection characteristics, mechanical strength characteristics, electrochemical characteristics, thermal conductivity characteristics, heat exchange characteristics, electrical conductivity characteristics, gas adsorption characteristics, gas purification performance, catalyst coating properties, and removal efficiency of substances captured in the porous body. The label may include one or more of these indicators. In addition, in this embodiment, the indicator included in the label is a material type intensity vector (x1, x2, . . . , xn) that represents the intensity of each pattern included in the porous body when the porous body is classified into n types of patterns, where n is an integer greater than or equal to 2. The material type intensity vector is a type of index that represents the shape of a porous body. The material type intensity vector will be described later. The label may include two or more of these various indexes. For example, the label may include two or more indexes that represent the shape of the porous body, or may include two or more indexes that represent the performance of the porous body, or may include one or more indexes that represent the shape of the porous body and one or more indexes that represent the performance of the porous body.

[0016] The machine learning unit 30 performs learning using a conditional generative adversarial network (CGAN) using a plurality of true data. The machine learning unit 30 includes a generator 31 and a classifier 32.

[0017] The generator 31 receives input of noise (also called a latent variable; a vector in which each element is a random number) and labels (also called a condition vector), and generates 3D image data based on the input. FIG. 2 is an explanatory diagram that schematically illustrates how the generator 31 generates 3D image data. As shown in the figure, the generator 31 is configured as a neural network having, as its main components, a fully connected layer and a transposed convolutional layer. When noise (e.g., a 400-dimensional vector) and labels are input to the generator 31, the noise is first fully connected to a series of 3D arrays (e.g., 96 8x4x4 3D arrays) that are feature maps of the 3D image. The noise is then concatenated with a group of arrays (e.g., three 8x4x4 3D arrays) with the same number of label elements, each of which has been upsampled to a 3D array of the same size, to generate a group of concatenated 3D arrays (e.g., 99 8x4x4 3D arrays). Next, the generator 31 repeatedly deconvolves the group of connected three-dimensional arrays, and ultimately generates one piece of three-dimensional image data (for example, one three-dimensional array of 256×128×128).

[0018] The classifier 32 inputs the label and 3D image data and outputs a "true image likelihood score taking label reproducibility into account," which is the sum of the degree to which the input 3D image data matches the porous body pattern indicated by the input label and a score representing the likelihood of the image being genuine. Figure 3 is an explanatory diagram schematically showing how the classifier 32 generates a true image likelihood score taking label reproducibility into account. The classifier 32 is configured as a neural network having a convolution layer and a fully connected layer as its main components. When the label and 3D image data are input to the classifier 32, the classifier 32 first repeatedly convolves the input 3D image data to convert it into a series of 3D arrays that are feature maps (e.g., 128 3D arrays of 16 × 8 × 8), and then further converts them into a single feature vector (e.g., a 48-dimensional vector) through full connection. Meanwhile, the classifier 32 converts the input label (e.g., 3D) into a vector of the same size (e.g., 48 dimensions) as the feature vector through full connection. The classifier 32 then outputs the sum of a scalar value (corresponding to label reproducibility) which is the inner product of the feature vector and the vector converted from the label, and a scalar value (corresponding to true image reproducibility) converted from the feature vector by full connection, as a true image reproducibility score taking the label reproducibility into consideration. For example, even if the generator 31 outputs an image that seems to be a true image, if the image is similar to a true image with a different label and seems to be a true image, then the learning of the generator 31 is insufficient, and label reproducibility has not been achieved. In order to have the generator 31 generate an image that seems to be a true image in line with the intention of the given label, the classifier 32 is designed as a network structure that calculates a true image reproducibility score taking label reproducibility into consideration.

[0019] As will be described in detail later, CGAN learning is performed in the machine learning unit 30, which adjusts and updates the values ​​of multiple (e.g., hundreds of thousands to hundreds of millions, or more depending on the problem) parameters such as weights and biases used in the fully connected layer and transposed convolutional layer of the generator 31 and the fully connected layer and convolutional layer of the classifier 32. The resulting trained generator 31 can generate realistic 3D image data based on the input labels that matches the porous body pattern represented by the label values.

[0020] The porous structure identification unit 35 uses the 3D image data generated by the trained generator 31 to identify 3D image data for which one or more parameters representing the shape and / or performance of the porous body represented by the 3D image data are suitable. The porous structure identification unit 35 includes an optimization processing unit 36 ​​and a parameter calculation unit 37. The parameter calculation unit 37 calculates one or more parameters representing the shape and / or performance of the porous body represented by the 3D image data based on the 3D image data generated by the trained generator 31. The optimization processing unit 36 ​​changes the label values ​​in various ways and inputs them to the trained generator 31, and causes the parameter calculation unit 37 to calculate parameters for each of the multiple 3D image data generated by the trained generator 31 based on the input. Based on the calculated parameters, the optimization processing unit 36 ​​identifies 3D image data for which one or more parameters are suitable from the multiple 3D image data generated by the trained generator 31. At this time, the optimization processing unit 36 ​​uses the labels input to the trained generator 31 as explanatory variables, and uses one or more types of parameters calculated by the parameter calculation unit 37 based on the 3D image data generated by the trained generator 31 based on the input as objective functions, and uses an optimization method to identify 3D image data for which one or more types of parameters are suitable.

[0021] Next, the operation of the design device 20 of this embodiment configured as described above, in particular the design method for a porous body executed by the design device 20, will be described. a learning step of performing learning using a conditional generative adversarial network using a plurality of true data in which three-dimensional image data of a porous body is associated with labels including one or more types of indicators representing the shape and / or performance of the porous body, to obtain a trained generator 31 that generates three-dimensional image data based on the labels; a porous structure identification step of changing the label values ​​in various ways and inputting them into the trained generator 31, calculating one or more parameters representing the shape and / or performance of the porous body represented by the three-dimensional image data for each of the multiple three-dimensional image data generated by the trained generator 31 based on the input, and identifying three-dimensional image data for which the one or more parameters are suitable from the multiple three-dimensional image data generated based on the calculated one or more parameters; Includes.

[0022] 4 is a flowchart showing an example of a porous body design routine executed by the design device 20. When this routine is started, the design device 20 first performs a process of generating a plurality of true data to be used in CGAN as a preparation process for the learning step (step S100).

[0023] As described above, the true data is a correspondence between the 3D image data of the porous body and the label, and the label is associated with the 3D image data that matches the label. Therefore, the 3D image data of the true data is also called a true image. The true data is used as input to the classifier 32 in the CGAN.

[0024] FIG. 5 is an explanatory diagram of true data. In this embodiment, the above-mentioned material type intensity vector (x1, x2, . . . , xn) is used as a label. The material type intensity vector represents the intensity of each pattern contained in a porous body when the porous body is classified into n types of patterns (material types), where n is an integer greater than or equal to 2. Intensity here refers to the magnitude of the components of each pattern of n types of porous bodies contained in a certain porous body. In other words, the material type intensity vector allows a certain porous body to be expressed as a hybrid material that combines the structures and characteristics of the n types of patterns contained in the porous body. Each component x1 to xn may have a value between 0 and 1, with 0 representing the absence of that component (lowest intensity) and 1 representing the highest intensity of that component. Furthermore, the sum of each component of the material type intensity vector (x1 + x2 + . . . + xn) may always be 1. Each of the multiple true data may include data associating the three-dimensional image data with one of n basis vectors of a material type intensity vector space constituted by the material type intensity vector, which is defined as representing the porous body pattern to which the three-dimensional image data belongs. Furthermore, the basis vector may be a vector in which the intensity of any one of the n types of porous body patterns in the material type intensity vector is a value other than 0 and the intensity of the (n-1) types of patterns is a value of 0. That is, the basis vector may be a vector in which the value of any one of the components x1, x2, . . . , xn of the material type intensity vector is a value other than 0 and the values ​​of the other components are 0. The basis vector may be a unit vector in which the value of any one of the components x1, x2, . . . , xn of the material type intensity vector is a value of 1 and the values ​​of the other components are 0. In this embodiment, the material type intensity vector associated with the true data is this unit vector.

[0025] An example of a material type intensity vector will be specifically described. In this embodiment, n = 3, and the three types of porous body patterns are a sintered simulated structure, a sphere-packed structure, and a sponge structure. The 3D image data on the left side of FIG. 5 is an example of a sintered simulated structure, the 3D image data in the center of FIG. 5 is an example of a sphere-packed structure, and the 3D image data on the right side of FIG. 5 is an example of a sponge structure. The sintered simulated structure is a structure that simulates the sintered structure of a porous body. The sphere-packed structure is a structure in which multiple particles (spheres) that are components of a porous body are packed. The sponge structure is a structure in which the particles and spaces of the sphere-packed structure are reversed. Unlike the sphere-packed structure, the sintered simulated structure has a structure in which multiple particles that make up the porous body are deformed and bonded. These three types of porous bodies were assigned to components x1, x2, and x3 of the material type intensity vector. That is, the strength of the sintered simulated structure was represented by x1, the strength of the sphere-packed structure by x2, and the strength of the sponge structure by x3. Furthermore, each component x1 to x3 takes a value between 0 and 1, with the value 0 being when that component is not included (lowest intensity) and the value 1 being when that component has the highest intensity. Therefore, as shown in Figure 5, the unit vector (1,0,0) is assigned as the material type intensity vector to the 3D image data of the sintered simulated structure. The unit vector (0,1,0) is assigned as the material type intensity vector to the 3D image data of the sphere packed structure. The unit vector (0,0,1) is assigned as the material type intensity vector to the 3D image data of the sponge structure.

[0026] In step S100, the real data generator 25 generates three-dimensional image data for each of the sintered-simulated structure, the sphere-packed structure, and the sponge structure. The three-dimensional image data may be a three-dimensional image of the structure of an actual porous body imaged by an X-ray CT scanner, or a three-dimensional image of the structure of a numerically generated virtual porous body. The three-dimensional image data representing the structure of the virtual porous body can be generated using, for example, the GRF (Gaussian Random Field) method or GeoDict (virtual material generation software) from Math2Market GmbH. In this embodiment, the real data generator 25 generates three-dimensional image data of the sintered-simulated structure using the GRF method, and generates three-dimensional image data of the sphere-packed structure and the sponge structure using GeoDict. In this embodiment, the function of the part of the real data generator 25 that executes the GRF method is realized using a program created using, for example, the programming language Python. However, other general-purpose programming languages ​​(e.g., C, Fortran, or Basic) may be used instead of Python.

[0027] The generation of 3D image data using the GRF method will now be described. The GRF method is a method for generating images of porous bodies with random skeletal structures and random pore surface structures according to a given random number sequence. The GRF method can generate images of porous bodies based on a set standard deviation σ and threshold γ. Figure 6 is an explanatory diagram showing how 3D image data is generated using the GRF method. For ease of explanation, Figure 6 shows an image of a cross section of a porous body in the 3D image data. When generating 3D image data using the GRF method, the true data generation unit 25 first generates a uniformly distributed random number sequence (each random number has a value extracted from a uniform probability distribution between 0 and 1) of the same size as the 3D image data to be generated, and then generates 3D image data in which each element of the generated random number sequence is arranged three-dimensionally (Figure 6(a)). Next, the true data generation unit 25 applies a Gaussian filter with a standard deviation σ to the generated 3D image data to perform convolution. As a result, the color shading in the convoluted 3D image is smoother than in the image before convolution, resulting in an image with a porous skeletal structure whose scale corresponds to the standard deviation σ (Figure 6(b)). For example, from Figure 6(a), which is an image corresponding to a uniformly distributed random number array, an image with smoothed color shading, as shown in Figure 6(b), is generated. The convolution result at this time varies depending on the value of the standard deviation σ. The three images in Figure 6(b) show examples of images after convolution when the standard deviation σ is set to three values: 2, 3, and 4 when convolving the image in Figure 6(a). Next, the true data generation unit 25 binarizes the color information of each voxel in the convoluted 3D image data using a threshold γ. The threshold γ is a value greater than 0 and less than 1. The color information value of each voxel (a value greater than or equal to 0 and less than 1) is compared with this threshold γ to determine which is larger, and the color information value is binarized to 0 or 1. This results in binarized 3D image data that indicates whether each voxel represents an internal space (pore) of the porous body or an object that constitutes the porous body (Fig. 6(c)). The binarization results vary depending on the value of the threshold γ.The three images in Figure 6(c) show examples of binarized images obtained by convolution of the image data in Figure 6(b) (the image on the right side of Figure 6(b)) with a standard deviation σ of 4, with the threshold γ set to three values: 0.48, 0.49, and 0.50. As can be seen from Figure 6, when generating 3D image data using the GRF method, changing the standard deviation σ and threshold γ can generate 3D image data of porous bodies with different structures and characteristics. For example, changing the standard deviation σ can generate 3D image data of porous bodies with different skeletal structure scales, and changing the threshold γ can generate 3D image data of porous bodies with different porosities and average pore diameters. Conversely, to generate multiple sets of 3D image data for porous bodies with similar structures and characteristics (e.g., porous bodies with a specific average pore size and porosity), the combination of the standard deviation σ and the threshold value γ can be adjusted for each of the different uniformly distributed random number sequences so that the sets have similar structures and characteristics (e.g., so that the sets have a specific average pore size and porosity), and the 3D image data can be generated. In this case, the standard deviation σ may be fixed and the threshold value γ may be adjusted.

[0028] The true data generator 25 may also perform a process to fine-tune the 3D image data generated by the GRF method, such as removing object portions that are floating from surrounding objects and cannot be actually created (changing the corresponding voxels from objects to space). When generating 3D image data using the GRF method, the true data generator 25 may also perform a process to generate a surface structure of the porous body so that the porosity of the outermost surfaces located at both ends of the porous body in the direction of internal fluid flow is greater than the porosity of the interior of the porous body. For example, when generating the uniformly distributed random number sequence for the above-mentioned 3D image data, the true data generator 25 may add regions with a length of 5 voxels to both ends of the flow direction relative to the size of the generated 3D image data, thereby generating a uniformly distributed random number sequence whose length along the flow direction is 10 voxels larger. The flow direction may be set, for example, as a direction parallel to one of the X, Y, and Z axes used for the position information of the voxels in the 3D image data. For example, if the size of the 3D image data is 256 x 128 x 128 voxels, the true data generation unit 25 generates a uniformly distributed random number array of 266 x 128 x 128 voxels. Next, the true data generation unit 25 applies a filter to the added region that attenuates from 1 to 0.9 along the flow direction, so that the random number value decreases toward both ends of the flow direction (i.e., the region is more likely to become porosity). Next, the true data generation unit 25 uses the standard deviation σ and threshold γ described above to generate binarized 3D image data including the added region, and then deletes the added region. By performing this processing, the porosity of the outermost surface located at both ends of the flow direction in the 3D image data becomes a value of 1 or close to that value, making it possible to generate 3D image data with a natural surface structure that more closely resembles that of an actual porous body.

[0029] In this embodiment, the true data generation unit 25 sets the standard deviation σ to a fixed value (value 4), adjusts (sets) the threshold value γ according to the distribution random number array so as to achieve the target porosity, and generates multiple 3D image data of the sintered simulated structure by the GRF method. The target porosity is a value randomly extracted from a normal distribution with an average of 0.55 and a standard deviation of 0.005, and is varied to some extent each time the 3D image data is generated.

[0030] The true data generator 25 also uses GeoDict, as described above, to generate multiple 3D image data for each of the packed-sphere structure and the sponge structure. Figure 7 is a conceptual diagram illustrating the generation of 3D image data for the packed-sphere structure. As shown in Figure 7, the packed-sphere structure is created by dropping multiple particles (spheres) that constitute the porous body from above into an area the size of the 3D image data, simulating the state in which multiple particles are packed into the area without performing particle expansion or contraction processing. Therefore, in the packed-sphere structure, adjacent particles are in point contact with each other. The sponge structure is created by filling an area with multiple particles, similar to the packed-sphere structure, and then inverting the particles and spaces to create spaces in the filled particle areas. However, if adjacent particles are only in point contact with each other, the connection of the spaces (pores) after inversion will be poor. Therefore, when creating the sponge structure, after filling the particles, a process is performed to slightly expand the diameter (e.g., by 2 voxels) of each particle without changing their center position, so that the particles partially overlap each other before inversion. The process of filling a region with particles as described above can be performed using, for example, the GrainGeo module in GeoDict, and the process of expanding or contracting particles can be performed using, for example, the ProcessGeo module in GeoDict.

[0031] The true data generator 25 generates multiple true data sets by associating the generated 3D image data of the sintered-simulated structure, sphere-packed structure, and sponge structure with their respective labels (here, material type intensity vectors). In step S100 of this embodiment, the true data generator 25 generates 5,000 pieces of 3D image data for each of the sintered-simulated structure, sphere-packed structure, and sponge structure, preparing a total of 15,000 pieces of true data. The 5,000 pieces of 3D image data of the same type are generated using the same data generation method, but at least some of the image data differ from each other. For example, the GRF method uses a uniformly distributed random number array with different values ​​each time, allowing for the generation of multiple 3D image data sets with at least some of the data differing from each other while maintaining the same generation method (while maintaining the same porous body pattern). When GeoDict is used, 3D image data sets with at least some of the data differing from each other while maintaining the same generation method can be obtained by randomizing the filling conditions, such as the particle drop position and particle size.

[0032] After generating multiple pieces of true data in step S100, the design device 20 performs a learning process in which a CGAN is used to learn the multiple pieces of true data to obtain a trained generator 31 (step S110). This step S110 corresponds to an example of the learning step described above. CGAN trains the generator 31 and the classifier 32 based on opposing loss functions to obtain a trained generator 31 that generates realistic images based on labels. In CGAN, the generator 31 trains the generator 31 to generate 3D image data that is closer to the true image based on the input labels, i.e., realistic 3D image data that matches the pattern of the porous body indicated by the input labels, and the classifier 32 then generates a true-image-likeness score for the 3D image data (also referred to as a fake image) that takes into account higher label reproducibility (the image is evaluated as realistic by the classifier 32). Furthermore, the classifier 32 is trained so as to maximize the difference between the true image likelihood score that takes into account label reproducibility output by the classifier 32 for 3D image data (true image) included in the true data and the true image likelihood score that takes into account label reproducibility output by the classifier 32 for 3D image data (fake image) generated by the generator 31 (so that fake images can be more accurately detected as fakes). In CGAN, the training of the generator 31 and the training of the classifier 32 are alternately repeated to obtain a trained generator 31 that evaluates images generated by the generator 31 as more likely to be real by the trained classifier 32.

[0033] This CGAN can be trained using a predetermined loss function. In this embodiment, the loss function formula (the following formulas (1) and (2)) of WGAN-gp (Wasserstein GAN-gradient penalty), which is one of the variations of GAN, is used as the loss function formula. However, other loss functions may also be used.

[0034]

number

[0035] A specific example of learning using CGAN will be described. FIG. 8 is an explanatory diagram of the machine learning unit 30. In step S110, the machine learning unit 30 first inputs 3 types of 20 pieces of true data out of the 15,000 pieces of true data described above, for a total of 60 pieces of true data, into the classifier 32. That is, 20 pieces of true data (combinations of labels and 3D image data) for each of the sintered-simulated structure, the sphere-packed structure, and the sponge structure are input to the classifier 32. At the same time, false data is input to the classifier 32, combining 3 types of 20 fake images generated by inputting labels and noise into the generator 31 at that point in the learning process with the labels input to the generator 31. The classifier 32 outputs a true image likelihood score for each of these 60 pieces of true data and 60 pieces of false data, taking label reproducibility into consideration. Then, the machine learning unit 30 calculates the original critic loss (original classifier loss function) of Equation (1) based on the output of the classifier 32. Specifically, the machine learning unit 30 calculates the average of the true image likelihood scores (the second term on the right-hand side of equation (1)) taking into account the reproducibility of the 60 labels output for each piece of true data, and calculates the average of the true image likelihood scores (the first term on the right-hand side of equation (1)) taking into account the reproducibility of the 60 labels output for each piece of false data, and defines the difference as the Original critic loss in equation (1). Furthermore, the machine learning unit 30 calculates the third term on the right-hand side of equation (1) (Gradient penalty). Specifically, the machine learning unit 30 divides the images in each pair of 60 image pairs consisting of the 60 true images and the 60 false images internally at the ratio of values ​​extracted from uniformly distributed random numbers between 0 and 1 to generate 60 interpolated images, and combines these with the label information of each image to generate 60 interpolated image data x i Further, the machine learning unit 30 obtains |y. i |y is the output of the discriminator 32, D(x i The gradient penalty is calculated by multiplying the average of the squared deviations of the L2 norm of the gradient of |y) from 1 by the coefficient λ. Then, the machine learning unit 30 calculates the sum of the calculated gradient penalty and the original critic loss as the loss function of the classifier 32 (L in Equation (1)). D) The coefficient λ is typically set to a value of 10, and is set to a value of 10 in this embodiment. The machine learning unit 30 then calculates the loss function L D Based on the loss function L D The classifier 32 is trained so that the value of σ is minimized, more specifically, so that the entire right-hand side of Equation (1) is minimized. Specifically, training the classifier 32 means updating the values ​​of multiple parameters used in the convolutional layer and fully connected layer of the classifier 32. As a result, the classifier 32 is trained so that the difference between the true image likelihood score that takes into account label reproducibility output by the classifier 32 for 3D image data (true image) included in the true data and the true image likelihood score that takes into account label reproducibility output by the classifier 32 for 3D image data (fake image) generated by the generator 31 is maximized (so that fake images can be more accurately identified as fakes). This training of the classifier 32 based on 60 pieces of true data is referred to as one iteration. The classifier 32 is trained 15,000 / 60 = 250 times, i.e., 250 iterations, using 15,000 pieces of true data.

[0036] Furthermore, every time the classifier 32 performs four iterations of learning, the generator 31 performs one iteration of learning. Learning one iteration of the generator 31 is performed as follows. First, the machine learning unit 30 inputs three types of labels and 20 noises to the generator 31. Next, the machine learning unit 30 inputs 60 pieces of fake data to the classifier 32 at that point in the learning process, which are combinations of 60 fake images (three types of labels × 20 noises) output by the generator 31 based on the combinations of the input labels and noises and the labels input to the generator 31 when each fake image was generated. Then, the machine learning unit 30 calculates the average value (= right side of equation (2)) of the outputs of the classifier 32 for the 60 pieces of fake data, and calculates the loss function (L in equation (2)) of the generator 31. G ) Then, the machine learning unit 30 calculates the loss function L GThe generator 31 is trained so that the value of is minimized. Specifically, training of the generator 31 means updating the values ​​of multiple parameters used in the fully connected layer and transposed convolution layer of the generator 31. As a result, training is performed so that the true image likelihood score that takes into account label reproducibility output by the classifier 32 for the 3D image data (fake image) included in the fake data is maximized (so that the fake image generated by the generator 31 becomes closer to the true image). This training of the generator 31 based on 60 fake data is called one iteration. The generator 31 trains one iteration for every four iterations of the classifier 32. In other words, the generator 31 trains 63 iterations while the classifier 32 trains 250 iterations.

[0037] The 20 noise elements used for training the generator 31 and the classifier 32 are random values ​​extracted from a normal distribution, but the 20 noise elements are different from each other. However, the same 20 noise elements are used for each label. Therefore, these 20 noise elements are also called fixed noise elements.

[0038] The process of training the classifier 32 for 250 iterations and the generator 31 for 63 iterations is called one epoch. The number of epochs is repeated until the fake image generated by the generator 31 becomes sufficiently close to the true image, thereby obtaining a trained generator 31. When the data shown in Figures 9 and 10 (described later) was obtained, the training was terminated after 920 iterations of the above one epoch because the fake image became sufficiently close to the true image.

[0039] The trained generator 31 obtained by training the CGAN in this way can efficiently generate multiple 3D image data representing various porous bodies according to the labels input, each of which includes one or more indices. More specifically, for an input of any label (here, a material type intensity vector), it can generate 3D image data that matches the structural pattern indicated by the label (more precisely, 3D image data that matches the structural pattern indicated by the label and is close to the true image). For example, when the trained generator 31 receives a material type intensity vector (1,0,0), it generates 3D image data that matches the pattern of the sintered simulated structure and is close to the true image. Furthermore, the trained generator 31 can generate 3D image data that matches the structural pattern indicated by any material type intensity vector (x1,x2,x3), not limited to the three types of material type intensity vectors (1,0,0), (0,1,0), and (0,0,1) that are the labels used for the true data, for an input of any material type intensity vector (x1,x2,x3), it can generate 3D image data that matches the structural pattern indicated by the input material type intensity vector. This allows the trained generator 31 to generate 3D image data of a hybrid material in which the structures and characteristics of n types of porous bodies (here, three types of porous bodies: sintered-like structure, sphere-packed structure, and sponge structure) are mixed in various proportions using the material type intensity vector. When the trained generator 31 is made to generate 3D image data, in addition to the labels, randomly generated noise is also input to the trained generator 31, as in the learning process of step S110.

[0040] The machine learning unit 30 that performs learning using CGAN as in step S110 above can be created, for example, using general-purpose libraries for deep learning such as TensorFlow and PyTorch on the programming language Python.

[0041] After performing step S110, the design device 20 performs processing (porous structure specifying processing) of steps S120 to S160. These steps S120 to S160 correspond to an example of the porous structure specifying step described above.

[0042] In the porous structure identification process of this embodiment, the porous structure identification unit 35 first performs steps S115 to S150 (search process). In this search process, the porous structure identification unit 35 first determines the label value to be input to the trained generator 31 (step S115). The porous structure identification unit 35 may, for example, randomly determine the label value, or may determine a value obtained from the operator via the input unit 22. The number of labels determined in step S115 may be one or more, and may be multiple. Next, the porous structure identification unit 35 inputs the label determined in step S115 to the trained generator 31, causing the trained generator to generate three-dimensional image data (step S120). The trained generator 31 generates multiple pieces of three-dimensional image data (20 pieces in this embodiment) based on the single label input from the porous structure identification unit 35 and the multiple (20 pieces in this embodiment) randomly generated fixed noises described above. If multiple label values ​​are determined in step S115, the trained generator 31 generates multiple pieces of 3D image data based on each of the multiple labels and the fixed noise. The 20 fixed noises have different values ​​for at least some of the elements in the noise. The same 20 fixed noises are used in step S120 regardless of the label values ​​input to the trained generator 31. The fixed noises used in step S120 do not need to be the same as the fixed noises used to train the CGAN. Next, the parameter calculation unit 37 of the porous structure identification unit 35 calculates one or more types of parameters (20 in this embodiment) that represent the shape and / or performance of the porous body represented by the 3D image data based on the generated 3D image data, and calculates the average of these parameters (step S130).

[0043] Here, various indices other than the material type intensity vector among the indices exemplified in the label described above can be used as the parameters of the porous body. Specifically, the parameters may include one or more of the following indices representing the shape (structural characteristics) of the porous body: porosity, solid fraction, specific surface area, pore diameter, particle diameter, structural uniformity of the pores or solid, pore chord length (the continuous length of the pores in a predetermined direction in the porous body), and solid chord length (the continuous length of the solid in a predetermined direction in the porous body). Examples of the parameters representing the performance of the porous body may include one or more of the pressure drop characteristics, collection characteristics, mechanical strength characteristics, electrochemical characteristics, thermal conductivity characteristics, heat exchange characteristics, electrical conductivity characteristics, gas adsorption characteristics, gas purification performance, catalyst coating properties, and removal efficiency of substances captured in the porous body. The parameters may include two or more of these various indices. For example, the parameters may include two or more indicators representing the shape of the porous body, or may include two or more indicators representing the performance of the porous body, or may include one or more indicators representing the shape of the porous body and one or more indicators representing the performance of the porous body. The parameters may include one or more of the pressure drop characteristics and collection characteristics of the porous body. In this embodiment, the parameters are the pressure drop characteristics and collection characteristics of the porous body.

[0044] The parameter calculation unit 37 calculates one or more parameters (here, the pressure loss characteristics and collection characteristics of the porous body) by performing a physical simulation based on each of the multiple 3D image data generated by the trained generator 31. The parameter calculation unit 37 calculates pressure loss [Pa] as the pressure loss characteristics and PM collection efficiency (unit: dimensionless) as the collection characteristics. In this embodiment, the parameter calculation unit 37 calculates the pressure loss and PM collection efficiency using FlowDict and FilterDict, which are additional modules for CFD (Computational Fluid Dynamics) calculations in GeoDict. FlowDict is a module that calculates the velocity of each point in the flow within the porous body, and FilterDict is a module that calculates the particle behavior of PM based on the obtained velocity field. The parameter calculation unit 37 may also calculate parameters using other methods. For example, the parameter calculation unit 37 may calculate the pressure loss [Pa] when a fluid passes through the porous body represented by the 3D image data by performing fluid analysis using the lattice Boltzmann method as a physical simulation based on the 3D image data. Such a method for calculating pressure loss is known, and is described, for example, in paragraph 0072 of Japanese Patent Application Laid-Open No. 2017-178729. The parameter calculation unit 37 may calculate the collection efficiency as follows. Specifically, the parameter calculation unit 37 first performs fluid analysis by the lattice Boltzmann method as a physical simulation based on the three-dimensional image data, thereby calculating the leakage amount [g / m ] of PM when a fluid containing PM passes through the inside of a porous body represented by the three-dimensional image data. 3 ] is calculated. 3 ] is the weight [g] of PM that passed through the porous medium, i.e., PM that was not captured by the porous medium, divided by the volume [m 3 ]. Such a method for calculating the amount of leakage of PM is known, and is described, for example, in paragraph 0071 of Japanese Patent Application Laid-Open No. 2017-178729. The parameter calculation unit 37 also calculates the amount of leakage of PM by dividing the total amount [g / m 3 ](unit volume of porous material [m 3Based on this, the collection efficiency (unit is dimensionless) is calculated using the relational expression: Collection efficiency = (total amount of PM - leakage amount of PM) / total amount of PM.

[0045] As described above, when the trained generator 31 generates 20 pieces of 3D image data in step S120, the parameter calculation unit 37 calculates one or more types of parameters based on each of the 20 pieces of 3D image data. The parameter calculation unit 37 also calculates the average for each type of parameter (here, the average of the pressure loss characteristics and the average of the collection characteristics). The calculated average is associated with the label at the time of generation of the 3D image data that was the basis for calculating the parameters. When multiple labels are input to the trained generator 31 in step S120, the average value of the parameters is calculated for each label.

[0046] When the parameter calculation unit 37 calculates one or more parameters in step S130, the porous structure identification unit 35 determines whether the termination condition for the search process is met (step S140). If the termination condition is not met, the porous structure identification unit 35 determines the value of the label to be input next to the trained generator 31 based on the parameters calculated in step S130 (step S150) and performs the processes from step S120 onwards. As a result, the porous structure identification unit 35 repeatedly performs the process of inputting a label to the trained generator 31 to generate 3D image data and the process of determining the label to be input next to the trained generator 31 based on parameters calculated from the generated 3D image data, thereby sequentially searching for porous bodies (3D image data). The fixed noise (20 fixed noises in this embodiment) used when repeatedly performing step S120 is the same value each time. In step S150, the porous structure identification unit 35 may determine the label to be input next to the trained generator 31 based on the parameters calculated in the most recent step S130. Furthermore, the porous structure identification unit 35 may determine the label to be input next to the trained generator 31 based on at least a portion of the parameters calculated in step S130, not just the most recent but multiple times over. The porous structure identification unit 35 may also determine the label to be input next to the trained generator based on all of the parameters calculated so far. The porous structure identification unit 35 may also randomly determine the label to be input next to the trained generator, regardless of the parameters calculated so far. Then, when the porous structure identification unit 35 determines in step S140 that the termination condition for the search process is met, it terminates the search process. Upon terminating the search process, the porous structure identification unit 35 identifies suitable 3D image data from the 3D image data generated during the search process (step S160) and terminates the porous structure identification process.

[0047] Furthermore, when performing the porous structure identification process, the porous structure identification unit 35 of this embodiment uses an optimization method to identify 3D image data for which one or more parameters are suitable, with the labels input to the trained generator 31 as explanatory variables and one or more parameters calculated for the porous body represented by the 3D image data generated by the trained generator 31 based on the input as objective functions. As the optimization method, for example, one or more of Bayesian optimization, genetic algorithm, and gradient method can be used. In this embodiment, Bayesian optimization is used. Furthermore, since this embodiment uses two parameters, the pressure drop characteristics and collection characteristics (more specifically, pressure drop and collection efficiency) of the porous body, multi-objective Bayesian optimization is used. Therefore, in this embodiment, the optimization processing unit 36 ​​of the porous structure identification unit 35 performs the above-mentioned search process using this multi-objective Bayesian optimization method. "Identifying three-dimensional image data having one or more suitable parameters using an optimization method" includes both cases where the optimization method is used to identify suitable three-dimensional image data, and cases where the optimization method is used to identify multiple suitable three-dimensional image data candidates (for example, multiple Pareto optimal solutions, described below, finally obtained by repeating steps S120 to S150). In the latter case, it is sufficient to identify suitable three-dimensional image data from the multiple suitable three-dimensional image data candidates using a method other than the optimization method.

[0048] Multi-objective Bayesian optimization is a method for finding a Pareto front (a set of Pareto-optimal solutions) when there is a trade-off relationship between multiple objective functions. A Pareto-optimal solution is a point that is not dominated by any other point in an objective function space defined by multiple objective functions. For example, in this embodiment, pressure loss and collection efficiency are used as objective functions, and a smaller pressure loss is preferable, and a higher collection efficiency is preferable. Therefore, point B, which has a larger pressure loss and a lower collection efficiency than point A in the objective function space, is dominated by point A. Such a point that is not dominated by other points is a Pareto-optimal solution.

[0049] In multi-objective Bayesian optimization, a Pareto front of a set of objective functions, each of which is one or more parameters calculated for a porous body represented by 3D image data generated based on all evaluated labels (explanatory variables), is selected using an acquisition function. Labels that have not yet been evaluated are selected using an acquisition function that has a high probability or expected value of improving the current Pareto front. If the objective function of the 3D image data generated from the selected labels improves the current Pareto front, the Pareto front is updated. By repeating this process, the Pareto-optimal solutions are updated, and multiple Pareto-optimal solutions are ultimately obtained. Various acquisition functions are known, including EHVI (Expected Hyper-Volume Improvement), HVPI (Hypervolume-based Probability of Improvement), and TS (Thompson Sampling). In this embodiment, EHVI is used as the acquisition function. EHVI is a function for acquiring the point with the largest expected value of the increase in Pareto hypervolume. The point with the largest expected value is selected as the next point to search.

[0050] Before starting the search, the search candidate labels to be evaluated may be discretely defined in advance within the range of possible label values. In this case, a Gaussian process regression equation for the relationship between the evaluated labels and the objective function is used to calculate an acquisition function (EHVI in this embodiment) for each of all unevaluated search candidate labels, and the label that gives the maximum value of the acquisition function is selected as the next label to be evaluated. In this embodiment, the range of possible values ​​for each element (x1, x2, and x3) of the material type intensity vector is set to 0 to 1, and 11 values ​​obtained by dividing this range into 10 at 0.1 intervals are selected as search candidate values ​​for each element. Therefore, 1331 (= 11 × 11 × 11) search candidate labels are defined in advance as search points in the explanatory variable space.

[0051] Therefore, the optimization processing unit 36 ​​performs the following process, for example, using the multi-objective Bayesian optimization technique in the above-described search process. First, in step S115 of the search process, the optimization processing unit 36 ​​selects an initial label to search from the previously discretely determined search candidate labels. In this embodiment, the optimization processing unit 36 ​​randomly selects the initial label to search. However, an operator may select the label. The number of labels selected in the initial step S115 may be one or more, and in this embodiment, ten labels are selected. Next, in step S120, the trained generator 31 generates 20 pieces of 3D image data based on each of the ten labels selected in step S115 (a total of 200 pieces of 3D image data). In the following step S130, the parameter calculation unit 37 calculates the average of the parameters of the 20 pieces of 3D image data for each label. That is, a total of ten parameter averages are calculated. In this embodiment, there are two types of parameters, pressure loss and filtering efficiency, so a total of ten combinations of the average pressure loss and the average filtering efficiency are calculated. The average of the 10 parameters calculated in this way (the combination of the average pressure loss value and the average collection efficiency value, i.e., a total of 10 sets of parameters) is the set of objective functions described above. Then, after determining in step S140 that the termination condition is not satisfied, the optimization processor 36 performs step S150. In step S150, the optimization processor 36 first identifies a Pareto front from the set of objective functions. Then, using a Gaussian process regression equation for the relationship between the evaluated labels (here, the 10 labels selected in step S115) and the objective functions, the optimization processor 36 calculates an acquisition function (EHVI in this embodiment) for each of all unevaluated labels among the search candidate labels, identifies one label that gives the maximum value of the acquisition function (the label with the highest expected value for improving the current Pareto front), and determines that label as the next label to be evaluated (i.e., the label to be input next to the trained generator 31).

[0052] In step S120, which is performed after step S150, the optimization processor 36 inputs the label to be evaluated next, determined in step S150, into the trained generator 31 to generate 20 pieces of 3D image data. In the following step S130, the optimization processor 36 causes the parameter calculation unit 37 to calculate the average of the parameters corresponding to the label. The optimization processor 36 adds the calculated average of the parameters (a combination of the average pressure loss and the average collection efficiency) to the set of objective functions. Then, in the next step S150, the optimization processor 36 determines whether the newly added objective function improves the Pareto front identified in the previous step S150 (the current Pareto front). If the current Pareto front improves, the optimization processor 36 updates the current Pareto front. That is, the optimization processor 36 adds the newly added objective function as one of the Pareto-optimal solutions, and excludes any existing Pareto-optimal solutions that are dominated by the newly added objective function from the Pareto-optimal solutions. The optimization processing unit 36 ​​then calculates an acquisition function (EHVI in this embodiment) for each of all unevaluated labels among the search candidate labels, and determines the label with the highest expected value for improving the current Pareto front as the label to be input to the trained generator 31 in the next step S120. The optimization processing unit 36 ​​repeatedly executes steps S120 to S150 in this manner until it is determined in step S140 that the termination condition is met. This repeatedly calculates parameters for unevaluated labels among the search candidate labels and updates the Pareto front based on the calculated parameters. The specified termination condition for step S140 of the search process may be, for example, the number of iterations (i.e., the number of searches) for repeating steps S120, S130, and S150, or when a state in which the Pareto front of the objective function does not change (a state in which no new Pareto optimal solutions are added and the Pareto front is not updated) continues for a specified number of searches, or when a state in which the Pareto hypervolume of the objective function does not increase continues for a specified number of searches, or when the Pareto hypervolume exceeds a specified threshold, or when the Pareto hypervolume exceeds a specified threshold and a state in which the Pareto hypervolume does not increase continues for a specified number of searches.When the determination in step S140 is made based on the Pareto hypervolume, the optimization processor 36 may update the Pareto front and calculate the Pareto hypervolume before step S140, rather than step S150.

[0053] The optimization processor 36 that performs the search process using Bayesian optimization as described above can be created using, for example, PHYSBO, a Python library for Bayesian optimization. The acquisition functions such as EHVI, HVPI, and TS described above can also be executed using the PHYSBO library.

[0054] When using the above-described multi-objective Bayesian optimization, in step S160, a Pareto-optimal solution having one or more suitable parameters (here, pressure loss and collection efficiency) is identified (selected) from among the multiple Pareto-optimal solutions finally obtained. Then, the 3D image data corresponding to the identified Pareto-optimal solution (the 3D image data used in step S130 to calculate the pressure loss and collection efficiency of the Pareto-optimal solution) is identified as the 3D image data having one or more suitable parameters. This identification process may be performed by the optimization processing unit 36 ​​based on a predetermined method, or may be performed by an operator.

[0055] As described above, in step S120, 20 pieces of 3D image data are generated for one label, and in step S130, an average value of the 20 pieces of 3D image data is calculated for each of one or more parameters. Therefore, in step S160, first, from among the multiple Pareto-optimal solutions finally obtained, the labels used when generating the 3D image data that were used to calculate the Pareto-optimal solution with the best one or more parameters (here, pressure loss and collection efficiency) may be identified. That is, the labels corresponding to the best Pareto-optimal solutions may be identified. Then, the 3D image data generated by the trained generator 31 based on the identified labels may be identified as 3D image data with the best one or more parameters. In this case, the best 3D image data may be identified from the 20 pieces of 3D image data already generated in step S120, or from one or more pieces of 3D image data newly generated by the trained generator 31 based on the identified labels and noises different from the 20 fixed noises used in step S120. By changing the noise, the trained generator 31 can generate countless 3D image data from a single label, and the parameter values ​​calculated from these 3D image data will differ to some extent. Therefore, a label capable of generating 3D image data with one or more suitable parameters may be first identified, and then 3D image data with one or more suitable parameters may be identified from among the multiple 3D image data generated based on the identified label. Furthermore, the multiple 3D image data generated based on the identified label can be considered to have suitable values ​​even if the values ​​of one or more parameters used in the objective function differ to some extent. Therefore, for each of the multiple 3D image data generated based on the identified label, an index (e.g., the above-mentioned indexes such as mechanical strength properties, pore structural uniformity, and solid structural uniformity) different from the one or more parameters used in the objective function may be calculated, and the 3D image data with the suitable index may be finally identified as the suitable 3D image data in step S160.

[0056] After completing the process of step S160, the porous structure identification unit 35 ends the porous structure identification process, performs an output process to output the results of the porous structure identification process as processing result data (step S170), and then ends this routine. The processing result data includes, for example, data associating the suitable 3D image data identified in step S160 with the labels and parameters of the 3D image data. The processing result data may also include data associating the 3D image data with the labels and parameters for each of the multiple Pareto-optimal solutions finally obtained in the search process. The processing result data may be output by storing the data in a storage device of the design device 20 or an external storage medium connected to the design device 20, or by outputting the processing result data to the output unit 23 based on an operator's instruction via the input unit 22.

[0057] The data obtained by actually performing the porous body design routine described above will be explained using Figures 9 and 10. Figure 9 is an explanatory diagram of the labels input to the trained generator 31 and the generated 3D image data and parameters. The image on the left side of Figure 9 shows an example of 3D image data output from the trained generator 31 when five material type intensity vectors, A (1, 0, 0), B (0.75, 0, 0.25), C (0.5, 0, 0.5), D (0.25, 0, 0.75), and E (0, 0, 1), are input to the trained generator 31 as labels. Note that this 3D image data was generated by inputting the above labels and one fixed noise into the trained generator 31. The image in Figure 9 is an image of the 3D image data corresponding to a cross section of a porous body. In the image in Figure 9, the white areas represent voids (pores), and the gray areas represent the object. The material type intensity vector A represents a sintered-simulated structure, and the material type intensity vector E represents a sponge structure. As shown in FIG. 9, when material type intensity vectors B to D with intermediate values ​​between A and E are input to the trained generator 31, the generated 3D image data can be 3D image data of a hybrid material that combines a sintered-simulated structure and a sponge structure. For example, the 3D image data generated based on material type intensity vector B is image data of a hybrid material that more closely resembles a sintered-simulated structure because the sintered-simulated structure has an intensity of 0.75 and the sponge structure has an intensity of 0.25. The 3D image data generated based on material type intensity vector D is image data of a hybrid material that more closely resembles a sponge structure because the sintered-simulated structure has an intensity of 0.25 and the sponge structure has an intensity of 0.75. The 3D image data generated based on material type intensity vector C is image data of a hybrid material that is intermediate between a sintered-simulated structure and a sponge structure because the sintered-simulated structure has an intensity of 0.5 and the sponge structure has an intensity of 0.5. The graph on the right side of FIG. 9 is a plot of the parameters calculated by the parameter calculation unit 37 based on the three-dimensional image data of each of the material type intensity vectors A to E, namely the pressure loss [Pa] and the collection efficiency [-].The graph on the right side of Figure 9 shows the average values ​​and standard deviation ranges of parameters of multiple 3D image data generated by inputting multiple fixed noises to the trained generator 31 along with the labels for each of the material type intensity vectors A to E. As shown in this graph, the parameter values ​​of the 3D image data generated by the trained generator 31 vary depending on the label. Therefore, by having the trained generator 31 generate 3D image data representing various porous bodies with different parameter values, it is possible to efficiently obtain 3D image data of various porous bodies. Therefore, it is possible to efficiently identify porous bodies having suitable parameters using the multiple generated 3D image data. Note that, as can be seen from the range of standard deviation indicated by the error bars in the graph in Figure 9, even if the input label is the same, there is a certain range in the parameters of the 3D image data generated by the trained generator 31. Therefore, by using multiple fixed noises as in the above-mentioned embodiment, it is preferable that the porous structure identification unit 35 calculates the average value of the parameters of multiple 3D image data (a number corresponding to the number of fixed noises, 20 in this case) generated based on one label and regards the calculated average value as the parameter value (representative value) of the 3D image data corresponding to the label. Then, as in the above-described embodiment, it is preferable that the porous structure specifying unit 35 performs step S150 of the search process based on this average value and specifies a label corresponding to a suitable Pareto optimal solution in step S160.

[0058] FIG. 10 is an explanatory diagram showing multiple Pareto-optimal solutions finally obtained by the search process, as well as a process of identifying suitable 3D image data from the multiple Pareto-optimal solutions. The square points in FIG. 10 represent the multiple Pareto-optimal solutions finally obtained by the search process. From these multiple Pareto-optimal solutions, suitable 3D image data can be identified, for example, as follows. First, among the multiple Pareto-optimal solutions, a Pareto-optimal solution having the most preferable value for each of multiple objective functions is identified. For example, in FIG. 10, a Pareto-optimal solution G with the lowest pressure loss and a Pareto-optimal solution F with the highest collection efficiency are identified. Then, a virtual point that combines the most preferable values ​​of the identified Pareto-optimal solutions is set as a utopia point. In FIG. 10, a point UP (circled in FIG. 10) that combines the pressure loss of Pareto-optimal solution G and the collection efficiency of Pareto-optimal solution F is set as the utopia point. Next, from among the multiple Pareto-optimal solutions finally obtained by the search process, the one closest to the utopia point is identified as the Pareto-optimal solution with the best pressure loss and collection efficiency, and the 3D image data corresponding to that Pareto-optimal solution is identified as the best 3D image data. In FIG. 10, the Pareto-optimal solution H identified as follows is set as the Pareto-optimal solution closest to the utopia point. First, the values ​​of the objective functions of the multiple Pareto-optimal solutions finally obtained by the search process are normalized so that the minimum value is 0 and the maximum value is 1. In other words, when the horizontal axis (pressure loss) of FIG. 10 is the x-axis and the vertical axis (collection efficiency) is the y-axis, the value of x (here, pressure loss) is normalized to (xx min ) / (x max -x min ) and normalize the y value (here, collection efficiency) as (yy min ) / (y max -y min) is normalized as the optimal pressure loss and collection efficiency. FIG. 10 also shows the values ​​0 and 1 on the vertical and horizontal axes after normalization. Next, among the points of each Pareto-optimal solution after normalization, the point closest to the line y = x or y = 1 - x passing through the utopia point (here, the Pareto-optimal solution H closest to the line y = 1 - x) is identified as the optimal Pareto-optimal solution. Then, one of the 20 pieces of 3D image data used to calculate the Pareto-optimal solution H is identified as the 3D image data with optimal pressure loss and collection efficiency. For example, among the 20 pieces of 3D image data after normalization, the 3D image data with the combination of pressure loss and collection efficiency closest to the combination of the average pressure loss and average collection efficiency of the Pareto-optimal solution H is identified as the 3D image data with optimal pressure loss and collection efficiency. In this embodiment, in step S160, the porous structure identifying unit 35 performs a process of identifying the optimal 3D image data using this method. However, the process of identifying the optimal 3D image data may be performed using other methods. For example, as described above, the porous structure identification unit 35 may first identify a label corresponding to the Pareto-optimal solution H, cause the trained generator 31 to generate multiple pieces of 3D image data based on the identified label, and identify 3D image data with optimal pressure loss and collection efficiency from among the multiple pieces of 3D image data generated. Alternatively, the porous structure identification unit 35 may identify the Pareto-optimal solution closest to the utopia point using another method. A target range may be set in advance for each objective function, and the porous structure identification unit 35 may identify a Pareto-optimal solution that satisfies all of the preset target ranges as a suitable Pareto-optimal solution from among the multiple Pareto-optimal solutions. For example, an upper limit for pressure loss and a lower limit for collection efficiency may be set in advance as target ranges, and the porous structure identification unit 35 may identify a Pareto-optimal solution that satisfies both the upper limit for pressure loss and the lower limit for collection efficiency as a suitable Pareto-optimal solution.

[0059] In addition, in this embodiment, a method for manufacturing a porous body is also carried out, which includes the above-mentioned method for designing a porous body. A design process for executing the porous body design method described above; a forming step of producing a porous body based on three-dimensional image data in which the one or more parameters specified in the design step are suitable; Includes.

[0060] In the design process, the porous body design method described above, for example, the porous body design routine of Fig. 4, is executed. For example, the porous body represented by the suitable three-dimensional image data identified in S160 of the porous body design routine described above becomes the designed porous body, i.e., the porous body to be manufactured.

[0061] In the forming step, a porous body is produced based on suitable 3D image data identified in the design step. In the forming step, a porous body based on the 3D image data may be produced using 3D modeling with a 3D printer. For 3D modeling, for example, additive manufacturing or stereolithography may be used. When the porous body is a sintered body, laser sintering may be used for 3D modeling. For example, the forming step includes a pore-forming material placement step in which a pore-forming material that forms pores in the porous body is placed, a raw material placement step in which raw materials that form the porous body are placed, and a sintering step in which the placed raw materials are sintered, and may include a process in which the pore-forming material placement step, raw material placement step, and sintering step are repeated multiple times. The pore-forming material may be removed simultaneously with the sintering of the raw materials in the sintering step.

[0062] In the forming process, a porous body based on 3D image data may be directly formed by a 3D modeling method. Alternatively, in the forming process, an inverted porous body, which is an inversion of the space and object of the 3D image data, may be formed by a 3D modeling method, and a porous body based on the 3D image data may be formed using the inverted porous body. For example, an unfired porous body may be formed by filling the space of the inverted porous body with a raw material slurry of the porous body, and the unfired porous body may be fired to burn off the inverted porous body to form the porous body. In this way, a porous body based on 3D image data can be formed, for example, even in cases where the raw material of the porous body cannot be directly formed using a 3D modeling method.

[0063] These methods for manufacturing porous bodies using three-dimensional modeling methods are known and are described, for example, in the above-mentioned Patent Document 1, JP-A No. 2017-051931, and JP-A No. 2017-052677.

[0064] According to the porous body design method of this embodiment described above in detail, by using the trained generator 31 prepared by training using CGAN, labels including one or more types of indicators can be input and multiple 3D image data representing various porous bodies according to the labels can be efficiently generated. Therefore, porous bodies having suitable parameters can be efficiently identified using the multiple generated 3D image data.

[0065] The label also includes a material type intensity vector (x1, x2, . . . , xn), which is an index representing the intensity of each pattern contained in the porous body when the porous body is classified into n types of patterns, where n is an integer greater than or equal to 2. Using this material type intensity vector, a porous body can be expressed as a hybrid material that combines the structures and characteristics of the n types of patterns contained in the porous body. Then, by performing a learning step using a label including this material type intensity vector, the trained generator 31 can generate 3D image data of porous bodies with various structures and characteristics, thereby broadening the search range for porous bodies with suitable parameters. As a result, it becomes easier to identify porous bodies with more suitable parameters.

[0066] Furthermore, in the porous structure identification step (steps S115 to S160 in FIG. 4 ), the labels input to the trained generator 31 are used as explanatory variables, and one or more parameters calculated for the porous body represented by the 3D image data generated by the trained generator 31 based on the input are used as objective functions. Using an optimization method in this way allows 3D image data with suitable parameters to be efficiently identified from a large number of 3D image data of porous bodies corresponding to various label values. For example, suitable 3D image data can be identified by calculating corresponding parameters for all search candidate labels without using the optimization method, i.e., performing a full point search. However, in this case, the time required for the search is likely to increase if the number of search candidate labels is large, and the accuracy of the search (the accuracy of identifying 3D image data with suitable parameters) is likely to decrease if the number of search candidate labels is small. By using the optimization method, suitable 3D image data can be efficiently identified while reducing the number of searches, even if the number of search candidate labels is large. This prevents an increase in processing time and a decrease in accuracy when identifying 3D image data with suitable parameters.

[0067] Furthermore, in the method for manufacturing a porous body of this embodiment, the porous body is produced based on the preferred three-dimensional image data identified by the above-mentioned porous body design method, and therefore a porous body having preferred parameters can be obtained.

[0068] It goes without saying that the present invention is not limited to the above-described embodiment, and can be embodied in various forms as long as they fall within the technical scope of the present invention.

[0069] For example, in the above-described embodiment, the true data generation unit 25 generates 3D image data of the sintered-simulated structure using the GRF method, and generates 3D image data of the sphere-packed structure and the sponge structure using GeoDict, and uses these as the true data. However, this is not limited to this. When a material type intensity vector is used as a label, the true data generation unit 25 only needs to generate 3D image data representing n types of porous body patterns (porous bodies corresponding to each of the n basis vectors of the material type intensity vector), the number of which is the same as the number of components of the material type intensity vector. For example, the true data generation unit 25 may generate n types of 3D image data using the GRF method by setting n combinations of target porosity and standard deviation σ to be used in the GRF method and associating each combination with the n material type intensity vectors used in the true data. Alternatively, the true data generation unit 25 may use GeoDict instead of the GRF method to fill an area the size of the 3D image data in the same manner as for a sphere-packed structure, and then perform particle expansion and contraction processing to simulate the behavior (movement, bonding, etc.) between adjacent particles during sintering, thereby generating 3D image data of the sintered simulated structure.The true data generation unit 25 is not limited to the GRF method or GeoDict, and may use any method to generate 3D image data representing the structure of a numerically generated virtual porous body.

[0070] As described above, the true data generating unit 25 may generate three-dimensional image data from the structure of an actual porous body imaged by an X-ray CT scanner. FIG. 11 is an explanatory diagram showing how three-dimensional image data is generated from an actual porous body using a CT scan. For example, a porous body obtained by cutting out a portion of the partition wall of an actual honeycomb filter may be prepared (left side of FIG. 11). A CT scan of the porous body may be performed to obtain multiple tomographic images (center of FIG. 11). Based on these multiple tomographic images, three-dimensional image data may be generated in which the position information and brightness value of each voxel are associated with each other (right side of FIG. 11). The generated three-dimensional image data may be binarized using a threshold determined automatically (e.g., by discriminant analysis (Otsu's binarization)) based on the distribution of brightness values ​​of each voxel. True data may then be generated using the binarized three-dimensional image data. Furthermore, regions of the generated three-dimensional image data where no porous body exists and only voids exist (e.g., regions I and J on the right side of FIG. 11) may be excluded from the three-dimensional image data. The true data generating unit 25 may generate three-dimensional image data based on a plurality of tomographic images input to the design device 20, for example.

[0071] When generating true data using 3D image data obtained based on an actual porous body and using a material type intensity vector as a label, multiple porous bodies with n different patterns, the number of which is the same as the number of components of the material type intensity vector, can be manufactured and used to generate the true data. In other words, while n different methods for generating 3D image data were used in the above-described embodiment, n different methods for manufacturing porous bodies can be similarly used. Each of the n different manufacturing methods can be associated with a material type intensity vector for each porous body pattern (here, manufacturing method). For example, n different manufacturing methods can be used, each differing from the others in one or more of the material of the constituent particles of the porous body, the average particle size of the constituent particles, the average particle size of the pore-forming material, and the blending ratio of the constituent particles to the pore-forming material. Multiple porous bodies can be actually manufactured using each of the n different manufacturing methods, and the 3D image data based on the resulting porous bodies can be associated with the material type intensity vector to generate the true data. Although multiple porous bodies manufactured using the same manufacturing method have similar structures and characteristics, they will not be exactly the same porous bodies. Therefore, by preparing multiple porous bodies manufactured using n different manufacturing methods, it is possible to obtain three-dimensional image data corresponding to each of the material type intensity vectors used in the true data (for example, in the above-mentioned embodiment, any of (1,0,0), (0,1,0), and (0,0,1)).

[0072] In the above-described embodiment, a material type intensity vector is used as the label included in the true data, but this is not limited to this. As described above, the label may include one or more indicators representing the shape and / or performance of the porous body. As described above, examples of indicators representing the shape of the porous body include the porosity, solid fraction, specific surface area, pore diameter, particle diameter, structural uniformity of the pores or solid, pore chord length, and solid chord length of the porous body. These values ​​may be measured based on the three-dimensional image data, may be measured based on the actual porous body that is the source of the three-dimensional image data, or may be measured based on the actual porous body manufactured based on the three-dimensional image data.

[0073] The porosity of a porous body may be calculated as the proportion of pore voxels in the total number of voxels in the three-dimensional image data. The solid fraction of a porous body may be calculated as the proportion of solid voxels in the total number of voxels in the three-dimensional image data. The porosity and solid fraction of a porous body may each be calculated using mercury intrusion porosimetry, Archimedes' method, or the like based on an actual porous body. The specific surface area of ​​a porous body may be the specific surface area per unit volume of the porous body, or the specific surface area per unit mass of the porous body. The specific surface area per unit volume of the porous body may be a value per total volume of the porous body, a value per volume of the pores (spaces) of the porous body, or a value per volume of the solid (object) of the porous body. The surface area of ​​the object portion used to calculate the specific surface area may be calculated based on, for example, the area of ​​the portion where solid voxels and pore voxels are adjacent in the three-dimensional image data. More specifically, the pore size of a porous body may be one or more of the average pore size, a representative value of the pore size distribution (e.g., D10, D50, D90, etc.), or a value representing the pore size distribution (standard deviation, maximum value, minimum value, etc.). Note that the pore sizes D10, D50, and D90 are also referred to as the 10% pore size, 50% pore size, and 90% pore size. The pore size D10 refers to the 10% pore size from the smallest pore size in the cumulative volumetric fraction of the pore size distribution measurement. The same applies to the pore sizes D50 and D90. These pore diameter values ​​may be calculated, for example, by dividing the pore (pore voxel) portion of the 3D image data into multiple pores by setting boundaries for the multiple pores using, for example, the WaterShed algorithm, calculating the pore diameter for each of the multiple pores as an equivalent spherical diameter, and then based on the distribution of the calculated pore diameters and statistical values ​​based on the distribution (e.g., mean, variance, maximum, minimum, etc.). These pore diameter values ​​may also be calculated using mercury intrusion porosimetry or the like based on an actual porous body. More specifically, the particle diameter of a porous body may be one or more of the average particle diameter, a representative value of the particle diameter distribution (e.g., D10, D50, D90, etc.), or a value representing the particle diameter distribution (e.g., standard deviation, maximum, minimum, etc.). Note that the particle diameters D10, D50, and D90 are also referred to as the 10% particle diameter, 50% particle diameter, and 90% particle diameter.The particle diameter D10 refers to the particle diameter of the smallest 10% of particle diameters in the volume-based cumulative fraction of particle diameter distribution measurement. The same applies to the particle diameters D50 and D90. These particle diameter values ​​may be calculated, for example, by inverting the pore and solid portions of the 3D image data and then using, for example, WaterShed segmentation, for the inverted pore portion in the same manner as described above. More specifically, the structural uniformity of the pores or solid of a porous body refers to the variance of the pore or solid values ​​calculated for each region after dividing the porous body into multiple regions. Examples of pore or solid values ​​calculated for each region include the porosity, solid fraction, specific surface area, pore diameter, and particle diameter described above. The pore chord length is the continuous length of the pore in a predetermined direction in the porous body. The predetermined direction may be, for example, a direction parallel to one of the X, Y, and Z axes used in the position information of the voxels in the 3D image data, i.e., one of the X, Y, and Z directions. Chord lengths may be calculated for two or more of the X, Y, and Z directions. More specifically, the pore code length may be one or more of the following: the average pore code length; a representative value of the pore code length distribution (e.g., L10, L50, L90); or a value representing the pore code length distribution (standard deviation, maximum value, minimum value, etc.). The pore code length L10 refers to the code length of the pores with the smallest 10% of pore code lengths in the length-based cumulative fraction of the pore code length distribution measurement. The same applies to the pore code lengths L50 and L90. For example, the value related to the pore code length in the X direction of a porous body can be calculated as follows: First, the 3D image data is divided into multiple cross sections parallel to the X direction (e.g., XY cross sections). The number of cross sections corresponds to the number of voxels in the Z direction of the 3D image data. Next, for each of the multiple cross sections, the voxels representing pores (pore voxels) are examined, and a group of pore voxels that are connected in a straight line in the X direction is identified as a single continuous pore voxel. The number of consecutive pore voxels, i.e., the pore code length, is counted for each of the multiple continuous pore voxels in the cross section. By counting the pore code lengths in this way for all cross sections, information on the distribution of pore code lengths in the porous body can be obtained.For example, it is possible to calculate the average value of the counted pore chord lengths, the standard deviation of the pore chord lengths, and the L90 value of the pore chord length. The chord length of a solid is the continuous length of a solid in a given direction in a porous body. More specifically, the chord length of a solid may be one or more of the average value of the solid chord length, a representative value of the distribution of the solid chord lengths (e.g., L10, L50, L90, etc.), or a value representing the distribution of the solid chord lengths (standard deviation, maximum value, minimum value, etc.). The L10 value of the solid chord length refers to the 10% of solids with the smallest chord lengths in the length-based cumulative fraction of the distribution measurement of the solid chord lengths. The same applies to the L50 and L90 values ​​of the solid chord lengths. Similar to the value related to the pore chord length, the value related to the solid chord length can be calculated by counting the number of consecutive voxels representing the solid (solid voxels). These indices representing the shape of porous bodies can be calculated using, for example, a module called PoroDict or a module called MatDict in GeoDict.

[0074] As described above, examples of indices representing the performance of a porous body include the pressure drop characteristics and trapping characteristics of the porous body used in the above-described embodiments, as well as the mechanical strength characteristics, electrochemical characteristics, thermal conductivity characteristics, heat exchange characteristics, electrical conductivity characteristics, gas adsorption characteristics, gas purification performance, catalytic coating properties, and removal efficiency of substances trapped in the porous body. These values ​​may be measured based on 3D image data, on the actual porous body that served as the source of the 3D image data, or on an actual porous body manufactured based on the 3D image data. For example, mechanical strength characteristics can be calculated using GeoDict's ElastoDict module. Thermal conductivity characteristics and electrical conductivity characteristics can be calculated using GeoDict's ConductoDict module. Electrochemical characteristics can be calculated using GeoDict's BatteryDict module. Gas adsorption characteristics can be calculated using GeoDict's AddiDict module. Catalyst coating properties can be calculated using the VOF method implemented in OpenFOAM, an open-source software for fluid simulation, or Ansys Fluent, a thermal-fluid analysis software from ANSYS. Heat exchange characteristics can be calculated using thermal fluid analysis implemented in OpenFOAM or Ansys Fluent.

[0075] For example, when the porosity of a porous body is used as a label, the true data generation unit 25 generates true data in step S100 by associating 3D image data with the porosity of the porous body represented by the 3D image data. The value of the label (porosity) used as true data can be, for example, a value in the range of 0% to less than 100%, or a value in the range of 1% to 99%. The true data generation unit 25 may generate 3D image data having various porosities using, for example, the GRF method described above, and use the generated data as true data. It is preferable that the true data generation unit 25 generates 3D image data having various porosity values ​​over a wider range to include the porosity range assumed for the porous body to be designed, and use the generated data as true data. By performing the learning process in step S110 using such true data, the trained generator 31 can generate 3D image data that matches the porosity indicated by the label (here, an arbitrary porosity value) when an arbitrary label is input (more precisely, 3D image data of a porous body having a porosity close to the porosity indicated by the label). In the porous structure identification step, the porosity is used as an input to the generator 31, allowing the generator 31 to efficiently generate multiple 3D image data representing porous bodies with various porosities. The label may include a material type intensity vector and a porosity. For example, a vector (x1, x2, x3, P) combining the material type intensity vector and the porosity P of the above-described embodiment may be used as a label. In this case, the label used as true data may be a vector in which one of x1 to x3 has a value of 1 and the rest have a value of 0, as in the above-described embodiment, and further combining this with the value of the porosity P. When the learning process of step S110 is performed using such true data, the trained generator 31 can generate 3D image data that matches the porous body indicated by the label (more precisely, 3D image data similar to the 3D image data of the porous body indicated by the label) for an input of any vector (x1, x2, x3, P).More specifically, the trained generator 31 can generate three-dimensional image data of a hybrid material that combines the structures and characteristics of three types of porous bodies, namely, a sintered simulated structure, a sphere-packed structure, and a sponge structure, in various proportions, and with the porosity P set to an arbitrary value.

[0076] For example, if the pressure loss of a porous body is used as a label, the true data generator 25 generates true data in step S100 by associating 3D image data with the pressure loss of the porous body represented by the 3D image data. The label (pressure loss) value used as true data can be, for example, various values ​​selected from the range of values ​​that the porous body can take. The true data generator 25 may, for example, generate multiple 3D image data, calculate the pressure loss for each 3D image data using the method described in step S130, and, if a label value within a predetermined range that can be used as true data is calculated, use that value and the 3D image data as true data. By performing the learning process in step S110 using such true data, the trained generator 31 can generate 3D image data that matches the pressure loss indicated by the label (here, an arbitrary pressure loss value) in response to input of the label (more precisely, 3D image data of a porous body having a pressure loss close to the pressure loss indicated by the label). In the porous structure identification step, the pressure loss is used as an input to the generator 31, which can efficiently generate multiple 3D image data representing porous bodies with various pressure losses. The label may contain only the pressure loss, or, similar to the case where the label contains the material type intensity vector and the porosity, the label may also contain the material type intensity vector and the pressure loss. Alternatively, the label may contain the material type intensity vector, the porosity, and the pressure loss. In this way, the label can contain an appropriate combination of one or more indicators representing the shape and / or performance of the porous body.

[0077] As with the label, the one or more parameters calculated in the porous structure determining step can be an appropriate combination of one or more indices representing the shape and / or performance of the porous body described above. The one or more indices included in the label and the one or more indices (parameters) calculated in the porous structure determining step may each contain an indices not included in the other, may be at least one different from each other, or may not contain the same type of indices.

[0078] In the above-described embodiment, in step S130, the parameter calculation unit 37 calculates one or more parameters by executing a physical simulation. However, this is not limited to this. The parameter calculation unit 37 may calculate one or more parameters by another method, or an operator or other device may calculate one or more parameters instead of the parameter calculation unit 37. For example, in step S130, an operator may fabricate porous bodies based on each of the multiple 3D image data generated by the trained generator 31 and calculate one or more parameters through experiments using the fabricated porous bodies. For example, an operator may fabricate porous bodies based on the 3D image data using three-dimensional modeling with a 3D printer. Then, the operator may input the parameters calculated through experiments into the design device 20, and the porous structure identification unit 35 may execute the processes from step S140 onward. Alternatively, in step S130, the parameter calculation unit 37 may calculate one or more parameters by applying a learning model. For example, a learning model can be constructed in advance as a model that directly calculates (predicts) one or more types of parameters when three-dimensional image data is input, by obtaining data on the correspondence between three-dimensional images and parameters based on the results of a physical simulation based on three-dimensional image data that has been conducted in advance or the results of an experiment on a porous body that has actually been created based on three-dimensional image data, and then learning that correspondence.The construction of such learning models is well known and is described, for example, in Moussa Tembely, Ali M. AlSumaiti, and Waleed Alameri, "A deep learning perspective on predicting permeability in porous media from network modeling to direct simulation," Comput Geosci 24 (2020) 1541-1556 DOI: 10.1007 / s10596-020-09963-4, and Serveh Kamrava, Pejman Tahmasebi, and Muhammad Sahimi, "Linking Morphology of Porous Media to Their Macroscopic Permeability by Deep Learning," Transport in Porous Media 131 (2020) 427-448 DOI: 10.1007 / s11242-019-01352-5. Alternatively, the learning model can be constructed in advance as a model that calculates feature quantities representing the shape of the porous body from 3D image data and calculates one or more parameters from the feature quantities. Such a learning model can be constructed, for example, using a support vector machine (SVM). Methods for constructing learning models using SVMs are well known and are described, for example, in Tomoki Yasuda, Shinichi Ookawara, Shiro Yoshikawa, and Hideyuki Matsumoto, "Machine learning and data-driven characterization framework for porous materials: Permeability prediction and channeling defect detection," Chemical Engineering Journal 420 (2021) 130069 DOI: 10.1016 / j.cej.2021.130069.

[0079] In the above-described embodiment, in the porous structure identification step, the porous structure identification unit 35 performs a search process using an optimization method to identify 3D image data with one or more suitable parameters. However, this is not limited to this. For example, in step S150 of the search process, an operator may determine the label value to be input next to the trained generator 31 based on the parameters calculated in step S130 without using an optimization method. In step S150 of the search process, the porous structure identification unit 35 may randomly determine the label value to be input next to the trained generator 31. Alternatively, instead of repeating steps S120 to S150 in the search process, the porous structure identification unit 35 may omit step S150 and perform steps S120 and S130 multiple times. That is, various labels may be input to the trained generator 31 to generate multiple 3D image data and calculate one or more parameters based on each of the 3D image data. For example, the porous structure identification unit 35 may perform steps S120 and S130 for all of the discretely determined search candidate labels described above. In this case as well, the porous structure identifying unit 35 or an operator may perform the process of step S160 based on the result of step S130 to identify suitable three-dimensional image data from the three-dimensional image data generated in step S120. For example, each parameter (e.g., pressure loss and collection efficiency) of the three-dimensional image data generated in step S120 may be plotted on a graph as shown in Fig. 10, and each parameter may be normalized to a range from 0 to 1, and the three-dimensional image data having parameters closest to the most suitable point (e.g., the point with the lowest pressure loss and the highest collection efficiency) may be identified as the suitable three-dimensional image data.

[0080] In the above-described embodiment, in step S160 of the porous structure identification process, three-dimensional image data having a porosity of 1% or more and 99% or less and having one or more suitable parameters may be identified from the plurality of three-dimensional image data generated in step S120. For example, the porous structure identification unit 35 may calculate the porosity of the plurality of three-dimensional image data generated in step S120, and if the porosity is not 1% or more and 99% or less, the three-dimensional image data may be excluded and not identified as suitable three-dimensional image data.

[0081] This specification also discloses the technical idea of ​​changing "the method for designing a porous body according to claim 1 or 2" in claim 4 originally filed to "the method for designing a porous body according to any one of claims 1 to 3." This specification also discloses the technical idea of ​​changing "the method for designing a porous body according to claim 1 or 2" in claim 5 originally filed to "the method for designing a porous body according to any one of claims 1 to 4." This specification also discloses the technical idea of ​​changing "the method for designing a porous body according to claim 1 or 2" in claim 6 originally filed to "the method for designing a porous body according to any one of claims 1 to 5." This specification also discloses the technical idea of ​​changing "the method for designing a porous body according to claim 1 or 2" in claim 7 originally filed to "the method for designing a porous body according to any one of claims 1 to 6." This specification also discloses the technical idea of ​​changing "the method for designing a porous body according to claim 1 or 2" in claim 8 originally filed to "the method for designing a porous body according to any one of claims 1 to 6." This specification also discloses the technical idea of ​​changing "the method for designing a porous body according to claim 1 or 2" in claim 9 originally filed to "the method for designing a porous body according to any one of claims 1 to 8." This specification also discloses the technical idea of ​​changing "the method for designing a porous body according to claim 1 or 2" in claim 11 originally filed to "the method for designing a porous body according to any one of claims 1 to 10." This specification also discloses the technical idea of ​​changing "a design process for carrying out the method for designing a porous body according to claim 1 or 2" in claim 12 originally filed to "a design process for carrying out the method for designing a porous body according to any one of claims 1 to 11."

[0082] This application claims priority from Japanese Patent Application No. 2022-40298, filed on March 15, 2022, the entire contents of which are incorporated herein by reference. [Industrial Applicability]

[0083] The present invention is applicable to the manufacturing industry of porous bodies used as filters for purifying exhaust gases emitted from automobile engines, stationary engines for construction machinery and industry, combustion appliances, etc. [Explanation of symbols]

[0084] 20 design device, 21 device main body, 22 input section, 23 output section, 25 true data generation section, 30 machine learning section, 31 generator, 32 discriminator, 35 porous structure identification section, 36 optimization processing section, 37 parameter calculation section.

Claims

1. a learning step of performing training using a conditional generative adversarial network using a plurality of true data in which three-dimensional image data of a porous body is associated with labels including one or more types of indices that represent the shape of the porous body, to obtain a trained generator that generates three-dimensional image data based on the labels; a porous structure identification step of changing the label values ​​in various ways and inputting them into the trained generator, calculating one or more parameters representing the performance of the porous body represented by the three-dimensional image data for each of the multiple three-dimensional image data generated by the trained generator based on the input, and identifying three-dimensional image data for which the one or more parameters are suitable from the multiple three-dimensional image data generated based on the calculated one or more parameters; Including, The label includes one or more of the following indicators: the porosity, solid fraction, specific surface area, pore diameter, particle diameter, structural uniformity of the pores or solid of the porous body; a pore code length which is the continuous length of the pores in a predetermined direction in the porous body; a solid code length which is the continuous length of the solid in a predetermined direction in the porous body; and a material type intensity vector (x1, x2, ..., xn) which represents the intensity of each pattern included in the porous body when the porous body is classified into n types of patterns, where n is an integer of 2 or more; The one or more parameters include one or more of the pressure drop characteristics, collection characteristics, mechanical strength characteristics, electrochemical characteristics, thermal conductivity characteristics, heat exchange characteristics, electrical conductivity characteristics, gas adsorption characteristics, gas purification performance, catalyst coating properties, and removal efficiency of substances collected in the porous body. How to design porous media.

2. In the porous structure identification step, the one or more types of parameters are calculated by performing a physical simulation or applying a learning model to each of the plurality of three-dimensional image data generated by the trained generator. A method for designing a porous body according to claim 1.

3. In the porous structure specifying step, a porous body is produced based on each of the plurality of three-dimensional image data generated by the trained generator, and the one or more types of parameters are calculated by an experiment using the produced porous body. A method for designing a porous body according to claim 1.

4. In the porous structure specifying step, The label to be input to the trained generator is used as an explanatory variable, and the one or more parameters calculated for the porous body represented by the three-dimensional image data generated by the trained generator based on the input are used as an objective function, and the three-dimensional image data for which the one or more parameters are suitable is identified using an optimization method. The method for designing a porous body according to any one of claims 1 to 3.

5. Bayesian optimization is used as the optimization method. The method for designing a porous body according to claim 4.

6. In the porous structure specifying step, three-dimensional image data having a porosity of 1% or more and 99% or less and having the one or more parameters suitable is specified from the generated plurality of three-dimensional image data. The method for designing a porous body according to any one of claims 1 to 3.

7. A design step of executing the porous body design method according to any one of claims 1 to 3; a forming step of producing a porous body based on three-dimensional image data in which the one or more parameters specified in the design step are suitable; A method for producing a porous body comprising the steps of:

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