Method for analyzing fluid forces and generating trained models

Abstract

This invention provides a method for easily identifying regions in the flow field after passing through an object that contribute significantly to the fluid force acting on the object. [Solution] This is a method for analyzing fluid forces. This method includes: a first step of performing a fluid analysis to calculate the flow field 20 after it has passed through a target object; a second step of obtaining multiple types of feature quantities from the physical quantity C of the flow field 20; a third step of estimating the fluid force using a trained model that has been trained to output the fluid force acting on the target object when the feature quantities are input; a fourth step of obtaining the contribution of each of the multiple types of feature quantities to the estimated fluid force; and a fifth step of mapping regions 39 that have a large contribution to the estimated fluid force on the flow field 20 or on coordinates corresponding to the flow field 20, based on the contribution.

Description

[Technical Field]

[0001] This invention relates to a method for analyzing fluid forces and a method for generating a trained model. [Background technology]

[0002] Non-patent document 1 below describes a method for predicting the aerodynamic performance of an automobile. In this method, a learning model capable of estimating the drag coefficient of an automobile is generated when a distance function determined from the shape of the automobile is input. [Prior art documents] [Patent Documents]

[0003] [Non-Patent Document 1] Kei Akasaka, Fangge Chen, and Takehito Teraguchi, "Development of a Surrogate Model for Predicting Automotive Aerodynamic Performance Using Machine Learning," [online], Transactions of the Society of Automotive Engineers of Japan, Society of Automotive Engineers of Japan, Vol. 52, No. 3, May 2021, pp. 621-626, [Retrieved August 28, 2024], Internet<URL:https: / / www.jstage.jst.go.jp / article / jsaeronbun / 52 / 3 / 52_20214248 / _pdf / -char / ja> [Overview of the project] [Problems that the invention aims to solve]

[0004] For example, when developing shapes for objects such as automobiles or tires that exhibit superior fluid resistance characteristics, it is necessary to carefully observe the flow field after the object has passed through it and identify the locations that significantly influence the fluid forces. However, such work has been problematic because it requires skilled techniques, effort, and time.

[0005] This invention was devised in view of the above-described circumstances, and its main objective is to provide a method that makes it possible to easily identify regions in the flow field after passing through an object that contribute significantly to the fluid force acting on the object. [Means for solving the problem]

[0006] The present invention is a method for analyzing fluid forces flowing around a target object using one or more processors, comprising: a first step of performing fluid analysis to calculate a flow field, which is the distribution of physical quantities of the fluid after it has passed through the target object; a second step of obtaining a plurality of types of feature quantities from the physical quantities of the flow field; a third step of estimating the fluid forces using a trained model that has been trained to output the fluid forces acting on the target object when the feature quantities are input; a fourth step of obtaining the estimated contribution to the fluid forces for each of the plurality of types of feature quantities; and a fifth step of mapping regions with large estimated contributions to the fluid forces on the flow field or on coordinates corresponding to the flow field based on the contributions. [Effects of the Invention]

[0007] By employing the above steps, the fluid force analysis method of the present invention makes it possible to easily identify regions in the flow field after passing through the target object that have a large contribution to the fluid force acting on the target object. [Brief explanation of the drawing]

[0008] [Figure 1] This is a block diagram showing an example of a fluid dynamics analysis device (a device for generating trained models). [Figure 2] This is a perspective view showing an example of the target object. [Figure 3] This flowchart shows an example of the processing steps for generating a pre-trained model. [Figure 4] This figure shows an example of an object model and space. [Figure 5] This figure shows an example of an object model and a computational grid. [Figure 6] This is a contour plot showing an example of the distribution of physical quantities in a flow field. [Figure 7] This figure shows an example of a physical quantity of a flow field. [Figure 8] (a) is a contour plot showing an example of a basis vector for the 0th mode, and (b) is a contour plot showing an example of a basis vector for the 2nd mode. [Figure 9] This graph shows the relationship between the coefficients and the unit time of the simulation. [Figure 10] This figure shows an example of a training dataset. [Figure 11] This figure shows an example of a pre-trained model (machine learning model). [Figure 12] This is a flowchart showing an example of the processing procedure for a fluid force analysis method. [Figure 13] This graph shows the relationship between multiple types of features and their contribution (SHAP value). [Figure 14] (a) is a contour map showing an example of the distribution of physical quantities in the flow field, and (b) is a diagram showing an example of the first mapping data where regions with a large contribution to fluid force are mapped. [Figure 15] This figure shows an example of second mapping data where regions with a large contribution to fluid forces are mapped onto the flow field. [Figure 16] Figures (a) through (e) show examples of multiple objects. [Figure 17] This figure shows an example of a second object model and space. [Figure 18] This figure shows an example of a second object model and a second computational grid. [Figure 19] This contour plot shows an example of a physical quantity calculated on the second computational grid. [Figure 20] This figure shows an example of a physical quantity calculated using a computational grid. [Figure 21] (a) is a contour plot showing an example of a basis vector for the 0th mode, and (b) is a contour plot showing an example of a basis vector for the 2nd mode. [Figure 22] (a) is a graph showing the relationship between the coefficients of the basis vector for the 0th mode and the unit time of the simulation, and (b) is a graph showing the relationship between the coefficients of the basis vector for the 2nd mode and the unit time of the simulation. [Figure 23] This figure shows an example of a training dataset. [Modes for carrying out the invention]

[0009] Embodiments of the present invention will be described below with reference to the drawings. It should be understood that the drawings contain exaggerations and representations that differ from the actual dimensional ratios of the structures in order to aid in understanding the content of the invention. Furthermore, the same or common elements are denoted by the same reference numerals throughout each embodiment, and redundant explanations are omitted. Moreover, the specific configurations shown in the embodiments and drawings are for the purpose of understanding the content of the present invention, and the present invention is not limited to the specific configurations shown in the drawings.

[0010] The fluid force analysis method of this embodiment (hereinafter sometimes referred to as the "analysis method") analyzes the fluid force flowing around a target object (the object being analyzed). The analysis method of this embodiment uses a fluid force analysis device (hereinafter sometimes referred to as the "analysis device"). The analysis device of this embodiment is also configured as a trained model generation device (hereinafter sometimes referred to as the "generation device"). Note that these analysis device and generation device may be configured separately. Figure 1 is a block diagram showing an example of the fluid force analysis device 1A (trained model generation device 1B).

[0011] [Fluid force analysis device (device for generating trained models)] The analysis device 1A (generation device 1B) of this embodiment is configured as a general-purpose computer 1. Examples of computer 1 include desktop computers, laptop computers, tablets, smartphones, and cloud servers.

[0012] The analysis device 1A (generation device 1B) of this embodiment includes an input device 3, an output device 4, and a calculation processing device 5.

[0013] [Input unit, output unit, arithmetic processing unit] Input device 3 is configured as an input device. An example of this input device is a keyboard or mouse. Output device 4 is configured as an output device. An example of this output device is a display device or printer. The arithmetic processing unit 5 is for predicting the performance of the target tire. The arithmetic processing unit 5 of this embodiment is configured to include one or more processors (arithmetic units) 5A that perform various calculations, a storage unit 5B in which data and programs are stored, and a working memory 5C.

[0014] [Processor] The processor 5A in this embodiment is configured as a central processing unit (CPU), but is not particularly limited and may be configured as a microprocessor or other processing unit, for example. In this embodiment, the analysis method and the method for generating a trained model (hereinafter sometimes referred to as the "generation method") are exemplified in which they are executed by a single processor 5A, but they may be executed by multiple processors (parallel processing).

[0015] [Storage] The storage unit 5B is a non-volatile information storage device, such as a magnetic disk, optical disk, or SSD. The storage unit 5B is provided with a data unit 7 and a program unit 8.

[0016] [Data Section] The data unit 7 of this embodiment is for storing data necessary for executing the analysis method and the generation method. The data unit 7 of this embodiment includes a model storage unit 7A, a flow field / hydrodynamic storage unit 7B, a basis vector / feature storage unit 7C, a training dataset storage unit 7D, a trained model storage unit 7E, a contribution storage unit 7F, and a mapping data storage unit 7G. The data unit 7 is not limited to this configuration, and may include storage units for other data as needed, or some of these may be omitted. The data stored in each storage unit 5B will be explained in each step of the prediction method and generation method described later.

[0017] [Programming Department] The program unit 8 in this embodiment is a program (application) necessary for executing the analysis method and the generation method. When such a program unit 8 is executed by the processor (arithmetic unit) 5A, the computer 1 (analysis device 1A and generation device 1B) can be made to function as a specific means. The program unit 8 in this embodiment includes a calculation unit 8A, a feature acquisition unit 8B, a preparation unit 8C, a learning unit 8D, an estimation unit 8E, a contribution acquisition unit 8F, a mapping unit 8G, and an evaluation unit 8H. Note that the program unit 8 is not limited to this configuration; other programs may be included as needed, or some of these may be omitted. Furthermore, the functions of each program unit 8 will be explained in each step of the prediction method and generation method described later.

[0018] [Target object] The object being analyzed is the object subject to fluid dynamics. This object is not particularly limited as long as it is subject to fluid dynamics analysis. Figure 2 is a perspective view showing an example of object 10.

[0019] In this embodiment, the target object 10 is exemplified as a columnar body 10A, but it is not limited to this configuration. The target object 10 may be, for example, a sphere, a tire, or an automobile.

[0020] The column 10A in this embodiment is constructed as a three-dimensional object including two parallel bottom surfaces 10a and a side surface (columnar surface) 10b connecting these bottom surfaces 10a. Such a column 10A is formed of, for example, steel, but is not particularly limited and may be formed of resin such as rubber, wood, or the like.

[0021] In this embodiment, the columnar body 10A is exemplified as being cylindrical, but is not limited to this form. The shape of the object 10 may be, for example, a square prism, an octagonal prism with chamfered edges, a triangular prism, or an elliptical prism.

[0022] [fluid] The fluid (not shown) is not particularly limited as long as it flows around the object 10 shown in Figure 2. Examples of fluids include air and liquid (water). In this embodiment, the fluid is air.

[0023] Fluid force is a physical quantity that acts on an object 10 as a fluid flows (passes through) the object 10. In this embodiment, the fluid force is the drag coefficient of air (C D An example is given where the value is (C). Note that the fluid force is the resistance coefficient (C D It is not limited to the value, for example, aerodynamic 6-component force (C L The values ​​may also be other values. Estimating such fluid forces is useful, for example, for evaluating the quality of the fluid resistance characteristics of the object 10.

[0024] Fluid force changes depending on the flow field. This flow field is the distribution of physical quantities (different from fluid force) of the fluid after it has passed through the target object 10. In this embodiment, the physical quantity is exemplified as the fluid pressure, but it is not limited to this form, and may be, for example, the fluid velocity. These physical quantities (in this example, pressure) are related to fluid force (in this example, the drag coefficient C). D It affects the value. Therefore, physical quantities have a strong correlation with fluid forces.

[0025] [Conventional problems and an overview of the analysis method in this embodiment] Incidentally, when developing the shape of an object (target object 10) with excellent fluid resistance characteristics, it is necessary to carefully observe the flow field after it passes through the target object 10 and identify the phenomena and their locations that have a significant influence on the fluid force. However, such work has the problem of requiring skilled techniques, effort, and time.

[0026] In the analysis method of this embodiment, by performing the processing procedure described later, regions in the flow field after passing through the target object 10 that contribute significantly to the fluid force (in this example, the drag coefficient) acting on the target object 10 can be easily identified.

[0027] The analysis method of this embodiment uses a trained model (machine-learned) generated based on the generation method described later. Therefore, if the trained model has not yet been generated at the time of execution of the analysis method, the trained model will be generated prior to the execution of the analysis method. If the trained model has already been generated at the time of execution of the analysis method, the execution of the generation method may be omitted.

[0028] [Method for generating a pre-trained model (First Embodiment)] Next, an example of the processing procedure for generating a pre-trained model will be described. The pre-trained model is a model for estimating the fluid force flowing around the target object 10. The pre-trained model in this embodiment is machine-learned so that when multiple types of features are input, the fluid force acting on the target object 10 is output. The multiple types of features are obtained from the physical quantities of the flow field after it has passed through the target object 10.

[0029] The physical quantities of the flow field and the fluid force of the object 10 change moment by moment. Therefore, it is preferable to calculate the physical quantities and fluid force at multiple time intervals (unit time of the simulation). Then, by training a machine learning model using multiple training datasets that combine multiple types of features obtained from the physical quantities of the flow field and the fluid force at each time interval, it becomes possible to generate a trained model that can accurately estimate the fluid force from multiple types of features.

[0030] Figure 3 is a flowchart showing an example of the processing steps for generating a trained model. Each step of the generation method in this embodiment is performed by one or more processors 5A included in the generation device 1B (computer 1) shown in Figure 1.

[0031] [Calculate flow field and fluid forces] In the generation method of this embodiment, first, a fluid analysis is performed to calculate at least the flow field after object 11 (shown in Figure 2) has passed through, and the fluid force acting on object 11 (step S11). As described above, the flow field is the distribution of physical quantities of the fluid after it has passed through object 11.

[0032] The flow field and fluid force calculated in step S11 of this embodiment are used to prepare a training dataset. For this reason, the object 11 targeted for fluid analysis in step S11 may have the same shape (in this example, a cylindrical shape) as the target object 10 (shown in Figure 2) analyzed by the analysis method described later. This allows for the calculation of a flow field and fluid force with the same tendencies as the target object 10. By using this training dataset based on the flow field and fluid force of such an object 11 in machine learning of the trained model, the accuracy of estimating the fluid force of the target object 10 is improved. Note that the object 11 is not limited to having the same shape as the target object 10; for example, an object with a shape similar to the target object 10 (e.g., a square prism or an octagonal prism) may be used. Since the flow field and fluid force similar to the target object 10 are calculated for these objects, the accuracy of estimating the fluid force of the target object 10 can be maintained by using this training dataset based on these flow fields and fluid forces in machine learning of the trained model.

[0033] In step S11 of this embodiment, first, the calculation unit 8A included in the program unit 8 shown in Figure 1 is loaded into the working memory 5C. The calculation unit 8A is a program for performing fluid analysis to calculate at least the flow field after the object 11 (shown in Figure 2) has passed through, and the fluid force acting on the object 11. When this calculation unit 8A is executed by the processor 5A, the computer 1 (generation device 1B) can be made to function as a means for performing fluid analysis and calculating the flow field and fluid force.

[0034] In this embodiment, the fluid analysis uses an object model that models the object 11 shown in Figure 2, and a computational grid for calculating the fluid flow field. Therefore, if the object model and computational grid have not yet been set up during the fluid analysis, they are set up prior to the fluid analysis. Figure 4 shows an example of the object model 13 and space 14. Figure 5 shows an example of the object model 13 and computational grid 15. In Figure 5, the selection region 21, which will be described later, is enclosed in a frame.

[0035] [Object Model] In this embodiment, the object model 13 is set as a two-dimensional model, but it is not limited to this configuration. The object model 13 may be set as a three-dimensional model, for example.

[0036] The object model 13 is a model of the object 11 shown in Figure 2. In this embodiment, the shape of object 11 is discretized using a finite number of elements F(i) (i=1, 2, ...). This allows the object model 13 to be defined. Each element F(i) is defined with numerical data such as an element number, a node number 17, and the coordinate values ​​of node 17.

[0037] In this embodiment, only the contour of the bottom surface 10a of the object 11 shown in Figure 2 is discretized, but this is not particularly limited. For example, the entire bottom surface 10a may be discretized, or the contour of the side surface 10b of the object 11 represented as a plane may be discretized. If the object model 13 is set as a three-dimensional model, the entire object 11 may be discretized. Furthermore, it is preferable to use commercially available software (such as "STAR-CCM+" from Siemens PLM Software) for discretization.

[0038] The object model 13 has an analytical coordinate system 18 associated with the shape of the object 11. This analytical coordinate system 18 is used, for example, to determine the position in space 14. Such an analytical coordinate system 18 is determined as appropriate, for example, as the centroid of the shape (base surface 10a) of the object 11. The object model 13 is input into the model storage unit 7A shown in Figure 1.

[0039] [Computational grid] As shown in Figure 5, the computational grid 15 has multiple nodes 19 in the space 14 surrounding the object model 13 for calculating the physical quantities of the fluid.

[0040] In this embodiment, the computational grid 15 is set as a two-dimensional model, similar to the object model 13, but it is not limited to this configuration. The computational grid 15 may be set as a three-dimensional model, for example.

[0041] The computational grid 15 is set in the space 14 surrounding the object model 13 shown in Figure 4. In this embodiment, the computational grid 15 is set excluding the area occupied by the object model 13 from the space 14, but it is not limited to this configuration. The computational grid 15 may, for example, be set including the area occupied by the object model 13.

[0042] In this embodiment, space 14 is large enough to completely surround the object model 13, but is not limited to this configuration. For example, space 14 may be large enough to surround only a portion of the object model 13, as long as it includes the region to be analyzed. Also, in this embodiment, space 14 is formed in a rectangular shape, but is not limited to this configuration. Depending on the purpose of fluid analysis, space 14 may be formed in a circular or triangular shape, for example.

[0043] As shown in Figure 4, the first length L1 and second length L2 of space 14 are set as appropriate depending on the purpose of the analysis. The first length L1 is the length in the direction of fluid flow (in this example, the x-axis direction). The second length L2 is the length in the direction perpendicular to the direction of fluid flow (in this example, the y-axis direction). In this embodiment, the first length L1 and the second length L2 are set to be approximately the same, but this is not particularly limited, and they may be different from each other. The first length L1 and the second length L2 can be set, for example, to 5 to 100 times the maximum width (not shown) of the bottom surface 10a of the object model 13.

[0044] A predetermined reference position 14a is set in space 14. The reference position 14a is set at any position within space 14, for example, at the origin of space 14 (where both the x-axis and y-axis coordinates are zero). Furthermore, a predetermined position 14b is identified in space 14 relative to the reference position 14a. The object model 13 is placed in space 14 such that the analytical coordinate system 18 of the object model 13 is located at this position 14b. Then, the space 14 surrounding the object model 13 is discretized by a finite number of elements G(i) (i=1, 2, ...) as shown in Figure 5. This sets up the computational grid 15 associated with the object model 13.

[0045] In this embodiment, each element G(i) is an Euler element capable of handling fluid (air) using the finite volume method. Each of these elements G(i) can be assigned the fluid (air) velocity, characteristics, etc. Furthermore, each element G(i) is provided with multiple nodes 19. These multiple nodes 19 can calculate physical quantities in the fluid (pressure in this example). In this embodiment, the nodes 19 of the computational grid 15 and the nodes 17 of the object model 13 (shown in Figure 4) are shared, but this is not particularly limited.

[0046] The computational grid 15 can be appropriately configured based on, for example, a known method (e.g., the procedure for setting up a sound space region as described in the Patent Document (Japanese Patent No. 4792049)). The above-mentioned software can be used for discretization. The computational grid 15 is input to the model storage unit 7A shown in Figure 1.

[0047] [Fluid analysis] Next, in step S11 of this embodiment, fluid analysis is performed using the computational grid 15 associated with the object model 13 shown in Figure 5. At a minimum, the flow field, which is the distribution of physical quantities of the fluid after it has passed through the object model 13 (object 11 shown in Figure 2), and the fluid forces acting on the object model 13 (object 11) are calculated.

[0048] Fluid analysis is performed under predetermined conditions based on known methods. The conditions in this embodiment include the Reynolds number Re and the flow velocity. The Reynolds number Re is a dimensionless number defined in fluid dynamics as the ratio of inertial force to viscous force. This Reynolds number Re is set appropriately according to the purpose of the analysis, for example, 4.0 × 10⁻⁶. 1 ~8.0×10 4 (In this example, 6.4 × 10 4 The flow rate is set to ). The flow rate is also set appropriately according to the purpose of the analysis, for example, to 5-30 m / s (10 m / s in this example).

[0049] In this embodiment, in the computational grid 15, an inflow F1 of fluid (air) is defined on the front wall 15f on one side in the fluid flow direction (x-axis direction). Furthermore, an outflow F2 of fluid (air) is defined on the rear wall 15b on the other side in the fluid flow direction (x-axis direction). As a result, in the computational grid 15, the fluid flowing along the flow direction is calculated for the object model 13, and a simulation (fluid analysis) can be performed in which the fluid (air) is in contact with the object model 13 (object 11). Note that the inflow F1 and outflow F2 of fluid are not limited to this configuration, and for example, they may be defined by swapping the front wall 15f and the rear wall 15b, or they may be defined in the vertical or diagonal direction.

[0050] In this embodiment, the motion of the fluid (air) flowing around the object model 13 can be calculated at each unit time (small time interval) of the simulation. For such simulations (fluid analysis), general-purpose fluid analysis software such as STAR-CCM+ from Siemens PLM Software or FLUNET from ANSYS can be used.

[0051] At each node 19 that constitutes the computational grid 15, a physical quantity of the fluid (in this example, air pressure) is calculated. Furthermore, based on the physical quantity of the fluid calculated at each node 19, the fluid force acting on the object model 13 (object 11 shown in Figure 2) is calculated. This fluid force is calculated using the air resistance coefficient (C DWhen the value) is calculated, first, in the fluid flow direction, the difference in pressure before and after the object model 13 and the shear stress of the fluid on the outer surface of the object model 13 are added together. Next, the added value is integrated over the surface area (the area of the outer surface) of the object model 13, and the air resistance coefficient (C D value) can be calculated.

[0052] The physical quantity (pressure) and fluid force (resistance coefficient) of each node 19 are calculated for each unit time (tiny time) from the start to the end of the simulation. The unit time is set to, for example, 0.5 to 5.0 μs (in this example, 1.0 μs). Also, the time from the start (t = t0) to the end (t = t n ) of the simulation is set to 1.0 to 10.0 seconds (in this example, 1.5 seconds).

[0053] In this embodiment, for each unit time, the physical quantities of a plurality of nodes 19 are arranged based on the coordinate values of each node 19. As a result, for each unit time, the distribution of physical quantities (matrix of physical quantities) is specified. These distributions of physical quantities can be specified as the fluid flow field after passing through the object 11 shown in FIG. 2 at each unit time.

[0054] FIG. 6 is a contour diagram showing an example of the distribution of the physical quantity C of the flow field 20. In FIG. 6, in the region (hereinafter sometimes referred to as the "selected region") 21 selected from the calculation grid 15 shown in FIG. 5, the distribution of the physical quantity C (flow field 20) calculated in one unit time is representatively shown. Details of the selected region 21 will be described later.

[0055] The flow field 20 can be input into the flow field - fluid force storage unit 7B shown in FIG. 1 for each unit time from the start (t = t0) to the end (t = t n ) of the simulation. Also, the fluid force (in this example, the resistance coefficient) acting on the object model 13 (the object 11 shown in FIG. 2) can be input into the flow field - fluid force storage unit 7B shown in FIG. 1 for each unit time from the start to the end of the simulation, similar to the flow field 20.

[0056] [Obtain multiple types of features] Next, in the generation method of this embodiment, multiple types of feature quantities are obtained from the physical quantity C of the flow field 20 shown in Figure 6 (step S12). In step S12 of this embodiment, multiple types of feature quantities are obtained from the physical quantity of the flow field 20 for each unit time (multiple time points) of the simulation.

[0057] In step S12 of this embodiment, first, the physical quantity C of the flow field 20 (shown in Figure 6), which is input to the flow field / fluid force memory unit 7B shown in Figure 1, and the feature quantity acquisition unit 8B included in the program unit 8 are loaded into the working memory 5C. The feature quantity acquisition unit 8B is a program for acquiring multiple types of feature quantities from the physical quantity C of the flow field 20. When this feature quantity acquisition unit 8B is executed by the processor 5A, the computer 1 (generation device 1B) can be made to function as a means for acquiring multiple types of feature quantities.

[0058] Multiple types of features may be obtained from physical quantities C calculated at all nodes 19 of the computational grid 15 shown in Figure 5. Generally, the fluid force acting on the object model 13 (in this example, the drag coefficient) tends to be greatly influenced by the physical quantity (pressure) C1 calculated at the nodes 19 closest to the object model 13. Furthermore, in the direction of fluid flow (in this example, the x-axis direction), the influence of physical quantities calculated at the downstream nodes 19 (right side in Figure 5) tends to be greater than that of physical quantities C calculated at the upstream nodes 19 (left side in Figure 5) of the object model 13. For this reason, multiple types of features may be obtained from the physical quantities C of the flow field 20, focusing on a select region 21 of the computational grid 15 that includes these nodes 19. By limiting feature acquisition to such a select region 21, features can be efficiently obtained from physical quantities C that have a significant influence on the fluid force.

[0059] In step S12 of this embodiment, first, a selection region 21 is selected from the computational grid 15 that includes a node 19 where a physical quantity C, which has a large influence on the fluid force, has been calculated. As described above, the fluid force tends to be more influenced by physical quantities calculated at nodes 19 close to the object model 13, and by physical quantities calculated at nodes 19 downstream of the object model 13 (on the right side in Figure 5). For this reason, in this embodiment, the selection region 21 is selected from the computational grid 15 such that it includes upstream nodes 19 close to the object model 13, while the number of downstream nodes 19 is relatively larger than the number of upstream nodes 19. The selection region 21 in this embodiment is formed in a rectangular shape, but is not limited to this configuration; for example, it may be formed in a circular or triangular shape depending on the purpose of fluid analysis.

[0060] Figure 7 shows an example of a physical quantity C in the flow field 20. In Figure 7, the physical quantity C is shown in a simplified form. In Figure 7, at multiple nodes 19 (shown in Figure 5) included in the selected region 21 shown in Figure 6, the physical quantity C of node 19 at the smallest coordinate value (x1, y1) is shown for each unit time t. 1t From there, the largest coordinate value (x z , y z ) Physical quantity C zt They are arranged vertically in ascending order. Furthermore, the physical quantity C 1t ~C zt However, from the smallest unit time (t=t0) to the largest unit time (t=t0) n The data is arranged horizontally in ascending order. This allows for the calculation of the physical quantity C at each unit time from the start to the end of the simulation at all nodes 19 included in the selected region 21. 10 ~C zn The matrix (multidimensional data of the physical quantity C) 22 can be identified.

[0061] Next, in step S12 of this embodiment, multiple types of feature quantities are obtained from the physical quantity C of the flow field 20 (in this example, the selected region 21). In this embodiment, multiple types of feature quantities are obtained at each unit time (multiple time points) t of the simulation.

[0062] As described above, multiple types of features are used as input to a trained model for estimating the fluid force acting on the target object 10. Therefore, as the number of multiple types of features increases, the number of training datasets required for machine learning also increases, thus requiring more time for machine learning. For this reason, features of lower dimension than the physical quantity C shown in Figures 6 and 7 (i.e., the physical quantity C included in matrix 22) are used. 10 ~C zn It is preferable to obtain fewer features than the number of elements in the simulation. Furthermore, it is important that multiple types of features have a strong correlation with the fluid force. However, since the physical quantity C (matrix 22) is calculated at multiple nodes 19 shown in Figure 5 for each unit time of the simulation, it constitutes complex and enormous data, making it difficult to obtain features that are lower dimensional than the physical quantity C and have a strong correlation with the fluid force.

[0063] In this embodiment, multiple types of features are obtained from the physical quantities C of the flow field 20 (in this example, the matrix 22 of physical quantities C in the selected region 21) based on Proper Orthogonal Decomposition (POD). Proper Orthogonal Decomposition is a method for extracting low-dimensional components from multidimensional data (in this example, the matrix 22 of physical quantities C). This Proper Orthogonal Decomposition is also called Principal Component Analysis (PCA), and can be decomposed into multiple basis vectors and multiple coefficients corresponding to each basis vector. These basis vectors and coefficients are extracted for each of the multiple modes (principal components).

[0064] The basis vectors (POD basis) are used to represent the spatial characteristics of the flow field 20 shown in Figure 6 for each of the multiple modes (principal components). These spatial characteristics (basis vectors) are used at each node 19 (shown in Figure 5) included in the flow field 20 (computational grid 15) from the start (t=t0) to the end (t=t0) of the simulation. n A characteristic physical quantity common to all units of time up to ) is identified. Therefore, one basis vector can be extracted for each of the multiple modes (in this example, the 0th to the 7th mode).

[0065] The coefficients (POD coefficients) are numerical values ​​that represent the strength of the basis vectors for each mode (in this example, modes 0 to 7), and are calculated from the start (t=t0) to the end (t=t0) of the simulation. n It is identified for each unit of time up to ). Therefore, the coefficients of each mode are constructed as time-series data that change over time (unit time).

[0066] Among the multiple modes (in this example, modes 0 to 7), the modes with relatively large changes in coefficients exhibit larger variances in the physical quantity C shown in Figures 6 and 7. Therefore, by comparing the coefficients of each mode, it becomes possible to identify characteristic parts of the flow field 20 shown in Figure 6. Since such characteristic parts of the flow field 20 tend to have a significant impact on the fluid force (in this example, the drag coefficient) acting on the object model 13 (object 11 shown in Figure 2), the coefficients of each mode that can identify these characteristic parts have a strong correlation with the fluid force. Therefore, the coefficients of each mode can be obtained as multiple types of feature quantities obtainable from the physical quantity C of the flow field 20. As mentioned above, the coefficients of each mode are time-series data. For this reason, the multiple types of feature quantities identified from the coefficients of each mode are also constructed as time-series data that change over time.

[0067] Furthermore, for each of the multiple modes (in this example, modes 0 to 7), the values ​​obtained by multiplying the basis vector by a coefficient at any unit time t are summed up for all modes, thereby determining the physical quantity C of the flow field 20 at any unit time t. 1t ~C zt It can be restored to its original form. For details of the intrinsic orthogonal decomposition, see, for example, Non-Patent Literature 2 (Kunihiko Taira, "Fluid Analysis by Intrinsic Orthogonal Decomposition: 1. Fundamentals," [online], flow, Japan Society of Fluid Mechanics, Vol. 30, 2011, pp. 115-123, [Retrieved August 29, 2024], Internet).<URL:https: / / www.nagare.or.jp / download / noauth.html?d=30-2rensai2.pdf&dir=54> It is described in ).

[0068] In this embodiment, eigenorthogonal decomposition (SnapshotPOD) is performed on all matrices 22 (multidimensional data) of the physical quantity C of the flow field 20 shown in Figure 7. This allows for the decomposition of each of the multiple modes (in this example, modes 0 to 7) into basis vectors and coefficients for each unit time.

[0069] Figure 8(a) is a contour plot showing an example of basis vector 23 for the 0th mode. Figure 8(b) is a contour plot showing an example of basis vector 23 for the 2nd mode. Figure 9 is a graph showing the relationship between coefficient 24 and the unit time of the simulation. In Figure 9, among the 0th to 7th modes, the coefficient 24 (feature D) for the 0th to 4th modes is shown. 0t ~D 4t ) is shown as a representative example. Note that feature D 0t ~D 4t This can be identified for each unit of time t (or multiple time points).

[0070] In step S12 of this embodiment, based on the intrinsic orthogonal decomposition, the physical quantity C calculated for each of the multiple nodes 19 included in the flow field 20 (selected region 21) shown in Figures 6 and 7 is used to obtain the multiple types of feature quantities D shown in Figure 9. 0t ~D 7t (The coefficients for the 8 modes, 24 in total) are obtained. This feature D 0t ~D 7t This is acquired at each unit time t (multiple time points) of the simulation. At each unit time t, the feature D 0t ~D 7t The number of these (8 in this example) is the physical quantity C shown in Figure 7. 1t ~C zt This is less than the number of elements (32,250 in this example). This prevents an increase in the number of training datasets required for machine learning of the trained model, while still allowing for the acquisition of features that have a strong correlation with hydrodynamics.

[0071] In step S12 of this embodiment, based on the intrinsic orthogonal decomposition, the physical quantity C of the flow field 20 shown in Figure 7 is used to obtain multiple types of feature quantities D shown in Figure 9. 0t ~D 7tWhile the above describes the acquisition of features, the invention is not limited to this embodiment. For example, multiple types of features (not shown) may be acquired from the physical quantity C of the flow field 20 based on at least one of a convolutional neural network, principal component analysis, and an autoencoder. Note that convolutional neural networks, principal component analysis, and autoencoders are all well-known.

[0072] A convolutional neural network (hereinafter sometimes referred to as "CNN") consists of convolutional layers, pooling layers, and fully connected layers. By using such a CNN, for example, multiple types of local features (not shown) can be extracted from the contour map of the physical quantity C of the flow field 20 shown in Figure 6 (i.e., fewer than the number of physical quantities C). Note that when using a CNN, unlike when using eigenorthogonal decomposition, supervised learning is required beforehand.

[0073] Principal component analysis (PCA) is a method for creating principal components by aggregating data with many variables. By using PCA, for example, multiple sets of principal components (not shown) can be obtained by transforming the physical quantity C based on multiple principal components obtained by aggregating the matrix (multidimensional data) 22 of the physical quantity C of the flow field 20 shown in Figure 7. These sets of principal components can be used to obtain multiple types of features from the physical quantity C of the flow field 20, fewer than the number of physical quantities C themselves.

[0074] An autoencoder is a technique for reducing the dimensionality of input data and compressing it. Using such an encoder, for example, the contour plot of the physical quantity C of the flow field 20 shown in Figure 6 can be compressed to extract its features. This allows for the acquisition of multiple types of features, fewer than the number of physical quantities, from the physical quantity C of the flow field 20. Note that, unlike when using eigenorthogonal decomposition, using an autoencoder requires prior unsupervised learning.

[0075] In step S12 of this embodiment, by using eigenorthogonal decomposition, multiple types of features D (in this example, feature D) that have a strong correlation with fluid force are generated without requiring prior machine learning such as CNN or autoencoder. 0t ~D 7t ) can be obtained. In this embodiment, multiple types of feature quantities D obtained for each unit time t (multiple time points) of the simulation are obtained. 0t ~D 7t In this example, the coefficient 24 shown in Figure 9 is input to the basis vector / feature memory unit 7C shown in Figure 1.

[0076] [Prepare the training dataset] Next, in the generation method of this embodiment, multiple types of feature quantities D (in this example, feature quantity D) are used as shown in Figure 9. 0t ~D 7t ) Then, a training dataset is prepared in which the fluid force is combined (step S13). The training dataset in this embodiment is used as training data for machine learning to output the fluid force from the feature D.

[0077] In step S13 of this embodiment, first, the feature quantity D (the feature quantity D shown in Figure 9) input to the basis vector / feature quantity storage unit 7C shown in Figure 1 is first processed. 0t ~D 7t The fluid forces input to the flow field / fluid force memory unit 7B are loaded into the working memory 5C. Furthermore, the preparation unit 8C included in the program unit 8 is loaded into the working memory 5C. The preparation unit 8C is a program for preparing a training dataset in which multiple types of feature quantities D and fluid forces are combined. When this preparation unit 8C is executed by the processor 5A, the computer 1 (generator 1B) can be made to function as a means for preparing the training dataset.

[0078] Figure 10 shows an example of the training dataset 26. In Figure 10, feature D 00 ~D n7 (Coefficient 24) is shown in a simplified form, and the fluid force E0~E n (C DThe values ​​are shown in a simplified form.

[0079] In step S13 of this embodiment, the simulation progresses from the start (t=t0) to the end (t=t0). n For every unit time t up to ), multiple types of features (in this example, feature D) 0t ~D 7t ) and fluid force E t These are combined. This creates multiple training datasets 26. Each of the training datasets 26 in this embodiment contains multiple types of features D, which are composed of coefficients 24 for multiple modes (in this example, from mode 0 to mode 7). 0t ~D 7t And, fluid force E t It includes.

[0080] Each of the multiple training datasets 26 in this embodiment is used to train a machine learning model in step S14 described later. This allows multiple types of feature quantities D obtained from the fluid flow field 20 after passing through the target object 10 (shown in Figure 2) in any unit time t. 0t ~D 7t When you input this, the fluid force E acting on the target object 10 will be calculated. t This enables the generation of a trained model capable of outputting the following. Multiple training datasets 26 are input to the training dataset storage unit 7D shown in Figure 1.

[0081] [Train the machine learning model] Next, in the generation method of this embodiment, a machine learning model is trained using the training dataset 26 shown in Figure 10 (step S14). In step S14, feature quantities D obtained from the fluid flow field 20 (for example, shown in Figure 6) after passing through the target object 10 shown in Figure 2 are acquired. 0t ~D 7t When this is input, the fluid force E acting on the target object 10 t The machine learning model is trained to produce the output shown.

[0082] In step S14 of this embodiment, first, the training dataset 26 (shown in Figure 10) stored in the training dataset storage unit 7D shown in Figure 1, and the learning unit 8D included in the program unit 8 are loaded into the working memory 5C. The learning unit 8D is a program that uses the training dataset 26 to train the machine learning model. When this learning unit 8D is executed by the processor 5A, the computer 1 (generator 1B) can be made to function as a means for training the machine learning model.

[0083] The machine learning model is not particularly limited, as long as it can be trained to output the fluid force E acting on the target object 10 when it receives feature quantities D obtained from the fluid flow field 20 (for example, shown in Figure 6) after the fluid has passed through the target object 10 shown in Figure 2. In this embodiment, it is desirable to use a deep learning model equipped with a neural network as the machine learning model. Such a machine learning model can be appropriately constructed based on known methods such as fully connected multilayer perceptrons, multiple regression, ridge regression, random forests, and Gaussian process regression.

[0084] Figure 11 shows an example of a trained model 29 (machine learning model 30). The machine learning model 30 in this embodiment is based on a fully connected multilayer perceptron. Since such a fully connected multilayer perceptron can infer regression problems, it is possible to accurately infer an unknown fluid force E based on past learning.

[0085] The machine learning model 30 is defined by an input layer 31, an output layer 32, and an intermediate layer (hidden layer) 33. The input layer 31 contains multiple types of features (coefficients 24), including the features D of the 0th to 7th modes. 0t ~D 7t However, this is input every unit time t. The output layer 32 receives the hydrodynamic force E acting on the target object 10 (shown in Figure 2). t However, it is possible to output every unit time t. The hidden layer 33 is generated by machine learning.

[0086] The hidden layer 33 contains a combination of multiple neurons (nodes) 34 arranged in a multi-level hierarchy and optimized weighting coefficients (parameters) 35. Each neuron 34 is connected by the weighting coefficients 35. Such a hidden layer 33 is called a neural network.

[0087] The weighting coefficient 35 is, for example, for each neuron 34, the input (feature quantities D of modes 0 to 7). 0t ~D 7t Output (hydrodynamic force) E t And the true output (hydrodynamic force E from training data) t The model is learned by adjusting the respective weight coefficients 35 to minimize the difference with ). This learning method is called backpropagation. By performing this learning on each of the multiple training datasets 26 (not shown in the figure), the machine learning model 30 can be optimized. This allows for the optimization of multiple types of features (in this example, feature D 0t ~D 7t ) is used as the explanatory variable, and the fluid force E t A pre-trained model 29 can be generated with the target variable as follows. For example, machine learning software (for example, the Python library "PyTorch") can be used to generate such a pre-trained model 29.

[0088] As described above, the fluid force E changes according to the flow field 20 shown in Figure 6. Therefore, the fluid force E t These are multiple types of feature quantities D obtained from the physical quantity C of the flow field 20 shown in Figure 7. 0t ~D 7t There is a tendency for it to correlate with (coefficient 24). Such multiple types of features D 0t ~D 7t However, by inputting this data into the trained model 29 shown in Figure 11, features for estimating the fluid force E can be effectively extracted. This makes it possible to generate a trained model 29 capable of accurately estimating the fluid force E.

[0089] In the machine learning of this embodiment, a plurality of learning datasets 26 shown in FIG. 10 are used. These learning datasets 26 are, for each unit time from the start (t = t0) to the end (t = t n ) of the simulation, a plurality of types of feature quantities D 0t ~D 7t and the fluid force E t are respectively combined. By using each of these learning datasets 26 for the machine learning of the machine learning model 30 shown in FIG. 11, it becomes possible to generate a learned model 29 that can accurately estimate the fluid force E that changes according to the flow field 20 shown in FIG. 6.

[0090] In the learned model 29 of this embodiment, when a plurality of types of feature quantities D 0t ~D 7t are input, the fluid force E t acting on the target object 10 is output. Therefore, it becomes possible to easily estimate the fluid force E acting on the target object 10 without the need for the experience and intuition of an expert.

[0091] Furthermore, in the learned model 29 (input layer 31), the feature quantities D 10 ~D zn obtained from the physical quantities C 0t ~C 7t (coefficients 24 of each mode with a lower dimension than the physical quantities C 1t ~C zt ) of the flow field 20 shown in FIG. 7 are input. For this reason, for example, compared with the case where the physical quantities C 1t ~C zt are directly input to the learned model 29 (input layer 31), the number of explanatory variables is reduced. As a result, in this embodiment, it becomes possible to reduce the number of teacher data required to create a learned model 29 having high prediction accuracy. Also, by reducing the number of teacher data, the creation time of the learned model 29 can be shortened. Furthermore, by reducing the number of teacher data, it is possible to suppress the occurrence of overlearning such as deviating greatly from the tendency originally suggested by the teacher data, and it becomes possible to infer (predict) the fluid force E with high accuracy. The learned model 29 is input to the learned model storage unit 7E shown in FIG. 1.

[0092] [Method for analyzing fluid forces (first embodiment)] Next, an example of the processing procedure for the fluid force analysis method will be described. In this analysis method, the fluid force E flowing around the target object 10 shown in Figure 2 is analyzed. In the analysis method of this embodiment, a trained model 29 (shown in Figure 11) generated based on the processing procedure of the generation method shown in Figure 3 is used. Figure 12 is a flowchart showing an example of the processing procedure for the fluid force analysis method. Each step of the analysis method of this embodiment is executed by one or more processors 5A included in the analysis device 1A (computer 1) shown in Figure 1.

[0093] [Calculate the flow field to be analyzed (Step 1)] In the analysis method of this embodiment, first, a fluid analysis is performed to calculate the flow field 20 (shown in Figure 6), which is the distribution of physical quantities of the fluid after it has passed through the target object 10 (first step S1). In the first step S1 of this embodiment, the flow field of the target object 10 is calculated based on the same processing procedure as in step S11 of the generation method shown in Figure 3.

[0094] In the first step S1 of this embodiment, first, the calculation unit 8A included in the program unit 8 shown in Figure 1 is loaded into the working memory 5C. The calculation unit 8A is a program that performs fluid analysis to calculate the flow field after at least the target object 10 (shown in Figure 2) has passed through. When this calculation unit 8A is executed by the processor 5A, the computer 1 (analysis device 1A) can be made to function as a means for performing fluid analysis and calculating the flow field 20.

[0095] In this embodiment, the fluid analysis uses a target object model that models the target object 10 and a computational grid for calculating the fluid flow field 20. Therefore, if the target object model and computational grid have not yet been set up during the fluid analysis, they are set up prior to the fluid analysis.

[0096] [Target object model] As shown in Figure 4, the target object model 16 in this embodiment, similar to the object model 13 set in step S11, is obtained by discretizing the shape of the target object 10 shown in Figure 3 using a finite number of elements F(i). This allows the target object model 16 to be set. The target object model 16 has an analytical coordinate system 18 associated with the shape of the target object 10. This analytical coordinate system 18 is identified, for example, as the centroid of the shape (base surface 10a) of the target object 10. The target object model 16 is input into the model storage unit 7A shown in Figure 1.

[0097] [Computational grid] As shown in Figure 5, the computational grid 15 in this embodiment is similar to the computational grid 15 set in step S11, in which the space 14 surrounding the target object model 16 shown in Figure 4 is discretized with a finite number of elements G(i). This sets up the computational grid 15 associated with the target object model 16. The computational grid 15 is input to the model storage unit 7A shown in Figure 1.

[0098] [Fluid analysis] Next, in the first step S1 of this embodiment, a fluid analysis is performed using the target object model 16 and the computational grid 15 shown in Figure 5. At a minimum, the flow field, which is the distribution of physical quantities of the fluid after it has passed through the target object model 16 (target object 10 shown in Figure 2), is calculated. The fluid analysis may be performed under the same conditions as in step S11 shown in Figure 3, or under different conditions (for example, different flow velocities). Thus, in the first step S1, the computational grid 15 can calculate the fluid flowing along the flow direction relative to the target object model 16. Furthermore, in the first step S1, a simulation (fluid analysis) may be performed in which a fluid (air) is brought into contact with the target object model 16 (target object 10).

[0099] At each node 19 constituting the computational grid 15 shown in Figure 5, a physical quantity of the fluid (in this example, air pressure) is calculated at each unit time (infinite time) from the start to the end of the simulation. By arranging these physical quantities at each node 19 based on the coordinate values ​​of each node 19, the distribution of physical quantities (a matrix of physical quantities) is identified. Such a distribution of physical quantities can be identified as the fluid flow field 20 after passing through the target object 10 shown in Figure 2. The physical quantity C of the flow field 20 may be obtained, for example, as a contour plot shown in Figure 6.

[0100] The flow field 20 is defined as follows: from the start of the simulation (t=t0) to the end (t=t0) n Up to that point, the flow field / hydrodynamic memory unit 7B shown in Figure 1 can be input at each unit time.

[0101] [Obtaining multiple types of features (Step 2)] Next, in the analysis method of this embodiment, multiple types of feature quantities D are obtained from the physical quantity C of the flow field 20 shown in Figure 6 (second step S2).

[0102] In the second step S2 of this embodiment, first, the physical quantity C of the flow field 20 (shown in Figure 6), which is input to the flow field / fluid force memory unit 7B shown in Figure 1, and the feature quantity acquisition unit 8B included in the program unit 8 are loaded into the working memory 5C. The feature quantity acquisition unit 8B is a program for acquiring multiple types of feature quantities D from the physical quantity C of the flow field 20. When this feature quantity acquisition unit 8B is executed by the processor 5A, the computer 1 (analysis device 1A) can be made to function as a means for acquiring multiple types of feature quantities D.

[0103] In the second step S2 of this embodiment, multiple types of feature quantities D can be obtained from the physical quantity C of the flow field of the target object 10 calculated in the first step S1, based on a procedure similar to that of step S12 of the generation method shown in Figure 3.

[0104] In the second step S2 of the present embodiment, similar to step S12 of the generation method shown in FIG. 3, first, a selection region 21 including nodes 19 where a physical quantity C having a large influence on the fluid force E is calculated is selected from the computational grid 15 shown in FIG. 5. In the present embodiment, the selection region 21 is selected from the computational grid 15 so as to include nodes 19 on the upstream side close to the target object model 16 and the number of nodes 19 on the downstream side is relatively larger than the number of nodes 19 on the upstream side. Then, at all nodes 19 included in the selection region 21, the physical quantity C (multidimensional data of the physical quantity C) calculated per unit time from the start to the end of the simulation can be specified.

[0105] Next, in the second step S2 of the present embodiment, a plurality of types of feature quantities D are obtained from the physical quantity C of the flow field 20 shown in FIGS. 6 and 7 (in this example, the selection region 21). In the present embodiment, a plurality of types of feature quantities D are obtained for each unit time (a plurality of times) of the simulation.

[0106] As described above, when the number of a plurality of types of feature quantities D increases, the number of learning datasets required for machine learning increases, so that a lot of time is required for machine learning. For this reason, it is important to obtain a plurality of types of feature quantities D that are feature quantities of a lower dimension than the physical quantity C shown in FIGS. 6 and 7 (that is, feature quantities fewer than the number of physical quantities C included in the matrix 22) and have a strong correlation with the fluid force E. However, since the physical quantity C (matrix 22) constitutes complex and huge data, it is difficult to obtain a feature quantity D that has a lower dimension than the physical quantity C and has a strong correlation with the fluid force E.

[0107] In the second step S2 of the present embodiment, proper orthogonal decomposition is performed on all matrices 22 of the physical quantity C of the flow field 20 shown in FIG. 7. As a result, in the second step S2, for each of a plurality of modes (in this example, mode 0 to mode 7), the basis vector 23 shown in FIG. 8 and the coefficient 24 for each unit time (feature quantity D shown in FIG. 9 0t ~D 7t ) can be decomposed. As described above, the coefficient 24 of each mode is the fluid force E tSince it has a strong correlation with multiple types of features D (in this example, feature D 0t ~D 7t ) are treated as such. As a result, there are fewer types of features D than the number of physical quantities C. 0t ~D 7t (In this example, the coefficients for the eight modes, 24 in total) are acquired at each unit time t (multiple time points) of the simulation. This prevents an increase in the number of training datasets required for machine learning of the trained model, while also acquiring features D that have a strong correlation with the fluid force E. 0t ~D 7t It can be obtained.

[0108] In the second step S2 of this embodiment, based on the intrinsic orthogonal decomposition, the physical quantity C of the flow field 20 shown in Figure 7 is used to obtain multiple types of feature quantities D shown in Figure 9. 0t ~D 7t While the above describes the obtained features, the method is not limited to this configuration. For example, multiple types of features may be obtained from the physical quantity C of the flow field 20 shown in Figures 6 and 7 based on at least one of a convolutional neural network (CNN), principal component analysis, and an autoencoder. Details of the CNN, principal component analysis, and autoencoder are as described above.

[0109] In the second step S2 of this embodiment, by using eigenorthogonal decomposition, multiple types of features D that have a strong correlation with the fluid force E can be obtained without the need to perform machine learning such as CNN or autoencoder in advance.

[0110] The basis vectors 23 of multiple modes (in this example, modes 0 to 7) are input to the basis vector / feature memory unit 7C shown in Figure 1. Furthermore, multiple types of feature quantities D 0t ~D 7t The coefficients (24 for each mode) are input to the basis vector / feature memory unit 7C shown in Figure 1 at each unit time t (multiple time points) of the simulation.

[0111] [Estimating the fluid force acting on the target object (Step 3)] Next, in the analysis method of this embodiment, the fluid force E acting on the target object 10 shown in Figure 2 is estimated (third step S3). In the third step S3, multiple types of feature quantities D obtained in step S2 are estimated. 0t ~D 7t The coefficients for each mode (24) and the trained model 29 (shown in Figure 11) generated based on the processing procedure of the generation method shown in Figure 3 are used.

[0112] In the third step S3 of this embodiment, first, multiple types of feature quantities D are input to the basis vector / feature quantity storage unit 7C shown in Figure 1. 0t ~D 7t The coefficients 24 for each mode are loaded into the working memory 5C. Furthermore, the trained model 29 (shown in Figure 11) input to the trained model storage unit 7E is loaded into the working memory 5C. Furthermore, the estimation unit 8E included in the program unit 8 is loaded into the working memory 5C. The estimation unit 8E is a program for estimating the fluid force acting on the target object 10 shown in Figure 2 using the trained model 29. When this estimation unit 8E is executed by the processor 5A, the computer 1 (analysis device 1A) can be made to function as a means for estimating the fluid force E acting on the target object 10.

[0113] As shown in Figure 11, the trained model 29 has multiple types of features D 0t ~D 7t When the coefficient for each mode (24) is input, the fluid force E acting on the target object 10 (shown in Figure 2) is calculated. t The machine learning is being used to produce the following output. Multiple types of features D obtained in step S2 are then applied to this pre-trained model 29. 0t ~D 7t However, when input at each unit time t, the fluid force E acting on the target object 10 tHowever, it can be estimated (output) at each unit time t. Therefore, the analysis method of this embodiment makes it possible to easily estimate the fluid force E acting on the target object 10 without requiring the experience or intuition of a skilled person. The fluid force E acquired at each unit time (multiple time points) of the simulation is input to the flow field / fluid force memory unit 7B shown in Figure 1.

[0114] [Obtain the contribution to fluid force] Next, in the analysis method of this embodiment, the multiple types of feature quantities D shown in Figure 11 are used. 0t ~D 7t For each of the (coefficients of each mode) the estimated hydrodynamic force E t The degree of contribution to is obtained (Step 4, S4).

[0115] In the fourth step S4 of this embodiment, first, multiple types of feature quantities D are input to the basis vector / feature quantity storage unit 7C shown in Figure 1. 0t ~D 7t The coefficients 24 for each mode and the fluid force Et input to the flow field / fluid force memory unit 7B are loaded into the working memory 5C. Furthermore, the trained model 29 input to the trained model memory unit 7E and the contribution acquisition unit 8F included in the program unit 8 are loaded into the working memory 5C. The contribution acquisition unit 8F contains multiple types of feature quantities D 0t ~D 7t For each of these, the estimated hydrodynamic force E t This is a program for obtaining the degree of contribution. This contribution acquisition unit 8F is executed by the processor 5A, which enables the computer 1 (analysis device 1A) to function as a means for obtaining the degree of contribution.

[0116] The contribution of this embodiment is the multiple types of feature quantities D 0t ~D 7t (In this example, each of the coefficients 24 for the 0th to 7th modes) represents the hydrodynamic force E according to the trained model 29. t This is output as an indicator (degree) showing how much it contributes to the estimation of multiple types of features D. 0t ~D7t (Of the 24 coefficients for modes 0 to 7, the fluid force E t Features D that have a relatively large influence (high importance) can be identified.

[0117] The contribution is the estimated hydrodynamic force E t An indicator (degree) showing the extent to which it contributes to the result can be obtained as appropriate. In this embodiment, multiple types of feature quantities D are obtained based on the known SHAP (Shapley Additive exPlanations). 0t ~D 7t (Coefficient of 24 for each mode) Each fluid force E t The degree of contribution to this can be obtained.

[0118] SHAP applies the Shapley value from game theory as XAI (eXplainable AI), a technique for interpreting machine learning. Such SHAP applies to each feature D of the prediction of the machine learning model 30, as shown in Figure 11. 0t ~D 7t It is used to evaluate the degree of contribution.

[0119] SHAP uses multiple types of features D 0t ~D 7t The degree to which each of these contributes to the estimation of the fluid force E can be easily calculated as a contribution (value). This contribution is indicated by its sign (positive or negative) and the magnitude of the numerical value. Multiple types of feature quantities D 0t ~D 7t Of each of these, feature D has the largest absolute value of contribution. 0t ~D 7t Approximately, fluid force E t This indicates a high impact. SHAP can be easily used, for example, by using publicly available software. Examples of such software include Python libraries.

[0120] In the fourth step S4 of this embodiment, multiple types of feature quantities D are generated based on SHAP. 0t ~D 7t Each of the fluid forces Et The contribution to this is obtained. This contribution is obtained using multiple types of features D obtained in the second step S2. 0t ~D 7t And the fluid force E estimated in the third step S3 t The trained model 29 is used. Furthermore, the contribution is calculated for each unit time t of the simulation, using multiple types of features D. 0t ~D 7t Multiple types of features D can be obtained at each unit time t of the simulation. 0t ~D 7t The contribution values ​​obtained for each instance are input into the contribution value storage unit 7F shown in Figure 1.

[0121] Figure 13 shows multiple types of feature quantities D. 0t ~D 7t This is a graph showing the relationship with the contribution S (SHAP value). In Figure 13, the darker the color, the greater the fluid force E. Also, multiple types of features D 0t ~D 7t The coefficients 24 for modes 0 through 7 and the mean field coefficients 24 are shown.

[0122] Figure 13 shows multiple types of features D at each unit time t of the simulation. 0t ~D 7t In this example, the contributions S0 to S7 (SHAP values) obtained for each of the 24 coefficients from mode 0 to mode 7 are plotted. Furthermore, the mean field feature D ave Contribution S obtained from (coefficient 24) ave The (SHAP values) are plotted. In this graph, the feature D of the second mode is shown. t2 The contribution S2 (the range of possible absolute values ​​of the SHAP value) of (coefficient 24) is the largest, indicating that it has the greatest influence on the fluid force E.

[0123] In the analysis method of this embodiment, the feature quantity D shown in Figure 9 is used. 0t ~D 7tBy referencing the coefficient 24 and the basis vector 23 shown in Figure 8, for example, in the flow field 20 shown in Figure 6, it is possible to estimate the location that has a significant influence on the estimated fluid force E (shown in Figure 11). However, the contributions S0 to S7 and feature D 0t ~D 7t Since the coefficient (24) changes with each unit of simulation time, such estimation presents the problem of requiring skilled techniques, effort, and time.

[0124] [Mapping regions that contribute significantly to fluid forces (Step 5)] Next, in the analysis method of this embodiment, based on the contributions S0 to S7 shown in Figure 13, regions with a large contribution to the estimated fluid force E (shown in Figure 11) are mapped onto the flow field 20 shown in Figure 6 or onto coordinates corresponding to the flow field 20 (5th step S5). Through such mapping, regions with a large contribution to the fluid force E can be easily identified in the flow field 20 after passing through the target object model 16 shown in Figure 6 (target object 10 shown in Figure 2), without the need for the above-mentioned references.

[0125] In the fifth step S5 of this embodiment, first, the basis vectors 23 (for example, shown in Figure 8) of multiple modes (in this example, mode 0 to mode 7) input to the basis vector / feature memory unit 7C shown in Figure 1 are loaded into the working memory 5C. Furthermore, multiple types of feature quantities D input to the basis vector / feature memory unit 7C are loaded. 0t ~D 7tThe coefficients 24 for each mode (shown in Figures 9 and 10) and the contributions S0 to S7 (shown in Figure 13) for each mode, which are input to the contribution memory unit 7F, are loaded into the working memory 5C. Furthermore, the mapping unit 8G included in the program unit 8 is loaded into the working memory 5C. This mapping unit 8G is a program for mapping regions that have a large contribution to the estimated fluid force E (shown in Figure 11) onto the flow field 20 shown in Figure 6 or onto coordinates corresponding to the flow field 20, based on the contributions S0 to S7. When this mapping unit 8G is executed by the processor 5A, the computer 1 (analysis device 1A) can function as a means for mapping regions that have a large contribution to the fluid force E.

[0126] Figure 14(a) is a contour plot showing an example of the distribution of the physical quantity C in the flow field 20. Figure 14(b) is a diagram showing an example of the first mapping data 41 in which the region 39 that contributes significantly to the fluid force E is mapped. Figure 14(a) shows the flow field 20 at a different unit time than the flow field 20 in Figure 6.

[0127] In the fifth step S5 of this embodiment, first, the region 39 that contributes significantly to the estimated fluid force E (shown in Figure 11) is mapped onto the coordinate system (in this example, the x and y axis coordinates) corresponding to the flow field 20 shown in Figure 14(a), as shown in Figure 14(b). That is, it is not directly mapped onto the flow field 20 shown in Figure 14(a), but is set separately from the flow field 20 and mapped onto the coordinate system (in this example, the x and y axis coordinates) corresponding to the flow field 20.

[0128] Mapping can be performed as appropriate if a region 39 with a large contribution to the hydrodynamic force E (shown in Figure 11) can be identified. As described above, for each of the multiple modes, the basis vector 23 and the coefficient 24 (feature quantity D) at any unit time are used. 0t ~D 7t The value obtained by multiplying by ) is summed up for all modes, resulting in the physical quantity C of the flow field 20 at any unit time t shown in Figure 7. 1t ~C zt It can be restored to the coefficient 24 (feature D).0t ~D 7t ) is a numerical value representing the strength of the basis vector 23, and is specified for each unit time, similar to the contribution to the fluid force E (SHAP value) S0~S7 shown in Figure 13. From this perspective, first, for each of the multiple modes in any unit time, the coefficient 24 (feature quantity D) is determined. 0t ~D 7t The absolute value of ) and the contribution (SHAP value) S0~S7 can be multiplied (Hadamard product). Next, for each of the multiple modes in any unit of time, the coefficient 24 (feature D) is calculated. 0t ~D 7t The absolute value of ) is multiplied by the contributions S0 to S7, and this value is then multiplied by the absolute value of the basis vector 23 shown in Figure 8, and the sum is applied to all modes. This allows for the acquisition of physical quantities of the flow field 20 (each node 19) considering the contributions S0 to S7. Since the larger the value of such physical quantities considering the contributions S0 to S7, the greater the contribution to the fluid force E (shown in Figure 11), it becomes possible to identify regions 39 that contribute greatly to the fluid force E.

[0129] In this embodiment, based on the following equation (1), regions 39 that have a large contribution to the estimated fluid force E are mapped onto the coordinates corresponding to the flow field 20.

[0130]

number

[0131] In equation (1) above, a physical quantity (matrix) considering the contribution S is obtained as a mask function M for any unit time. This mask function M is used to identify regions 39 (coordinate values) on the coordinates corresponding to the flow field 20 shown in Figure 14(a) in which the estimated fluid force E has a large contribution.

[0132] In equation (1) above, the variable k is replaced with a number that identifies each mode (in this example, modes 0 through 7). Then, for each of the multiple modes in any given unit of time, the absolute value Z of coefficient 24 (feature D) shown in Figure 10 is calculated. k And the contribution (SHAP value) S shown in Figure 13 k These are multiplied (the Hadamard product is applied). As a result, at any given time, the contribution S for each of the multiple modes is determined. k Features that take these factors into consideration (hereinafter sometimes referred to as "contributing features") are obtained.

[0133] Next, for each of the multiple modes, the absolute value U of the basis vector 23 is determined for each of the multiple modes in any given unit of time. k and the contributing features (i.e., the absolute value Z) k and contribution S k (The product of and) is multiplied by and. As a result, for any given unit of time, physical quantities of the flow field 20 (each node 19) considering the contribution S are obtained for each of the multiple modes. Then, for any given unit of time, the physical quantities of all modes are summed up to obtain the physical quantities of the flow field 20 (each node 19) considering the contribution S. These physical quantities are obtained as a mask function M for any given unit of time.

[0134] At any given unit of time, at node 19 (shown in Figure 5), where the absolute value of the physical quantity (mask function M) considering the contribution S is relatively small, the basis vector 23 (absolute value U k ), Feature D 0t ~D 7t (Absolute value Z) k ) and contribution S0~S7(S kAt least one of the following is small. At such a node 19, the contribution to the fluid force E shown in Figure 11 can be considered small in the flow field 20 (selected region 21) after passing through the target object model 16 (target object 10) shown in Figure 14(a). On the other hand, at a node 19 where the absolute value of the physical quantity (mask function M) considering the contribution S is relatively large, the basis vector 23 (absolute value U k ), Feature D 0t ~D 7t (Absolute value Z) k ) and contribution S0~S7(S k At least one of the following is larger. At such a node 19, it can be considered that the contribution to the fluid force E is large in the flow field 20 after passing through the target object model 16 (target object 10). Therefore, the mask function M can identify the region (coordinate values) where the estimated contribution to the fluid force E is large.

[0135] In the fifth step S5 of this embodiment, based on equation (1) above, regions that contribute significantly to the estimated fluid force E are mapped onto the coordinates corresponding to the flow field 20. The mapping is performed as appropriate.

[0136] In the fifth step S5 of this embodiment, at any given unit of time, first color information (transparent in this example) 43 is assigned to nodes 19 (shown in Figure 5) where the absolute value of the mask function M (recovered physical quantity) is greater than or equal to a predetermined threshold, as shown in Figure 14(b). By assigning such first color information 43, regions 39 that contribute significantly to the estimated hydrodynamic force E (shown in Figure 11) can be mapped onto the coordinates corresponding to the flow field 20 (selected region 21) shown in Figure 14(a). By comparing these regions 39 with the flow field 20, it becomes possible to easily find locations in the flow field 20 that have a significant influence on the hydrodynamic force E (for example, locations where Karman vortices grow) and physical quantities C, etc., without requiring skilled techniques, effort, or time. The threshold is set appropriately according to the purpose of the analysis, for example, to 5% to 20% of the maximum value among the absolute values ​​of each value in the matrix (nodes 19) that constitute the mask function M.

[0137] On the other hand, in the fifth step S5 of this embodiment, second color information (in this example, semi-transparent gray) 44 is assigned to nodes 19 (shown in Figure 5) where the absolute value of the mask function M (restored physical quantity) is less than a predetermined threshold in any given unit of time. By assigning such second color information 44, regions 40 that have a small contribution to the estimated fluid force E (shown in Figure 11) can be mapped onto the coordinates corresponding to the flow field 20 (selected region 21) shown in Figure 14(a). By comparing these regions 40 with the flow field 20 shown in Figure 14(a), it becomes possible to easily find positions and physical quantities C, etc., in the flow field 20 that have a small influence on the fluid force E, without requiring skilled techniques, effort, or time.

[0138] In the fifth step S5 of this embodiment, based on a similar procedure, the first color information 43 and the second color information 44 are assigned to the coordinates corresponding to the flow field 20 (selected region 21) shown in Figure 14(a) for each unit time from the start to the end of the simulation. This makes it easy to find the positions and physical quantities C, etc., that have a significant influence on the fluid force E shown in Figure 11 in the flow field 20 for each unit time.

[0139] In the fifth step S5, the mapping of the region 39 that contributes significantly to the estimated fluid force E (shown in Figure 11) onto the coordinates corresponding to the flow field 20 is not limited to the configuration shown in Figure 14(b). For example, the region 39 that contributes significantly to the fluid force E may be mapped onto the flow field 20 shown in Figure 14(a). In this case, if the first color information 43 and the second color information 44 are replaced with the color information of the flow field 20 (contour diagram) based on the procedure described above, it becomes difficult to grasp the physical quantity C of the flow field (contour diagram) 20. On the other hand, the first mapping data 41 in this embodiment is assigned transparent first color information 43 and semi-transparent second color information 44. By superimposing such first mapping data 41 onto the flow field 20 shown in Figure 14(a), the region 39 that contributes significantly to the fluid force E can be mapped while allowing the color information representing the physical quantity C of the flow field 20 to pass through. For example, commercially available image processing software can be used to perform the operation of superimposing such first mapping data 41.

[0140] Figure 15 shows an example of second mapping data 42 in which a region 39 that contributes significantly to the fluid force E (shown in Figure 11) is mapped onto the flow field 20. In the second mapping data 42, the first mapping data 41 shown in Figure 14(b) is superimposed on the flow field 20 shown in Figure 14(a). This eliminates the need to separately compare the region 39 of the first mapping data 41 with the flow field 20, making it easier to identify locations and physical quantities C that significantly influence the estimation of the fluid force E shown in Figure 11 within the flow field 20. Furthermore, it is preferable that the first mapping data 41 is superimposed on the flow field 20 for each unit of time from the start to the end of the simulation. This makes it possible to grasp the locations and physical quantities C that significantly influence the estimation of the fluid force E in a time series (as a video) for each unit of time. The first mapping data 41 and the second mapping data 42 are input to the mapping data storage unit 7G shown in Figure 1.

[0141] [Evaluate the fluid forces of the target object] Next, in the analysis method of this embodiment, the quality of the fluid force E (shown in Figure 11) of the target object 10 shown in Figure 2 is evaluated (step S6). The evaluation of the fluid force E may be performed by the analysis device 1A (computer 1) shown in Figure 1, or by an operator or the like. The quality of the fluid force E is evaluated as appropriate. In this embodiment, the fluid force E is evaluated as good if it is below a predetermined threshold. The threshold can be set as appropriate, for example, according to the performance required of the target object 10 (e.g., air resistance). Furthermore, the quality of the fluid force E may be evaluated considering the region 39 that contributes greatly to the fluid force E, based on the contribution S0 to S7 (SHAP value) shown in Figure 13, the first mapping data 41 shown in Figure 14(b), and the second mapping data 42 shown in Figure 15.

[0142] In step S6 of this embodiment, first, the fluid force E of the target object 10 (target object model 16) input to the flow field / fluid force memory unit 7B shown in Figure 1, and the evaluation unit 8H included in the program unit 8 are loaded into the working memory 5C. The evaluation unit 8H is a program for evaluating the quality of the fluid force E of the target object 10. When this evaluation unit 8H is executed by the processor 5A, the computer 1 (analysis device 1A) can be made to function as a means for evaluating the fluid force E.

[0143] If the fluid force E of the target object 10 is determined to be good (Yes in step S6), the target object 10 determined to be good is manufactured (step S7). On the other hand, if the fluid force E of the target object 10 is determined to be poor (No in step S6), the shape of the target object 10 is changed (step S8), and the first steps S1 to S6 are performed again. In step S7, for example, based on the first mapping data 41 shown in Figure 14(b) and the second mapping data 42 shown in Figure 15, it is preferable that the shape of the target object 10 is changed to reduce the fluid force E, taking into account the region 39 that contributes greatly to the fluid force E. This ensures that a target object 10 with reduced fluid force (air resistance) E is reliably designed and manufactured.

[0144] [Method for analyzing fluid forces (Second Embodiment)] In the analysis method of the previous embodiment, in the second step S2 shown in Figure 12, multiple types of feature quantities D are calculated from the calculation result of the physical quantity C (shown in Figure 6) of the flow field 20 in the first step S1. 0t ~D 7t (As shown in Figure 9) was obtained, but the method is not limited to this. As described above, multiple types of feature quantities D 0t ~D 7t This is time-series data that changes over time (unit time t). In this time-series data, the feature D 0t ~D 7t If the changes are periodic, in the second step S2, based on the trend of the time series data, future features (i.e., the end time of the simulation t=t) are calculated. n (Features of a unit time t after a later period) D 0t ~D 7t This may include a step to predict the future feature D. 0t ~D 7t Because this is obtained virtually, the computation time for fluid analysis (simulation) can be reduced.

[0145] In this embodiment, the third step S3 involves the future feature quantity D predicted in the second step S2. 0t ~D 7t (Figure not shown) is input into the trained model 29 shown in Figure 11 to determine the future fluid force E t The step may include estimating the future fluid forces acting on the object 10 (i.e., the end time of the simulation t=t) without requiring the experience or intuition of an expert. n (Fluid force at a later unit time t) E t This makes it possible to easily estimate the value.

[0146] Furthermore, in the fourth step S4 of this embodiment, multiple types of future features D 0t ~D 7t For each of these, the estimated future fluid force E tThe contributions S0 to S7 (shown in Figure 13) may be obtained. Furthermore, in the fifth step S5, based on the contributions S0 to S7, the estimated future fluid force E is obtained as shown in Figures 14(b) and 15. t Region 39 with a large contribution to the fluid force E may be mapped. In this embodiment, in the future flow field 20 after passing through the target object 10, the fluid force E t Region 39, which has a large contribution to this, can be easily identified.

[0147] [Method for generating a pre-trained model (Second Embodiment)] In previous embodiments, the flow field 20 (shown in Figure 6) and the fluid force E (not shown) after passing through one object 11 shown in Figure 2 are obtained, and multiple types of feature quantities D are obtained from the physical quantity C of the flow field 20. 0t ~D 7t (As shown in Figure 9) was obtained, but the method is not limited to this configuration. For example, the flow field 20 and fluid force E of multiple objects 11 with different shapes may be obtained, and multiple types of feature quantities D common to the flow field 20 of each of the multiple objects 11 may be obtained. Then, for each of the multiple objects 11, a training dataset may be prepared in which the common feature quantities D and the fluid force E are combined, and machine learning may be performed. This can generate a trained model 29 (as shown in Figure 11) that can accurately output the fluid force E acting on target objects 10 of various shapes.

[0148] [Multiple objects] The multiple objects 11 are not particularly limited as long as their shapes differ from each other. Figures 16(a) to (e) show examples of multiple objects 11.

[0149] While the multiple objects 11 are exemplified as columnar bodies 10A, similar to the target object 10 (object 11) shown in Figure 2, they are not limited to this configuration. For example, they may be spheres, tires, vehicles, etc. Details of the columnar bodies 10A are as described above.

[0150] As shown in Figures 16(a) to (e), the multiple objects 11 include the first object 11A, the second object 11B, the third object 11C, the fourth object 11D, and the fifth object 11E, but the configuration is not limited to this. The multiple objects 11 may include other objects 11 different from the first object 11A to the fifth object 11E, or some of these objects 11A to 11E may be omitted. Furthermore, the shape of at least one of the multiple objects 11 may be the same as the shape of the target object 10 (shown in Figure 2) analyzed by the analysis method, or the shapes of all objects 11 may be different from the shapes of the target object 10.

[0151] The first object 11A has the same shape as the target object 10 (object 11) shown in Figure 2. The second object 11B is a regular square prism. The third object 11C is an octagonal prism obtained by chamfering a regular square prism. The fourth object 11D is a regular octagonal prism. The fifth object 11E is an octagonal prism with a larger chamfer than the regular octagonal prism. Therefore, the shapes of the first object 11A to the fifth object 11E are different from each other. Note that the first object 11A to the fifth object 11E are not limited to these shapes; for example, they may be triangular prisms or elliptical prisms.

[0152] [Calculate flow field and fluid forces] In the generation method of this embodiment, in step S11 shown in Figure 3, a fluid analysis is performed to obtain the flow field 20 shown in Figure 6 and the fluid force E shown in Figure 10 for each of the multiple objects 11 shown in Figure 16. For the fluid analysis, as in previous embodiments, multiple object models 13, each modeling one of the multiple objects 11, and a computational grid 15 (shown in Figure 5) for calculating the fluid flow field 20 are used. Details of the object models 13 are as described above.

[0153] Figure 17 shows an example of the second object model 13B and space 14. Figure 18 shows an example of the second object model 13B and second computational grid 15B. In Figure 18, the common computational grid area 46, which will be described later, is enclosed in a white frame.

[0154] As shown in Figures 17 and 18, the multiple object models 13 include a first object model (not shown), a second object model 13B, a third object model (not shown), a fourth object model (not shown), and a fifth object model (not shown). These first to fifth object models are modeled after the first to fifth objects 11A to 11E shown in Figures 16(a) to 16(e), respectively. The details of the object models 13 are as described above and are input into the model storage unit 7A shown in Figure 1.

[0155] As shown in Figure 18, the computational grid 15 has multiple nodes 19 for calculating the physical quantities of the fluid in the space 14 surrounding the object models 13 (each of the first to fifth object models) shown in Figure 17.

[0156] The computational grid 15 includes the first computational grid (not shown), the second computational grid 15B, the third computational grid (not shown), the fourth computational grid (not shown), and the fifth computational grid (not shown). These first to fifth computational grids are set in the space 14 (shown in Figure 17) that surrounds each of the first to fifth object models.

[0157] As shown in Figure 17, a predetermined reference position 14a is set in space 14. The analytical coordinate systems 18 for the first to fifth object models are placed at a predetermined position 14b relative to this reference position 14a. Details of the computational grid 15 (shown in Figure 18) are as described above.

[0158] In this embodiment, unlike previous embodiments, when the analytical coordinate systems 18 of the first to fifth object models are aligned, as shown in Figure 18, the first to fifth computational grids include a common computational grid area 46 where the nodes 19 are in the same positions. In these common computational grid areas 46, the physical quantities of the fluid are calculated at the same positions in the first to fifth computational grids, respectively, so feature quantities can be obtained from the physical quantities calculated at the same positions.

[0159] The common computational grid area 46 can be set as appropriate. In this embodiment, prior to the discretization of the first to fifth computational grids by element G(i), virtual regions 45, which have the same shape as the common computational grid area 46, are set in the space 14 shown in Figure 17. At this time, each virtual region 45 is positioned apart from the first to fifth object models and is positioned at the same position with respect to the reference position 14a in each space 14.

[0160] Next, in the respective spaces 14 where the first to fifth object models are arranged in the same analytical coordinate system 18, each virtual region 45 (common computational grid area 46) is discretized by element G(i) such that the nodes 19 within each virtual region 45 are in the same position. As described above, since each virtual region 45 is spaced apart from the first to fifth object models, it can be discretized by element G(i) without sharing any nodes 19 within the first to fifth object models. Therefore, each virtual region 45 (common computational grid area 46) can be easily discretized by element G(i) such that the nodes 19 within each virtual region 45 are in the same position. As a result, a common computational grid area 46 is set in the first to fifth computational grids. Such discretization can be easily performed by adjusting the parameters of the software described above.

[0161] The common computational grid area 46 (virtual region 45) is preferably set downstream (to the right in the figure) in the direction of fluid flow relative to the first to fifth object models. This common computational grid area 46 enables the analysis of the physical quantities of the fluid after it has collided with and been affected by each of the first object 11A (first object model) to the fifth object 11E (fifth object model) shown in Figure 16. In this embodiment, the common computational grid area 46 (virtual region 45) is set in a U-shape surrounding the first to fifth object models, but it is not limited to this configuration, and may be set in an inverted C-shape, for example.

[0162] Next, in the space 14 where the common computational grid area 46 is set, the region between the object model 13 and the common computational grid area 46 (i.e., the region other than the common computational grid area 46) is discretized by element G(i). This sets up the first to fifth computational grids.

[0163] The first computational grid is associated with the first object model. As shown in Figure 18, the second computational grid 15B is associated with the second object model 13B. The third computational grid is associated with the third object model. The fourth computational grid is associated with the fourth object model. The fifth computational grid is associated with the fifth object model. These computational grids 15 are input to the model storage unit 7A shown in Figure 1.

[0164] Next, in step S11 of this embodiment, fluid analysis is performed using the computational grid 15 associated with the object model 13 shown in Figure 18, as in previous embodiments. At a minimum, the flow field 20, which is the distribution of physical quantities of the fluid after it has passed through the object model 13 (object 11 shown in Figure 16), and the fluid force E acting on the object model 13 (object 11) are calculated.

[0165] In this embodiment, fluid analysis is performed for each of the first to fifth computational grids. The details of the fluid analysis are as described above. Figure 19 is a contour plot showing an example of a physical quantity (hereinafter referred to as the "second physical quantity") C2 calculated in the second computational grid 15B. In Figure 19, the second physical quantity C2 of the common computational grid area 46 shown in Figure 18 is shown.

[0166] The flow fields 20 calculated in each of the first to fifth computational grids are used from the start of the simulation (t=t0) to the end (t=t0). n Up to the end of the simulation, the flow field / hydroforce memory unit 7B shown in Figure 1 can be input at each unit time. Also, the hydroforces (in this example, drag coefficients) E1 to E5 acting on the first to fifth object models can be input at each unit time from the start to the end of the simulation, similar to the flow field 20, into the flow field / hydroforce memory unit 7B shown in Figure 1.

[0167] [Obtaining a plurality of types of feature quantities] Next, in the generation method of this embodiment, a plurality of types of feature quantities are obtained from the physical quantities of the flow field 20 of the computational grids (the first computational grid to the fifth computational grid) (step S12). In step S12 of this embodiment, for each unit time (a plurality of times) of the simulation, a plurality of types of feature quantities common to the flow fields 20 of the plurality of objects (the first object 11A to the fifth object 11E) are obtained.

[0168] The plurality of types of feature quantities may be obtained from the physical quantities calculated at all the nodes 19 of the computational grid 15 shown in FIG. 18. As described above, in the common computational grid area 46, the physical quantities of the fluid that have collided with and fluctuated for each of the first object 11A (the first object model) to the fifth object 11E (the fifth object model) shown in FIG. 16 are calculated at the same positions in the first computational grid to the fifth computational grid. Therefore, in step S12, for each of the first computational grid to the fifth computational grid, it is preferable to obtain a plurality of types of feature quantities from the physical quantities of the flow field 20 for the common computational grid area 46.

[0169] FIG. 20 is a diagram showing an example of the physical quantity C calculated by the computational grid 15. In FIG. 20, the first physical quantity C1, the second physical quantity C2, and the fifth physical quantity C5 are shown as representatives. Also, in FIG. 20, the physical quantities are shown in a simplified manner (only the signs). The first physical quantity C1 is the physical quantity calculated in the common computational grid area of the first computational grid not shown. The second physical quantity C2 is the physical quantity calculated in the common computational grid area 46 of the second computational grid 15B shown in FIG. 18. The third physical quantity C3 (not shown) is the physical quantity calculated in the common computational grid area of the third computational grid not shown. The fourth physical quantity C4 (not shown) is the physical quantity calculated in the common computational grid area of the fourth computational grid not shown. The fifth physical quantity C5 is the physical quantity calculated in the common computational grid area of the fifth computational grid not shown.

[0170] In FIG. 20, the first physical quantity C1 calculated at each node 19 of the common calculation grid area 46 shown in FIG. 18 is the physical quantity C1 at the smallest coordinate values (x1, y1) every unit time t 1t from, the physical quantity C1 at the largest coordinate values (x z , y z ). They are arranged vertically in ascending order zt . Furthermore, the first physical quantity C1 1t ~C1 zt are arranged horizontally in ascending order from the smallest unit time (t = t0) to the largest unit time (t = t n ). As a result, for all nodes 19 included in the common calculation grid area 46, the first physical quantity C1 10 ~C1 zn calculated every unit time from the start to the end of the simulation can be identified as a matrix (multidimensional data) 22. Furthermore, based on the same procedure as the first physical quantity C1, matrices (multidimensional data) 22 of the second physical quantity C2 to the fifth physical quantity C5 can be identified

[0171] Next, in step S12 of this embodiment, a plurality of types of feature quantities are obtained from the physical quantities of the flow field 20 (in this example, the common calculation grid area 46). In this embodiment, based on proper orthogonal decomposition, for each unit time t (a plurality of times) of the simulation, a plurality of types of feature quantities common to the flow field 20 after passing through a plurality of objects (the first object 11A to the fifth object 11E shown in FIG. 16) are obtained

[0172] For example, when each of the physical quantities C1 (C1 10 ~C1 zn ) to the fifth physical quantity C5 (C5 10 ~C5 zn ) is independently subjected to proper orthogonal decomposition, in each mode, it is decomposed into different basis vectors and coefficients corresponding to each basis vector. Therefore, it is impossible to obtain a plurality of types of feature quantities common to the flow field 20 (the first calculation grid to the fifth calculation grid) after passing through a plurality of objects (the first object 11A to the fifth object 11E shown in FIG. 16) respectively

[0173] In this embodiment, a known Global POD (hereinafter sometimes referred to as "G-POD") is performed, which is a method for aligning the basis vectors of each mode (obtaining common basis vectors). In G-POD, as shown in Figure 20, for all units of time, an intrinsic orthogonal decomposition is performed on the matrix obtained by combining all of the matrices 22A of the first physical quantity C1 to the matrices 22E of the fifth physical quantity. As a result, the first physical quantity C1 to the fifth physical quantity C5 can be decomposed into a plurality of common basis vectors (i.e., common basis vectors in each mode) 23 and a plurality of coefficients 24 corresponding to each of the plurality of basis vectors.

[0174] Figure 21(a) is a contour plot showing an example of the basis vector 23 for the 0th mode. Figure 21(b) is a contour plot showing an example of the basis vector 23 for the 2nd mode. Figure 22(a) is a graph showing the relationship between the coefficients 24 of the basis vector 23 for the 0th mode and the unit time of the simulation. Figure 22(b) is a graph showing the relationship between the coefficients 24 of the basis vector 23 for the 2nd mode and the unit time of the simulation. As shown in Figure 22, the coefficients 24 can be specified for each unit time (multiple time points).

[0175] In step S12, an intrinsic orthogonal decomposition (G-POD in this example) is performed on the first physical quantity C1 to the fifth physical quantity C5 shown in Figure 20. As a result, the first physical quantity C1 to the fifth physical quantity C5 can be decomposed into a common basis vector 23 (shown in Figure 21) and the coefficients 24 of each basis vector 23 (shown in Figure 22).

[0176] The basis vectors 23 shown in Figure 21 represent the characteristic parts (parts with large variance) common to the first physical quantity C1 to the fifth physical quantity C5 shown in Figure 20. Corresponding to these basis vectors 23, each of the first physical quantity C1 to the fifth physical quantity C5 is decomposed into coefficients 24 for each mode. Then, the coefficients 24 for each mode decomposed from each of the first physical quantity C1 to the fifth physical quantity C5 are used to determine the multiple types of characteristic quantities D1 (D1) for each of the first physical quantity C1 to the fifth physical quantity C5. 0t ~D1 20t )~D5(D50t ~D5 20t These can be obtained as ). These multiple types of features D are obtained at each unit of time (multiple time points) of the simulation.

[0177] Multiple types of features D1(D1 0t ~D1 20t )~D5(D5 0t ~D5 20t The number of ) is the first physical quantity C1(C1) shown in Figure 20. 1t ~C1 zt ) ~ 5th physical quantity C5 (C5 1t ~C5 zt This is less than the number of ) elements. This prevents an increase in the number of training datasets required for machine learning of the trained model 29, while allowing the acquisition of features D1 to D5 that have a strong correlation with the fluid force E. Multiple types of features D1 to D5 (coefficient 24) are input to the basis vector / feature memory unit 7C shown in Figure 1.

[0178] In this embodiment, multiple types of features D1 to D5 were obtained based on intrinsic orthogonal decomposition, but the embodiment is not limited to this. For example, multiple types of features may be obtained based on at least one of a convolutional neural network, principal component analysis, and an autoencoder.

[0179] [Prepare the training dataset] Next, in the generation method of this embodiment, a training dataset is prepared in which multiple types of feature quantities D1 to D5 and the fluid force E are combined (step S13). The training dataset of this embodiment is used as training data for machine learning to output the fluid force E from the feature quantities D1 to D5.

[0180] Figure 23 shows an example of the training dataset 26. In Figure 23, the feature D1(D1 0t ~D1 20t )~D5(D5 0t ~D5 20t ) is shown in a simplified form, and the fluid force E1 (E10~E1 n )~E5(E50~E5 n) is shown in a simplified form.

[0181] In step S13 of this embodiment, in multiple modes, the simulation is run from the start (t=t0) to the end (t=t0). n For every unit time t up to ), multiple types of feature quantities (coefficients) D1 are decomposed from the first physical quantity C1 shown in Figure 20. 0t ~D1 20t And the fluid force E1 acting on the first object model t These are combined. Furthermore, in multiple modes, for each unit time t, multiple types of feature quantities (coefficients) D2 are decomposed from the second physical quantity C2 shown in Figure 20. 0t ~D2 20t And the fluid force E2 acting on the second object model t These are combined. Furthermore, in multiple modes, for each unit time t, multiple types of feature quantities (coefficients) D3 are decomposed from a third physical quantity C3 (not shown). 0t ~D3 20t And the fluid force E3 acting on the third object model t These are combined. Furthermore, in multiple modes, for each unit time t, multiple types of feature quantities (coefficients) D4 are decomposed from the fourth physical quantity C4 (not shown). 0t ~D4 20t And the fluid force E4 acting on the fourth object model t These are combined. Furthermore, in multiple modes, for each unit time t, multiple types of feature quantities (coefficients) D5 are decomposed from the fifth physical quantity C5 shown in Figure 20. 0t ~D5 20t And the fluid force E5 acting on the fifth object model t These are combined. As a result, multiple training datasets 26 are created. The multiple training datasets 26 are input to the training dataset storage unit 7D shown in Figure 1.

[0182] [Train the machine learning model] Next, in the generation method of this embodiment, a machine learning model is trained using the training dataset 26 shown in Figure 23 (step S14). In step S14, when feature quantities D obtained from the fluid flow field 20 after passing through the target object 10 (for example, shown in Figure 19) are input, the machine learning model is trained to output the fluid force E acting on the target object 10.

[0183] In this embodiment, the machine learning uses multiple training datasets 26 shown in Figure 23. These training datasets 26 consist of multiple types of feature quantities (coefficients) D1 to D5 decomposed from each of the first physical quantity C1 to the fifth physical quantity C5 shown in Figure 20, and fluid forces E1 to E5 acting on the first to fifth object models, from the start (t=t0) to the end (t=t0) of the simulation. n These are combined for each unit of time up to ). The first physical quantity C1 to the fifth physical quantity C5 and the fluid forces E1 to E5 are obtained from multiple objects 11 with different shapes (the first object 11A to the fifth object 11E shown in Figure 16). By using each of these training datasets 26 in machine learning, it becomes possible to generate a trained model 29 that can accurately estimate the fluid force E acting on an object 10 having any shape, without being limited to an object 10 having a specific shape.

[0184] The trained model 29 (input layer 31) shown in Figure 11 contains the physical quantity C1 of the flow field 20 shown in Figure 20. 1t ~C1 zt ) and the fifth physical quantity C5(C5 1t ~C5 zt Fewer (lower-dimensional) features than D1(D1 0t ~D1 20t ) and D5 (D5 0t ~D5 20t The following is input. This reduces the number of training data required to create a trained model 29 with high prediction accuracy, while also potentially shortening the time required to create the trained model 29. The trained model 29 is input to the trained model storage unit 7E shown in Figure 1.

[0185] In the analysis method using the trained model 29 of this embodiment, in the fourth step S4 shown in Figure 12, the contribution S to the fluid force E estimated by the trained model 29 (for example, shown in Figure 13) is obtained for each of the multiple types of feature quantities D. By obtaining these contribution S values, it is possible to identify feature quantities D (mode coefficients 24) that have a high influence on the fluid force E for an object 10 having an arbitrary shape.

[0186] Furthermore, in the fifth step S5, based on the contribution S, regions 39 that have a large contribution to the estimated fluid force E are mapped onto the flow field 20 shown in Figure 19 or onto coordinates corresponding to the flow field 20, as shown in Figures 14(b) and 15. This makes it possible to easily find locations and physical quantities C, etc., that have a large influence on the fluid force E in the flow field 20 that has passed through an object 10 of any shape, without requiring skilled techniques, effort, or time. By considering such regions 39, for example, by changing the shape of the object 10, an object 10 with reduced fluid force (air resistance) E can be reliably designed and manufactured.

[0187] Although particularly preferred embodiments of the present invention have been described in detail above, the present invention is not limited to the illustrated embodiments and can be implemented in various modified forms. [Examples]

[0188] Based on the processing procedure shown in Figure 3, a trained model was generated to estimate the fluid forces flowing around the target object shown in Figure 2 (Example 1, Example 2).

[0189] In Example 1, the flow field and fluid force after passing through the object shown in FIG. 2 were acquired, and characteristic quantities of various types were acquired from the physical quantities of the flow field. Next, a training dataset (shown in FIG. 10) in which a plurality of types of characteristic quantities and fluid forces were combined was prepared. Then, learning of the machine learning model was performed such that when the characteristic quantity acquired from the flow field of the fluid after passing through the target object was input, the fluid force acting on the target object was output. As a result, in Example 1, a learned model based on the training dataset acquired from the object shown in FIG. 2 was generated.

[0190] In Example 2, the flow field and fluid force after passing through each of the five objects shown in FIGS. 16(a) to (e) were acquired, and characteristic quantities of various types were acquired from the physical quantities of the flow field. Next, a training dataset (shown in FIG. 23) in which a plurality of types of characteristic quantities and fluid forces were combined was prepared. Then, learning of the machine learning model was performed such that when the characteristic quantity acquired from the flow field of the fluid after passing through the target object was input, the fluid force acting on the target object was output. As a result, in Example 2, a learned model based on the training dataset acquired from the five objects shown in FIGS. 16(a) to (e) was generated.

[0191] Next, based on the processing procedure shown in FIG. 12, the fluid force flowing around the target object shown in FIG. 2 was analyzed (Examples 1 and 2). In Examples 1 and 2, the flow field and fluid force after passing through the target object shown in FIG. 2 were acquired, and characteristic quantities of various types were acquired from the physical quantities of the flow field. Next, the characteristic quantity was input to the learned model generated in each of Examples 1 and 2, and the fluid force of the target object was estimated. Then, for each of the plurality of types of characteristic quantities, the degree of contribution to the fluid force was acquired, and based on the degree of contribution, a region where the contribution to the estimated fluid force was large was mapped on the flow field or on the coordinates corresponding to the flow field. The common specifications of the fluid analysis are as follows. Software: STAR-CCM+ manufactured by Siemens PLM Software Unsteady turbulent flow model: SST k-ω Reynolds number Re: 6.4×10 4

[0192] For both Example 1 and Example 2, the coefficient of determination R² between the fluid force estimated by the trained model (estimated value) and the fluid force calculated by the simulation (correct value) was 0.999 or higher in both cases. Therefore, the trained models in both Example 1 and Example 2 were able to estimate the fluid force with good accuracy. Furthermore, in Example 2, compared to Example 1, the fluid force could be estimated with better accuracy without being affected by the shape of the target object.

[0193] Figure 14(b) shows an example of first mapping data where regions with a large contribution to fluid force are mapped. Figure 15 shows an example of second mapping data where regions with a large contribution to fluid force are mapped onto the flow field. Examples 1 and 2 were able to map regions with a large estimated contribution to fluid force onto the flow field or onto coordinates corresponding to the flow field. As a result, Examples 1 and 2 were able to easily identify regions with a large contribution to fluid force acting on the target object in the flow field after it has passed through the target object, without requiring skilled techniques, effort, or time.

[0194] [Note] The present invention includes the following embodiments.

[0195] [Invention 1] A method for analyzing fluid forces flowing around an object using one or more processors, The first step involves performing a fluid analysis to calculate the flow field, which is the distribution of physical quantities of the fluid after it has passed through the target object. A second step involves obtaining multiple types of feature quantities from the physical quantities of the flow field, A third step involves estimating the fluid force using a pre-trained model that has been machine-trained to output the fluid force acting on the target object when the aforementioned features are input. A fourth step involves obtaining the estimated contribution to the fluid force for each of the aforementioned multiple types of features, A fifth step includes mapping regions where the estimated contribution to the fluid force is large onto the flow field or onto coordinates corresponding to the flow field, based on the aforementioned contributions. Methods for analyzing fluid forces. [Invention 2] The second step is to obtain the multiple types of feature quantities based on intrinsic orthogonal decomposition, as described in the first invention, for the fluid force analysis method. [Invention 3] The second step is to obtain the plurality of feature quantities based on at least one of a convolutional neural network, principal component analysis, and an autoencoder, as described in the first invention, for the fluid force analysis method according to the present invention. [4th Invention] The aforementioned multiple types of features are time-series data that change over time. The second step includes predicting future features based on the trends of the time series data, The fluid force analysis method according to any one of inventions 1 to 3, wherein the third step includes inputting the future features into the trained model to estimate the future fluid force. [5th ​​Invention] The aforementioned physical quantity includes the pressure of the fluid, The fluid force analysis method according to any one of inventions 1 to 4, wherein the fluid force includes a drag coefficient. [Invention 6] A method for generating a trained model for estimating the fluid forces flowing around a target object, The process involves performing a fluid analysis to calculate at least the flow field, which is the distribution of physical quantities of the fluid after it has passed through an object, and the fluid forces acting on the object. The steps include obtaining multiple types of feature quantities from the physical quantities of the flow field, The steps include: preparing a training dataset in which the aforementioned multiple types of features and the aforementioned fluid force are combined; The process includes the step of training a machine learning model using the aforementioned training dataset so that when features obtained from the fluid flow field after passing through the target object are input, the fluid force acting on the target object is output. Method for generating a pre-trained model. [7th Invention] The step of calculating the flow field and the fluid force includes the step of calculating the flow field and the fluid force for each of a plurality of objects with different shapes from one another. The method for generating a trained model according to the present invention, wherein the step of acquiring the aforementioned features includes the step of acquiring multiple types of features common to the flow fields of each of the multiple objects. [8th Invention] The step of acquiring the aforementioned features is to acquire the aforementioned multiple types of features based on eigenorthogonal decomposition, a method for generating a trained model according to item 6 or 7 of the present invention. [Invention 9] The method for generating a trained model according to claim 6 or 7 of the present invention, wherein the step of acquiring the aforementioned features is to acquire the aforementioned multiple types of features based on at least one of a convolutional neural network, principal component analysis, and an autoencoder. [Explanation of Symbols]

[0196] 20 Flow field 39 areas

Claims

1. A method for analyzing the fluid forces flowing around an object using one or more processors, The first step involves performing a fluid analysis to calculate the flow field, which is the distribution of physical quantities of the fluid after it has passed through the target object. A second step involves obtaining multiple types of feature quantities from the physical quantities of the flow field, A third step involves estimating the fluid force using a pre-trained model that has been machine-trained to output the fluid force acting on the target object when the aforementioned features are input. A fourth step involves obtaining the estimated contribution to the fluid force for each of the aforementioned multiple types of features, A fifth step includes mapping regions where the estimated contribution to the fluid force is large onto the flow field or onto coordinates corresponding to the flow field, based on the aforementioned contributions. Methods for analyzing fluid forces.

2. The second step is to obtain the plurality of feature quantities based on intrinsic orthogonal decomposition, as described in claim 1, for the fluid force analysis method.

3. The fluid force analysis method according to claim 1, wherein the second step is to obtain the plurality of types of features based on at least one of a convolutional neural network, principal component analysis, and an autoencoder.

4. The aforementioned multiple types of features are time-series data that change over time. The second step includes predicting future features based on the trends of the time series data, The fluid force analysis method according to claim 1, wherein the third step includes inputting the future features into the trained model to estimate the future fluid force.

5. The aforementioned physical quantity includes the pressure of the fluid, The fluid force analysis method according to claim 1, wherein the fluid force includes a drag coefficient.

6. A method for generating a trained model for estimating the fluid forces flowing around a target object, The process involves performing a fluid analysis to calculate at least the flow field, which is the distribution of physical quantities of the fluid after it has passed through an object, and the fluid forces acting on the object. A step of obtaining multiple types of feature quantities from the physical quantities of the flow field, The steps include: preparing a training dataset in which the aforementioned multiple types of features and the aforementioned fluid force are combined; The process includes the step of training a machine learning model using the aforementioned training dataset so that when features obtained from the fluid flow field after passing through the target object are input, the fluid force acting on the target object is output. Method for generating a pre-trained model.

7. The step of calculating the flow field and the fluid force includes the step of calculating the flow field and the fluid force for each of a plurality of objects with different shapes from one another. The method for generating a trained model according to claim 6, wherein the step of acquiring the aforementioned features includes the step of acquiring a plurality of types of features common to the flow fields of each of the plurality of objects.

8. The method for generating a trained model according to claim 6, wherein the step of acquiring the aforementioned features is to acquire the plurality of types of features based on eigenorthogonal decomposition.

9. The method for generating a trained model according to claim 6, wherein the step of acquiring the features is to acquire the plurality of types of features based on at least one of a convolutional neural network, principal component analysis, and an autoencoder.

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